m high, at an average rate of 1.50 × 10 kg/s. If all the potential energy of thi

Question

m high, at an average rate of 1.50 × 10 kg/s. If all the potential energy of this water were converted to electric energy, how much power would be produced by these falls? 1255 The water going over the falls has gravitatanal potential energy relative to the base of the falls. As the water falls, the falling water acquires kinetic the falls; its energy is entirely kinetic. The rate at which energy is delivered to the base of the falis is given by the time derivative of the work done. energy until, at the base of

Explanation / Answer

suppose a water of mass m is taken out and it is then released form the height h , then the amount of potential energy lost by the water is equal to the gain in the kinetic energy which is used to do work

hence

W= mgh

If it takes time T to take out water,then the rate at which this work is done or the rate of conversion into kinetic energy is given by

P=W/T = mgh/T

where m/T is the rate of flow of water

putting all values, we get

P= (1.5*10^6)(9.8)(128) = 1.8816 * 10^6 kW

since all potential energy is converted, hence power = 1.8816 * 10^6 kW = 1882 MW

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