1000 kg of water falls per second from a dam of height 30m. An electric generator at the foot of the dam uses kinetic energy of this water to generate electricity. Under ideal conditions (assuming there is no loss of energy) determine how many mega joules of energy can be produced in 10 seconds. Also, find the magnitude of power developed.
Answers
Explanation:
The velocity of the energy-sapped water is therefore sqrt(1 − η). So if we pull 96% of the energy out of the water, its flow velocity is 20% of the free-flow value (13 m/s in the foregoing example). Or we can grab 99% at a 10% exit speed (7 m/s, or 15 m.p.h.). Hydroelectric dams exploit storage of gravitational potential energy. A mass, m, raised a height, h against gravity, g = 10 m/s², is given a potential energy E = mgh. The result will be in Joules if the input is expressed in meters, kilograms, and seconds (MKS, or SI units). Water has a density of ρ = 1000 kg/m³, so if we know how many cubic meters of water flow through the dam each second (F), the power available to the dam will be P = ηρFgh. We have inserted η to represent the efficiency of the dam—usually around 90% (η≈0.90).