in a dam generatingpower station water falls at a rate of 1000kg/sfroma height of 10mit is 69% effecient power

Question

in a dam generatingpower station water falls at a rate of 1000kg/s froma height of 10m.it is 60% effecient . find the power generated?

Answer 1

First solve this problem for 100% efficiency, then it will be no problem to go back and find 69% and 60% efficiency (or was that just a typo?).

This dam power generating plant works on the principle that the water initially have some gravitational potential energy which, as it falls, is converted into kinetic energy which is used to turn the turbines and generate electrical energy.
If everything in this process worked perfectly, all the PE would convert to KE which would then all convert to electrical energy.

1000 kg of water at a height of 10 meters would have a gravitational potential energy equal to,
PE = mgh
PE = 1000 kg * 9.81 m/s^2 * 10 m
PE = 98100 Joules (a unit of energy)

So if 1000 kg of water is falling per second, then 98100 Joules per second could potentially be generated,
Power = 98100 Joules / second
Power = 98100 Watts (a unit of power)

So if everything was 100% efficient, the power output would be 98100 Watts.
But it isn't 100% efficient, it is 60% (or 69%) efficient.
So to find the adjusted, inefficient, power output, just multiply the efficiency percentage as a decimal by the max power output.

Under 60% efficiency,
Power = .60 * 98100 = 58860 Watts
Under 69% efficiency,
Power = .69 * 98100 = 67689 Watts

Answer 2

Potential energy of 1000 kg water at a heightr of 10m
=1000*10*9.81 = 98100 Joule (g=9.81 m/s/s)
Power is the energy per unit time
Power generated at 69% efficiency =98100*0.69 =67689 Watt