A hydroelectric dam holds back a lake of surface area 3.1×10 6 m2 that has verti

Question

A hydroelectric dam holds back a lake of surface area 3.1×106 m2 that has vertical sides below the water level. The water level in the lake is a height 150 mabove 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 93 %efficiency.

Part A

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 .

Part B

What volume of water must pass through the dam to produce an amount of electrical energy totalling 1000 kilowatthours of electrical energy?

Express your answer using two significant figures.

Part C

What distance does the level of water in the lake fall when this much water passes through the dam?

Express your answer using two significant figures.

Explanation / Answer

a) Energy is stored in the top meter of the water in the lake

3.1x106 m2 x 160 m x 1000 kg/m3 x 9.8 m/s2 x 150 m = 4.7 x 1011J

b) The volume of water must pass through the dam to produce an amount of electrical energy totalling 1000 kilowatthours of electrical energy

1000000 W x 60s/min x 60 min/hr x 1 hr = .86 x 9.8 m/s^2 x 160 m x kg => 2570000 kg =>2.7x103 m^3

c) The Distance does the level of water in the lake fall when this much water passes through the dam

2.7x103 m3 / 3.1 x 10^6 m^2 => 8.3x10-4 m.

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