A solar-powered pump is to be used in Arizona to pump underground water for wild

Question

A solar-powered pump is to be used in Arizona to pump underground water for wildlife from a depth of220 mutant average rate of 450 L/day with a 50-m head loss in the length of piping. Assume the electrical-to-mechanical pumping efficiency is 82 percent. Determine the size of the solar-panel array that needs to be installed in m^2 Assume the solar input to the panel is 1000 W per square meter of panel area and the solar panel efficiency is 15 percent, so that a 1 -m^2 surface can provide 150 W of electricity on average each day. Assume that the water is pumped from an underground supply which is at atmospheric pressure.

Explanation / Answer

Total pump head = 220 + 50 = 270 m

Pump power = rho * Q * g * pump head      ( Q = 450 * 10^-3 m^3/day)

                    = 1000 * 450 * 10^-3 * 9.8 * 270

                     = 1190700 J / day

Electrical power required = 1190700 / 0.82   = 1452073.17 J/day

Area of solar panel required = 1452073.17 / 150

                                          = 9680.5   m^2

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