A hydroelectric dam holds back a lake of surface area 3.0×10 6 m2 that has verti

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 .

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

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

Explanation / Answer

  a) 3.0x10^6 m^2 x 140 m x 1000 kg/m^3 x 9.8 m/s^2 x 140 m = 5.76 x 10^14 J
b) 1000000 W x 60s/min x 60 min/hr x 1 hr = .95 x 9.8 m/s^2 x 140 m x kg => 1432 m^3
c) 1432 m^3 / 3.0x 10^6 m^2 => 4.77*10^-4 m.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.