Subtopic: Sources of power on the farm – human, animal, mechanical, electrical, wind, solar and biomass
Question Statement:
A solar photovoltaic pumping system delivers a discharge of $Q = 18\text{ m}^3/\text{h}$ of irrigation water against a total dynamic head of $H = 40\text{ m}$. Water density is $\rho = 1000\text{ kg/m}^3$ and $g = 9.81\text{ m/s}^2$. The combined efficiency of the motor-pump unit and controller/inverter is $\eta_{sys} = 60\%$ ($0.60$). The minimum electrical power rating ($W_p$) of the solar PV array required to operate this pump in $\text{kW}$ is ________ (round off to 2 decimal places).
Answer Key:
3.27
Step-by-Step Solution & Explanation
1. Water discharge rate in $\text{m}^3/\text{s}$:
$Q = \frac{18}{3600} = 0.005\text{ m}^3/\text{s}$
2. Hydraulic power ($P_{hyd}$):
$P_{hyd} = \rho g Q H = 1000 \times 9.81 \times 0.005 \times 40 = 1962\text{ W} = 1.962\text{ kW}$
3. Solar PV array peak power required ($P_{PV}$):
$P_{PV} = \frac{P_{hyd}}{\eta_{sys}} = \frac{1.962\text{ kW}}{0.60} = 3.27\text{ kW}$