Question

Water falls from a height of $60\text{m}$ at a rate of $15\text{kg/s}$ to operate a turbine. If the energy loss due to friction is $10\%$ of the total energy, how much power is generated by the turbine? $\left[1\text{mark}\right]$

A. $12.3\text{kW}$
B. $7.0\text{kW}$
C. $8.1\text{kW}$
D. $10.2\text{kW}$

Answer 1

Correct answer$:$ option C $-$ $8.1\text{kW}$

Solution:
The mass of the water falling/second, $m$ = $15\text{kg/s}$

The height of the water fall, $h$ = $60\text{m}$

Energy loss is $10\%$, therefore $90\%$ of the water's energy can be used by the turbine to generate power.

The power generated = $\frac{90}{100}\times mgh$
= $0.9\times 15\times 10\times 60=8100\text{W}=8.1\text{kW}$