Question

At a hydroelectric power plant, the water pressure head is at a height of $300m$ and the water flow available is $100m^3{s}^{-1}$. If the turbine generator efficiency is $60\mathrm{\%}$, estimate the electric power available from the plant. $($Given $g=9.8{ms}^{-2})$

• (A) $176.4MW$
• (B) $170.4MW$
• (C) $172.4MW$
• (D) $160.4MW$

Answer 1

The Correct Option is A

Explanation:
Here given,Height of water pressure head, $h=300m$Volume of the water flowing per second,$100m^3{s}^{-1}$Mass of water flowing per second,$m=100\times {10}^{3}kg$$={10}^{5}kg$Acceleration due to gravity, $g=9.8{ms}^{-2}$Potential energy of water fall during one second,$=mgh={10}^5\times 9.8\times 300$$=2.94\times {10}^8\mathrm{J}$The efficiency of the turbine $=60\mathrm{\%}$Therefore, input power $=2.94\times {10}^8{Js}^{-1}$Efficiency, $\eta =\frac{\text{ output power }}{\text{ input power }}$Output power $=\eta \times$ input power$=0.6\times 2.94\times {10}^8$$=1.764\times {10}^{8}W$$=176.4MW$Hence, the correct option is (A).