Water falls from a height of 60 m at the rate of $15 \mathrm{~kg} / \mathrm{s}$ to operate a turbine

Question

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 $20 \%$ of the input energy. How much power is generated by the turbine? ( $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )\

Professor PC Thomas Classes · Answer

Given, $h=60 \mathrm{~m}$ Now, water falls at the rate of 15 kg is\ i.e., $\frac{m}{t}=15 \mathrm{~kg} / \mathrm{s}$\ $g=10 \mathrm{~m} / \mathrm{s}^{2}$\ As loss due to friction is $20 \%$, therefore only $80 \%$ of input energy is used to generate power.\ $	herefore \quad P=g h \frac{m}{t} 	imes \frac{80}{100}$\ $P=10 	imes 60 	imes 15 	imes \frac{80}{100}=7200 \mathrm{~W} \Rightarrow P=7.2 \mathrm{~kW}$\