Pumped Energy Storage. A water reservoir has surface area A and depth D. The water flows down pipes and through turbines to generate electric power. The bottom of the reservoir is at height H above the turbines. The depth D of water in the reservoir decreases at a rate d. (a) Calculate the total gravitational potential energy U. (b) Calculate the available power P = |dU/dt|, i.e., available for conversion to electric power.
DATA: A = 8 ×105 m2; D = 17 m; H = 103 m; d = 0.55 m per hour; density = 1.0 ×103 kg/m3.