Water falls from a height of $60\text{m}$ at the rate of $15\text{kg/s}$ to operate a turbine. The losses due to frictional forces are $10\%$ of the energy. How much power is generated by the turbine? (Take $g=10{\text{m/s}}^2$)

1. Calculate the input power (rate of potential energy provided):The formula for potential energy is $U=mgh$. Power is the rate of energy change:
$$P_{\text{in}}=\frac{dm}{dt}\cdot gh$$
Given $\frac{dm}{dt}=15\text{kg/s}$, $g=10{\text{m/s}}^2$, and $h=60\text{m}$:
$$P_{\text{in}}=15\times 10\times 60=9000\text{W}=9\text{kW}$$
Account for losses:The losses are $10\%$, which means the efficiency ($\eta$) is $100\%-10\%=90\%$.
$$\eta =0.9$$
Calculate generated power:
$$P_{\text{out}}=\eta \times P_{\text{in}}$$
$$P_{\text{out}}=0.9\times 9\text{kW}=8.1\text{kW}$$