Subtopic: Sources of power on the farm – human, animal, mechanical, electrical, wind, solar and biomass
Question Statement:
A solar photovoltaic (SPV) water pumping system lifts water through a total static plus friction head of $H = 25\text{ m}$. The system discharges water at a steady rate of $Q = 144\text{ m}^3/\text{day}$ over an equivalent effective peak sunshine duration of $t = 6\text{ hours/day}$. The density of water is $\rho = 1000\text{ kg/m}^3$ and $g = 9.81\text{ m/s}^2$. If the combined wire-to-water efficiency of the inverter, motor, and pump set is $\eta = 50\%$, the minimum required peak power rating ($W_p$) of the solar PV panel array in $\text{kW}_p$ is ________ (round off to 2 decimal places).
Answer Key:
3.27
Step-by-Step Solution & Explanation
```
Solar Water Pumping System:
Daily volume: Q_d = 144 m^3
Peak sunshine: t = 6 h = 21600 s
Flow rate: Q = 144 / 21600 = 6.667 * 10^-3 m^3/s
Head: H = 25 m
Efficiency: eta = 50% = 0.50
```
**Step-by-step Calculation:**
1. Average volumetric discharge during operating hours:
$Q = \frac{144\text{ m}^3}{6 \times 3600\text{ s}} = \frac{144}{21600} = 0.006667\text{ m}^3/\text{s} = 6.667\text{ L/s}$
2. Hydraulic power required to lift water ($P_h$):
$P_h = \rho g Q H = 1000\text{ kg/m}^3 \times 9.81\text{ m/s}^2 \times 0.006667\text{ m}^3/\text{s} \times 25\text{ m}$
$P_h = 9810 \times 0.006667 \times 25 = 1635\text{ W} = 1.635\text{ kW}$
3. Peak solar array rating ($P_{\text{pv}}$):
$P_{\text{pv}} = \frac{P_h}{\eta} = \frac{1.635\text{ kW}}{0.50} = 3.27\text{ kW}_p$