Question

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 force are $10\%$ of the input energy. How much power is generated by the turbine?

$g=10{\text{m/s}}^2$

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

Answer 1

The correct option is C $8.1\text{kW}$

Incident power on turbine,

$P=\frac{d\left(mgh\right)}{dt}$

$\Rightarrow P=gh\frac{dm}{dt}$

$\Rightarrow P=10\times 60\times 15$

$\Rightarrow P=9000\text{W}$

Now, losses due to frictional forces are $10\%$.

$\therefore$ Power generated, $=(1-\frac{10}{100})\times 9000$

$=8100\text{W}$

$=8.1\text{kW}$

Hence, option $\left(C\right)$ is the correct answer.