A hydroelectric dam holds back a lake of surface area 3.0×106 m2 that has vertic

Question

A hydroelectric dam holds back a lake of surface area 3.0×106 m2 that has vertical sides below the water level. The water level in the lake is a height 140 m above the base of the dam. When the water passes through turbines at the base of the dam, its mechanical energy is converted into electrical energy with 95 % efficiency.

If gravitational potential energy is taken to be zero at the base of the dam, how much energy is stored in the top meter of the water in the lake? The density of water is 1000 kg/m3 .

Express your answer using two significant figures.

Explanation / Answer

PE = mass*g*height

mass= density*volume

volume = Area*dh

Stored energy will be

PE = mgh = rho*V*g*h = rho*A*dh*g*h

stored energy = 1000*3*10^6*1*9.81*140

Stored energy = 4.12*10^12 J

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