Q. Water falls from a height of $60\ m$ at the rate of $15\ kg/s$ to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine $(g = 10\ m/s^{2})$
A) $12.3\ kW$
B) $7.0\ kW$
C) $8.1\ kW$
D) $10.2\ kW$
Explanation
(c) Power given to turbine $= \frac{mgh}{t}$
$P_{in} = \left( \frac{m}{t} \right) \times g \times h \Rightarrow P_{in} = 15 \times 10 \times 60$
$\Rightarrow P_{in} = 9000\ W \Rightarrow P_{in} = 9\ kW$
As efficiency of turbine is 90% therefore power generated = 90% of $9\ kW$
$P_{out} = 9 \times \frac{90}{100} \Rightarrow P_{out} = 8.1\ kW$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.