When water falls from a height of 80 ~m at the rate of 20 ~kg ~s ⁻¹ to operate a turbine the losses due to frictional force are 20 % of input energy. How much power is generated by the turbine?

Step-by-step solution

The potential energy of the water falling per unit time is the input power, given by P_ in = mgh t = ( m t )gh . Given m t = 20 kg s ⁻¹ , g = 10 m s ⁻² , and h = 80 m , we have P_ in = 20 10 80 = 16000 W = 16 kW . The losses due to frictional force are 20 % of the input energy, so the efficiency of the turbine is 100 % - 20 % = 80 % . The power generated by the turbine is P_ out = 80 % of P_ in = 0.8 16 kW = 12.8 kW . Answer: 12.8 KW