Pumped Energy Storage. A water reservoir has surface area A and depth D. The wat

Question

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.

Explanation / Answer

total gravitational pe (U)=mgh..
h=H+D/2,
m=density()*volume=AD,

so

U=*A*D*g*(H+D/2)

U=1607186868 J.

power(P)=|dU/dt|=|Ag(H*dD/dt+D*dD/dt)|; and

dD/dt=-d

P=|Ag(-H*d-D*d)|=Agd(H+D)

P=2.014600896*1011 J/s..

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