Question

Water falls from a height of $80\text{m}$ at the rate of $20\text{kg/s}$ to operate a turbine. The losses due to frictional force are $20$ % of the energy. How much power is generated by the turbine? $(g=10\frac{m}{s^2})$

• A. $12.3\text{kW}$
• B. $7.0\text{kW}$
• C. $12.8\text{kW}$
• D. $10.2\text{kW}$

Answer 1

The correct option is C $12.8\text{kW}$

Power given to turbine $=\frac{mgh}{t}$
$P_{in}=\left(\frac{m}{t}\right)gh\Rightarrow P_{in}=20\times 10\times 80$
$\Rightarrow P_{in}=16000\text{W}$
$\Rightarrow P_{in}=16\text{kW}$
Frictional losses mount to $20\%$, efficiency of turbine is $80\%$ Therefore, power generated by turbine $=80\%of16\text{kW}$
$\Rightarrow P_{out}=16\times \frac{80}{100}$
$\Rightarrow P_{out}=12.8\text{kW}$