One method used to store energy during times of low demand is by pumping water uphill into a reservoir. When energy demand exceeds the output produced by power plants, the water is released, moves downhill, and is converted into electricity by a turbine. During a 142.0 minute long period of low usage, 62.0 MW is used to pump water up an elevation of 56.7 m in a series of 1.00 m diameter pipes. The friction loss in the pipe going to the upper reservoir is 30.2 m2/s2.
What is the mass flow rate, , of water during the low usage period?
What is the total mass of water raised 56.7 m during this 142.0 minute period?
How long can the turbines produce 335.0 MW of power from the release of the mass of stored water calculated above? Assume the water sustains a friction loss of 30.2 m2/s2 on the way down to the turbine.
What is the efficiency of this process? (Assume that the pump and tubines operate at 100% efficiency, and the only loses are due to frictional loses within the pipes.)