Question: 15. Water falls from a height of 60 m at the rate of 15 \mathrm{~kg} / \mathrm{s} to operate a turbine. The losses due to frictional force are 10 \% of the input energy. How much power is generated by the turbine?
(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2})(1) 10.2 kW
(2) 8.1 kW
(3) 12.3 kW
(4) 7.0 kW
Answer: Option (2)
Explanation:
The input power supplied by falling water is equal to the rate of loss of gravitational potential energy.
Mass of water falling per second is m = 15\,\text{kg s}^{-1} and height is h = 60\,\text{m}.
The input power is given by P_{\text{input}} = mgh.
Substituting the given values, P_{\text{input}} = 15 \times 10 \times 60 = 9000\,\text{W}.
The losses due to friction are 10\% of the input power,
so the useful power obtained is 90\% of the input power.
Thus, the power generated by the turbine is P = 0.9 \times 9000 = 8100\,\text{W}.
Converting into kilowatts, P = 8.1\,\text{kW}.
Therefore, the correct answer is Option (2).