Design and Modeling of a Solar-Powered Water System for Real-Time Microbial Detection and Treatment

2.1 Materials and reagents

Nitric acid was used for preservation of water samples during heavy-metal analysis. Concentrated nitric acid (65–69% w/w) was added at 2 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).

Sodium thiosulfate was used to neutralize residual chlorine in microbiological water samples. A volume of 0.1 mL of 10% (w/v) sodium thiosulfate solution was added per 100 mL of sample. Sodium thiosulfate was supplied by Sigma-Aldrich (Catalogue No. S8503).

Membrane filters with a pore size of 0.45 μm and a diameter of 47 mm were used for chemical filtration and microbial analysis. Filters were obtained from Merck Millipore, USA (Catalogue No. HAWP04700).

Eosin Methylene Blue (EMB) agar was used for selective culturing of Escherichia coli. EMB agar powder was prepared at 37 g/L of distilled water according to the manufacturer’s instructions and sterilized by autoclaving at 121 °C for 15 minutes. The medium was supplied by Oxoid Ltd. (Thermo Fisher Scientific, UK; Catalogue No. CM0069).

Sterile sampling bottles (100 mL capacity), pre-dosed with sodium thiosulfate, and were supplied by VWR International (Catalogue No. 215–1590).

2.2 Characterization of physical, chemical, and biological pollutants in rural surface water sources

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.¹⁰ To identify the number of water samples to be used, a statistical technique is used.

2.2.1 Statistical Sampling Techniques

Equation 1 is used to determine the number of water samples to use based on the sources. Table 1 presents the standard score values of Z, e, and r.^12,22

Where.

n is the required sample size.

Z is the score (1.96 for 95% confidence, 1.645 for 90%).

r is the estimated proportion of contamination (0.5 is used if unknown; it’s the most conservative).

e is the margin of error in proportion (0.05).

Using Equation 3.1 and Table 1, for example, considering the confidence 95%. Z = 1.96, e = 0.005, r = 0.5

n = 384 water samples.

Each water sample is tested for heavy metals, E. coli, pharmaceuticals, organic debris, pesticides, and salts.

2.2.2 Characterisation of Physical Water Contaminants

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.¹¹

Parameters such as turbidity, Total Suspended Solids, environmental temperature, and organic debris are considered. The methods of testing physical water parameters are shown in Table 2.¹²

Gravimetric Filtration Procedure.¹³

The measurement is done in each perspective and the Total Suspended Solids (mg/L), TSS are determined in Equation 2.

Where;

$W_{\mathit{\text{initial}}}$ is the Weight of the clean, dry filter (mg).

$W_{\mathit{\text{final}}}$ is the Weight of dried filter plus solids (mg).

$V$ is the Volume of water sample filtered (mL).

2.2.3 Characterization of Chemical Contaminants, such as Heavy Metals, Pharmaceuticals, Salts, and Pesticides.

Each chemical contaminant type is identified through experimental testing and recorded.¹³

Testing of heavy metals in each water sample.

Equation 3 describes the quality rating for a heavy metal measured such as Zinc or Iron.

$C_i$ is the measured concentration of metal in (mg/L).

$Q_i$ is the Quality rating for a heavy metal i.

$S_i$ is the Standard value for metal i (mg/L)

Where $W_i$ is the unit weight of a heavy metal tested.

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 Equation 5 and Table 3.

Heavy Metal Water Quality Index (HMWQI)

After the procedure Table 4 can be used to guide in determining the WHO standard concentrations.¹³

How to Test Pharmaceutical contaminants in water

Water samples are collected from the water source and stored at a temperature of 4°c for 2 days. Some solid particles were filtered using a micro filter with a minimum porous diameter of 0.45 μm. Liquid Chromatography – Tandem Mass Spectrometry is used to detect the pharmaceutical contaminants.¹⁴

The Pharmaceutical classes targeted are Analgesics, Antibiotics, and Antidepressants. WHO does not specify the quantitative standards of pharmaceuticals in water.¹⁴ Table 5 elaborates the physiochemical parameters of water for each water sample.

How to test salt in water

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 (μS/cm).¹⁵ Salts are found in water sources as their standard concentrations as identified by WHO are elaborated in Table 6.

However, the WHO standards of TDS are 300 mg/L/ and it doesn’t specify EC.¹⁶

How to test pesticides in water

Gas Chromatography–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 μg/L.¹⁷

2.2.4 Characterization of Biological Contaminants such as Bacteria

The characterization is done for the bacteria specialized as in Table 7.

Materials and equipment used to test bacteria

Procedures for testing¹²

Table 8 indicates examples of bacteria involved in drinking water.¹⁷

2.3 Design a water treatment system that will be capable of removing the physical, chemical, and microbial water pollutants

The model will consist of the components below, as shown in Figure 1.^17,30

Figure 1. Model for the water treatment system.^30,20

Figure 1 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.

The system will be supported by solar power and its design will be done in the following ways:

The loads of the pumps, evaporator and condenser are shown in Table 9. Whereas Table 10 indicates loads of two motor pumps, 1 evaporator and 1 condenser.

2.3.1 Energy Balance on a Solar Collector

This accounts for the solar energy received, absorbed, stored, and lost at the collector surface.

Where;

$Q_{\mathit{net}}$ is the useful heat gain in Watts

$Q_{\mathit{\text{Solar}}}$ is the incident solar energy absorbed in Watts

$Q_{\mathit{\text{lOSS}}}$ is the total heat losses (W), including convection, conduction, and radiation

2.3.2 Absorbed Solar Radiation

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 Equation 7.

Where;

A is the absorber area (m²)

G is the incident solar radiation (W/m²)

α\alphaα is the absorptivity of the surface (dimensionless)

2.3.3 Convective Heat Loss

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. Equation 8 describes the heat transfer and panel surface temperature.

Where;

hc is a convective heat transfer coefficient in W/m²·K

Ts is a surface temperature measured in Kelvin (K)

Ta is the ambient temperature measured in Kelvin (K)

2.3.4 Radiative Heat Loss

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 Equation 9.

ϵ is the Emissivity of the surface, σ is the Stefan-Boltzmann constant $5.67\times {10}^{-8}$ W/m².K⁴

The total heat loss is given in Equation 10

This calls for the energy balance in a Water Volume (Lumped System)

Where;

m is mass of water (kg)

cp is the specific heat capacity of water (J/kg·K)

$\frac{\mathit{dT}}{\mathit{dt}}$ is the Rate of temperature change (K/s)

2.3.5 Solar Collector Efficiency

Where;

η = Efficiency of the solar collector

2.3.6 The overall load current and the operational time

The normal operating voltage will be 12-24 V. Table 9 shows the loads in the water purification system and their daily working rates.

The total current, $T_C=\sum \frac{P_i}{V}$ = $\left(\frac{(250+250+1000+800)}{(230+230+230+230)}\right)=\mathbf{2.5}\mathit{A}\mathit{}$

The Total Energy Demand per Day (E_D) will be given in Equation 13.

Where;

$P_i$ is the power rating of the i^th load (in watts)

$T_i$ is the Time, the i^th load is operated per day

Battery capacity, B _C

$\text{Operational Time Estimate}\left(\mathrm{hr}\right),$ which is described in Equation 14.

Where;

$P_T$ is the total load power in watts

DoD is the Depth of Discharge, which is usually a capacity of 80%

2.3.7 How to Calculate Total PV System Losses

Figure 2,^18–31 describes electrical components used in water treatment. The components helps in identifying the system power losses through determining load for each.

Figure 2. An off-grid solar circuit for powering a water treatment system.³¹

A schematic of the solar PV array charging system. 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.

2.3.7.1 Losses Inverter

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 Equation 15.¹⁸

Where $I_{\mathit{eff}}$ 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 2–5% and efficiency ranges 95 to 98%.

2.3.7.2 Soiling Losses

Accumulation of dust and dirt on the solar panels may cause losses, which are called soiling losses. Soil losses are identified using Equation 3.9

The formula for soiling losses (S_L) will be given by

Where ${\mathit{E}}_{\mathit{\text{soiled}}}$ is the production energy when the PV has dirt (Joules)

${\mathit{E}}_{\mathit{\text{cleaned}}}$ is the production energy when the PV is clean from dirt in J or Watts

2.3.7.3 Losses caused by Temperature (T _L)

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. Equation 3.10 describes the factors that lead to temperature losses of the PV system.

Where;

$Q_{\mathit{Deg}}$ is the module quality degradation factor

$P_{\mathit{STC}}$ is the maximum energy/power at standard test conditions (Watts)

$C_{\mathit{\text{Temp}}}$ is the temperature coefficient

$T_C$ is the module temperature (⁰ C)

2.3.7.4 DC and AC cabling losses

The DC losses obtained in a PV system cannot be directly determined. For this solar water treatment system, the maximum current, I_M, and maximum voltage are determined first to determine the cabling losses.¹⁹

Maximum current I _M

Maximum Voltage ${\mathit{V}}_{\mathit{M}}$

Where $V_t=\frac{N_{sk{T}_C}}{q,}$ where k is the Boltzmann constant 1.3806503 × 10⁻²³ J/°C, q = 1.60217646 × 10⁻²³ C is the charge of an electron. $T_C$ and G are temperatures (°C). $G_{\mathit{STC}}$ =1000 W/m² = irradiance of the standard testing condition. The other parameters will be used from the manufacturer’s manual.

The voltage difference in this DC will be obtained from Equation 19.

Where

$V_{\mathit{DC}}$ is the measured voltage in volts. Measured at the inverter’s input.

The cabling losses (C_DCL) are given in Equation 21.

Where $I_{\mathit{DC}}$ the DC is current measured at the input point of the inverter.

$Q_{\mathit{Deg}}$ is the PV module quality degradation factor.

2.3.7.5 Mismatch and wiring losses

This occurs when uneven panel performance and inter-cell/inter-module ohmic losses are obtained in the PV system. Equation 22 describes mismatch losses.

Where;

$P_a$ is the Power of the array with mismatch

$P_i$ is the Power of a perfectly matched array

Pa and Pi will be simulated using PVsyst

2.3.7.6 Wiring loss

Wire losses are caused by current with the wire, resistivity, and area of the wire as defined in Equation 23.

Where;

$\mathrm{\rho }$ is the Resistivity of the wire material (Ω·m)

$A$ is the area of the cable wire (m²)

$I$ is the length of cable wire (m)

2.3.7.7 Degradation (annual)

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.

2.3.7.8 Performance Ratio (PR)

This will help to determine the system’s availability. This will give the amount of sunlight required by the solar panel and convert to AC

According to,²¹

Where t is the time interval in hours

T is the total number of intervals

${P_t}^{\mathit{\text{In Output}}}$ is the measured or actual AC output power of the PV system

$P_{\mathit{STC}}$ is the rated power output of the PV module or system under Standard Test Conditions (STC)

$G_t$ is the Irradiance on the plane of the array at time t

$G_{\mathit{STC}}$ is the Standard irradiance under STC, usually taken as 1000 W/m²

2.3.7.9 Shading Losses

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 Equation 25.

${\mathit{E}}_{\mathit{\text{Shadded}}}$ is the energy output of a PV system with shade (W/m²).

${\mathit{E}}_{\mathit{\text{Unshadded}}}$ is the energy output of a PV system without shade (W/m²).

Extraterrestrial Solar Irradiance on a Horizontal Surface ( ${\mathbf{H}}_{\mathbf{o}})$

The amount of solar energy received per unit area on a horizontal surface at the top of the Earth’s atmosphere during a given time is described in Equation 26

Where:

G_s is the Solar constant (W/m²)

n is Day of the year (1–365)

Φ is Latitude (radians or degrees)

δ is the Solar declination (radians or degrees)

ω is the Sunset hour angle (radians or degrees)

The declination angle can be given as

Sunset Hour Angle

2.3.7.10 Solar Irradiation on an inclined plane (H_t)

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 Equation 29.

Where H is the measured global radiation on the surface that is horizontal

$\beta$ is the Tilt angle

${\mathit{HG}}_r$ is the ground reflectance (typically 0.2)

H_b is the estimated beam

R_b is the ratio of the beam radiation on a tilted surface to a horizontal surface

H_d diffuse beam

2.3.7.11 Total Solar Irradiance on Collector Surface ( ${\mathit{I}}_{\mathit{t}}$ )

Where

$I_t$ is the total irradiance on the tilted surface [W/m²]

$\mathrm{I}$ is the direct irradiance on horizontal [W/m²]

$I_d$ is the diffuse irradiance on horizontal [W/m²]

$I_r=\mathrm{\rho g}(\mathrm{I}+I_d)$ : Reflected irradiance, where ρ_g is ground reflectivity (0.2)

Β is the Tilt angle of the collector

R is the Ratio of the beam irradiance on tilted to horizontal

The current requirement will be determined by using the formula.

The system will be a 24 V voltage system

2.3.7.12 Solar Panel & Battery Sizing

Time required to treatment water per day

Daily energy = Total Load × Time required to treat water per day

The PV system is for 12 V

Proposed battery sizing = 25 Ah × 1.5 (safety factor) = 40 Ah

3.1 Design of the source of water

To determine the required capacity of the source, the daily water demand is estimated first.

Where N is the population of people to receive water

D is in m³/day

Q is per capita water consumption (Liters/person/day)

The flow rate, $Q(\mathrm{m}3/\mathrm{h})=D/T$

Where T is the number of operating hours

Where

$D_V$ is the average daily demand?

${\mathit{P}}_{\mathit{D}}$ is the peak demand factor, usually 1.8

Source capacity

Where $V_S$ the storage volume is used (m³)

$A_S$ is the surface area of the water body (m²)

$H_e$ is the effective depth of water (m)

3.2 Hydraulic design of the intake pipe

Sizing the intake pipe,

Where A is the cross-sectional area of a pipe

Q is the flow rate

V is the velocity determined by the pump of the manufacturer

3.2.1 Pump Design

Where Q is the pump flow rate (m³/s)

D is the pump daily demand (m^3/day)

T is the operating hours in a day

Where;

$H_S$ is the Suction head (vertical lift from source to pump)

$H_D$ is the delivery head (vertical height to the highest point in the system)

$H_F$ is the friction loss in the pipe

Determine Pump Power, H_P

Or where Q is the flow (m³/s)

H is the Head (m)

$H_P$ = Water horsepower (Watts)

1 Horse power = 746 Watts

3.2.2 Hydraulic Power

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.

Static hydraulic power from one height to another is given by,

Where $\mathrm{P}$ _s is the hydraulic power (W)

H is the maximum lift in meters. This is the head at the outlet

Q is mass flow rate (m³/s), $\mathrm{\rho }\text{is the density of fluid}\mathrm{kg}/{\mathrm{m}}^3$

g is acceleration due to gravity, which is equivalent to 9.81 m/s²

h is the differential height

Where m is mass (kg)

Time, t, is in seconds

P_S = Q $\mathrm{\rho gh}$ , and Q = AV. Where A is area and V is velocity

Where A is the area of the cross-section and U is the initial velocity of water

The dynamic hydraulic power of a pump as water flows from one to another is given by,

$\mathrm{Pd}=\frac{\mathrm{\rho A}{\mathrm{U}}^3}{2}$ , but $\mathrm{V}=⎷\left(2\mathrm{gh}\right)$ so, ${\mathrm{V}}^2=2\mathrm{gh}$ , $P_D=\text{Qρgh}$ , maximum lift h.

Therefore static power of a water pump is equivalent to the dynamic power of a water pump.

3.2.3 Efficiency of a Pump ( $\mathbf{\eta p}$ )

Comparing electrical power with hydraulic power Water Pump, the efficiency of a pump must be greater than the efficiency of the system. Figure 3 illustrates a schematic of a pump, having a suction and an outlet pipe.³²

Figure 3. Architecture of Hydraulic Pump.³²

The architecture of Hydraulic Pump involving the direction of flow of liquid.

Electric power input of the motor will be equivalent to the electric power input Pe, of the pump. Considering the Figure 4 indicating a suction head of a pump, Sh, discharge head, Hs and total head Ht.³²

Figure 4. Pump head determination.³²

The architecture, show the total head pump.

Total head, Ht = Dh + Hs

From Equation 43 $\mathrm{Ps}=\text{Qρgh}$

Considering the hydraulic power at a height of … … Therefore, power loss is

Efficiency of the system, $\text{ηsytem}=\left(\frac{\mathrm{Ph}-\text{Ploss}}{\mathrm{Pe}}\right)\times 100$

$\mathrm{e}\mathrm{are}\mathrm{all}\text{in}\mathrm{KW}$ . Therefore, $\mathrm{\eta p}>\text{ηsyst}$

The type of flow will be determined by

Where

ρ is fluid density (kg/m³)

u is the average fluid velocity (m/s)

D is the pipe diameter (m)

μ is the dynamic viscosity (Pa·s)

3.2.4 Modelling water flow using Navier-Stokes Equations

The vector form Equation is

∇ is the Divergence operator

ρ is the fluid density (kg/m³)

u is the velocity vector of the fluid (m/s)

t is time (s)

For incompressible fluids

$\nabla ·\mathrm{u}=0$ . This means density is constant, $\mathit{\rho t}=0$

Since the pipe is a 3D component, water will flow in 3D, and for 3D flow

Where u, v, w: velocity components in x, y, z directions

Conservation of momentum will be given as

Where;

f is the body forces

$\mathrm{\mu }$ is the dynamic viscosity

ρ is the fluid density

p is the pressure

According to Roiti-Gromeka-Szymański ´nski Solution, the pressure gradient of laminar flow of water is given by the 51

Where r is the pipe radius, G is the pressure gradient.

4.1 Temperature rise

The increase in temperature can kill more bacteria and micro-organisms. The heat energy required to kill bacteria is described in Equation 52.

Where;

$Q_a$ is the amount of amount heat added. It is measured in Joules

m is the mass of water in kg

cp is the specific heat of water, which is equivalent to 4186 J/kg·°C)

ΔT is the temperature change in °C

When a phase change occurs, water boils, and the heat energy is converted as in Equation 53.

Where,

$L_v$ is the latent heat of vaporization

4.1.1 Inactivation models of microbial organisms

First-order of inactivation is described in Equation 54.

Where;

$N_O$ is the initial number of organisms

N is the number after time, t

K is the inactivation rate constant in 1/s

It is time in (s)

4.1.2 Time required to reduce microbial organisms (D value)

The higher the energy to inactivate bacteria, the less the time of inactivation.

Where;

D is the time required at a specific temperature to eliminate microbes by 90%

The temperature will change to the D-value

Where Z is the temperature increase needed to reduce the D-value by a log cycle

4.2 Thermodynamic efficiency

Where Q_input is the total heat supplied

4.2.1 Rate of Heat Transfer

q is the heat transfer rate in Watts

h is convective heat transfer coefficient in W/m²·K

A, area in m²

Ts, Tw are surface and water temperatures, respectively, in K

4.2.2 Fourier’s Law (Conduction)

Fourier’s law of heat conduction describes how heat flows through a solid material due to a temperature change, and it’s described in Equation 59.

Where K is thermal conductivity in W/m·K

$\frac{\mathit{dT}}{\mathit{dx}}$ is the temperature gradient

4.2.3 Transient Heat Transfer

Water is heated to an extent of it being unstable. The temperature change is explained in Equation 60.

Where

T₀ is the initial temperature in Kelvin

$T_{\infty }$ is the Surrounding temperature

Ρ is the density of water

V is volume in cubic meters

T is time in seconds

5.1 Radiation Heat Transfer

ε is emissivity, σ is Stefan-Boltzmann constant (5.67 × 10⁸ W/m²·K⁴)

7.1 Baseline environmental characterization (n = 384)

Microbial Load: Baseline analysis of 384 samples from Ishaka Municipality revealed critical levels of contamination. Escherichia coli was present in 72–85% of spring and wetland samples, with a mean concentration of 48–210 CFU/100 mL, significantly exceeding the WHO limit of 0 CFU/100 mL.

7.1.1 Chemical & Physical Profile: Turbidity levels ranged from 9 to 146 NTU (WHO limit <5 NTU), while Total Suspended Solids (TSS) were recorded between 18 and 92 mg/L. Chemical analysis detected heavy metals, including Lead (0.03–0.11 mg/L) and Arsenic (0.011–0.024 mg/L), alongside emerging contaminants like pharmaceutical residues (ibuprofen at 18–44 ng/L) and DDT pesticides (2–9 ng/L).

7.2 Multi-stage treatment performance

7.2.1 Solar Thermal Inactivation: Heating water to ≥70–100 °C achieved a Log Reduction Value (LRV) of 4–6 for E. coli. Complete bacterial inactivation was consistently reached within 8–12 minutes of sustained boiling.

7.2.2 Combined System Efficiency: The integrated system (Sedimentation + Filtration + RO + Thermal) achieved a cumulative removal efficiency of >95% across all contaminant classes.

Comparative Water Quality

Turbidity: Reduced from baseline 45–140 NTU to <2 NTU.

Heavy Metals: Lead and Arsenic concentrations were lowered to <0.005 mg/L and < 0.003 mg/L, respectively, well below regulatory thresholds.

7.3 Real-time microbial monitoring (BOD biosensor)

7.3.1 Biosensor Validation: The integrated BOD biosensor exhibited a linear response range of 0–30 mg/L. Validation against standard laboratory BOD tests showed a high correlation coefficient (R² = 0.89–0.94).

7.3.2 Response Dynamics: The sensor provided rapid real-time feedback with a response time of 45–90 seconds. Post-treatment monitoring showed a reduction in BOD from 4.8–11.3 mg/L to 0.9–1.8 mg/L, providing immediate verification of water safety.

7.4 Solar energy & system modeling

7.4.1 PV Efficiency: The photovoltaic array produced 1.2–1.6 kWh/day, consistently meeting 100% of the system’s operational energy demand (1.0–1.3 kWh) even during low-irradiance periods.

7.4.2 Loss & Performance Analysis: Detailed loss modeling accounted for soiling (4–6%), temperature (3–5%), and inverter inefficiencies (2–3%), resulting in a final Performance Ratio (PR) of 0.84 to 0.88.

7.4.3 Hydraulic Stability: Navier–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.