How much total energy is stored in the lake in Problem? As in that problem, take the gravitational potential energy to be zero at the base of the dam. Express your answer in joules and in kilowatt-hours. (?Hint?: Break the lake up into infinitesimal horizontal layers of thickness ?dy?, and integrate to find the total potential energy.) Problem: 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 150 m above the base of the dam. When the water passes through turbines at the base of the dam, its mechanical energy is converted to electrical energy with 90% efficiency. (a) lf 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. (b) What volume of water must pass through the dam to produce 1000 kilowatt-hours of electrical energy? What distance does the level of water in the lake fall when this much water passes through the dam?

Solution 80P Step 1: We have Area A = 3 × 10 m 2 Height h = 150 m 3 Density = 1000 kg /m Thus we have 6 Volume v = 3 × 10 m × 150 m v = 4.5 × 10 m 3 Potential energy is given by PE = mgh We can find mass of the water as m = v × Substituting values we get m = 4.5 × 10 m × 1000 kg /m = 4.5 × 10 kg 11 Using this we get PE we get 11 PE = 4.5 × 10 kg × 9.8 × 150 14 PE = 6.615 × 10 J Hence we get energy as 6.615 × 10 J 14