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The demand for electric power is usually much higher duringthe day than it is at night, and utility companies often sell powerat night at much lower prices to encourage consumers to use theavailable power generation capacity and to avoid building newexpensive power plants that will be used only a short time duringpeak periods. Utilities are also willing to purchase power producedduring the day from private parties at a high price.

Suppose a utility company is selling electric power for$0.06/kWh at night and is willing to pay $0.13/kWh for powerproduced during the day. To take advantage of this opportunity, anentrepreneur is considering building a large reservoir 50 m abovethe lake level, pumping water from the lake to the reservoir atnight using cheap power, and letting the water flow from thereservoir back to the lake during the day, producing power as thepump–motor operates as a turbine–generator during reverse flow.Preliminary analysis shows that a water flow rate of 2 m3/s can beused in either direction, and the irreversible head loss of thepiping system is 2.6 m. The combined pump–motor andturbine–generator efficiencies are expected to be 75 percent each.Assuming the system operates for 10 h each in the pump and turbinemodes during a typical day, determine the potential revenue thispump–turbine system can generate per year.