The Grand Coulee Dam is 1270 m long and 170 m high. The electrical power output from generators at its base is approximately 2000 MW. How many cubic meters of water must flow from the top of the dam per second to produce this amount of power if 92% of the work done on the water by gravity is con-verted to electrical energy? (Each cubic meter of water has a mass of 1000 kg.)
Solution 94P Step 1: Height of the dam, h = 170 m Suppose, a cubic metre of water is moving from 170 m height to the generator. The energy of this 1 cubic metre water can be calculated. Mass of 1 cubic metre water, m = 1000 kg Acceleration due to gravity, g = 9.8 m/s 2 Therefore, potential energy of 1 cubic metre water at the top, U = mgh U = 1000 kg × 9.8 m/s × 170 m = 1666000 J Step 2: Provided, the generator can convert 92% of work done by the water as electrical energy. That means, the efficiency of the generator is 92%. 1 cubic metre of water can do 1666000 J of work. So, the amount of electrical energy produced from it will be, E = 0.92 × W = 0.92 × 1666000 J = 1532720 J So, 1 cubic metre of water can generate 1532720 J of electrical energy.