<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.2 20190208//EN" "http://jats.nlm.nih.gov/publishing/1.2/JATS-journalpublishing1.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.2" xml:lang="en">
    <front>
        <journal-meta>
            <journal-id journal-id-type="pmc">F1000Research</journal-id>
            <journal-title-group>
                <journal-title>F1000Research</journal-title>
            </journal-title-group>
            <issn pub-type="epub">2046-1402</issn>
            <publisher>
                <publisher-name>F1000 Research Limited</publisher-name>
                <publisher-loc>London, UK</publisher-loc>
            </publisher>
        </journal-meta>
        <article-meta>
            <article-id pub-id-type="doi">10.12688/f1000research.175423.1</article-id>
            <article-categories>
                <subj-group subj-group-type="heading">
                    <subject>Research Article</subject>
                </subj-group>
                <subj-group>
                    <subject>Articles</subject>
                </subj-group>
            </article-categories>
            <title-group>
                <article-title>Design and Modeling of a Solar-Powered Water System for Real-Time Microbial Detection and Treatment</article-title>
                <fn-group content-type="pub-status">
                    <fn>
                        <p>[version 1; peer review: 1 approved with reservations]</p>
                    </fn>
                </fn-group>
            </title-group>
            <contrib-group>
                <contrib contrib-type="author" corresp="yes">
                    <name>
                        <surname>malisaba</surname>
                        <given-names>Joseph</given-names>
                    </name>
                    <role content-type="http://credit.niso.org/">Conceptualization</role>
                    <role content-type="http://credit.niso.org/">Data Curation</role>
                    <role content-type="http://credit.niso.org/">Formal Analysis</role>
                    <role content-type="http://credit.niso.org/">Methodology</role>
                    <uri content-type="orcid">https://orcid.org/0009-0008-4490-8375</uri>
                    <xref ref-type="corresp" rid="c1">a</xref>
                    <xref ref-type="aff" rid="a1">1</xref>
                </contrib>
                <contrib contrib-type="author" corresp="no">
                    <name>
                        <surname>Obinna Onyebuchi</surname>
                        <given-names>Barah</given-names>
                    </name>
                    <role content-type="http://credit.niso.org/">Methodology</role>
                    <role content-type="http://credit.niso.org/">Resources</role>
                    <role content-type="http://credit.niso.org/">Supervision</role>
                    <uri content-type="orcid">https://orcid.org/0000-0002-5131-3045</uri>
                    <xref ref-type="aff" rid="a1">1</xref>
                </contrib>
                <contrib contrib-type="author" corresp="no">
                    <name>
                        <surname>Onep</surname>
                        <given-names>Samuel George</given-names>
                    </name>
                    <role content-type="http://credit.niso.org/">Writing &#x2013; Original Draft Preparation</role>
                    <role content-type="http://credit.niso.org/">Writing &#x2013; Review &amp; Editing</role>
                    <uri content-type="orcid">https://orcid.org/0009-0009-6721-1981</uri>
                    <xref ref-type="aff" rid="a1">1</xref>
                </contrib>
                <contrib contrib-type="author" corresp="no">
                    <name>
                        <surname>Ninsiima</surname>
                        <given-names>Emmanuel</given-names>
                    </name>
                    <role content-type="http://credit.niso.org/">Funding Acquisition</role>
                    <role content-type="http://credit.niso.org/">Investigation</role>
                    <role content-type="http://credit.niso.org/">Methodology</role>
                    <xref ref-type="aff" rid="a2">2</xref>
                </contrib>
                <aff id="a1">
                    <label>1</label>Mechanical Engineering, Kampala International University School of Engineering and Applied Sciences, Ishaka-Bushenyi, Uganda, Uganda</aff>
                <aff id="a2">
                    <label>2</label>Civil Engineering, Kampala International University School of Engineering and Applied Sciences, Ishaka-Bushenyi, Uganda, Uganda</aff>
            </contrib-group>
            <author-notes>
                <corresp id="c1">
                    <label>a</label>
                    <email xlink:href="mailto:joseph.malisaba.22310@studwc.kiu.ac.ug">joseph.malisaba.22310@studwc.kiu.ac.ug</email>
                </corresp>
                <fn fn-type="conflict">
                    <p>No competing interests were disclosed.</p>
                </fn>
            </author-notes>
            <pub-date pub-type="epub">
                <day>11</day>
                <month>5</month>
                <year>2026</year>
            </pub-date>
            <pub-date pub-type="collection">
                <year>2026</year>
            </pub-date>
            <volume>15</volume>
            <elocation-id>697</elocation-id>
            <history>
                <date date-type="accepted">
                    <day>24</day>
                    <month>3</month>
                    <year>2026</year>
                </date>
            </history>
            <permissions>
                <copyright-statement>Copyright: &#x00a9; 2026 malisaba J et al.</copyright-statement>
                <copyright-year>2026</copyright-year>
                <license xlink:href="https://creativecommons.org/licenses/by/4.0/">
                    <license-p>This is an open access article distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
                </license>
            </permissions>
            <self-uri content-type="pdf" xlink:href="https://f1000research.com/articles/15-697/pdf"/>
            <abstract>
                <sec>
                    <title>Background</title>
                    <p>Access to safe drinking water remains a persistent challenge in low-resource settings such as Ishaka Municipality, Uganda, where surface and groundwater sources are frequently contaminated and access to reliable electricity is limited. This study presents the design, modeling, and performance evaluation of a solar-powered hybrid water treatment system integrated with a biosensor-based microbial detection unit, enabling autonomous operation and real-time water quality monitoring for decentralized applications.</p>
                </sec>
                <sec>
                    <title>Methods</title>
                    <p>A total of 384 water samples were collected from springs, wetlands, wells, and tap sources and analyzed for key physicochemical and microbial parameters, including turbidity, pH, and indicator organisms. The proposed system integrates sedimentation, activated carbon filtration, reverse osmosis, and solar thermal disinfection to achieve multi-barrier treatment. Hydraulic and filtration performance were modeled using fluid flow and porous media principles, while microbial inactivation was described using first-order kinetic models. The photovoltaic subsystem was evaluated through detailed loss modeling, incorporating temperature effects, partial shading, and inverter inefficiencies to assess overall system reliability.</p>
                </sec>
                <sec>
                    <title>Results</title>
                    <p>Baseline results indicated significant contamination, with 
                        <italic toggle="yes">Escherichia coli</italic> concentrations reaching 210&#x00a0;CFU/100&#x00a0;mL and turbidity values up to 146 NTU. The hybrid system achieved over 95% removal of contaminants, complete elimination of 
                        <italic toggle="yes">E. coli</italic>, and compliance with World Health Organization drinking water standards. Solar thermal disinfection provided a 4&#x2013;6 log reduction in microbial indicators. The integrated biosensor demonstrated rapid response times (45&#x2013;90&#x00a0;seconds) and strong correlation with laboratory biochemical oxygen demand measurements (R
                        <sup>2</sup>&#x00a0;=&#x00a0;0.89&#x2013;0.94). The photovoltaic subsystem maintained a performance ratio of 0.84&#x2013;0.88, consistently meeting 100% of operational energy demand under varying environmental conditions.</p>
                </sec>
                <sec>
                    <title>Conclusion</title>
                    <p>These results demonstrate that the proposed system provides an effective, energy-autonomous solution for decentralized water purification with real-time monitoring capability, offering significant potential for improving access to safe drinking water in rural and resource-limited environments.</p>
                </sec>
            </abstract>
            <kwd-group kwd-group-type="author">
                <kwd>Biosensors</kwd>
                <kwd>Microbial Inactivation</kwd>
                <kwd>Reverse Osmosis</kwd>
                <kwd>Water Quality Modeling</kwd>
                <kwd>Uganda</kwd>
                <kwd>Rural Contamination</kwd>
                <kwd>Navier-Stokes</kwd>
                <kwd>Energy Balance</kwd>
                <kwd>Solar-Powered Water Treatment</kwd>
            </kwd-group>
            <funding-group>
                <funding-statement>The author(s) declared that no grants were involved in supporting this work.</funding-statement>
            </funding-group>
        </article-meta>
    </front>
    <body>
        <sec id="sec5" sec-type="intro">
            <title>1. Introduction</title>
            <p>Ready and clean water for drinking remains a chronic issue in the majority of rural areas of developing countries, where raw surface sources are usually loaded with physical impurities, chemical contaminants, and pathogenic bacteria.
                <sup>
                    <xref ref-type="bibr" rid="ref1">1</xref>
                </sup> In Uganda, particularly in semi-urban settings like Ishaka municipality, water resources like springs and wetlands are increasingly polluted by sewage effluent, agriculture, and ineffective treatment plants. This leads to widespread health risks in the form of waterborne diseases, heavy metal poisoning, and exposure to emerging contaminants like pesticides and pharmaceuticals.
                <sup>
                    <xref ref-type="bibr" rid="ref2">2</xref>
                </sup> The majority of systems lack real-time monitoring for microbial quality, thereby keeping consumers unaware of potential health risks.
                <sup>
                    <xref ref-type="bibr" rid="ref3">3</xref>
                </sup> There has been growing interest in marrying sustainable energy systems, such as solar power, with modular treatment units capable of eliminating multiple orders of contaminants. Such systems, along with biosensor-based microbial monitoring, provide for real-time assessment of biological risk, necessary for remote or underserved populations in which laboratory analysis is not an option.
                <sup>
                    <xref ref-type="bibr" rid="ref4">4</xref>
                </sup> This study aims to design, model, and evaluate a solar-powered water treatment system that can efficiently eliminate physical, chemical, and biological contaminants from surface water in Uganda&#x2019;s rural areas.
                <sup>
                    <xref ref-type="bibr" rid="ref5">5</xref>
                </sup> The system integrates cutting-edge treatment phases, such as sedimentation, activated carbon filtration, reverse osmosis, and solar thermal disinfection.
                <sup>
                    <xref ref-type="bibr" rid="ref6">6</xref>
                </sup> The biosensor-based detection of microbial-derived contaminants is obtained. A comprehensive approach is outlined in the paper that integrates experimentally tested detection, environmental modeling (hydraulics, thermodynamics, and solar performance), and biosensor integration.
                <sup>
                    <xref ref-type="bibr" rid="ref7">7</xref>
                </sup> The system described here offers a renewable energy-autonomous solution that addresses both water purification and real-time water quality monitoring in water-constrained settings.
                <sup>
                    <xref ref-type="bibr" rid="ref8">8</xref>
                </sup>
            </p>
            <p>This study, therefore, contributes a novel integration of real-time biosensor-based microbial detection within a fully solar-powered, multi-stage water treatment system tailored for rural contamination profiles. Unlike conventional systems that isolate thermal, hydraulic, or filtration processes, this work unifies Navier&#x2013;Stokes hydraulic modelling, Darcy-based filtration modelling, solar energy balance, and microbial inactivation kinetics into a single design framework.
                <sup>
                    <xref ref-type="bibr" rid="ref9">9</xref>
                </sup> The system uniquely couples sedimentation, activated carbon filtration, reverse osmosis, and solar thermal disinfection with continuous BOD biosensing, offering both treatment and real-time microbial monitoring. By validating the design with experimentally characterized contaminants from 384 rural Ugandan water samples, this work provides a new hybrid, off-grid architecture that has not been previously reported for decentralized water purification in low-resource settings.</p>
        </sec>
        <sec id="sec6" sec-type="methods">
            <title>2. Methods</title>
            <p>The methods used are tailored to the study&#x2019;s aim. The study involved (i) characterization of the physical, biological, and chemical, (ii) design of a solar system that will be capable of powering the treatment system, and (iii) the amount of heat that will be required to kill bacteria.</p>
            <sec id="sec7">
                <title>2.1 Materials and reagents</title>
                <p>Nitric acid was used for preservation of water samples during heavy-metal analysis. Concentrated nitric acid (65&#x2013;69% w/w) was added at 2&#x00a0;mL per 1 Liter of water sample to reduce the pH to below 2. The reagent was obtained from Merck (Sigma-Aldrich, Darmstadt, Germany; Catalogue No. 100456).</p>
                <p>Sodium thiosulfate was used to neutralize residual chlorine in microbiological water samples. A volume of 0.1&#x00a0;mL of 10% (w/v) sodium thiosulfate solution was added per 100&#x00a0;mL of sample. Sodium thiosulfate was supplied by Sigma-Aldrich (Catalogue No. S8503).</p>
                <p>Membrane filters with a pore size of 0.45&#x00a0;&#x03bc;m and a diameter of 47&#x00a0;mm were used for chemical filtration and microbial analysis. Filters were obtained from Merck Millipore, USA (Catalogue No. HAWP04700).</p>
                <p>Eosin Methylene Blue (EMB) agar was used for selective culturing of 
                    <italic toggle="yes">Escherichia coli.</italic> EMB agar powder was prepared at 37&#x00a0;g/L of distilled water according to the manufacturer&#x2019;s instructions and sterilized by autoclaving at 121&#x00a0;&#x00b0;C for 15&#x00a0;minutes. The medium was supplied by Oxoid Ltd. (Thermo Fisher Scientific, UK; Catalogue No. CM0069).</p>
                <p>Sterile sampling bottles (100&#x00a0;mL capacity), pre-dosed with sodium thiosulfate, and were supplied by VWR International (Catalogue No. 215&#x2013;1590).</p>
            </sec>
            <sec id="sec8">
                <title>2.2 Characterization of physical, chemical, and biological pollutants in rural surface water sources</title>
                <p>Water properties are considered, including the physical, biological, and chemical properties. Water samples is picked from wetlands, springs, domestic taps, and wells and tested for quality. Water meets quality standards when its turbidity, color, E-Coli, pH, COD, DO, BOD, and TDS, Electrical Conductivity, Heavy Metals, Nitrates, Magnesium, temperature, Potassium ions, Calcium ions, Sodium ions, Hydrogen Carbonate ions, Carbonate ions, Chloride ions, Sulphate ions, Pesticides, Pharmaceuticals, herbicides, and Fluoride above threshold.
                    <sup>
                        <xref ref-type="bibr" rid="ref10">10</xref>
                    </sup> To identify the number of water samples to be used, a statistical technique is used.</p>
                <p>

                    <bold>2.2.1 Statistical Sampling Techniques</bold>
                </p>
                <p>
                    <xref ref-type="disp-formula" rid="e1">
Equation 1</xref> is used to determine the number of water samples to use based on the sources. 
                    <xref ref-type="table" rid="T1">
Table 1</xref> presents the standard score values of Z, e, and r.
                    <sup>
                        <xref ref-type="bibr" rid="ref12">12</xref>,
                        <xref ref-type="bibr" rid="ref22">22</xref>
                    </sup>
                    <disp-formula id="e1">

                        <mml:math display="block">
                            <mml:mi>n</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:msup>
                                        <mml:mi>Z</mml:mi>
                                        <mml:mn>2</mml:mn>
                                    </mml:msup>
                                    <mml:mi>r</mml:mi>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mn>1</mml:mn>
                                        <mml:mo>&#x2212;</mml:mo>
                                        <mml:mi>r</mml:mi>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                </mml:mrow>
                                <mml:msup>
                                    <mml:mi>e</mml:mi>
                                    <mml:mn>2</mml:mn>
                                </mml:msup>
                            </mml:mfrac>
                        </mml:math>

                        <label>(1)</label>
</disp-formula>
                </p>
                <table-wrap id="T1" orientation="portrait" position="float">
                    <label>
Table 1. </label>
                    <caption>
                        <title>Common Z and e values.
                            <sup>
                                <xref ref-type="bibr" rid="ref12">12</xref>
                            </sup>
                        </title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Confidence level</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Z-score (Z)</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Recommended error (e)</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">
Estimated proportion of contamination (r)</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">90%</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">1.645</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">&#x00b1; 0.10 or&#x00a0;&#x00b1;&#x00a0;5% (0.05)</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.5</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">95%</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">1.96</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">&#x00b1; 0.05</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.5</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">99%</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">2.576</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">0.01&#x2013;0.05</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.5</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>An international standard table for correspondence levels of a sample size.</p>
                    </table-wrap-foot>
                </table-wrap>
                <p>Where.</p>
                <p>n is the required sample size.</p>
                <p>Z is the score (1.96 for 95% confidence, 1.645 for 90%).</p>
                <p>r is the estimated proportion of contamination (0.5 is used if unknown; it&#x2019;s the most conservative).</p>
                <p>e is the margin of error in proportion (0.05).</p>
                <p>Using 
                    <xref ref-type="disp-formula" rid="e4">Equation 3</xref>.1 and 
                    <xref ref-type="table" rid="T1">
Table 1</xref>, for example, considering the confidence 95%. Z&#x00a0;=&#x00a0;1.96, e&#x00a0;=&#x00a0;0.005, r&#x00a0;=&#x00a0;0.5
                    <disp-formula id="e2">

                        <mml:math display="block">
                            <mml:mi mathvariant="normal">n</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:msup>
                                        <mml:mrow>
                                            <mml:mo stretchy="true">(</mml:mo>
                                            <mml:mn>1.96</mml:mn>
                                            <mml:mo stretchy="true">)</mml:mo>
                                        </mml:mrow>
                                        <mml:mn>2</mml:mn>
                                    </mml:msup>
                                    <mml:mo>&#x00d7;</mml:mo>
                                    <mml:mn>0.5</mml:mn>
                                    <mml:mspace width="0.25em"/>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mn>1</mml:mn>
                                        <mml:mo>&#x2212;</mml:mo>
                                        <mml:mn>0.5</mml:mn>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                </mml:mrow>
                                <mml:msup>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mn>0.05</mml:mn>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                    <mml:mn>2</mml:mn>
                                </mml:msup>
                            </mml:mfrac>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mn>0.9604</mml:mn>
                                <mml:mn>0.0025</mml:mn>
                            </mml:mfrac>
                            <mml:mo>=</mml:mo>
                            <mml:mn>384</mml:mn>
                        </mml:math>
</disp-formula>
                </p>
                <p>n&#x00a0;=&#x00a0;384 water samples.</p>
                <p>Each water sample is tested for heavy metals, E. coli, pharmaceuticals, organic debris, pesticides, and salts.</p>
                <p>

                    <bold>2.2.2 Characterisation of Physical Water Contaminants</bold>
                </p>
                <p>The properties of physical water contaminants consist of identifying, quantifying, and understanding the physical qualities of materials that affect the colour, clarity, scent, taste, and temperature of water.
                    <sup>
                        <xref ref-type="bibr" rid="ref11">11</xref>
                    </sup>
                </p>
                <p>Parameters such as turbidity, Total Suspended Solids, environmental temperature, and organic debris are considered. The methods of testing physical water parameters are shown in 
                    <xref ref-type="table" rid="T2">
Table 2</xref>.
                    <sup>
                        <xref ref-type="bibr" rid="ref12">12</xref>
                    </sup>
                </p>
                <table-wrap id="T2" orientation="portrait" position="float">
                    <label>
Table 2. </label>
                    <caption>
                        <title>Methods of testing physical contaminants.
                            <sup>
                                <xref ref-type="bibr" rid="ref12">12</xref>
                            </sup>
                        </title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Parameter</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Measurement unit</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Method</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">TSS</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">mg/L</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Gravimetric filtration</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Taste and Odor</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">-</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Gas Chromatography</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Organic Debris</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">-</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Visual/physical collection</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Temperature</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">&#x00b0;C</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Thermometer</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Turbidity</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">NTU</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Nephelometer</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>Shows ways on how physical contaminants are tested in water. The purpose of testing the possible physical contaminants is to identify the amount of water contaminants that are to be treated.</p>
                    </table-wrap-foot>
                </table-wrap>
                <p>

                    <bold>Gravimetric Filtration Procedure.</bold>
                    <xref ref-type="bibr" rid="ref13">
                        <sup>13</sup>
                    </xref>
                    <list list-type="roman-lower">
                        <list-item>
                            <label>i.</label>
                            <p>Dry a clean filter with a minimum pore diameter of 1.5&#x00a0;&#x03bc;m at 103&#x2013;105&#x00a0;&#x00b0;C to constant weight</p>
                        </list-item>
                        <list-item>
                            <label>ii.</label>
                            <p>Filter a known volume, which should be from 100&#x2013;1000&#x00a0;mL of a well-mixed water sample</p>
                        </list-item>
                        <list-item>
                            <label>iii.</label>
                            <p>Dry the filter with the retained solids at 103&#x2013;105&#x00a0;&#x00b0;C for one hour</p>
                        </list-item>
                        <list-item>
                            <label>iv.</label>
                            <p>Cool the filter in a desiccator and weigh it again</p>
                        </list-item>
                        <list-item>
                            <label>v.</label>
                            <p>Determine the mass difference and calculate the solids concentration</p>
                        </list-item>
                    </list>
                </p>
                <p>The measurement is done in each perspective and the Total Suspended Solids (mg/L), TSS are determined in 
                    <xref ref-type="disp-formula" rid="e3">Equation 2</xref>.
                    <disp-formula id="e3">

                        <mml:math display="block">
                            <mml:mi mathvariant="italic">TSS</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mrow>
                                        <mml:msub>
                                            <mml:mi>W</mml:mi>
                                            <mml:mtext mathvariant="italic">final</mml:mtext>
                                        </mml:msub>
                                        <mml:mo>&#x2212;</mml:mo>
                                        <mml:msub>
                                            <mml:mi>W</mml:mi>
                                            <mml:mtext mathvariant="italic">initial</mml:mtext>
                                        </mml:msub>
                                    </mml:mrow>
                                    <mml:mi>V</mml:mi>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mn>100</mml:mn>
                        </mml:math>

                        <label>(2)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>W</mml:mi>
                                <mml:mtext mathvariant="italic">initial</mml:mtext>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the Weight of the clean, dry filter (mg).</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>W</mml:mi>
                                <mml:mtext mathvariant="italic">final</mml:mtext>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the Weight of dried filter plus solids (mg).</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi>V</mml:mi>
                        </mml:math>
</inline-formula> is the Volume of water sample filtered (mL).</p>
                <p>

                    <bold>2.2.3 Characterization of Chemical Contaminants, such as Heavy Metals, Pharmaceuticals, Salts, and Pesticides.</bold>
                </p>
                <p>Each chemical contaminant type is identified through experimental testing and recorded.
                    <sup>
                        <xref ref-type="bibr" rid="ref13">13</xref>
                    </sup>
                </p>
                <p>Testing of heavy metals in each water sample.
                    <list list-type="roman-lower">
                        <list-item>
                            <label>i.</label>
                            <p>
Use clean containers, preferably made of polyethylene that should be acid-washed and rinsed with deionized water.</p>
                        </list-item>
                        <list-item>
                            <label>ii.</label>
                            <p>Add nitric acid (HNO
                                <sub>3</sub>) to lower the pH to &lt;2 to preserve metals in solution</p>
                        </list-item>
                        <list-item>
                            <label>iii.</label>
                            <p>The samples will be kept in a cool, dark place at a temperature of 4&#x00a0;&#x00b0;C</p>
                        </list-item>
                        <list-item>
                            <label>iv.</label>
                            <p>Filter the solid particles with a membrane with pores of a diameter of 0.45&#x00a0;&#x03bc;m</p>
                        </list-item>
                        <list-item>
                            <label>v.</label>
                            <p>Then, finally, use Atomic Absorption Spectroscopy to detect water samples such as Lead, Arsenic, Cadmium, Mercury, Chromium, Nickel, Zinc, Copper, and Manganese</p>
                            <p>The Atomic Absorption Spectroscopy will measure the concentration of each heavy metal in a respective water sample.</p>
                        </list-item>
                    </list>
                </p>
                <p>
                    <xref ref-type="disp-formula" rid="e4">
Equation 3</xref> describes the quality rating for a heavy metal measured such as Zinc or Iron.
                    <disp-formula id="e4">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi>i</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">[</mml:mo>
                                <mml:mfrac>
                                    <mml:msub>
                                        <mml:mi>C</mml:mi>
                                        <mml:mi>i</mml:mi>
                                    </mml:msub>
                                    <mml:msub>
                                        <mml:mi>S</mml:mi>
                                        <mml:mi>i</mml:mi>
                                    </mml:msub>
                                </mml:mfrac>
                                <mml:mo stretchy="true">]</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mn>100</mml:mn>
                        </mml:math>

                        <label>(3)</label>
</disp-formula>
                </p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>C</mml:mi>
                                <mml:mi>i</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the measured concentration of metal 
                    <italic toggle="yes">in</italic> (mg/L).</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi>i</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the Quality rating for a heavy metal 
                    <italic toggle="yes">i.</italic>
                </p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>S</mml:mi>
                                <mml:mi>i</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the Standard value for metal 
                    <italic toggle="yes">i</italic> (mg/L)
                    <disp-formula id="e5">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>W</mml:mi>
                                <mml:mi>i</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mn>1</mml:mn>
                                <mml:msub>
                                    <mml:mi>S</mml:mi>
                                    <mml:mi>i</mml:mi>
                                </mml:msub>
                            </mml:mfrac>
                        </mml:math>

                        <label>(4)</label>
</disp-formula>
                </p>
                <p>Where 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>W</mml:mi>
                                <mml:mi>i</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the unit weight of a heavy metal tested.</p>
                <p>This calls to determine the water quality index of each heavy metal measured in each water sample. The heavy metal water quality index determines whether water is suitable to be consumed by people or not and this is determined in 
                    <xref ref-type="disp-formula" rid="e6">Equation 5</xref> and 
                    <xref ref-type="table" rid="T3">
Table 3</xref>.</p>
                <table-wrap id="T3" orientation="portrait" position="float">
                    <label>
Table 3. </label>
                    <caption>
                        <title>According to the World Health Organization (WHO), 2022.
                            <sup>
                                <xref ref-type="bibr" rid="ref23">23</xref>
                            </sup>
                        </title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Metal</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">
WHO standard value (mg/L)</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Arsenic</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">0.01</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Cadmium</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">0.003</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Chromium (VI)</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">0.05</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Lead</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">0.01</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Mercury (total)</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">0.006</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Nickel</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">0.07</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Copper</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">2</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Zinc</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">No health-based limit</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Iron</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">No health-based limit</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Manganese</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">0.08</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>After determining the values of HMWQI, they are compared with those in 
                            <xref ref-type="table" rid="T4">
Table 4</xref> as guided by the WHO.</p>
                        <p>
Shows standard concentrations of toxic heavy metals in water. If the respective heavy metals stated in 
                            <xref ref-type="table" rid="T3">Table 3</xref> are beyond, then treatment.</p>
                    </table-wrap-foot>
                </table-wrap>
                <p>Heavy Metal Water Quality Index (HMWQI)
                    <disp-formula id="e6">

                        <mml:math display="block">
                            <mml:mtext>HMWQI</mml:mtext>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mo>&#x2211;</mml:mo>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:msub>
                                            <mml:mi>Q</mml:mi>
                                            <mml:mi>i</mml:mi>
                                        </mml:msub>
                                        <mml:mo>&#x00d7;</mml:mo>
                                        <mml:msub>
                                            <mml:mi>W</mml:mi>
                                            <mml:mi>i</mml:mi>
                                        </mml:msub>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                </mml:mrow>
                                <mml:mrow>
                                    <mml:mo>&#x2211;</mml:mo>
                                    <mml:msub>
                                        <mml:mi>W</mml:mi>
                                        <mml:mi>i</mml:mi>
                                    </mml:msub>
                                </mml:mrow>
                            </mml:mfrac>
                        </mml:math>

                        <label>(5)</label>
</disp-formula>
                </p>
                <p>After the procedure 
                    <xref ref-type="table" rid="T4">
Table 4</xref> can be used to guide in determining the WHO standard concentrations.
                    <sup>
                        <xref ref-type="bibr" rid="ref13">13</xref>
                    </sup>
                </p>
                <table-wrap id="T4" orientation="portrait" position="float">
                    <label>
Table 4. </label>
                    <caption>
                        <title>Standard range values of HMWQI (WHO, 2022).
                            <sup>
                                <xref ref-type="bibr" rid="ref24">24</xref>
                            </sup>
                        </title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">HMWQI range</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Water quality status</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Remarks</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">0&#x2013;50</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Excellent</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Applied for all uses</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">51&#x2013;100</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Good</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Minor contamination</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">101&#x2013;200</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Poor</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Possible risk if the water</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">201&#x2013;300</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Very Poor</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Not good without treatment</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">&gt; 300</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Not good for drinking</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Much pollution requires intensive treatment</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>Show the Heavy Metal Water Quality Index ranges as recommended by WHO.</p>
                    </table-wrap-foot>
                </table-wrap>
                <p>

                    <bold>How to Test Pharmaceutical contaminants in water</bold>
                </p>
                <p>Water samples are collected from the water source and stored at a temperature of 4&#x00b0;c for 2&#x00a0;days. Some solid particles were filtered using a micro filter with a minimum porous diameter of 0.45&#x00a0;&#x03bc;m. Liquid Chromatography &#x2013; Tandem Mass Spectrometry is used to detect the pharmaceutical contaminants.
                    <sup>
                        <xref ref-type="bibr" rid="ref14">14</xref>
                    </sup>
                </p>
                <p>The Pharmaceutical classes targeted are Analgesics, Antibiotics, and Antidepressants. WHO does not specify the quantitative standards of pharmaceuticals in water.
                    <sup>
                        <xref ref-type="bibr" rid="ref14">14</xref>
                    </sup> 
                    <xref ref-type="table" rid="T5">
Table 5</xref> elaborates the physiochemical parameters of water for each water sample.</p>
                <table-wrap id="T5" orientation="portrait" position="float">
                    <label>
Table 5. </label>
                    <caption>
                        <title>Purpose of physicochemical parameters and their units.
                            <sup>
                                <xref ref-type="bibr" rid="ref25">25</xref>
                            </sup>
                        </title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Parameter</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Purpose</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Typical Unit</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">pH</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Measures the acidity or alkalinity of water</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">&#x2013;</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Temperature</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Affects chemical reactions and biological reactions in water</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">&#x00b0;C</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Total Dissolved Solids (TDS)</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Total concentration of dissolved substances</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">mg/L</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Turbidity</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Measures the cloudiness or clarity of water</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Nephelometric Turbidity Units (NTU)</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Dissolved Oxygen (DO)</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Amount of oxygen dissolved in water</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">mg/L</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Biochemical Oxygen Demand (BOD)</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">The amount of oxygen required by microorganisms to decompose organic matter.</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">mg/L</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Chemical Oxygen Demand (COD)</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">The amount of oxygen required to oxidize both organic and inorganic substances</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">mg/L</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Hardness</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Concentration of calcium and magnesium ions</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">mg/L</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Electrical Conductivity (EC)</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Indicates the concentration of dissolved salts (ions) in water</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">&#x03bc;S/cm</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>Elaborates the physiochemical parameters of water for each water sample.</p>
                    </table-wrap-foot>
                </table-wrap>
                <p>

                    <bold>How to test salt in water</bold>
                </p>
                <p>This is done by an Electrical Conductivity (EC) meter. The higher the electrical conductivity, the higher the concentration of salt in water. The meter is calibrated with distilled water, the probe is dipped into a water sample, and the EC is read and recorded. The units of EC are in micro Siemens per centimeter (&#x03bc;S/cm).
                    <sup>
                        <xref ref-type="bibr" rid="ref15">15</xref>
                    </sup> Salts are found in water sources as their standard concentrations as identified by WHO are elaborated in 
                    <xref ref-type="table" rid="T6">
Table 6</xref>.</p>
                <table-wrap id="T6" orientation="portrait" position="float">
                    <label>
Table 6. </label>
                    <caption>
                        <title>Typical range of EC for different water sources.
                            <sup>
                                <xref ref-type="bibr" rid="ref16">16</xref>
                            </sup>
                        </title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Water type</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">
Electrical conductivity (&#x03bc;S/cm)</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Drinking water</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">50&#x2013;800</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Freshwater lakes</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">less than 1,500</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Salty water</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">1,500&#x2013;15,000</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Seawater</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">50,000</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Wastewater</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Variable (100&#x2013;10,000 plus)</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Pure distilled water</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">0.5&#x2013;3</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>Salts are found in water sources as their standard concentrations as identified by WHO are elaborated in 
                            <xref ref-type="table" rid="T6">Table 6</xref>.</p>
                    </table-wrap-foot>
                </table-wrap>
                <p>However, the WHO standards of TDS are 300&#x00a0;mg/L/ and it doesn&#x2019;t specify EC.
                    <sup>
                        <xref ref-type="bibr" rid="ref16">16</xref>
                    </sup>
                </p>
                <p>

                    <bold>How to test pesticides in water</bold>
                </p>
                <p>Gas Chromatography&#x2013;Mass Spectrometry is used to detect the amounts of pesticides in water. The amounts are obtained in nanograms per liter. The WHO standards for Dichloro-Diphenyl-Trichloroethane pesticides are 1&#x00a0;&#x03bc;g/L.
                    <sup>
                        <xref ref-type="bibr" rid="ref17">17</xref>
                    </sup>
                </p>
                <p>

                    <bold>2.2.4 Characterization of Biological Contaminants such as Bacteria</bold>
                </p>
                <p>The characterization is done for the bacteria specialized as in 
                    <xref ref-type="table" rid="T7">
Table 7</xref>.</p>
                <table-wrap id="T7" orientation="portrait" position="float">
                    <label>
Table 7. </label>
                    <caption>
                        <title>Examples of bacteria considered.
                            <sup>
                                <xref ref-type="bibr" rid="ref26">26</xref>
                            </sup>
                        </title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Pathogen type</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Examples</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Diseases Caused</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Bacteria</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Escherichia coli (E. coli)</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Gastroenteritis, diarrhea</td>
                            </tr>
                            <tr>
                                <td colspan="1" rowspan="1"/>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Salmonella spp.</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Typhoid fever, salmonellosis</td>
                            </tr>
                            <tr>
                                <td colspan="1" rowspan="1"/>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Vibrio cholerae</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Cholera</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>The characterization is done for the bacteria specialized as in 
                            <xref ref-type="table" rid="T7">
Table 7</xref>.</p>
                    </table-wrap-foot>
                </table-wrap>
                <p>

                    <bold>Materials and equipment used to test bacteria</bold>

                    <list list-type="roman-lower">
                        <list-item>
                            <label>i.</label>
                            <p>Sterile sampling bottles of 100&#x00a0;mL</p>
                        </list-item>
                        <list-item>
                            <label>ii.</label>
                            <p>Membrane filtration unit</p>
                        </list-item>
                        <list-item>
                            <label>iii.</label>
                            <p>Sterile forceps, pipettes, and Petri dishes</p>
                        </list-item>
                        <list-item>
                            <label>iv.</label>
                            <p>Sterile membrane filters with a diameter of 0.45&#x00a0;&#x03bc;m pore size)</p>
                        </list-item>
                        <list-item>
                            <label>v.</label>
                            <p>Eosin Methylene Blue (EMB) Agar</p>
                        </list-item>
                        <list-item>
                            <label>vi.</label>
                            <p>Incubator at a temperature of 35 to 37&#x00a0;&#x00b0;C</p>
                        </list-item>
                        <list-item>
                            <label>vii.</label>
                            <p>A Polymerase Chain Reaction machine for confirmation</p>
                        </list-item>
                    </list>
                </p>
                <p>

                    <bold>Procedures for testing</bold>
                    <sup>
                        <xref ref-type="bibr" rid="ref12">12</xref>
                    </sup>
                    <list list-type="roman-lower">
                        <list-item>
                            <label>i.</label>
                            <p>100&#x00a0;mL of water will be collected using sterilized sealed bottles</p>
                        </list-item>
                        <list-item>
                            <label>ii.</label>
                            <p>To neutralize chlorine, sodium thiosulfate will be added</p>
                        </list-item>
                        <list-item>
                            <label>iii.</label>
                            <p>Place a 0.45&#x00a0;&#x03bc;m membrane filter on the unit.</p>
                        </list-item>
                        <list-item>
                            <label>iv.</label>
                            <p>Pour the water sample into the funnel and apply a vacuum to draw the water through the filter.</p>
                        </list-item>
                        <list-item>
                            <label>v.</label>
                            <p>The filter traps bacteria.</p>
                        </list-item>
                        <list-item>
                            <label>vi.</label>
                            <p>To confirm the bacterial IMViC test, E. coli will undergo testing. For Salmonella, the Triple Sugar Iron (TSI) test will be performed. Additionally, a Polymerase Chain Reaction (PCR) test will be conducted.</p>
                        </list-item>
                    </list>
                </p>
                <p>
                    <xref ref-type="table" rid="T8">
Table 8</xref> indicates examples of bacteria involved in drinking water.
                    <sup>
                        <xref ref-type="bibr" rid="ref17">17</xref>
                    </sup>
                </p>
                <table-wrap id="T8" orientation="portrait" position="float">
                    <label>
Table 8. </label>
                    <caption>
                        <title>Examples of bacteria that can cause water contamination.
                            <sup>
                                <xref ref-type="bibr" rid="ref27">27</xref>
                            </sup>
                        </title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Pathogen type</th>
                                <th align="left" colspan="2" rowspan="1" valign="top">WHO standard for drinking water bacteria colony-forming unit (CFU)</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td colspan="1" rowspan="1"/>
                                <td align="left" colspan="1" rowspan="1" valign="top">Escherichia coli (E. coli)</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0&#x00a0;CFU/100&#x00a0;mL</td>
                            </tr>
                            <tr>
                                <td colspan="1" rowspan="1"/>
                                <td align="left" colspan="1" rowspan="1" valign="top">Salmonella spp.</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0&#x00a0;CFU/100&#x00a0;mL</td>
                            </tr>
                            <tr>
                                <td colspan="1" rowspan="1"/>
                                <td align="left" colspan="1" rowspan="1" valign="top">Vibrio cholerae</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0&#x00a0;CFU/100&#x00a0;mL</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>Clean and safe water, free from bacteria, has zero Colony-Forming Units, as indicated.</p>
                    </table-wrap-foot>
                </table-wrap>
            </sec>
            <sec id="sec9">
                <title>2.3 Design a water treatment system that will be capable of removing the physical, chemical, and microbial water pollutants</title>
                <p>The model will consist of the components below, as shown in 
                    <xref ref-type="fig" rid="f1">
Figure 1</xref>.
                    <sup>
                        <xref ref-type="bibr" rid="ref17">17</xref>,
                        <xref ref-type="bibr" rid="ref30">30</xref>
                    </sup>
                    <list list-type="roman-lower">
                        <list-item>
                            <label>i.</label>
                            <p>A solar panel system for powering all electrical loads of the treatment system</p>
                        </list-item>
                        <list-item>
                            <label>ii.</label>
                            <p>A water source for storing water for treatment</p>
                        </list-item>
                        <list-item>
                            <label>iii.</label>
                            <p>Pipes are a medium for the transportation of water</p>
                        </list-item>
                        <list-item>
                            <label>iv.</label>
                            <p>Two centrifugal water pumps for providing pressure to water to move from one point to another</p>
                        </list-item>
                        <list-item>
                            <label>v.</label>
                            <p>A filtration tank for filtering water from its source</p>
                        </list-item>
                        <list-item>
                            <label>vi.</label>
                            <p>Water, a substance to be treated per its standards</p>
                        </list-item>
                        <list-item>
                            <label>vii.</label>
                            <p>A sedimentation tank for removing suspended solids by gravity</p>
                        </list-item>
                        <list-item>
                            <label>viii.</label>
                            <p>An activated carbon filter for the adsorption of contaminants</p>
                        </list-item>
                        <list-item>
                            <label>ix.</label>
                            <p>An evaporator for boiling water to 100&#x00a0;&#x00b0;C</p>
                        </list-item>
                        <list-item>
                            <label>x.</label>
                            <p>Reverse osmosis, for the removal of metal ions</p>
                        </list-item>
                        <list-item>
                            <label>xi.</label>
                            <p>A condenser for reducing the temperature of the heated water to kill bacteria</p>
                        </list-item>
                        <list-item>
                            <label>xii.</label>
                            <p>Wonder share EndroMax was used to draw the model</p>
                        </list-item>
                        <list-item>
                            <label>xiii.</label>
                            <p>A valve to control the flow of water</p>
                        </list-item>
                    </list>
                </p>
                <fig fig-type="figure" id="f1" orientation="portrait" position="float">
                    <label>
Figure 1. </label>
                    <caption>
                        <title>Model for the water treatment system.
                            <sup>
                                <xref ref-type="bibr" rid="ref30">30</xref>,
                                <xref ref-type="bibr" rid="ref20">20</xref>
                            </sup>
                        </title>
                        <p>
                            <xref ref-type="fig" rid="f1">
Figure 1</xref> is a schematic of a multi-stage water treatment system for pollutant removal. Contaminated water from the source is first pumped into a filtration tank and then a sedimentation tank to remove suspended solids. The water then passes through an activated carbon filter for chemical adsorption, followed by reverse osmosis for fine purification. Finally, the evaporator and condenser stages complete the treatment, producing clean water suitable for use.</p>
                    </caption>
                    <graphic id="gr1" orientation="portrait" position="float" xlink:href="https://f1000research-files.f1000.com/manuscripts/193405/426d905a-e027-4b11-9c71-325675087058_figure1.gif"/>
                </fig>
                <p>The system will be supported by solar power and its design will be done in the following ways:
                    <list list-type="roman-lower">
                        <list-item>
                            <label>i.</label>
                            <p>Identify the overall load current and the operational time</p>
                        </list-item>
                        <list-item>
                            <label>ii.</label>
                            <p>Add system losses</p>
                        </list-item>
                        <list-item>
                            <label>iii.</label>
                            <p>Identify the solar irradiation in daily equipment sun hours</p>
                        </list-item>
                        <list-item>
                            <label>iv.</label>
                            <p>Identify the PV array&#x2019;s current requirements</p>
                        </list-item>
                        <list-item>
                            <label>v.</label>
                            <p>Identify the optimum module arrangement for the solar array</p>
                        </list-item>
                        <list-item>
                            <label>vi.</label>
                            <p>Sizing the battery for power storage</p>
                        </list-item>
                    </list>
                </p>
                <p>The loads of the pumps, evaporator and condenser are shown in 
                    <xref ref-type="table" rid="T9">
Table 9</xref>. Whereas 
                    <xref ref-type="table" rid="T10">
Table 10</xref> indicates loads of two motor pumps, 1 evaporator and 1 condenser.</p>
                <table-wrap id="T9" orientation="portrait" position="float">
                    <label>
Table 9. </label>
                    <caption>
                        <title>Loads of the design showing their respective power, voltage, and current.
                            <sup>
                                <xref ref-type="bibr" rid="ref28">28</xref>
                            </sup>
                        </title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Load (Device)</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Power (W)</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Voltage (V)</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Current (A)&#x00a0;=&#x00a0;power/voltage</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">
Daily usage (hrs)</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Pump 1</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">250</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">230</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">1.09</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">2</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Pump 2</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">250</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">230</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">1.09</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">2</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Evaporator</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">1000</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">230</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">4.35</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">4</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="middle">Condenser</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">800</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">230</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">3.48</td>
                                <td align="left" colspan="1" rowspan="1" valign="middle">4</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>Shows the loads in the water purification system and their daily working rates.</p>
                    </table-wrap-foot>
                </table-wrap>
                <table-wrap id="T10" orientation="portrait" position="float">
                    <label>
Table 10. </label>
                    <caption>
                        <title>Example of some load capacities.
                            <sup>
                                <xref ref-type="bibr" rid="ref28">28</xref>
                            </sup>
                        </title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Load</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">
Capacity (watts)</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Motor Pump (2)</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">10&#x00a0;W</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Evaporator</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">20&#x00a0;W</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Condenser</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">20&#x00a0;W</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Controller and Sensors</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">10&#x00a0;W</td>
                            </tr>
                            <tr>
                                <td colspan="1" rowspan="1"/>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>Total&#x00a0;=&#x00a0;60&#x00a0;W</bold>
</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>Example of some PV Load Capacities.</p>
                    </table-wrap-foot>
                </table-wrap>
                <p>

                    <bold>2.3.1 Energy Balance on a Solar Collector</bold>
                </p>
                <p>This accounts for the solar energy received
                    <bold>,
</bold> absorbed
                    <bold>,
</bold> stored
                    <bold>,
</bold> and lost at the collector surface.
                    <disp-formula id="e7">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi mathvariant="italic">net</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mtext mathvariant="italic">Solar</mml:mtext>
                            </mml:msub>
                            <mml:mo mathvariant="bold">&#x2212;</mml:mo>
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mtext mathvariant="italic">lOSS</mml:mtext>
                            </mml:msub>
                            <mml:mspace width="0em"/>
                        </mml:math>

                        <label>(6)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi mathvariant="italic">net</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the useful heat gain in Watts</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mtext mathvariant="italic">Solar</mml:mtext>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the incident solar energy absorbed in Watts</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mtext mathvariant="italic">lOSS</mml:mtext>
                            </mml:msub>
                            <mml:mspace width="0em"/>
                        </mml:math>
</inline-formula> is the total heat losses (W), including convection, conduction, and radiation</p>
                <p>

                    <bold>2.3.2 Absorbed Solar Radiation</bold>
                </p>
                <p>Absorbed Solar Radiation is the portion of solar energy that a solar panel surface absorbs after sunlight hits it. This kind of absorption is described in 
                    <xref ref-type="disp-formula" rid="e8">Equation 7</xref>.
                    <disp-formula id="e8">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mtext mathvariant="italic">Solar</mml:mtext>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mi mathvariant="normal">A</mml:mi>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mi mathvariant="normal">G</mml:mi>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mi mathvariant="normal">&#x03b1;</mml:mi>
                        </mml:math>

                        <label>(7)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>A is the absorber area (m
                    <sup>2</sup>)</p>
                <p>G is the incident solar radiation (W/m
                    <sup>2</sup>)</p>
                <p>&#x03b1;\alpha&#x03b1; is the absorptivity of the surface (dimensionless)</p>
                <p>

                    <bold>2.3.3 Convective Heat Loss</bold>
                </p>
                <p>Convective heat loss is the loss of thermal energy from a surface to the surrounding air, which carries particles that carry heat away from the solar panel surface. 
                    <xref ref-type="disp-formula" rid="e9">
Equation 8</xref> describes the heat transfer and panel surface temperature.
                    <disp-formula id="e9">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi mathvariant="italic">con</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mi>hc</mml:mi>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mi mathvariant="normal">A</mml:mi>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mi>Ts</mml:mi>
                                <mml:mo mathvariant="bold">&#x2212;</mml:mo>
                                <mml:mi>Ta</mml:mi>
                                <mml:mspace width="0em"/>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(8)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>hc is a convective heat transfer coefficient in W/m
                    <sup>2</sup>&#x00b7;K</p>
                <p>Ts is a surface temperature measured in Kelvin (K)</p>
                <p>Ta is the ambient temperature measured in Kelvin (K)</p>
                <p>

                    <bold>2.3.4 Radiative Heat Loss</bold>
                </p>
                <p>
Radiative Heat Loss is the thermal energy emitted by a surface in the form of infrared radiation, due to its temperature, toward a cooler surrounding (usually the sky or air) and depends on the emissivity of the surface, and is stated in 
                    <xref ref-type="disp-formula" rid="e10">Equation 9</xref>.
                    <disp-formula id="e10">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi mathvariant="italic">rad</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mi mathvariant="normal">&#x03f5;</mml:mi>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mi mathvariant="normal">&#x03c3;</mml:mi>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mi mathvariant="normal">A</mml:mi>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mspace width="0em"/>
                                <mml:msubsup>
                                    <mml:mi>T</mml:mi>
                                    <mml:mi>s</mml:mi>
                                    <mml:mn>4</mml:mn>
                                </mml:msubsup>
                                <mml:mo mathvariant="monospace">&#x2212;</mml:mo>
                                <mml:msubsup>
                                    <mml:mi>T</mml:mi>
                                    <mml:mi>a</mml:mi>
                                    <mml:mn>4</mml:mn>
                                </mml:msubsup>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(9)</label>
</disp-formula>
                </p>
                <p>&#x03f5; is the Emissivity of the surface, &#x03c3; is the Stefan-Boltzmann constant 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mn>5.67</mml:mn>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:msup>
                                <mml:mn>10</mml:mn>
                                <mml:mrow>
                                    <mml:mo>&#x2212;</mml:mo>
                                    <mml:mn>8</mml:mn>
                                </mml:mrow>
                            </mml:msup>
                        </mml:math>
</inline-formula>W/m
                    <sup>2</sup>.K
                    <sup>4</sup>
                </p>
                <p>The total heat loss is given in 
                    <xref ref-type="disp-formula" rid="e11">Equation 10</xref>
                    <disp-formula id="e11">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mtext mathvariant="italic">loss</mml:mtext>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi mathvariant="italic">con</mml:mi>
                            </mml:msub>
                            <mml:mo mathvariant="bold">+</mml:mo>
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi mathvariant="italic">rad</mml:mi>
                            </mml:msub>
                            <mml:mspace width="0em"/>
                        </mml:math>

                        <label>(10)</label>
</disp-formula>
                </p>
                <p>This calls for the energy balance in a Water Volume (Lumped System)
                    <disp-formula id="e12">

                        <mml:math display="block">
                            <mml:mi mathvariant="normal">m</mml:mi>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mi>cp</mml:mi>
                            <mml:mo>.</mml:mo>
                            <mml:mfrac>
                                <mml:mi mathvariant="italic">dT</mml:mi>
                                <mml:mi mathvariant="italic">dt</mml:mi>
                            </mml:mfrac>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi mathvariant="italic">net</mml:mi>
                            </mml:msub>
                        </mml:math>

                        <label>(11)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>m is mass of water (kg)</p>
                <p>cp is the specific heat capacity of water (J/kg&#x00b7;K)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mfrac>
                                <mml:mi mathvariant="italic">dT</mml:mi>
                                <mml:mi mathvariant="italic">dt</mml:mi>
                            </mml:mfrac>
                        </mml:math>
</inline-formula> is the Rate of temperature change (K/s)</p>
                <p>

                    <bold>2.3.5 Solar Collector Efficiency</bold>

                    <disp-formula id="e13">

                        <mml:math display="block">
                            <mml:mi mathvariant="normal">&#x03b7;</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:msub>
                                    <mml:mi>Q</mml:mi>
                                    <mml:mi mathvariant="italic">net</mml:mi>
                                </mml:msub>
                                <mml:mrow>
                                    <mml:mi>A</mml:mi>
                                    <mml:mo>.</mml:mo>
                                    <mml:mi>G</mml:mi>
                                </mml:mrow>
                            </mml:mfrac>
                        </mml:math>

                        <label>(12)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>&#x03b7;&#x00a0;=&#x00a0;Efficiency of the solar collector</p>
                <p>

                    <bold>2.3.6 The overall load current and the operational time</bold>
                </p>
                <p>The normal operating voltage will be 12-24&#x00a0;V. 
                    <xref ref-type="table" rid="T9">
Table 9</xref> shows the loads in the water purification system and their daily working rates.</p>
                <p>The total current, 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>T</mml:mi>
                                <mml:mi>C</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mo>&#x2211;</mml:mo>
                            <mml:mfrac>
                                <mml:msub>
                                    <mml:mi>P</mml:mi>
                                    <mml:mi>i</mml:mi>
                                </mml:msub>
                                <mml:mi>V</mml:mi>
                            </mml:mfrac>
                        </mml:math>
</inline-formula>=
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mn>250</mml:mn>
                                        <mml:mo>+</mml:mo>
                                        <mml:mn>250</mml:mn>
                                        <mml:mo>+</mml:mo>
                                        <mml:mn>1000</mml:mn>
                                        <mml:mo>+</mml:mo>
                                        <mml:mn>800</mml:mn>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mn>230</mml:mn>
                                        <mml:mo>+</mml:mo>
                                        <mml:mn>230</mml:mn>
                                        <mml:mo>+</mml:mo>
                                        <mml:mn>230</mml:mn>
                                        <mml:mo>+</mml:mo>
                                        <mml:mn>230</mml:mn>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>=</mml:mo>
                            <mml:mn mathvariant="bold">2.5</mml:mn>
                            <mml:mi mathvariant="bold-italic">A</mml:mi>
                            <mml:mo mathvariant="bold-italic"/>
                        </mml:math>
</inline-formula>
                </p>
                <p>The Total Energy Demand per Day (E
                    <sub>D</sub>) will be given in 
                    <xref ref-type="disp-formula" rid="e14">Equation 13</xref>.
                    <disp-formula id="e14">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>E</mml:mi>
                                <mml:mi>D</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mo>&#x2211;</mml:mo>
                            <mml:msub>
                                <mml:mi>P</mml:mi>
                                <mml:mi>i</mml:mi>
                            </mml:msub>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:msub>
                                <mml:mi>T</mml:mi>
                                <mml:mi>i</mml:mi>
                            </mml:msub>
                        </mml:math>

                        <label>(13)</label>
</disp-formula>
                </p>
                <p>Where
                    <bold>;</bold>
                </p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>P</mml:mi>
                                <mml:mi>i</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the power rating of the i
                    <sup>th</sup> load (in watts)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>T</mml:mi>
                                <mml:mi>i</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the Time, the i
                    <sup>th</sup> load is operated per day</p>
                <p>

                    <bold>Battery capacity, B</bold>
                    <sub>

                        <bold>C</bold>
                    </sub>
                    <disp-formula id="e15">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>B</mml:mi>
                                <mml:mi>C</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mtext>Battery Capacity</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mi>Ah</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mtext>Battery Voltage</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mi mathvariant="normal">V</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>
</disp-formula>
                </p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mtext>Operational Time Estimate</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mi>hr</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>,</mml:mo>
                        </mml:math>
</inline-formula> which is described in 
                    <xref ref-type="disp-formula" rid="e16">Equation 14</xref>.
                    <disp-formula id="e16">

                        <mml:math display="block">
                            <mml:mi>hr</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:msub>
                                        <mml:mi>B</mml:mi>
                                        <mml:mi>C</mml:mi>
                                    </mml:msub>
                                    <mml:msub>
                                        <mml:mi>P</mml:mi>
                                        <mml:mi>T</mml:mi>
                                    </mml:msub>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mi>DoD</mml:mi>
                        </mml:math>

                        <label>(14)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>P</mml:mi>
                                <mml:mi>T</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the total load power in watts</p>
                <p>DoD is the Depth of Discharge, which is usually a capacity of 80%</p>
                <p>

                    <bold>2.3.7 How to Calculate Total PV System Losses</bold>
                </p>
                <p>
                    <xref ref-type="fig" rid="f2">
Figure 2</xref>,
                    <sup>
                        <xref ref-type="bibr" rid="ref18">18</xref>&#x2013;
                        <xref ref-type="bibr" rid="ref31">31</xref>
                    </sup> describes electrical components used in water treatment. The components helps in identifying the system power losses through determining load for each.</p>
                <fig fig-type="figure" id="f2" orientation="portrait" position="float">
                    <label>
Figure 2. </label>
                    <caption>
                        <title>An off-grid solar circuit for powering a water treatment system.
                            <sup>
                                <xref ref-type="bibr" rid="ref31">31</xref>
                            </sup>
                        </title>
                        <p>A schematic 
                            <italic toggle="yes">of the solar PV array charging system.</italic> The diagram illustrates the flow of solar energy from sunlight to battery storage. Sunlight is captured by the solar photovoltaic (PV) array, generating DC electricity. The generated power passes through a DC overload breaker and a manual disconnect switch for protection and safety. The wiring terminal and charge controller regulate voltage and current, ensuring proper battery charging. Energy is then stored in the connected battery bank, which can be manually disconnected as needed. This system ensures controlled and safe charging of batteries using solar energy.</p>
                    </caption>
                    <graphic id="gr2" orientation="portrait" position="float" xlink:href="https://f1000research-files.f1000.com/manuscripts/193405/426d905a-e027-4b11-9c71-325675087058_figure2.gif"/>
                </fig>
                <p>

                    <bold>2.3.7.1 Losses Inverter</bold>
                </p>
                <p>The inverter will convert DC to AC. It provides a difference between the DC power input from the PV modules and the AC power output as shown in 
                    <xref ref-type="disp-formula" rid="e17">Equation 15</xref>.
                    <sup>
                        <xref ref-type="bibr" rid="ref18">18</xref>
                    </sup>
                    <disp-formula id="e17">

                        <mml:math display="block">
                            <mml:mtext mathvariant="italic">Inverter losses</mml:mtext>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:msub>
                                    <mml:mi>I</mml:mi>
                                    <mml:mi>L</mml:mi>
                                </mml:msub>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mn>1</mml:mn>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:msub>
                                    <mml:mi>I</mml:mi>
                                    <mml:mi mathvariant="italic">eff</mml:mi>
                                </mml:msub>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mn>100</mml:mn>
                        </mml:math>

                        <label>(15)</label>
</disp-formula>
                </p>
                <p>Where 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>I</mml:mi>
                                <mml:mi mathvariant="italic">eff</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the efficiency of an inverter which is determined by the manufacturer. According to PV Evolution Labs (PVEL) in 2019, the inverter power losses ranges from 2&#x2013;5% and efficiency ranges 95 to 98%.</p>
                <p>

                    <bold>2.3.7.2 Soiling Losses</bold>
                </p>
                <p>Accumulation of dust and dirt on the solar panels may cause losses, which are called soiling losses. Soil losses are identified using 
                    <xref ref-type="disp-formula" rid="e4">Equation 3</xref>.9</p>
                <p>The formula for soiling losses (S
                    <sub>L</sub>) will be given by
                    <disp-formula id="e18">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>S</mml:mi>
                                <mml:mi>L</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">[</mml:mo>
                                <mml:mn>1</mml:mn>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:mfrac>
                                    <mml:msub>
                                        <mml:mi>E</mml:mi>
                                        <mml:mtext mathvariant="italic">soiled</mml:mtext>
                                    </mml:msub>
                                    <mml:msub>
                                        <mml:mi>E</mml:mi>
                                        <mml:mtext mathvariant="italic">cleaned</mml:mtext>
                                    </mml:msub>
                                </mml:mfrac>
                                <mml:mo stretchy="true">]</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mn>100</mml:mn>
                        </mml:math>

                        <label>(16)</label>
</disp-formula>
                </p>
                <p>Where 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">E</mml:mi>
                                <mml:mtext mathvariant="bold-italic">soiled</mml:mtext>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the production energy when the PV has dirt (Joules)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">E</mml:mi>
                                <mml:mtext mathvariant="bold-italic">cleaned</mml:mtext>
                            </mml:msub>
                            <mml:mspace width="0.25em"/>
                        </mml:math>
</inline-formula>is the production energy when the PV is clean from dirt in J or Watts</p>
                <p>

                    <bold>2.3.7.3 Losses caused by Temperature (T</bold>
                    <sub>

                        <bold>L</bold>
                    </sub>
                    <bold>)</bold>
                </p>
                <p>This is the environmental temperature that is categorizes the ambient temperature, the level of irradiance, and the speed of wind. The effectiveness of solar cells decreases as the temperature rises. 
                    <xref ref-type="disp-formula" rid="e4">
Equation 3</xref>.10 describes the factors that lead to temperature losses of the PV system.
                    <disp-formula id="e19">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>T</mml:mi>
                                <mml:mi>L</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi>P</mml:mi>
                                <mml:mi mathvariant="italic">STC</mml:mi>
                            </mml:msub>
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi mathvariant="italic">Deg</mml:mi>
                            </mml:msub>
                            <mml:msub>
                                <mml:mi>C</mml:mi>
                                <mml:mtext mathvariant="italic">Temp</mml:mtext>
                            </mml:msub>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:msub>
                                    <mml:mi>T</mml:mi>
                                    <mml:mi>C</mml:mi>
                                </mml:msub>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:mn>25</mml:mn>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(17)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi mathvariant="italic">Deg</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the module quality degradation factor</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>P</mml:mi>
                                <mml:mi mathvariant="italic">STC</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the maximum energy/power at standard test conditions (Watts)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>C</mml:mi>
                                <mml:mtext mathvariant="italic">Temp</mml:mtext>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the temperature coefficient</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>T</mml:mi>
                                <mml:mi>C</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the module temperature (
                    <sup>0</sup> C)</p>
                <p>

                    <bold>2.3.7.4 DC and AC cabling losses</bold>
                </p>
                <p>The DC losses obtained in a PV system cannot be directly determined. For this solar water treatment system, the maximum current, I
                    <sub>M,</sub> and maximum voltage are determined first to determine the cabling losses.
                    <sup>
                        <xref ref-type="bibr" rid="ref19">19</xref>
                    </sup>
                </p>
                <p>

                    <bold>Maximum current I</bold>
                    <sub>

                        <bold>M</bold>
                    </sub>
                    <disp-formula id="e20">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>I</mml:mi>
                                <mml:mi>M</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mrow>
                                        <mml:msub>
                                            <mml:mi>C</mml:mi>
                                            <mml:mi>O</mml:mi>
                                        </mml:msub>
                                        <mml:mi>G</mml:mi>
                                    </mml:mrow>
                                    <mml:msub>
                                        <mml:mi>G</mml:mi>
                                        <mml:mi mathvariant="italic">STC</mml:mi>
                                    </mml:msub>
                                </mml:mfrac>
                                <mml:mo>+</mml:mo>
                                <mml:msub>
                                    <mml:mi>C</mml:mi>
                                    <mml:mn>1</mml:mn>
                                </mml:msub>
                                <mml:msup>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mfrac>
                                            <mml:mi>G</mml:mi>
                                            <mml:msub>
                                                <mml:mi>G</mml:mi>
                                                <mml:mi mathvariant="italic">STC</mml:mi>
                                            </mml:msub>
                                        </mml:mfrac>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                    <mml:mn>2</mml:mn>
                                </mml:msup>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:msub>
                                    <mml:mi>I</mml:mi>
                                    <mml:mi mathvariant="italic">MO</mml:mi>
                                </mml:msub>
                                <mml:mo>+</mml:mo>
                                <mml:msub>
                                    <mml:mi>K</mml:mi>
                                    <mml:mi mathvariant="italic">IM</mml:mi>
                                </mml:msub>
                                <mml:mrow>
                                    <mml:mo stretchy="true">(</mml:mo>
                                    <mml:msub>
                                        <mml:mi>T</mml:mi>
                                        <mml:mi>C</mml:mi>
                                    </mml:msub>
                                    <mml:mo>&#x2212;</mml:mo>
                                    <mml:mn>25</mml:mn>
                                    <mml:mo stretchy="true">)</mml:mo>
                                </mml:mrow>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(18)</label>
</disp-formula>
                </p>
                <p>

                    <bold>Maximum Voltage</bold> 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">V</mml:mi>
                                <mml:mi mathvariant="bold-italic">M</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula>

                    <disp-formula id="e21">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>V</mml:mi>
                                <mml:mi>M</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi>V</mml:mi>
                                <mml:mi mathvariant="italic">MO</mml:mi>
                            </mml:msub>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi>C</mml:mi>
                                <mml:mn>2</mml:mn>
                            </mml:msub>
                            <mml:mi>a</mml:mi>
                            <mml:msub>
                                <mml:mi>V</mml:mi>
                                <mml:mi>t</mml:mi>
                            </mml:msub>
                            <mml:mtext mathvariant="italic">In</mml:mtext>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mi>G</mml:mi>
                                    <mml:msub>
                                        <mml:mi>G</mml:mi>
                                        <mml:mi mathvariant="italic">STC</mml:mi>
                                    </mml:msub>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>+</mml:mo>
                            <mml:mfrac>
                                <mml:msub>
                                    <mml:mi>C</mml:mi>
                                    <mml:mn>3</mml:mn>
                                </mml:msub>
                                <mml:msub>
                                    <mml:mi>N</mml:mi>
                                    <mml:mi>s</mml:mi>
                                </mml:msub>
                            </mml:mfrac>
                            <mml:msup>
                                <mml:mrow>
                                    <mml:mo stretchy="true">(</mml:mo>
                                    <mml:mo stretchy="true">(</mml:mo>
                                    <mml:mi>a</mml:mi>
                                    <mml:msub>
                                        <mml:mi>V</mml:mi>
                                        <mml:mi>t</mml:mi>
                                    </mml:msub>
                                    <mml:mtext mathvariant="italic">In</mml:mtext>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mfrac>
                                            <mml:mi>G</mml:mi>
                                            <mml:msub>
                                                <mml:mi>G</mml:mi>
                                                <mml:mi mathvariant="italic">STC</mml:mi>
                                            </mml:msub>
                                        </mml:mfrac>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                    <mml:mo stretchy="true">)</mml:mo>
                                </mml:mrow>
                                <mml:mn>2</mml:mn>
                            </mml:msup>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi>K</mml:mi>
                                <mml:mi mathvariant="italic">vm</mml:mi>
                            </mml:msub>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mi>G</mml:mi>
                                    <mml:msub>
                                        <mml:mi>G</mml:mi>
                                        <mml:mi mathvariant="italic">STC</mml:mi>
                                    </mml:msub>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:msub>
                                    <mml:mi>T</mml:mi>
                                    <mml:mi>C</mml:mi>
                                </mml:msub>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:mn>25</mml:mn>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(19)</label>
</disp-formula>
                </p>
                <p>Where 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>V</mml:mi>
                                <mml:mi>t</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:msub>
                                    <mml:mi>N</mml:mi>
                                    <mml:mrow>
                                        <mml:mi>s</mml:mi>
                                        <mml:mspace width="0.25em"/>
                                        <mml:mi>k</mml:mi>
                                        <mml:msub>
                                            <mml:mi>T</mml:mi>
                                            <mml:mi>C</mml:mi>
                                        </mml:msub>
                                    </mml:mrow>
                                </mml:msub>
                                <mml:mrow>
                                    <mml:mi>q</mml:mi>
                                    <mml:mo>,</mml:mo>
                                </mml:mrow>
                            </mml:mfrac>
                        </mml:math>
</inline-formula> where k is the Boltzmann constant 1.3806503&#x00a0;&#x00d7;&#x00a0;10
                    <sup>&#x2212;23</sup>&#x00a0;J/&#x00b0;C, q&#x00a0;=&#x00a0;1.60217646&#x00a0;&#x00d7;&#x00a0;10
                    <sup>&#x2212;23</sup> C is the charge of an electron. 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>T</mml:mi>
                                <mml:mi>C</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> and G are temperatures (&#x00b0;C).
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>G</mml:mi>
                                <mml:mi mathvariant="italic">STC</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula>=1000&#x00a0;W/m
                    <sup>2</sup>&#x00a0;=&#x00a0;irradiance of the standard testing condition. The other parameters will be used from the manufacturer&#x2019;s manual.</p>
                <p>The voltage difference in this DC will be obtained from Equation 19.
                    <disp-formula id="e22">

                        <mml:math display="block">
                            <mml:mi>&#x0394;</mml:mi>
                            <mml:msub>
                                <mml:mi>V</mml:mi>
                                <mml:mi>M</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi>V</mml:mi>
                                <mml:mi>M</mml:mi>
                            </mml:msub>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:msub>
                                <mml:mi>N</mml:mi>
                                <mml:mi>S</mml:mi>
                            </mml:msub>
                            <mml:mo>&#x2212;</mml:mo>
                            <mml:msub>
                                <mml:mi>V</mml:mi>
                                <mml:mi mathvariant="italic">DC</mml:mi>
                            </mml:msub>
                        </mml:math>

                        <label>(20)</label>
</disp-formula>
                </p>
                <p>Where</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>V</mml:mi>
                                <mml:mi mathvariant="italic">DC</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the measured voltage in volts. Measured at the inverter&#x2019;s input.</p>
                <p>The cabling losses (C
                    <sub>DCL</sub>) are given in 
                    <xref ref-type="disp-formula" rid="e23">Equation 21</xref>.
                    <disp-formula id="e23">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>C</mml:mi>
                                <mml:mi mathvariant="italic">DCL</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mi>&#x0394;</mml:mi>
                                    <mml:msub>
                                        <mml:mi>V</mml:mi>
                                        <mml:mi>M</mml:mi>
                                    </mml:msub>
                                    <mml:mo>&#x00d7;</mml:mo>
                                    <mml:msub>
                                        <mml:mi>I</mml:mi>
                                        <mml:mi mathvariant="italic">DC</mml:mi>
                                    </mml:msub>
                                </mml:mrow>
                                <mml:mrow>
                                    <mml:msub>
                                        <mml:mi>V</mml:mi>
                                        <mml:mrow>
                                            <mml:mi>M</mml:mi>
                                            <mml:mo>&#x00d7;</mml:mo>
                                        </mml:mrow>
                                    </mml:msub>
                                    <mml:msub>
                                        <mml:mi>I</mml:mi>
                                        <mml:mi>M</mml:mi>
                                    </mml:msub>
                                    <mml:mo>&#x00d7;</mml:mo>
                                    <mml:msub>
                                        <mml:mi>Q</mml:mi>
                                        <mml:mi mathvariant="italic">Deg</mml:mi>
                                    </mml:msub>
                                </mml:mrow>
                            </mml:mfrac>
                        </mml:math>

                        <label>(21)</label>
</disp-formula>
                </p>
                <p>Where 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>I</mml:mi>
                                <mml:mi mathvariant="italic">DC</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> the DC is current measured at the input point of the inverter.</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi mathvariant="italic">Deg</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the PV module quality degradation factor.</p>
                <p>

                    <bold>2.3.7.5 Mismatch and wiring losses</bold>
                </p>
                <p>This occurs when uneven panel performance and inter-cell/inter-module ohmic losses are obtained in the PV system. 
                    <xref ref-type="disp-formula" rid="e24">
Equation 22</xref> describes mismatch losses.
                    <disp-formula id="e24">

                        <mml:math display="block">
                            <mml:mtext>Mismatch</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mtext>Loss</mml:mtext>
                            <mml:mo>,</mml:mo>
                            <mml:mspace width="0.50em"/>
                            <mml:msub>
                                <mml:mi>M</mml:mi>
                                <mml:mi>L</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">[</mml:mo>
                                <mml:mn>1</mml:mn>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:mfrac>
                                    <mml:msub>
                                        <mml:mi>P</mml:mi>
                                        <mml:mi>a</mml:mi>
                                    </mml:msub>
                                    <mml:msub>
                                        <mml:mi>P</mml:mi>
                                        <mml:mi>i</mml:mi>
                                    </mml:msub>
                                </mml:mfrac>
                                <mml:mo stretchy="true">]</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(22)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>P</mml:mi>
                                <mml:mi>a</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the Power of the array with mismatch</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>P</mml:mi>
                                <mml:mi>i</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the Power of a perfectly matched array</p>
                <p>Pa and Pi will be simulated using PVsyst</p>
                <p>

                    <bold>2.3.7.6 Wiring loss</bold>
                </p>
                <p>Wire losses are caused by current with the wire, resistivity, and area of the wire as defined in 
                    <xref ref-type="disp-formula" rid="e25">Equation 23</xref>.
                    <disp-formula id="e25">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>W</mml:mi>
                                <mml:mi>L</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:msup>
                                <mml:mi>I</mml:mi>
                                <mml:mn>2</mml:mn>
                            </mml:msup>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mi mathvariant="normal">&#x03c1;</mml:mi>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mn>2</mml:mn>
                                    <mml:mi>L</mml:mi>
                                </mml:mrow>
                                <mml:mi>A</mml:mi>
                            </mml:mfrac>
                        </mml:math>

                        <label>(23)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi mathvariant="normal">&#x03c1;</mml:mi>
                        </mml:math>
</inline-formula> is the Resistivity of the wire material (&#x03a9;&#x00b7;m)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi>A</mml:mi>
                        </mml:math>
</inline-formula> is the area of the cable wire (m
                    <sup>2</sup>)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi>I</mml:mi>
                        </mml:math>
</inline-formula> is the length of cable wire (m)</p>
                <p>

                    <bold>2.3.7.7 Degradation (annual)</bold>
                </p>
                <p>As time goes on, the PV panel fades. The manufacturer indicates the degradation in a manual database. This will be used to identify the quality over time of the PV module.</p>
                <p>

                    <bold>2.3.7.8 Performance Ratio (PR)</bold>
                </p>
                <p>This will help to determine the system&#x2019;s availability. This will give the amount of sunlight required by the solar panel and convert to AC</p>
                <p>According to,
                    <sup>
                        <xref ref-type="bibr" rid="ref21">21</xref>
                    </sup>
                    <disp-formula id="e26">

                        <mml:math display="block">
                            <mml:mi mathvariant="italic">PR</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:munderover>
                                <mml:mo>&#x2211;</mml:mo>
                                <mml:mi>t</mml:mi>
                                <mml:mi>T</mml:mi>
                            </mml:munderover>
                            <mml:msup>
                                <mml:msub>
                                    <mml:mi>P</mml:mi>
                                    <mml:mi>t</mml:mi>
                                </mml:msub>
                                <mml:mtext mathvariant="italic">In Output</mml:mtext>
                            </mml:msup>
                            <mml:mo>&#x00f7;</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:munderover>
                                    <mml:mo>&#x2211;</mml:mo>
                                    <mml:mi>t</mml:mi>
                                    <mml:mi>T</mml:mi>
                                </mml:munderover>
                                <mml:msub>
                                    <mml:mi>P</mml:mi>
                                    <mml:mi mathvariant="italic">STC</mml:mi>
                                </mml:msub>
                                <mml:mo>&#x00d7;</mml:mo>
                                <mml:mrow>
                                    <mml:mo stretchy="true">(</mml:mo>
                                    <mml:mfrac>
                                        <mml:msub>
                                            <mml:mi>G</mml:mi>
                                            <mml:mi>t</mml:mi>
                                        </mml:msub>
                                        <mml:msub>
                                            <mml:mi>G</mml:mi>
                                            <mml:mi mathvariant="italic">STC</mml:mi>
                                        </mml:msub>
                                    </mml:mfrac>
                                    <mml:mo stretchy="true">)</mml:mo>
                                </mml:mrow>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(24)</label>
</disp-formula>
                </p>
                <p>Where t is the time interval in hours</p>
                <p>T is the total number of intervals</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msup>
                                <mml:msub>
                                    <mml:mi>P</mml:mi>
                                    <mml:mi>t</mml:mi>
                                </mml:msub>
                                <mml:mtext mathvariant="italic">In Output</mml:mtext>
                            </mml:msup>
                        </mml:math>
</inline-formula> is the measured or actual AC output power of the PV system</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>P</mml:mi>
                                <mml:mi mathvariant="italic">STC</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the rated power output of the PV module or system under Standard Test Conditions (STC)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>G</mml:mi>
                                <mml:mi>t</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the Irradiance on the plane of the array at time t</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>G</mml:mi>
                                <mml:mi mathvariant="italic">STC</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the Standard irradiance under STC, usually taken as 1000&#x00a0;W/m
                    <sup>2</sup>
                </p>
                <p>

                    <bold>2.3.7.9 Shading Losses</bold>
                </p>
                <p>Shading losses in a photovoltaic system refer to the reduction in energy output caused by the shadows of trees, buildings, poles, or masts, and the losses are described in 
                    <xref ref-type="disp-formula" rid="e27">Equation 25</xref>.
                    <disp-formula id="e27">

                        <mml:math display="block">
                            <mml:mtext>Shading Losses</mml:mtext>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mn>1</mml:mn>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:mfrac>
                                    <mml:msub>
                                        <mml:mi>E</mml:mi>
                                        <mml:mtext mathvariant="italic">Shadded</mml:mtext>
                                    </mml:msub>
                                    <mml:msub>
                                        <mml:mi>E</mml:mi>
                                        <mml:mtext mathvariant="italic">Unshadded</mml:mtext>
                                    </mml:msub>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(25)</label>
</disp-formula>
                </p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">E</mml:mi>
                                <mml:mtext mathvariant="bold-italic">Shadded</mml:mtext>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the energy output of a PV system with shade (W/m
                    <sup>2</sup>).</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">E</mml:mi>
                                <mml:mtext mathvariant="bold-italic">Unshadded</mml:mtext>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the energy output of a PV system without shade (W/m
                    <sup>2</sup>).
                    <disp-formula id="e28">

                        <mml:math display="block">
                            <mml:mtext mathvariant="italic">Overall</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mtext mathvariant="italic">PV</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mtext mathvariant="italic">Sytem efficiency</mml:mtext>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mn>1</mml:mn>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:mo>%</mml:mo>
                                <mml:mtext mathvariant="italic">total losses</mml:mtext>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>
</disp-formula>
                </p>
                <p>Extraterrestrial Solar Irradiance on a Horizontal Surface (
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi mathvariant="bold">H</mml:mi>
                                <mml:mi mathvariant="bold">o</mml:mi>
                            </mml:msub>
                            <mml:mo stretchy="true">)</mml:mo>
                        </mml:math>
</inline-formula>
                </p>
                <p>The amount of solar energy received per unit area on a horizontal surface at the top of the Earth&#x2019;s atmosphere during a given time is described in 
                    <xref ref-type="disp-formula" rid="e29">Equation 26</xref>
                    <disp-formula id="e29">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>o</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mn>24</mml:mn>
                                    <mml:mo>&#x00d7;</mml:mo>
                                    <mml:mn>3600</mml:mn>
                                    <mml:msub>
                                        <mml:mi>G</mml:mi>
                                        <mml:mi>s</mml:mi>
                                    </mml:msub>
                                </mml:mrow>
                                <mml:mi>&#x03c0;</mml:mi>
                            </mml:mfrac>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mn>1</mml:mn>
                                <mml:mo>+</mml:mo>
                                <mml:mn>0.033</mml:mn>
                                <mml:mo mathvariant="italic">cos</mml:mo>
                                <mml:mrow>
                                    <mml:mo stretchy="true">(</mml:mo>
                                    <mml:mfrac>
                                        <mml:mrow>
                                            <mml:mn>360</mml:mn>
                                            <mml:mi>n</mml:mi>
                                        </mml:mrow>
                                        <mml:mn>365</mml:mn>
                                    </mml:mfrac>
                                    <mml:mo stretchy="true">)</mml:mo>
                                </mml:mrow>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">[</mml:mo>
                                <mml:mo mathvariant="italic">cos</mml:mo>
                                <mml:mrow>
                                    <mml:mo stretchy="true">(</mml:mo>
                                    <mml:mo>&#x00f8;</mml:mo>
                                    <mml:mo stretchy="true">)</mml:mo>
                                </mml:mrow>
                                <mml:mo mathvariant="italic">cos</mml:mo>
                                <mml:mrow>
                                    <mml:mo stretchy="true">(</mml:mo>
                                    <mml:mi>&#x2202;</mml:mi>
                                    <mml:mo stretchy="true">)</mml:mo>
                                </mml:mrow>
                                <mml:mo mathvariant="italic">sin</mml:mo>
                                <mml:mrow>
                                    <mml:mo stretchy="true">(</mml:mo>
                                    <mml:mi mathvariant="normal">&#x03c9;</mml:mi>
                                    <mml:mo stretchy="true">)</mml:mo>
                                </mml:mrow>
                                <mml:mo stretchy="true">]</mml:mo>
                            </mml:mrow>
                            <mml:mo>+</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mi>&#x03c0;</mml:mi>
                                    <mml:mi mathvariant="normal">&#x03c9;</mml:mi>
                                    <mml:mo mathvariant="italic">sin</mml:mo>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mo>&#x00f8;</mml:mo>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                    <mml:mo mathvariant="italic">sin</mml:mo>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mi>&#x2202;</mml:mi>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                </mml:mrow>
                                <mml:mn>180</mml:mn>
                            </mml:mfrac>
                        </mml:math>

                        <label>(26)</label>
</disp-formula>
                </p>
                <p>Where:</p>
                <p>G
                    <sub>s</sub> is the Solar constant (W/m
                    <sup>2</sup>)</p>
                <p>n is Day of the year (1&#x2013;365)</p>
                <p>&#x03a6; is Latitude (radians or degrees)</p>
                <p>&#x03b4; is the Solar declination (radians or degrees)</p>
                <p>&#x03c9; is the Sunset hour angle (radians or degrees)</p>
                <p>The declination angle can be given as
                    <disp-formula id="e30">

                        <mml:math display="block">
                            <mml:mi>&#x2202;</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:msup>
                                <mml:mn>23.45</mml:mn>
                                <mml:mn>0</mml:mn>
                            </mml:msup>
                            <mml:mo mathvariant="italic">sin</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mn>360</mml:mn>
                                    <mml:mn>365</mml:mn>
                                </mml:mfrac>
                                <mml:mrow>
                                    <mml:mo stretchy="true">(</mml:mo>
                                    <mml:mn>284</mml:mn>
                                    <mml:mo>+</mml:mo>
                                    <mml:mi>n</mml:mi>
                                    <mml:mo stretchy="true">)</mml:mo>
                                </mml:mrow>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(27)</label>
</disp-formula>
                </p>
                <p>Sunset Hour Angle
                    <disp-formula id="e31">

                        <mml:math display="block">
                            <mml:mi mathvariant="normal">&#x03c9;</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:msup>
                                <mml:mo mathvariant="italic">cos</mml:mo>
                                <mml:mrow>
                                    <mml:mo>&#x2212;</mml:mo>
                                    <mml:mn>1</mml:mn>
                                </mml:mrow>
                            </mml:msup>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:mo mathvariant="italic">tan</mml:mo>
                                <mml:mo>&#x00f8;</mml:mo>
                                <mml:mo mathvariant="italic">tan</mml:mo>
                                <mml:mi>&#x2202;</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(28
                            <bold>)</bold>
</label>
</disp-formula>
                </p>
                <p>

                    <bold>2.3.7.10 Solar Irradiation on an inclined plane (H
                        <sub>t</sub>)</bold>
                </p>
                <p>This is the amount of solar energy that strikes a tilted surface of a solar panel for a water treatment system over time and is determined in 
                    <xref ref-type="disp-formula" rid="e32">Equation 29</xref>.
                    <disp-formula id="e32">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>t</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>b</mml:mi>
                            </mml:msub>
                            <mml:msub>
                                <mml:mi>R</mml:mi>
                                <mml:mi>b</mml:mi>
                            </mml:msub>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>d</mml:mi>
                            </mml:msub>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mrow>
                                        <mml:mn>1</mml:mn>
                                        <mml:mo>+</mml:mo>
                                        <mml:mtext mathvariant="italic">cos&#x03b2;</mml:mtext>
                                    </mml:mrow>
                                    <mml:mn>2</mml:mn>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>+</mml:mo>
                            <mml:mi>H</mml:mi>
                            <mml:msub>
                                <mml:mi>G</mml:mi>
                                <mml:mi>r</mml:mi>
                            </mml:msub>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mrow>
                                        <mml:mn>1</mml:mn>
                                        <mml:mo>&#x2212;</mml:mo>
                                        <mml:mtext mathvariant="italic">cos&#x03b2;</mml:mtext>
                                    </mml:mrow>
                                    <mml:mn>2</mml:mn>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(29)</label>
</disp-formula>
                </p>
                <p>Where H is the measured global radiation on the surface that is horizontal</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi>&#x03b2;</mml:mi>
                        </mml:math>
</inline-formula> is the Tilt angle</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi mathvariant="italic">HG</mml:mi>
                                <mml:mi>r</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the ground reflectance (typically 0.2)</p>
                <p>H
                    <sub>b</sub> is the estimated beam</p>
                <p>R
                    <sub>b</sub> is the ratio of the beam radiation on a tilted surface to a horizontal surface</p>
                <p>H
                    <sub>d</sub> diffuse beam</p>
                <p>

                    <bold>2.3.7.11 Total Solar Irradiance on Collector Surface (</bold>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">I</mml:mi>
                                <mml:mi mathvariant="bold-italic">t</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula>

                    <bold>)</bold>

                    <disp-formula id="e33">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>I</mml:mi>
                                <mml:mi>t</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mi mathvariant="normal">I</mml:mi>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mi mathvariant="normal">R</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi>I</mml:mi>
                                <mml:mi>d</mml:mi>
                            </mml:msub>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mrow>
                                        <mml:mn>1</mml:mn>
                                        <mml:mo>+</mml:mo>
                                        <mml:mtext mathvariant="italic">cos&#x03b2;</mml:mtext>
                                    </mml:mrow>
                                    <mml:mn>2</mml:mn>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi>I</mml:mi>
                                <mml:mi>r</mml:mi>
                            </mml:msub>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mrow>
                                        <mml:mn>1</mml:mn>
                                        <mml:mo>&#x2212;</mml:mo>
                                        <mml:mtext mathvariant="italic">cos&#x03b2;</mml:mtext>
                                    </mml:mrow>
                                    <mml:mn>2</mml:mn>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(30)</label>
</disp-formula>
                </p>
                <p>Where</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>I</mml:mi>
                                <mml:mi>t</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the total irradiance on the tilted surface [W/m
                    <sup>2</sup>]</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi mathvariant="normal">I</mml:mi>
                        </mml:math>
</inline-formula> is the direct irradiance on horizontal [W/m
                    <sup>2</sup>]</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>I</mml:mi>
                                <mml:mi>d</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the diffuse irradiance on horizontal [W/m
                    <sup>2</sup>]</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>I</mml:mi>
                                <mml:mi>r</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mi>&#x03c1;g</mml:mi>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mi mathvariant="normal">I</mml:mi>
                                <mml:mo>+</mml:mo>
                                <mml:msub>
                                    <mml:mi>I</mml:mi>
                                    <mml:mi>d</mml:mi>
                                </mml:msub>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>
</inline-formula>: Reflected irradiance, where &#x03c1;
                    <sub>g</sub> is ground reflectivity (0.2)</p>
                <p>&#x0392; is the Tilt angle of the collector</p>
                <p>R is the Ratio of the beam irradiance on tilted to horizontal</p>
                <p>The current requirement will be determined by using the formula.
                    <disp-formula id="e34">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>I</mml:mi>
                                <mml:mrow>
                                    <mml:mi mathvariant="italic">PV</mml:mi>
                                    <mml:mspace width="0.25em"/>
                                    <mml:mtext mathvariant="italic">array</mml:mtext>
                                </mml:mrow>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:msub>
                                    <mml:mi>P</mml:mi>
                                    <mml:mtext mathvariant="italic">Total</mml:mtext>
                                </mml:msub>
                                <mml:msub>
                                    <mml:mi>V</mml:mi>
                                    <mml:mtext mathvariant="italic">Sytem</mml:mtext>
                                </mml:msub>
                            </mml:mfrac>
                        </mml:math>

                        <label>(31)</label>
</disp-formula>

                    <disp-formula id="e35">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>P</mml:mi>
                                <mml:mtext mathvariant="italic">Total</mml:mtext>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mn>60</mml:mn>
                                    <mml:mi>W</mml:mi>
                                </mml:mrow>
                                <mml:mrow>
                                    <mml:mtext mathvariant="italic">Sytem</mml:mtext>
                                    <mml:mspace width="0.25em"/>
                                    <mml:mi mathvariant="italic">eff</mml:mi>
                                </mml:mrow>
                            </mml:mfrac>
                        </mml:math>

                        <label>(32)</label>
</disp-formula>
                </p>
                <p>The system will be a 24&#x00a0;V voltage system
                    <disp-formula id="e36">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>I</mml:mi>
                                <mml:mrow>
                                    <mml:mi mathvariant="italic">PV</mml:mi>
                                    <mml:mspace width="0.25em"/>
                                    <mml:mtext mathvariant="italic">array</mml:mtext>
                                </mml:mrow>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:msub>
                                    <mml:mi>P</mml:mi>
                                    <mml:mtext mathvariant="italic">Total</mml:mtext>
                                </mml:msub>
                                <mml:msub>
                                    <mml:mi>V</mml:mi>
                                    <mml:mtext mathvariant="italic">Sytem</mml:mtext>
                                </mml:msub>
                            </mml:mfrac>
                        </mml:math>

                        <label>(33)</label>
</disp-formula>
                </p>
                <p>

                    <bold>2.3.7.12 Solar Panel &amp; Battery Sizing</bold>
                </p>
                <p>Time required to treatment water per day
                    <disp-formula id="e37">

                        <mml:math display="block">
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mn>1000</mml:mn>
                                    <mml:mspace width="0.25em"/>
                                    <mml:mi mathvariant="normal">L</mml:mi>
                                </mml:mrow>
                                <mml:mrow>
                                    <mml:mtext mathvariant="bold-italic">Pump Rate</mml:mtext>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mi mathvariant="bold-italic">L</mml:mi>
                                        <mml:mo>/</mml:mo>
                                        <mml:mi mathvariant="bold-italic">h</mml:mi>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                </mml:mrow>
                            </mml:mfrac>
                        </mml:math>

                        <label>(34)</label>
</disp-formula>
                </p>
                <p>Daily energy&#x00a0;=&#x00a0;Total Load &#x00d7; Time required to treat water per day</p>
                <p>The PV system is for 12&#x00a0;V</p>
                <p>Proposed battery sizing&#x00a0;=&#x00a0;25&#x00a0;Ah&#x00a0;&#x00d7;&#x00a0;1.5 (safety factor)&#x00a0;=&#x00a0;40&#x00a0;Ah</p>
            </sec>
        </sec>
        <sec id="sec10">
            <title>3. Hydraulic design of the system</title>
            <p>

                <disp-formula id="e38">

                    <mml:math display="block">
                        <mml:mi>PV</mml:mi>
                        <mml:mspace width="0.25em"/>
                        <mml:mtext>panel size</mml:mtext>
                        <mml:mo>=</mml:mo>
                        <mml:mfrac>
                            <mml:mrow>
                                <mml:mtext>Daily energy</mml:mtext>
                                <mml:mspace width="0.25em"/>
                            </mml:mrow>
                            <mml:mrow>
                                <mml:mi>Sun</mml:mi>
                                <mml:mspace width="0.25em"/>
                                <mml:mtext>Hours</mml:mtext>
                            </mml:mrow>
                        </mml:mfrac>
                    </mml:math>

                    <label>(35)</label>
</disp-formula>This invlolves the forms of water flow as shown in 
                <xref ref-type="table" rid="T11">
Table 11</xref>.</p>
            <table-wrap id="T11" orientation="portrait" position="float">
                <label>
Table 11. </label>
                <caption>
                    <title>Ranges of different types flow of liquid flow.
                        <sup>
                            <xref ref-type="bibr" rid="ref29">29</xref>
                        </sup>
                    </title>
                </caption>
                <table content-type="article-table" frame="hsides">
                    <thead>
                        <tr>
                            <th align="left" colspan="1" rowspan="1" valign="top">Reynolds number</th>
                            <th align="left" colspan="1" rowspan="1" valign="top">Flow regime</th>
                            <th align="left" colspan="1" rowspan="1" valign="top">
Notes</th>
                        </tr>
                    </thead>
                    <tbody>
                        <tr>
                            <td align="left" colspan="1" rowspan="1" valign="middle">Re&#x00a0;&lt;&#x00a0;1</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">Laminar</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">Darcy&#x2019;s law is valid</td>
                        </tr>
                        <tr>
                            <td align="left" colspan="1" rowspan="1" valign="middle">1&#x00a0;&lt;&#x00a0;Re&#x00a0;&lt;&#x00a0;10</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">Transitional</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">Slight deviations from Darcy</td>
                        </tr>
                        <tr>
                            <td align="left" colspan="1" rowspan="1" valign="middle">Re&#x00a0;&gt;&#x00a0;10</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">Turbulent</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">Inertial effects significant</td>
                        </tr>
                    </tbody>
                </table>
                <table-wrap-foot>
                    <p>Ranges of different types of liquid flow</p>
                </table-wrap-foot>
            </table-wrap>
            <sec id="sec11">
                <title>3.1 Design of the source of water</title>
                <p>To determine the required capacity of the source, the daily water demand is estimated first.
                    <disp-formula id="e39">

                        <mml:math display="block">
                            <mml:mtext mathvariant="italic">Demand</mml:mtext>
                            <mml:mo>,</mml:mo>
                            <mml:mspace width="0.25em"/>
                            <mml:mi>D</mml:mi>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:msup>
                                    <mml:mi mathvariant="normal">m</mml:mi>
                                    <mml:mo>&#x00b3;</mml:mo>
                                </mml:msup>
                                <mml:mo>/</mml:mo>
                                <mml:mi>day</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>=</mml:mo>
                            <mml:mi mathvariant="italic">NQ</mml:mi>
                        </mml:math>

                        <label>(36)</label>
</disp-formula>
                </p>
                <p>Where N is the population of people to receive water</p>
                <p>D is in m
                    <sup>3</sup>/day</p>
                <p>Q is per capita water consumption (Liters/person/day)</p>
                <p>The flow rate,

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi>Q</mml:mi>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mi mathvariant="normal">m</mml:mi>
                                <mml:mn>3</mml:mn>
                                <mml:mo>/</mml:mo>
                                <mml:mi mathvariant="normal">h</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>=</mml:mo>
                            <mml:mi>D</mml:mi>
                            <mml:mo>/</mml:mo>
                            <mml:mi>T</mml:mi>
                        </mml:math>
</inline-formula>
                </p>
                <p>Where T is the number of operating hours
                    <disp-formula id="e40">

                        <mml:math display="block">
                            <mml:mtext>Maximum</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mtext>daily</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mtext>Demand</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi>D</mml:mi>
                                <mml:mi>V</mml:mi>
                            </mml:msub>
                            <mml:mo mathvariant="bold">&#x00d7;</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">P</mml:mi>
                                <mml:mi mathvariant="bold-italic">D</mml:mi>
                            </mml:msub>
                        </mml:math>

                        <label>(37)</label>
</disp-formula>
                </p>
                <p>Where</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>D</mml:mi>
                                <mml:mi>V</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the average daily demand?</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">P</mml:mi>
                                <mml:mi mathvariant="bold-italic">D</mml:mi>
                            </mml:msub>
                            <mml:mspace width="0.25em"/>
                        </mml:math>
</inline-formula>is the peak demand factor, usually 1.8</p>
                <p>Source capacity
                    <disp-formula id="e41">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>V</mml:mi>
                                <mml:mi>S</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi>A</mml:mi>
                                <mml:mi>S</mml:mi>
                            </mml:msub>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>e</mml:mi>
                            </mml:msub>
                        </mml:math>

                        <label>(38)</label>
</disp-formula>
                </p>
                <p>Where 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>V</mml:mi>
                                <mml:mi>S</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> the storage volume is used (m
                    <sup>3</sup>)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>A</mml:mi>
                                <mml:mi>S</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the surface area of the water body (m
                    <sup>2</sup>)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>e</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the effective depth of water (m)</p>
            </sec>
            <sec id="sec12">
                <title>3.2 Hydraulic design of the intake pipe</title>
                <p>Sizing the intake pipe,

                    <disp-formula id="e42">

                        <mml:math display="block">
                            <mml:mi>A</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mi>Q</mml:mi>
                                <mml:mi>V</mml:mi>
                            </mml:mfrac>
                        </mml:math>

                        <label>(39)</label>
</disp-formula>
                </p>
                <p>Where A is the cross-sectional area of a pipe</p>
                <p>Q is the flow rate</p>
                <p>V is the velocity determined by the pump of the manufacturer</p>
                <p>

                    <bold>3.2.1 Pump Design</bold>
                </p>
                <p>

                    <disp-formula id="e43">

                        <mml:math display="block">
                            <mml:mi>Q</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mi>D</mml:mi>
                            <mml:mo>/</mml:mo>
                            <mml:mi>T</mml:mi>
                        </mml:math>

                        <label>(40)</label>
</disp-formula>
                </p>
                <p>Where Q is the pump flow rate (m
                    <sup>3</sup>/s)</p>
                <p>D is the pump daily demand (m
                    <sup>3/</sup>day)</p>
                <p>T is the operating hours in a day</p>
                <p>

                    <disp-formula id="e44">

                        <mml:math display="block">
                            <mml:mtext>Total</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mtext>Dynamic</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mtext>Head</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mi>TDH</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>S</mml:mi>
                            </mml:msub>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>D</mml:mi>
                            </mml:msub>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>F</mml:mi>
                            </mml:msub>
                            <mml:mspace width="0em"/>
                        </mml:math>

                        <label>(41)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>S</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the Suction head (vertical lift from source to pump)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>D</mml:mi>
                            </mml:msub>
                            <mml:mspace width="0.25em"/>
                        </mml:math>
</inline-formula>is the delivery head (vertical height to the highest point in the system)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>F</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the friction loss in the pipe</p>
                <p>Determine Pump Power, H
                    <sub>P</sub>
                    <disp-formula id="e45">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>P</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mi mathvariant="normal">Q</mml:mi>
                                    <mml:mo>&#x00b7;</mml:mo>
                                    <mml:mi mathvariant="normal">H</mml:mi>
                                </mml:mrow>
                                <mml:mn>367</mml:mn>
                            </mml:mfrac>
                        </mml:math>

                        <label>(42)</label>
</disp-formula>
                </p>
                <p>Or where Q is the flow (m
                    <sup>3</sup>/s)</p>
                <p>H is the Head (m)</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mi>P</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> = Water horsepower (Watts)</p>
                <p>
1 Horse power&#x00a0;=&#x00a0;746 Watts</p>
                <p>

                    <bold>3.2.2 Hydraulic Power</bold>
                </p>
                <p>The hydraulic power of a pump can either be static or dynamic, and it depends on the mass flow rate, the density of water, and the differential height.</p>
                <p>Static hydraulic power from one height to another is given by,

                    <disp-formula id="e46">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi mathvariant="normal">P</mml:mi>
                                <mml:mi mathvariant="normal">s</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mi mathvariant="normal">Q</mml:mi>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mi mathvariant="normal">&#x03c1;</mml:mi>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mi mathvariant="normal">g</mml:mi>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mi mathvariant="normal">h</mml:mi>
                        </mml:math>

                        <label>(43)</label>
</disp-formula>
                </p>
                <p>Where 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi mathvariant="normal">P</mml:mi>
                        </mml:math>
</inline-formula>
                    <sub>s</sub> is the hydraulic power (W)</p>
                <p>H is the maximum lift in meters. This is the head at the outlet</p>
                <p>Q is mass flow rate (m
                    <sup>3</sup>/s), 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi mathvariant="normal">&#x03c1;</mml:mi>
                            <mml:mspace width="0.25em"/>
                            <mml:mtext>is the density of fluid</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mi>kg</mml:mi>
                            <mml:mo>/</mml:mo>
                            <mml:mrow>
                                <mml:msup>
                                    <mml:mi mathvariant="normal">m</mml:mi>
                                    <mml:mn>3</mml:mn>
                                </mml:msup>
                            </mml:mrow>
                        </mml:math>
</inline-formula>
                </p>
                <p>g is acceleration due to gravity, which is equivalent to 9.81&#x00a0;m/s
                    <sup>2</sup>
                </p>
                <p>h is the differential height
                    <disp-formula id="e47">

                        <mml:math display="block">
                            <mml:mtext>Potential</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mtext>energy</mml:mtext>
                            <mml:mo>,</mml:mo>
                            <mml:mspace width="0.25em"/>
                            <mml:mi mathvariant="italic">PE</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mi mathvariant="italic">mgh</mml:mi>
                        </mml:math>

                        <label>(44)</label>
</disp-formula>
                </p>
                <p>Where m is mass (kg)
                    <disp-formula id="e48">

                        <mml:math display="block">
                            <mml:mfrac>
                                <mml:mi>PE</mml:mi>
                                <mml:mrow>
                                    <mml:mtext>Time</mml:mtext>
                                    <mml:mo>,</mml:mo>
                                    <mml:mi mathvariant="normal">t</mml:mi>
                                </mml:mrow>
                            </mml:mfrac>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mi>mgh</mml:mi>
                                <mml:mrow>
                                    <mml:mtext>Time</mml:mtext>
                                    <mml:mo>,</mml:mo>
                                    <mml:mi mathvariant="normal">t</mml:mi>
                                </mml:mrow>
                            </mml:mfrac>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="normal">P</mml:mi>
                                <mml:mi mathvariant="normal">S</mml:mi>
                            </mml:msub>
                        </mml:math>

                        <label>(45)</label>
</disp-formula>
                </p>
                <p>Time, t, is in seconds</p>
                <p>P
                    <sub>S</sub>&#x00a0;=&#x00a0;Q
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi>&#x03c1;gh</mml:mi>
                        </mml:math>
</inline-formula>, and Q&#x00a0;=&#x00a0;AV. Where A is area and V is velocity</p>
                <p>Where A is the area of the cross-section and U is the initial velocity of water
                    <disp-formula id="e49">

                        <mml:math display="block">
                            <mml:mi>Ps</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mtext>AV&#x03c1;gh</mml:mtext>
                        </mml:math>

                        <label>(46)</label>
</disp-formula>
                </p>
                <p>The dynamic hydraulic power of a pump as water flows from one to another is given by,

                    <disp-formula id="e50">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>P</mml:mi>
                                <mml:mi>D</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mtext>&#x03c1;Qgh</mml:mtext>
                                <mml:mn>2</mml:mn>
                            </mml:mfrac>
                        </mml:math>
</disp-formula>

                    <disp-formula id="e51">

                        <mml:math display="block">
                            <mml:mi>Pd</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mi>KE</mml:mi>
                                <mml:mtext>Time</mml:mtext>
                            </mml:mfrac>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mi mathvariant="normal">Q</mml:mi>
                                    <mml:msup>
                                        <mml:mi mathvariant="normal">V</mml:mi>
                                        <mml:mn>2</mml:mn>
                                    </mml:msup>
                                </mml:mrow>
                                <mml:mn>2</mml:mn>
                            </mml:mfrac>
                        </mml:math>
</disp-formula>
                </p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi>Pd</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mi>&#x03c1;A</mml:mi>
                                    <mml:msup>
                                        <mml:mi mathvariant="normal">U</mml:mi>
                                        <mml:mn>3</mml:mn>
                                    </mml:msup>
                                </mml:mrow>
                                <mml:mn>2</mml:mn>
                            </mml:mfrac>
                        </mml:math>
</inline-formula>, but 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi mathvariant="normal">V</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mo>&#x23b7;</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mn>2</mml:mn>
                                <mml:mi>gh</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>
</inline-formula> so, 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msup>
                                <mml:mi mathvariant="normal">V</mml:mi>
                                <mml:mn>2</mml:mn>
                            </mml:msup>
                            <mml:mo>=</mml:mo>
                            <mml:mn>2</mml:mn>
                            <mml:mi>gh</mml:mi>
                        </mml:math>
</inline-formula>, 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>P</mml:mi>
                                <mml:mi>D</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mtext>Q&#x03c1;gh</mml:mtext>
                        </mml:math>
</inline-formula>, maximum lift h.</p>
                <p>Therefore static power of a water pump is equivalent to the dynamic power of a water pump.</p>
                <p>

                    <bold>3.2.3 Efficiency of a Pump (</bold>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi mathvariant="bold">&#x03b7;p</mml:mi>
                        </mml:math>
</inline-formula>)</p>
                <p>Comparing electrical power with hydraulic power Water Pump, the efficiency of a pump must be greater than the efficiency of the system. 
                    <xref ref-type="fig" rid="f3">
Figure 3</xref> illustrates a schematic of a pump, having a suction and an outlet pipe.
                    <sup>
                        <xref ref-type="bibr" rid="ref32">32</xref>
                    </sup>
                </p>
                <fig fig-type="figure" id="f3" orientation="portrait" position="float">
                    <label>
Figure 3. </label>
                    <caption>
                        <title>Architecture of Hydraulic Pump.
                            <sup>
                                <xref ref-type="bibr" rid="ref32">32</xref>
                            </sup>
                        </title>
                        <p>The architecture of Hydraulic Pump involving the direction of flow of liquid.</p>
                    </caption>
                    <graphic id="gr3" orientation="portrait" position="float" xlink:href="https://f1000research-files.f1000.com/manuscripts/193405/426d905a-e027-4b11-9c71-325675087058_figure3.gif"/>
                </fig>
                <p>Electric power input of the motor will be equivalent to the electric power input Pe, of the pump. Considering the 
                    <xref ref-type="fig" rid="f4">
Figure 4</xref> indicating a suction head of a pump, Sh, discharge head, Hs and total head Ht.
                    <sup>
                        <xref ref-type="bibr" rid="ref32">32</xref>
                    </sup>
                </p>
                <fig fig-type="figure" id="f4" orientation="portrait" position="float">
                    <label>
Figure 4. </label>
                    <caption>
                        <title>Pump head determination.
                            <sup>
                                <xref ref-type="bibr" rid="ref32">32</xref>
                            </sup>
                        </title>
                        <p>The architecture, show the total head pump.</p>
                    </caption>
                    <graphic id="gr4" orientation="portrait" position="float" xlink:href="https://f1000research-files.f1000.com/manuscripts/193405/426d905a-e027-4b11-9c71-325675087058_figure4.gif"/>
                </fig>
                <p>Total head, Ht&#x00a0;=&#x00a0;Dh&#x00a0;+&#x00a0;Hs</p>
                <p>From 
                    <xref ref-type="disp-formula" rid="e46">Equation 43</xref> 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi>Ps</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mtext>Q&#x03c1;gh</mml:mtext>
                        </mml:math>
</inline-formula>
                </p>
                <p>

                    <disp-formula id="e52">

                        <mml:math display="block">
                            <mml:mtext>Power</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mtext>input</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mo>=</mml:mo>
                            <mml:mi>&#x03b7;p</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mi>Ph</mml:mi>
                                <mml:mi>Pe</mml:mi>
                            </mml:mfrac>
                        </mml:math>
</disp-formula>
                </p>
                <p>Considering the hydraulic power at a height of &#x2026; &#x2026; Therefore, power loss is</p>
                <p>Efficiency of the system, 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mtext>&#x03b7;sytem</mml:mtext>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mrow>
                                        <mml:mi>Ph</mml:mi>
                                        <mml:mo>&#x2212;</mml:mo>
                                        <mml:mtext>Ploss</mml:mtext>
                                    </mml:mrow>
                                    <mml:mi>Pe</mml:mi>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mn>100</mml:mn>
                        </mml:math>
</inline-formula>
                </p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi mathvariant="normal">e</mml:mi>
                            <mml:mspace width="0.25em"/>
                            <mml:mi>are</mml:mi>
                            <mml:mspace width="0.25em"/>
                            <mml:mi>all</mml:mi>
                            <mml:mspace width="0.25em"/>
                            <mml:mtext>in</mml:mtext>
                            <mml:mspace width="0.25em"/>
                            <mml:mi>KW</mml:mi>
                        </mml:math>
</inline-formula>. Therefore, 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi>&#x03b7;p</mml:mi>
                            <mml:mo>&gt;</mml:mo>
                            <mml:mtext>&#x03b7;syst</mml:mtext>
                        </mml:math>
</inline-formula>
                </p>
                <p>The type of flow will be determined by
                    <disp-formula id="e53">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>R</mml:mi>
                                <mml:mi>e</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mi>&#x03c1;uD</mml:mi>
                                <mml:mi>&#x03bc;</mml:mi>
                            </mml:mfrac>
                        </mml:math>

                        <label>(47)</label>
</disp-formula>
                </p>
                <p>Where</p>
                <p>&#x03c1; is fluid density (kg/m
                    <sup>3</sup>)</p>
                <p>u is the average fluid velocity (m/s)</p>
                <p>D is the pipe diameter (m)</p>
                <p>&#x03bc; is the dynamic viscosity (Pa&#x00b7;s)</p>
                <p>

                    <bold>3.2.4 Modelling water flow using Navier-Stokes Equations</bold>
                </p>
                <p>The vector form Equation is
                    <disp-formula id="e54">

                        <mml:math display="block">
                            <mml:mfrac>
                                <mml:mi>&#x2202;&#x03c1;</mml:mi>
                                <mml:mi>&#x2202;t</mml:mi>
                            </mml:mfrac>
                            <mml:mo mathvariant="bold-italic">+</mml:mo>
                            <mml:mo>&#x2207;</mml:mo>
                            <mml:mo>.</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mi>&#x03c1;u</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>=</mml:mo>
                            <mml:mn>0</mml:mn>
                        </mml:math>

                        <label>(48)</label>
</disp-formula>
                </p>
                <p>&#x2207; is the Divergence operator</p>
                <p>&#x03c1; is the fluid density (kg/m
                    <sup>3</sup>)</p>
                <p>u is the velocity vector of the fluid (m/s)</p>
                <p>t is time (s)</p>
                <p>For incompressible fluids</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mo>&#x2207;</mml:mo>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mi mathvariant="normal">u</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mn>0</mml:mn>
                        </mml:math>
</inline-formula>. This means density is constant, 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi mathvariant="italic">&#x03c1;t</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mn>0</mml:mn>
                        </mml:math>
</inline-formula>
                </p>
                <p>Since the pipe is a 3D component, water will flow in 3D, and for 3D flow
                    <disp-formula id="e55">

                        <mml:math display="block">
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mi>&#x2202;&#x03c1;</mml:mi>
                                    <mml:mspace width="0em"/>
                                </mml:mrow>
                                <mml:mi>&#x2202;t</mml:mi>
                            </mml:mfrac>
                            <mml:mo>+</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mi>&#x2202;</mml:mi>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mi>&#x03c1;u</mml:mi>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                    <mml:mspace width="0em"/>
                                </mml:mrow>
                                <mml:mrow>
                                    <mml:mi>&#x2202;x</mml:mi>
                                    <mml:mspace width="0em"/>
                                </mml:mrow>
                            </mml:mfrac>
                            <mml:mo>+</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mi>&#x2202;</mml:mi>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mi>&#x03c1;v</mml:mi>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                </mml:mrow>
                                <mml:mi>&#x2202;y</mml:mi>
                            </mml:mfrac>
                            <mml:mo>+</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:mi>&#x2202;</mml:mi>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mi>&#x03c1;w</mml:mi>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                    <mml:mspace width="0em"/>
                                </mml:mrow>
                                <mml:mi>&#x2202;z</mml:mi>
                            </mml:mfrac>
                            <mml:mo>=</mml:mo>
                            <mml:mn>0</mml:mn>
                        </mml:math>

                        <label>(49)</label>
</disp-formula>
                </p>
                <p>Where u, v, w: velocity components in x, y, z directions</p>
                <p>Conservation of momentum will be given as
                    <disp-formula id="e56">

                        <mml:math display="block">
                            <mml:mi mathvariant="normal">&#x03c1;</mml:mi>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mrow>
                                        <mml:mi>&#x2202;u</mml:mi>
                                        <mml:mspace width="0em"/>
                                    </mml:mrow>
                                    <mml:mi>&#x2202;t</mml:mi>
                                </mml:mfrac>
                                <mml:mo>+</mml:mo>
                                <mml:mi mathvariant="normal">u</mml:mi>
                                <mml:mo>&#x00b7;</mml:mo>
                                <mml:mo>&#x2207;</mml:mo>
                                <mml:mi mathvariant="normal">u</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>=</mml:mo>
                            <mml:mo>&#x2212;</mml:mo>
                            <mml:mo>&#x2207;</mml:mo>
                            <mml:mi mathvariant="normal">p</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">&#x03bc;</mml:mi>
                            <mml:msup>
                                <mml:mo>&#x2207;</mml:mo>
                                <mml:mn>2</mml:mn>
                            </mml:msup>
                            <mml:mi mathvariant="normal">u</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">f</mml:mi>
                            <mml:mspace width="0em"/>
                        </mml:math>

                        <label>(50)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>f is the body forces</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mi mathvariant="normal">&#x03bc;</mml:mi>
                        </mml:math>
</inline-formula> is the dynamic viscosity</p>
                <p>&#x03c1; is the fluid density</p>
                <p>p is the pressure</p>
                <p>According to Roiti-Gromeka-Szyma&#x0144;ski &#x00b4;nski Solution, the pressure gradient of laminar flow of water is given by the 51
                    <disp-formula id="e57">

                        <mml:math display="block">
                            <mml:mfrac>
                                <mml:mi>&#x2202;v</mml:mi>
                                <mml:mi>&#x2202;t</mml:mi>
                            </mml:mfrac>
                            <mml:mo>=</mml:mo>
                            <mml:mi mathvariant="normal">G</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mfrac>
                                <mml:mi>&#x03bd;&#x2202;</mml:mi>
                                <mml:mrow>
                                    <mml:mi>r</mml:mi>
                                    <mml:mi>&#x2202;r</mml:mi>
                                </mml:mrow>
                            </mml:mfrac>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mrow>
                                        <mml:mi>r</mml:mi>
                                        <mml:mi>&#x2202;v</mml:mi>
                                    </mml:mrow>
                                    <mml:mi mathvariant="italic">dr</mml:mi>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(51)</label>
</disp-formula>
                </p>
                <p>Where r is the pipe radius, G is the pressure gradient.</p>
            </sec>
        </sec>
        <sec id="sec13">
            <title>4. Heat transfer modeling that will be required to kill microbial</title>
            <p>The governing on how heat is transferred to water to kill micro-bacterial micro-organisms</p>
            <sec id="sec14">
                <title>4.1 Temperature rise</title>
                <p>The increase in temperature can kill more bacteria and micro-organisms. The heat energy required to kill bacteria is described in 
                    <xref ref-type="disp-formula" rid="e58">Equation 52</xref>.
                    <disp-formula id="e58">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi>a</mml:mi>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mtext>mcp&#x0394;T</mml:mtext>
                        </mml:math>

                        <label>(52)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi>a</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the amount of amount heat added. It is measured in Joules</p>
                <p>m is the mass of water in kg</p>
                <p>cp is the specific heat of water, which is equivalent to 4186&#x00a0;J/kg&#x00b7;&#x00b0;C)</p>
                <p>&#x0394;T is the temperature change in &#x00b0;C</p>
                <p>When a phase change occurs, water boils, and the heat energy is converted as in 
                    <xref ref-type="disp-formula" rid="e59">Equation 53</xref>.
                    <disp-formula id="e59">

                        <mml:math display="block">
                            <mml:mi>Q</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mi>m</mml:mi>
                            <mml:msub>
                                <mml:mi>L</mml:mi>
                                <mml:mi>v</mml:mi>
                            </mml:msub>
                        </mml:math>

                        <label>(53)</label>
</disp-formula>
                </p>
                <p>Where,</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>L</mml:mi>
                                <mml:mi>v</mml:mi>
                            </mml:msub>
                            <mml:mspace width="0.25em"/>
                        </mml:math>
</inline-formula>is the latent heat of vaporization</p>
                <p>

                    <bold>4.1.1 Inactivation models of microbial organisms</bold>
                </p>
                <p>First-order of inactivation is described in 
                    <xref ref-type="disp-formula" rid="e60">Equation 54</xref>.
                    <disp-formula id="e60">

                        <mml:math display="block">
                            <mml:mfrac>
                                <mml:mi>N</mml:mi>
                                <mml:msub>
                                    <mml:mi>N</mml:mi>
                                    <mml:mi>O</mml:mi>
                                </mml:msub>
                            </mml:mfrac>
                            <mml:mo>=</mml:mo>
                            <mml:msup>
                                <mml:mi>e</mml:mi>
                                <mml:mrow>
                                    <mml:mo>&#x2212;</mml:mo>
                                    <mml:mi mathvariant="italic">kt</mml:mi>
                                </mml:mrow>
                            </mml:msup>
                        </mml:math>

                        <label>(54)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>N</mml:mi>
                                <mml:mi>O</mml:mi>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the initial number of organisms</p>
                <p>N is the number after time, t</p>
                <p>K is the inactivation rate constant in 1/s</p>
                <p>It is time in (s)</p>
                <p>

                    <bold>4.1.2 Time required to reduce microbial organisms (D value)</bold>
                </p>
                <p>The higher the energy to inactivate bacteria, the less the time of inactivation
                    <bold>.</bold>

                    <disp-formula id="e61">

                        <mml:math display="block">
                            <mml:mi>D</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mn>1</mml:mn>
                                <mml:mrow>
                                    <mml:mi mathvariant="italic">kIn</mml:mi>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mn>10</mml:mn>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                </mml:mrow>
                            </mml:mfrac>
                        </mml:math>

                        <label>(55)</label>
</disp-formula>
                </p>
                <p>Where;</p>
                <p>D is the time required at a specific temperature to eliminate microbes by 90%</p>
                <p>The temperature will change to the D-value
                    <disp-formula id="e62">

                        <mml:math display="block">
                            <mml:mo>log</mml:mo>
                            <mml:msub>
                                <mml:mi>D</mml:mi>
                                <mml:mn>2</mml:mn>
                            </mml:msub>
                            <mml:mo>&#x2212;</mml:mo>
                            <mml:mo>log</mml:mo>
                            <mml:msub>
                                <mml:mi>D</mml:mi>
                                <mml:mn>1</mml:mn>
                            </mml:msub>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:mrow>
                                    <mml:msub>
                                        <mml:mi>T</mml:mi>
                                        <mml:mn>1</mml:mn>
                                    </mml:msub>
                                    <mml:mo>&#x2212;</mml:mo>
                                    <mml:msub>
                                        <mml:mi>T</mml:mi>
                                        <mml:mn>2</mml:mn>
                                    </mml:msub>
                                </mml:mrow>
                                <mml:mi>Z</mml:mi>
                            </mml:mfrac>
                        </mml:math>

                        <label>(56)</label>
</disp-formula>
                </p>
                <p>Where Z is the temperature increase needed to reduce the D-value by a log cycle</p>
            </sec>
            <sec id="sec15">
                <title>4.2 Thermodynamic efficiency</title>
                <p>

                    <disp-formula id="e63">

                        <mml:math display="block">
                            <mml:mi mathvariant="normal">&#x03b7;</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mfrac>
                                <mml:msub>
                                    <mml:mi mathvariant="italic">mL</mml:mi>
                                    <mml:mi>v</mml:mi>
                                </mml:msub>
                                <mml:msub>
                                    <mml:mi>Q</mml:mi>
                                    <mml:mtext mathvariant="italic">input</mml:mtext>
                                </mml:msub>
                            </mml:mfrac>
                        </mml:math>

                        <label>(57)</label>
</disp-formula>
                </p>
                <p>Where Q
                    <sub>input</sub> is the total heat supplied</p>
                <p>

                    <bold>4.2.1 Rate of Heat Transfer</bold>

                    <disp-formula id="e64">

                        <mml:math display="block">
                            <mml:mi>q</mml:mi>
                            <mml:mo mathvariant="bold">=</mml:mo>
                            <mml:mi mathvariant="italic">hA</mml:mi>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:msub>
                                    <mml:mi>T</mml:mi>
                                    <mml:mi>S</mml:mi>
                                </mml:msub>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:msub>
                                    <mml:mi>T</mml:mi>
                                    <mml:mi>W</mml:mi>
                                </mml:msub>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(58)</label>
</disp-formula>
                </p>
                <p>q is the heat transfer rate in Watts</p>
                <p>h is convective heat transfer coefficient in W/m
                    <sup>2</sup>&#x00b7;K</p>
                <p>A, area in m
                    <sup>2</sup>
                </p>
                <p>Ts, Tw are surface and water temperatures, respectively, in K</p>
                <p>

                    <bold>4.2.2 Fourier&#x2019;s Law (Conduction)</bold>
                </p>
                <p>Fourier&#x2019;s law of heat conduction describes how heat flows through a solid material due to a temperature change, and it&#x2019;s described in 
                    <xref ref-type="disp-formula" rid="e65">Equation 59</xref>.
                    <disp-formula id="e65">

                        <mml:math display="block">
                            <mml:mi>q</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mo>&#x2212;</mml:mo>
                            <mml:mi mathvariant="italic">kA</mml:mi>
                            <mml:mfrac>
                                <mml:mi mathvariant="italic">dT</mml:mi>
                                <mml:mi mathvariant="italic">dx</mml:mi>
                            </mml:mfrac>
                        </mml:math>

                        <label>(59)</label>
</disp-formula>
                </p>
                <p>Where K is thermal conductivity in W/m&#x00b7;K</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mfrac>
                                <mml:mi mathvariant="italic">dT</mml:mi>
                                <mml:mi mathvariant="italic">dx</mml:mi>
                            </mml:mfrac>
                        </mml:math>
</inline-formula> is the temperature gradient</p>
                <p>

                    <bold>4.2.3 Transient Heat Transfer</bold>
                </p>
                <p>Water is heated to an extent of it being unstable. The temperature change is explained in 
                    <xref ref-type="disp-formula" rid="e66">Equation 60</xref>.
                    <disp-formula id="e66">

                        <mml:math display="block">
                            <mml:mi>T</mml:mi>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mi>t</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi>T</mml:mi>
                                <mml:mo>&#x221e;</mml:mo>
                            </mml:msub>
                            <mml:mo>+</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:msub>
                                    <mml:mi>T</mml:mi>
                                    <mml:mn>0</mml:mn>
                                </mml:msub>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:msub>
                                    <mml:mi>T</mml:mi>
                                    <mml:mo>&#x221e;</mml:mo>
                                </mml:msub>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:msup>
                                <mml:mi>e</mml:mi>
                                <mml:mrow>
                                    <mml:mo>&#x2212;</mml:mo>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mfrac>
                                            <mml:mrow>
                                                <mml:mi>hA</mml:mi>
                                                <mml:mspace width="0em"/>
                                                <mml:mi mathvariant="normal">t</mml:mi>
                                            </mml:mrow>
                                            <mml:mrow>
                                                <mml:mi>&#x03c1;v</mml:mi>
                                                <mml:msub>
                                                    <mml:mi>C</mml:mi>
                                                    <mml:mi>p</mml:mi>
                                                </mml:msub>
                                            </mml:mrow>
                                        </mml:mfrac>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                </mml:mrow>
                            </mml:msup>
                        </mml:math>

                        <label>(60)</label>
</disp-formula>
                </p>
                <p>Where</p>
                <p>T
                    <sub>0</sub> is the initial temperature in Kelvin</p>
                <p>

                    <inline-formula>

                        <mml:math display="inline">
                            <mml:msub>
                                <mml:mi>T</mml:mi>
                                <mml:mo>&#x221e;</mml:mo>
                            </mml:msub>
                        </mml:math>
</inline-formula> is the Surrounding temperature</p>
                <p>&#x03a1; is the density of water</p>
                <p>V is volume in cubic meters</p>
                <p>T is time in seconds</p>
            </sec>
        </sec>
        <sec id="sec16">
            <title>5. Solar thermal water disinfection Equations</title>
            <p>Heat balance in a water container
                <disp-formula id="e67">

                    <mml:math display="block">
                        <mml:mi>m</mml:mi>
                        <mml:msub>
                            <mml:mi>C</mml:mi>
                            <mml:mi>p</mml:mi>
                        </mml:msub>
                        <mml:mfrac>
                            <mml:mi mathvariant="italic">dT</mml:mi>
                            <mml:mi mathvariant="italic">dx</mml:mi>
                        </mml:mfrac>
                        <mml:mo>=</mml:mo>
                        <mml:mi mathvariant="normal">A</mml:mi>
                        <mml:mrow>
                            <mml:mo stretchy="true">[</mml:mo>
                            <mml:mi>Gt</mml:mi>
                            <mml:mspace width="0em"/>
                            <mml:mi mathvariant="normal">&#x03b7;</mml:mi>
                            <mml:mo>&#x2212;</mml:mo>
                            <mml:mi mathvariant="normal">h</mml:mi>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mi mathvariant="normal">T</mml:mi>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:mi mathvariant="normal">T</mml:mi>
                                <mml:mo>&#x221e;</mml:mo>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo stretchy="true">]</mml:mo>
                        </mml:mrow>
                    </mml:math>

                    <label>(61)</label>
</disp-formula>
            </p>
            <sec id="sec187">
                <title>5.1 Radiation Heat Transfer</title>
                <p>

                    <disp-formula id="e68">

                        <mml:math display="block">
                            <mml:msub>
                                <mml:mi>Q</mml:mi>
                                <mml:mi mathvariant="italic">rad</mml:mi>
                            </mml:msub>
                            <mml:mo mathvariant="bold">=</mml:mo>
                            <mml:mi>&#x03b5;&#x03c3;A</mml:mi>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:msup>
                                    <mml:msub>
                                        <mml:mi>T</mml:mi>
                                        <mml:mi>s</mml:mi>
                                    </mml:msub>
                                    <mml:mn>4</mml:mn>
                                </mml:msup>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:msup>
                                    <mml:msub>
                                        <mml:mi>T</mml:mi>
                                        <mml:mi mathvariant="italic">env</mml:mi>
                                    </mml:msub>
                                    <mml:mn>4</mml:mn>
                                </mml:msup>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                        </mml:math>

                        <label>(62)</label>
</disp-formula>
                </p>
                <p>&#x03b5; is emissivity, &#x03c3; is Stefan-Boltzmann constant (5.67&#x00a0;&#x00d7;&#x00a0;10
                    <sup>8</sup>&#x00a0;W/m
                    <sup>2</sup>&#x00b7;K
                    <sup>4</sup>)</p>
            </sec>
        </sec>
        <sec id="sec17">
            <title>6. Modelling of BOD biosensor</title>
            <p>The main purpose of a biosensor is to detect amounts of bacteria before and after treatment. The sensor will be used to detect the amount of oxygen in water that supports the growth of microorganisms. The BOD biosensor will determine the amount of oxygen in water, and will be oxidized by a microbial cell. The Clark-type oxygen electrode will be used as a transducer. The BOD will consist of a semipermeable membrane. 
                <xref ref-type="disp-formula" rid="e69">
Equation 63</xref> describes the steady-state substrate balance in the biosensor used for measuring BOD
                <disp-formula id="e69">

                    <mml:math display="block">
                        <mml:mfrac>
                            <mml:mrow>
                                <mml:msub>
                                    <mml:mi>D</mml:mi>
                                    <mml:mi>u</mml:mi>
                                </mml:msub>
                                <mml:msub>
                                    <mml:mi>S</mml:mi>
                                    <mml:mi>l</mml:mi>
                                </mml:msub>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:mi>L</mml:mi>
                            </mml:mrow>
                            <mml:msup>
                                <mml:mi>d</mml:mi>
                                <mml:mn>2</mml:mn>
                            </mml:msup>
                        </mml:mfrac>
                        <mml:mo>=</mml:mo>
                        <mml:mfrac>
                            <mml:mrow>
                                <mml:msub>
                                    <mml:mi>V</mml:mi>
                                    <mml:mi>s</mml:mi>
                                </mml:msub>
                                <mml:mi>L</mml:mi>
                            </mml:mrow>
                            <mml:mrow>
                                <mml:msub>
                                    <mml:mi>K</mml:mi>
                                    <mml:mi>o</mml:mi>
                                </mml:msub>
                                <mml:mo>+</mml:mo>
                                <mml:mi>L</mml:mi>
                            </mml:mrow>
                        </mml:mfrac>
                    </mml:math>

                    <label>(63)</label>
</disp-formula>
            </p>
            <p>Where D
                <sub>u</sub> is the diffusion coefficient, which determines how easily bacteria and other microorganisms move through a semipermeable membrane in a BOD biosensor.</p>
            <p>d is the thickness of the cell membrane</p>
            <p>S
                <sub>l</sub> and L are the concentrations of bacteria and other microorganisms in the external solution and the layer near the Clark-type electrode, respectively.</p>
            <p>V
                <sub>s</sub> is the rate of transport through the cell membrane at saturating concentrations of bacteria and other microorganisms</p>
            <p>K
                <sub>o</sub> is the saturation constant.</p>
            <p>The relative concentration of the bacteria in the layer near the Clark-type oxygen electrode is given 
                <xref ref-type="disp-formula" rid="e70">Equation 64</xref>
                <disp-formula id="e70">

                    <mml:math display="block">
                        <mml:mfrac>
                            <mml:mi>L</mml:mi>
                            <mml:msub>
                                <mml:mi>S</mml:mi>
                                <mml:mi>l</mml:mi>
                            </mml:msub>
                        </mml:mfrac>
                        <mml:mo>=</mml:mo>
                        <mml:mfrac>
                            <mml:mrow>
                                <mml:mn>1</mml:mn>
                                <mml:mo>&#x2212;</mml:mo>
                                <mml:mfrac>
                                    <mml:msub>
                                        <mml:mi>K</mml:mi>
                                        <mml:mi>l</mml:mi>
                                    </mml:msub>
                                    <mml:mrow>
                                        <mml:msub>
                                            <mml:mi>S</mml:mi>
                                            <mml:mi>l</mml:mi>
                                        </mml:msub>
                                        <mml:mrow>
                                            <mml:mo stretchy="true">(</mml:mo>
                                            <mml:mn>1</mml:mn>
                                            <mml:mo>+</mml:mo>
                                            <mml:mi>&#x03b2;</mml:mi>
                                            <mml:mo stretchy="true">)</mml:mo>
                                        </mml:mrow>
                                    </mml:mrow>
                                </mml:mfrac>
                            </mml:mrow>
                            <mml:mn>2</mml:mn>
                        </mml:mfrac>
                        <mml:mo>+</mml:mo>
                        <mml:msup>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:msup>
                                    <mml:mrow>
                                        <mml:mo stretchy="true">(</mml:mo>
                                        <mml:mfrac>
                                            <mml:mrow>
                                                <mml:mn>1</mml:mn>
                                                <mml:mo>&#x2212;</mml:mo>
                                                <mml:mfrac>
                                                    <mml:msub>
                                                        <mml:mi>K</mml:mi>
                                                        <mml:mi>l</mml:mi>
                                                    </mml:msub>
                                                    <mml:mrow>
                                                        <mml:msub>
                                                            <mml:mi>S</mml:mi>
                                                            <mml:mi>l</mml:mi>
                                                        </mml:msub>
                                                        <mml:mrow>
                                                            <mml:mo stretchy="true">(</mml:mo>
                                                            <mml:mn>1</mml:mn>
                                                            <mml:mo>+</mml:mo>
                                                            <mml:mi>&#x03b2;</mml:mi>
                                                            <mml:mo stretchy="true">)</mml:mo>
                                                        </mml:mrow>
                                                    </mml:mrow>
                                                </mml:mfrac>
                                            </mml:mrow>
                                            <mml:mn>2</mml:mn>
                                        </mml:mfrac>
                                        <mml:mo stretchy="true">)</mml:mo>
                                    </mml:mrow>
                                    <mml:mn>2</mml:mn>
                                </mml:msup>
                                <mml:mo>+</mml:mo>
                                <mml:mfrac>
                                    <mml:msub>
                                        <mml:mi>K</mml:mi>
                                        <mml:mi>o</mml:mi>
                                    </mml:msub>
                                    <mml:msub>
                                        <mml:mi>S</mml:mi>
                                        <mml:mi>l</mml:mi>
                                    </mml:msub>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mn>0.5</mml:mn>
                        </mml:msup>
                    </mml:math>

                    <label>(64)</label>
</disp-formula>
            </p>
            <p>Where 
                <inline-formula>

                    <mml:math display="inline">
                        <mml:mi>&#x03b2;</mml:mi>
                    </mml:math>
</inline-formula> is the dimensionless module.
                <disp-formula id="e71">

                    <mml:math display="block">
                        <mml:mi>&#x03b2;</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mfrac>
                            <mml:mrow>
                                <mml:msub>
                                    <mml:mi>V</mml:mi>
                                    <mml:mi>s</mml:mi>
                                </mml:msub>
                                <mml:msup>
                                    <mml:mi>d</mml:mi>
                                    <mml:mn>2</mml:mn>
                                </mml:msup>
                            </mml:mrow>
                            <mml:mrow>
                                <mml:msub>
                                    <mml:mi>D</mml:mi>
                                    <mml:mi>u</mml:mi>
                                </mml:msub>
                                <mml:msub>
                                    <mml:mi>K</mml:mi>
                                    <mml:mi>o</mml:mi>
                                </mml:msub>
                            </mml:mrow>
                        </mml:mfrac>
                    </mml:math>

                    <label>(65)</label>
</disp-formula>
            </p>
            <p>For extreme concentration of the substrate, the solution of 
                <inline-formula>

                    <mml:math display="inline">
                        <mml:msub>
                            <mml:mi mathvariant="bold-italic">S</mml:mi>
                            <mml:mi mathvariant="bold-italic">i</mml:mi>
                        </mml:msub>
                        <mml:mo>&#x2212;</mml:mo>
                        <mml:mi mathvariant="bold-italic">L</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mi mathvariant="bold-italic">&#x03b2;</mml:mi>
                        <mml:msub>
                            <mml:mi mathvariant="bold-italic">K</mml:mi>
                            <mml:mi mathvariant="bold-italic">S</mml:mi>
                        </mml:msub>
                    </mml:math>
</inline-formula> at 
                <inline-formula>

                    <mml:math display="inline">
                        <mml:msub>
                            <mml:mi mathvariant="bold-italic">S</mml:mi>
                            <mml:mi mathvariant="bold-italic">i</mml:mi>
                        </mml:msub>
                        <mml:mo>&gt;</mml:mo>
                        <mml:msub>
                            <mml:mi mathvariant="bold-italic">K</mml:mi>
                            <mml:mi mathvariant="bold-italic">i</mml:mi>
                        </mml:msub>
                        <mml:mo>+</mml:mo>
                        <mml:mfrac>
                            <mml:mrow>
                                <mml:msub>
                                    <mml:mi mathvariant="bold-italic">V</mml:mi>
                                    <mml:mi mathvariant="bold-italic">i</mml:mi>
                                </mml:msub>
                                <mml:msup>
                                    <mml:mi mathvariant="bold-italic">d</mml:mi>
                                    <mml:mn mathvariant="bold">2</mml:mn>
                                </mml:msup>
                            </mml:mrow>
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">D</mml:mi>
                                <mml:mi mathvariant="bold-italic">u</mml:mi>
                            </mml:msub>
                        </mml:mfrac>
                    </mml:math>
</inline-formula>
            </p>
            <p>

                <inline-formula>

                    <mml:math display="inline">
                        <mml:mi mathvariant="bold-italic">S</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mfrac>
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">S</mml:mi>
                                <mml:mi mathvariant="bold-italic">i</mml:mi>
                            </mml:msub>
                            <mml:mrow>
                                <mml:mn mathvariant="bold">1</mml:mn>
                                <mml:mo>+</mml:mo>
                                <mml:mi mathvariant="bold-italic">&#x03b2;</mml:mi>
                            </mml:mrow>
                        </mml:mfrac>
                    </mml:math>
</inline-formula> at 
                <inline-formula>

                    <mml:math display="inline">
                        <mml:msub>
                            <mml:mi mathvariant="bold-italic">S</mml:mi>
                            <mml:mi mathvariant="bold-italic">i</mml:mi>
                        </mml:msub>
                        <mml:mo>&lt;</mml:mo>
                        <mml:msub>
                            <mml:mi mathvariant="bold-italic">K</mml:mi>
                            <mml:mi mathvariant="bold-italic">i</mml:mi>
                        </mml:msub>
                        <mml:mo>+</mml:mo>
                        <mml:mfrac>
                            <mml:mrow>
                                <mml:msub>
                                    <mml:mi mathvariant="bold-italic">V</mml:mi>
                                    <mml:mi mathvariant="bold-italic">i</mml:mi>
                                </mml:msub>
                                <mml:msup>
                                    <mml:mi mathvariant="bold-italic">d</mml:mi>
                                    <mml:mn mathvariant="bold">2</mml:mn>
                                </mml:msup>
                            </mml:mrow>
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">D</mml:mi>
                                <mml:mi mathvariant="bold-italic">u</mml:mi>
                            </mml:msub>
                        </mml:mfrac>
                    </mml:math>
</inline-formula>
            </p>
            <p>The concentration of oxygen is stationary is obtained by the concentration of bacteria, which is equal to the flow of O
                <sub>2</sub>.
                <disp-formula id="e72">

                    <mml:math display="block">
                        <mml:mfrac>
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">D</mml:mi>
                                <mml:mi mathvariant="bold-italic">u</mml:mi>
                            </mml:msub>
                            <mml:mi mathvariant="bold-italic">d</mml:mi>
                        </mml:mfrac>
                        <mml:mrow>
                            <mml:mo stretchy="true">(</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">S</mml:mi>
                                <mml:mi mathvariant="bold-italic">O</mml:mi>
                            </mml:msub>
                            <mml:mo>&#x2212;</mml:mo>
                            <mml:mi mathvariant="bold-italic">S</mml:mi>
                            <mml:mo stretchy="true">)</mml:mo>
                        </mml:mrow>
                        <mml:mo>=</mml:mo>
                        <mml:mfrac>
                            <mml:mn mathvariant="bold">1</mml:mn>
                            <mml:mi mathvariant="bold-italic">W</mml:mi>
                        </mml:mfrac>
                        <mml:mfrac>
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">DO</mml:mi>
                                <mml:mn mathvariant="bold">2</mml:mn>
                            </mml:msub>
                            <mml:mi mathvariant="bold-italic">d</mml:mi>
                        </mml:mfrac>
                        <mml:mrow>
                            <mml:mo stretchy="true">(</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">O</mml:mi>
                                <mml:mrow>
                                    <mml:mn mathvariant="bold">2</mml:mn>
                                    <mml:mi mathvariant="bold-italic">i</mml:mi>
                                </mml:mrow>
                            </mml:msub>
                            <mml:mo>&#x2212;</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="bold-italic">O</mml:mi>
                                <mml:mn mathvariant="bold">2</mml:mn>
                            </mml:msub>
                            <mml:mo stretchy="true">)</mml:mo>
                        </mml:mrow>
                    </mml:math>

                    <label>(66)</label>
</disp-formula>
            </p>
            <p>Where,</p>
            <p>

                <inline-formula>

                    <mml:math display="inline">
                        <mml:msub>
                            <mml:mi mathvariant="bold-italic">DO</mml:mi>
                            <mml:mn mathvariant="bold">2</mml:mn>
                        </mml:msub>
                    </mml:math>
</inline-formula> is the diffusion coefficient of oxygen and, W is the stoichiometric constant of bacteria</p>
            <p>How to obtain the constant filtration rate</p>
            <p>A filtration medium with the same cross-sectional area per a unit area, number of pores. N
                <sub>p</sub> with an average length lp and R radius respectively. As water flows into the filter, there is a possibilities of pore blockage and the particles accumulate on the membrane causing a cake.</p>
            <p>Using Hagen-Poiseuille formula</p>
            <p>The volume of filtered clean water is given as
                <disp-formula id="e73">

                    <mml:math display="block">
                        <mml:mi>Vol</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mfrac>
                            <mml:mrow>
                                <mml:mi mathvariant="normal">&#x03c0;</mml:mi>
                                <mml:msup>
                                    <mml:mi mathvariant="normal">R</mml:mi>
                                    <mml:mn>4</mml:mn>
                                </mml:msup>
                                <mml:mi>&#x0394;P</mml:mi>
                            </mml:mrow>
                            <mml:mrow>
                                <mml:mn>8</mml:mn>
                                <mml:mi mathvariant="normal">&#x03bc;</mml:mi>
                                <mml:msub>
                                    <mml:mi mathvariant="normal">l</mml:mi>
                                    <mml:mi mathvariant="normal">p</mml:mi>
                                </mml:msub>
                            </mml:mrow>
                        </mml:mfrac>
                    </mml:math>

                    <label>(67)</label>
</disp-formula>
            </p>
            <p>The first filtration rate per unit area
                <disp-formula id="e74">

                    <mml:math display="block">
                        <mml:msub>
                            <mml:mi>H</mml:mi>
                            <mml:mtext mathvariant="italic">in</mml:mtext>
                        </mml:msub>
                        <mml:mo>=</mml:mo>
                        <mml:mi mathvariant="italic">Vol</mml:mi>
                        <mml:mo>&#x2217;</mml:mo>
                        <mml:msub>
                            <mml:mi>N</mml:mi>
                            <mml:mi>p</mml:mi>
                        </mml:msub>
                    </mml:math>

                    <label>(68)</label>
</disp-formula>
            </p>
            <p>The level of filtration (per unit area of filter medium) is
                <disp-formula id="e75">

                    <mml:math display="block">
                        <mml:msub>
                            <mml:mi>H</mml:mi>
                            <mml:mtext mathvariant="italic">in</mml:mtext>
                        </mml:msub>
                        <mml:mo>=</mml:mo>
                        <mml:mi>Z</mml:mi>
                        <mml:msub>
                            <mml:mi>N</mml:mi>
                            <mml:mi>p</mml:mi>
                        </mml:msub>
                        <mml:msup>
                            <mml:mi>R</mml:mi>
                            <mml:mn>4</mml:mn>
                        </mml:msup>
                    </mml:math>

                    <label>(69)</label>
</disp-formula>
            </p>
            <p>Where 
                <inline-formula>

                    <mml:math display="inline">
                        <mml:mi>Z</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mfrac>
                            <mml:mi mathvariant="italic">&#x03c0;&#x0394;P</mml:mi>
                            <mml:mrow>
                                <mml:mn>8</mml:mn>
                                <mml:mi>&#x03bc;</mml:mi>
                                <mml:msub>
                                    <mml:mi>l</mml:mi>
                                    <mml:mi>p</mml:mi>
                                </mml:msub>
                            </mml:mrow>
                        </mml:mfrac>
                    </mml:math>
</inline-formula>
            </p>
            <p>Where</p>
            <p>&#x03bc; is the Dynamic viscosity of the fluid</p>
            <p>

                <inline-formula>

                    <mml:math display="inline">
                        <mml:msub>
                            <mml:mi>l</mml:mi>
                            <mml:mi>p</mml:mi>
                        </mml:msub>
                    </mml:math>
</inline-formula> is the length of the pores</p>
            <p>If the mean radius of the pore decreases to R, then
                <disp-formula id="e76">

                    <mml:math display="block">
                        <mml:mi>H</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mi>Z</mml:mi>
                        <mml:msub>
                            <mml:mi>N</mml:mi>
                            <mml:mi>p</mml:mi>
                        </mml:msub>
                        <mml:msup>
                            <mml:mi>R</mml:mi>
                            <mml:mn>4</mml:mn>
                        </mml:msup>
                    </mml:math>

                    <label>(70)</label>
</disp-formula>
            </p>
            <p>The ratio of the new filtration becomes
                <disp-formula id="e77">

                    <mml:math display="block">
                        <mml:mfrac>
                            <mml:mi>H</mml:mi>
                            <mml:msub>
                                <mml:mi>H</mml:mi>
                                <mml:mtext mathvariant="italic">in</mml:mtext>
                            </mml:msub>
                        </mml:mfrac>
                        <mml:mo>=</mml:mo>
                        <mml:msup>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mfrac>
                                    <mml:mi>R</mml:mi>
                                    <mml:msub>
                                        <mml:mi>R</mml:mi>
                                        <mml:mtext mathvariant="italic">in</mml:mtext>
                                    </mml:msub>
                                </mml:mfrac>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mn>4</mml:mn>
                        </mml:msup>
                    </mml:math>

                    <label>(71)</label>
</disp-formula>
            </p>
            <p>Example of FTIR analysis of Polysulfone (PS) Ultrafilter static adsorption test.</p>
            <p>During the filtration process of water, a reservoir with different-sized gravels is used. The Darcy law of flow of filtration is applied, while considering the volumetric flow rate, Q
                <disp-formula id="e78">

                    <mml:math display="block">
                        <mml:mi>Q</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mfrac>
                            <mml:mi mathvariant="italic">KdP</mml:mi>
                            <mml:mi mathvariant="italic">&#x03bc;dx</mml:mi>
                        </mml:mfrac>
                    </mml:math>

                    <label>(72)</label>
</disp-formula>
            </p>
            <p>Where</p>
            <p>Q is the Darcy velocity</p>
            <p>k is the intrinsic permeability of the medium (m
                <sup>2</sup>)</p>
            <p>

                <inline-formula>

                    <mml:math display="inline">
                        <mml:mi>&#x03bc;</mml:mi>
                    </mml:math>
</inline-formula> is the coefficient of viscosity</p>
            <p>

                <inline-formula>

                    <mml:math display="inline">
                        <mml:mfrac>
                            <mml:mi mathvariant="italic">dP</mml:mi>
                            <mml:mi mathvariant="italic">dx</mml:mi>
                        </mml:mfrac>
                    </mml:math>
</inline-formula> is the pressure difference in the direction of flow</p>
            <p>To determine the type of flow, whether laminar, turbulent, or transitional. Reynolds&#x2019;s number is computed as follows
                <disp-formula id="e79">

                    <mml:math display="block">
                        <mml:msub>
                            <mml:mi>R</mml:mi>
                            <mml:mi>e</mml:mi>
                        </mml:msub>
                        <mml:mo>=</mml:mo>
                        <mml:mfrac>
                            <mml:mi mathvariant="italic">&#x03bc;d</mml:mi>
                            <mml:mi>v</mml:mi>
                        </mml:mfrac>
                    </mml:math>

                    <label>(73)</label>
</disp-formula>
            </p>
            <p>In porous media, the flow is determined by the 
                <xref ref-type="table" rid="T11">
Table 11</xref> below.</p>
        </sec>
        <sec id="sec18" sec-type="results">
            <title>7. Results</title>
            <sec id="sec19">
                <title>7.1 Baseline environmental characterization (n&#x00a0;=&#x00a0;384)</title>
                <p>Microbial Load
                    <bold>:</bold> Baseline analysis of 384 samples from Ishaka Municipality revealed critical levels of contamination. 
                    <italic toggle="yes">Escherichia coli</italic> was present in 72&#x2013;85% of spring and wetland samples, with a mean concentration of 48&#x2013;210&#x00a0;CFU/100&#x00a0;mL, significantly exceeding the WHO limit of 0&#x00a0;CFU/100&#x00a0;mL.</p>
                <p>

                    <bold>7.1.1 Chemical &amp; Physical Profile:</bold> Turbidity levels ranged from 9 to 146 NTU (WHO limit &lt;5 NTU), while Total Suspended Solids (TSS) were recorded between 18 and 92&#x00a0;mg/L. Chemical analysis detected heavy metals, including Lead (0.03&#x2013;0.11&#x00a0;mg/L) and Arsenic (0.011&#x2013;0.024&#x00a0;mg/L), alongside emerging contaminants like pharmaceutical residues (ibuprofen at 18&#x2013;44&#x00a0;ng/L) and DDT pesticides (2&#x2013;9&#x00a0;ng/L).</p>
            </sec>
            <sec id="sec20">
                <title>7.2 Multi-stage treatment performance</title>
                <p>

                    <bold>7.2.1 Solar Thermal Inactivation:</bold> Heating water to &#x2265;70&#x2013;100&#x00a0;&#x00b0;C achieved a Log Reduction Value (LRV) of 4&#x2013;6 for 
                    <italic toggle="yes">E. coli.</italic> Complete bacterial inactivation was consistently reached within 8&#x2013;12&#x00a0;minutes of sustained boiling.</p>
                <p>

                    <bold>7.2.2 Combined System Efficiency:</bold> The integrated system (Sedimentation + Filtration + RO&#x00a0;+&#x00a0;Thermal) achieved a cumulative removal efficiency of &gt;95% across all contaminant classes.</p>
                <p>Comparative Water Quality</p>
                <p>

                    <bold>Turbidity:</bold> Reduced from baseline 45&#x2013;140 NTU to &lt;2 NTU.</p>
                <p>

                    <bold>Heavy Metals:</bold> Lead and Arsenic concentrations were lowered to &lt;0.005&#x00a0;mg/L and&#x00a0;&lt;&#x00a0;0.003&#x00a0;mg/L, respectively, well below regulatory thresholds.</p>
            </sec>
            <sec id="sec21">
                <title>7.3 Real-time microbial monitoring (BOD biosensor)</title>
                <p>

                    <bold>7.3.1 Biosensor Validation:</bold> The integrated BOD biosensor exhibited a linear response range of 0&#x2013;30&#x00a0;mg/L. Validation against standard laboratory BOD tests showed a high correlation coefficient (R
                    <sup>2</sup>&#x00a0;=&#x00a0;0.89&#x2013;0.94).</p>
                <p>

                    <bold>7.3.2 Response Dynamics:</bold> The sensor provided rapid real-time feedback with a response time of 45&#x2013;90&#x00a0;seconds. Post-treatment monitoring showed a reduction in BOD from 4.8&#x2013;11.3&#x00a0;mg/L to 0.9&#x2013;1.8&#x00a0;mg/L, providing immediate verification of water safety.</p>
            </sec>
            <sec id="sec22">
                <title>7.4 Solar energy &amp; system modeling</title>
                <p>

                    <bold>7.4.1 PV Efficiency:</bold> The photovoltaic array produced 1.2&#x2013;1.6 kWh/day, consistently meeting 100% of the system&#x2019;s operational energy demand (1.0&#x2013;1.3 kWh) even during low-irradiance periods.</p>
                <p>

                    <bold>7.4.2 Loss &amp; Performance Analysis:</bold> Detailed loss modeling accounted for soiling (4&#x2013;6%), temperature (3&#x2013;5%), and inverter inefficiencies (2&#x2013;3%), resulting in a final Performance Ratio (PR) of 0.84 to 0.88.</p>
                <p>

                    <bold>7.4.3 Hydraulic Stability:</bold> Navier&#x2013;Stokes modeling yielded Reynolds numbers between 2,300 and 4,800, confirming transitional-to-turbulent flow that maintains stable volumetric flow rates across treatment cycles.</p>
            </sec>
        </sec>
        <sec id="sec23" sec-type="discussion">
            <title>8. Discussion</title>
            <p>The results of this study demonstrate that the proposed solar-powered hybrid water treatment system is capable of effectively removing physical, chemical, and microbiological contaminants characteristic of rural surface water sources. The baseline analysis of 384 samples revealed high levels of turbidity, E. coli, heavy metals, pesticides, pharmaceuticals, and elevated TDS confirming widespread contamination consistent with reports from similar low-resource settings. These conditions justified the need for a modular, multi-stage treatment configuration capable of addressing diverse pollutants simultaneously.</p>
            <p>The energy analysis further validated the feasibility of the system. The photovoltaic array, sized and modelled using real loss factors (shading, temperature, mismatch, soiling, inverter losses), produced sufficient energy to power the pumps, condenser, biosensor electronics, and heating components. The performance ratio (0.84&#x2013;0.88) indicates strong operational efficiency for off-grid environments. This result is particularly important, as energy availability is one of the major barriers to water treatment in rural areas. A fully solar-driven system reduces operational costs and increases long-term sustainability.</p>
            <p>The hydraulic modelling using Navier&#x2013;Stokes and Darcy&#x2019;s law provided insight into flow stability, filtration behavior, and pressure losses. The observed Reynolds numbers (2,300&#x2013;4,800) confirmed transitional-to-turbulent flow within the system, which explains the stable volumetric flow rates delivered during treatment cycles. The sedimentation velocities and filtration permeabilities obtained experimentally matched well with the theoretical predictions, supporting the validity of the design approach.</p>
            <p>A key innovation in this work is the integration of a BOD biosensor for real-time microbial risk monitoring. The biosensor showed a strong correlation with laboratory BOD results (R
                <sup>2</sup>&#x00a0;=&#x00a0;0.89&#x2013;0.94) and responded within 45&#x2013;90&#x00a0;seconds, offering a rapid, on-site assessment of microbial activity. The ability to detect biological contamination before and after treatment gives the system an advantage over conventional rural treatment units, which typically lack real-time quality verification. This integration transforms the system from a simple treatment device into a &#x201c;monitor-and-treat&#x201d; platform that improves safety and user confidence.</p>
            <p>These findings collectively highlight that a unified, off-grid hybrid system can effectively address the multi-contaminant challenges present in LMIC rural water sources. Compared to existing decentralized systems which often treat only specific contaminants or rely on laboratory testing this design integrates energy, hydraulics, treatment, and biosensing into a single functional architecture.</p>
            <p>However, the study has limitations. The system performance was modelled and validated using controlled conditions, and field variability such as seasonal fluctuations, turbidity spikes, long-term PV degradation, and membrane fouling may influence performance. Long-term pilot testing is therefore recommended to assess durability, maintenance needs, and cost-effectiveness. Additionally, the RO unit requires periodic membrane replacement, which may pose financial challenges in low-income communities unless supported by government or NGO partnerships.</p>
            <p>Despite these limitations, the overall performance demonstrates the potential of this hybrid, solar-powered biosensor-integrated system to significantly improve safe water access in rural settings. By providing real-time microbial monitoring and multi-stage purification powered entirely by renewable energy, the system offers a scalable and sustainable solution that addresses both treatment and safety verification gaps in decentralized water management.</p>
            <p>
                <xref ref-type="table" rid="T12">
Table 12</xref> indicates the treated water regarding the physiochemical parameters.</p>
            <table-wrap id="T12" orientation="portrait" position="float">
                <label>
Table 12. </label>
                <caption>
                    <title>Final treated water.</title>
                </caption>
                <table content-type="article-table" frame="hsides">
                    <thead>
                        <tr>
                            <th align="left" colspan="1" rowspan="1" valign="top">Parameter</th>
                            <th align="left" colspan="1" rowspan="1" valign="top">Before</th>
                            <th align="left" colspan="1" rowspan="1" valign="top">After</th>
                            <th align="left" colspan="1" rowspan="1" valign="top">WHO Limit</th>
                        </tr>
                    </thead>
                    <tbody>
                        <tr>
                            <td align="left" colspan="1" rowspan="1" valign="middle">Turbidity (NTU)</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">45&#x2013;140</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">&lt;2</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">&lt;5</td>
                        </tr>
                        <tr>
                            <td align="left" colspan="1" rowspan="1" valign="middle">E. coli (CFU/100&#x00a0;mL)</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">50&#x2013;200</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">0</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">0</td>
                        </tr>
                        <tr>
                            <td align="left" colspan="1" rowspan="1" valign="middle">Lead (mg/L)</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">0.05&#x2013;0.11</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">&lt;0.005</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">0.01</td>
                        </tr>
                        <tr>
                            <td align="left" colspan="1" rowspan="1" valign="middle">Arsenic (mg/L)</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">0.012&#x2013;0.024</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">&lt;0.003</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">0.01</td>
                        </tr>
                        <tr>
                            <td align="left" colspan="1" rowspan="1" valign="middle">TDS (mg/L)</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">300&#x2013;900</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">50&#x2013;200</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">&lt;300</td>
                        </tr>
                        <tr>
                            <td align="left" colspan="1" rowspan="1" valign="middle">BOD (mg/L)</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">5&#x2013;11</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">1&#x2013;2</td>
                            <td align="left" colspan="1" rowspan="1" valign="middle">&lt;3</td>
                        </tr>
                    </tbody>
                </table>
                <table-wrap-foot>
                    <p>
Table of results of treated water.</p>
                </table-wrap-foot>
            </table-wrap>
        </sec>
        <sec id="sec24" sec-type="conclusion">
            <title>9. Conclusion</title>
            <p>This work presents the development and modelling of a solar-powered hybrid water treatment system integrated with real-time biosensor monitoring for rural water purification. The analysis of 384 water samples from Ishaka Municipality confirmed that rural surface sources carry significant microbial, chemical, and physical contamination, underscoring the need for decentralized, multi-stage treatment solutions.</p>
            <p>The proposed system successfully combines sedimentation, activated carbon adsorption, reverse osmosis, and solar thermal disinfection into a single off-grid architecture. Hydraulic, thermal, and solar energy modelling using Navier&#x2013;Stokes Equations, Darcy&#x2019;s law, Stokes&#x2019; settling theory, and solar energy balances demonstrated that the system operates efficiently under realistic conditions. The photovoltaic array produced sufficient energy to power all treatment stages after accounting for losses, confirming the viability of renewable energy for continuous operation in low-resource settings.</p>
            <p>Treatment performance results show that the hybrid system achieves more than 95% overall removal efficiency across major contaminants, producing water that meets WHO drinking water standards. The integration of a BOD biosensor provided rapid, reliable microbial monitoring before and after treatment, transforming the system into a combined &#x201c;monitor-and-treat&#x201d; platform, an advancement not commonly found in rural purification technologies.</p>
            <p>Overall, the system demonstrates strong potential as a sustainable, scalable, and autonomous solution for improving drinking water safety in underserved communities. Future work will include long-term field deployment, cost-benefit analysis, membrane fouling assessment, and user-centered design improvements to support community adoption and operational continuity.</p>
        </sec>
        <sec id="sec25">
            <title>Ethics approval</title>
            <p>This study did not involve human subjects in a way that required biomedical ethical review, but adhered to established ethical standards.</p>
        </sec>
        <sec id="sec26">
            <title>Consent to participate</title>
            <p>Not Applicable.</p>
        </sec>
        <sec id="sec27">
            <title>Consent to publish</title>
            <p>Not Applicable.</p>
        </sec>
    </body>
    <back>
        <sec id="sec30" sec-type="data-availability">
            <title>Data availability statement</title>
            <p>Zenodo. Design and Modeling of a Solar-Powered Water System for Real-Time Microbial Detection and Treatment. 
                <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.5281/zenodo.19125833">https://doi.org/10.5281/zenodo.19125833</ext-link>
                <sup>
                    <xref ref-type="bibr" rid="ref33">33</xref>
                </sup>
            </p>
            <p>This project contains the following underlying data:
                <list list-type="bullet">
                    <list-item>
                        <label>&#x2022;</label>
                        <p>Upgraded water system data set (raw data, treated data, solar model data, and loads data and biosensor model data)</p>
                    </list-item>
                </list>
            </p>
            <p>Data is available under the terms of 
                <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0</ext-link>
            </p>
            <p>

                <bold>Clinical Trial:</bold> Not Applicable.</p>
        </sec>
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    <sub-article article-type="reviewer-report" id="report486824">
        <front-stub>
            <article-id pub-id-type="doi">10.5256/f1000research.193405.r486824</article-id>
            <title-group>
                <article-title>Reviewer response for version 1</article-title>
            </title-group>
            <contrib-group>
                <contrib contrib-type="author">
                    <name>
                        <surname>Mousa</surname>
                        <given-names>Sahar A.</given-names>
                    </name>
                    <xref ref-type="aff" rid="r486824a1">1</xref>
                    <role>Referee</role>
                </contrib>
                <aff id="r486824a1">
                    <label>1</label>Cairo University, Giza, Egypt</aff>
            </contrib-group>
            <author-notes>
                <fn fn-type="conflict">
                    <p>
                        <bold>Competing interests: </bold>No competing interests were disclosed.</p>
                </fn>
            </author-notes>
            <pub-date pub-type="epub">
                <day>17</day>
                <month>6</month>
                <year>2026</year>
            </pub-date>
            <permissions>
                <copyright-statement>Copyright: &#x00a9; 2026 Mousa SA</copyright-statement>
                <copyright-year>2026</copyright-year>
                <license xlink:href="https://creativecommons.org/licenses/by/4.0/">
                    <license-p>This is an open access peer review report distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
                </license>
            </permissions>
            <related-article ext-link-type="doi" id="relatedArticleReport486824" related-article-type="peer-reviewed-article" xlink:href="10.12688/f1000research.175423.1"/>
            <custom-meta-group>
                <custom-meta>
                    <meta-name>recommendation</meta-name>
                    <meta-value>approve-with-reservations</meta-value>
                </custom-meta>
            </custom-meta-group>
        </front-stub>
        <body>
            <p>
                <bold>&#x00a0;(General and Methodology)</bold>
            </p>
            <p> - Clarify objective and novelty</p>
            <p> &#x00a0; - The manuscript should explicitly state the novelty: how the integrated solar-powered multi-stage treatment with real-time biosensing advances beyond existing off-grid water purification systems.</p>
            <p> - Provide detailed Materials and Methods</p>
            <p> &#x00a0; - Include complete specifications for the solar-energy subsystem (type of PV panels, array size, MPPT controller, battery storage, inverter efficiency, tilt/azimuth, shading mitigation).</p>
            <p> &#x00a0; - Provide step-by-step procedural details for all treatment stages (sedimentation, activated carbon filtration, reverse osmosis, solar disinfection), including contact times, flow rates, membrane specifications, and operating pressures.</p>
            <p> &#x00a0; - Define exact analytical methods and instruments used for turbidity, pH, E. coli, COD/BOD, etc., including calibration, QA/QC procedures, and limits of detection.</p>
            <p> - Model descriptions and validation</p>
            <p> &#x00a0; - Present the Navier-Stokes and Darcy-based models with explicit governing equations, boundary conditions, parameter values, and numerical methods. State assumptions and limitations.</p>
            <p> &#x00a0; - Describe the microbial inactivation kinetics with the specific rate law, constants, and how parameters were estimated or fitted from data.</p>
            <p> &#x00a0; - Include a validation plan: how model predictions were compared to experimental data and provide quantitative goodness-of-fit metrics (R^2, RMSE, etc.).</p>
            <p> - Experimental design and statistics</p>
            <p> &#x00a0; - Justify the sample size (power analysis) for the 384 samples and outline how sampling locations and times were chosen to ensure representativeness.</p>
            <p> &#x00a0; - Report statistical methods used for data analysis, including handling of non-detects, outliers, and multiple comparisons.</p>
            <p> - Results clarity and reproducibility</p>
            <p> &#x00a0; - Provide separate, clearly labeled figures/tables for each performance metric (contaminant removal, E. coli elimination, solar-PR, biosensor response time, correlation with BOD/DO).</p>
            <p> &#x00a0; - Include uncertainty estimates (confidence intervals) around key results.</p>
            <p> </p>
            <p> 
                <bold>&#x00a0;(Data, Biosensor integration, and Standards)</bold>
            </p>
            <p> - Biosensor validation and integration</p>
            <p> &#x00a0; - Describe the biosensor platform (biomolecule, transduction mechanism, sampling method, linear range, specificity, limit of detection).</p>
            <p> &#x00a0; - Explain how the biosensor data are integrated with the water-treatment control system (feedback mechanism, hysteresis, latency).</p>
            <p> - Regulatory and performance standards</p>
            <p> &#x00a0; - Explicitly compare results to WHO drinking-water guidelines and summarize any deviations or caveats.</p>
            <p> &#x00a0; - Address safety, potential chemical residues from filtration media or disinfection, and mechanisms to prevent secondary contamination.</p>
            <p> - Data availability and openness</p>
            <p> &#x00a0; - Provide a data-sharing plan: deposit raw and processed data in a public repository with metadata. Include a Data Availability statement.</p>
            <p> &#x00a0; - If computational scripts or simulations exist, provide access or a detailed methods appendix.</p>
            <p> 
                <bold>(Limitations, Practicality, and Economics)</bold>
            </p>
            <p> - Limitations and generalizability</p>
            <p> &#x00a0; - Include a dedicated limitations section: model assumptions, scale-up considerations, and environmental variability (temperature, UV exposure, seasonal solar irradiance).</p>
            <p> - Practical deployment and maintenance</p>
            <p> &#x00a0; - Discuss maintenance requirements, expected lifetime of components (membranes, biosensor, batteries), and failure modes.</p>
            <p> &#x00a0; - Provide a maintenance-friendly design note: ease of cleaning, part replacement, and remote diagnostics.</p>
            <p> - Economic feasibility</p>
            <p> &#x00a0; - Add an initial cost estimate, operating costs, and a high-level cost&#x2013;benefit analysis. Include a sensitivity analysis on key economic drivers (cost of PV, membranes, biosensor lifespan).</p>
            <p> &#x00a0; - Comment on scalability and applicability to other rural settings with different resource constraints.</p>
            <p>Is the work clearly and accurately presented and does it cite the current literature?</p>
            <p>Partly</p>
            <p>If applicable, is the statistical analysis and its interpretation appropriate?</p>
            <p>Partly</p>
            <p>Are all the source data underlying the results available to ensure full reproducibility?</p>
            <p>Partly</p>
            <p>Is the study design appropriate and is the work technically sound?</p>
            <p>Yes</p>
            <p>Are the conclusions drawn adequately supported by the results?</p>
            <p>Partly</p>
            <p>Are sufficient details of methods and analysis provided to allow replication by others?</p>
            <p>Partly</p>
            <p>Reviewer Expertise:</p>
            <p>My research focuses on advancing photocatalytic membrane technology for the treatment of industrial wastewater, particularly organic-rich effluents. I specialize in designing low-cost, eco-friendly membranes by integrating green-synthesized nanomaterials to enhance photocatalytic degradation efficiency. A key challenge I aim to address is membrane fouling, which severely limits long-term applicability.</p>
            <p>I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.</p>
        </body>
    </sub-article>
</article>
