Water falls from a height of 50 m at the rate of $20 \mathrm{~kg} / \mathrm{s}$ to operate a turbine

Question

Water falls from a height of 50 m at the rate of $20 \mathrm{~kg} / \mathrm{s}$ to operate a turbine. The losses due to frictional force are $10 \%$ of the input energy. How much power is generated by the turbine? ( $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

Professor PC Thomas Classes · Answer

(a) : Given, $h=50 \mathrm{~m}$. Water falls at the rate of $m/t = 20 \mathrm{~kg} / \mathrm{s}$. Acceleration due to gravity $g=10 \mathrm{~m} / \mathrm{s}^{2}$. As loss due to friction is $10\%$, only $90\%$ of input energy is converted to power. $P = g h \frac{m}{t} 	imes \frac{90}{100} = 10 	imes 50 	imes 20 	imes 0.9 = 9000 \mathrm{~W} \Rightarrow P = 9.0 \mathrm{~kW}$.