A hydroelectric power plant situated at a distance of 20 km from a town. Whose energy demand is 100 MW at 240 V. At hydro electric power plant, the water pressure head is at a height of 400 m and the water flow available is \( 100\,\mathrm{m^3/s} \). Electrical energy generated in power plant is transmitted to the town with the use of transformers voltage output of the AC generator at power plant is stepped up and is there transmitted over long distances to a sub-station near the consumers in town. Sub-stations and utility poles steps down the voltage finally the 240 V which finally reaches the houses.
If the efficiency of turbine is 70% the electric power generated in plant is (Take \( g = 10\,\mathrm{m/s^2} \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 280 MW
The power available from falling water is the loss of potential energy per second: a volume flow \( Q \) of water of density \( \rho \) falling through a height \( h \) gives \( \rho Q g h \). The electric power is this times the efficiency.
\( \rho = 1000\,\mathrm{kg\,m^{-3}} \)
\( Q = 100\,\mathrm{m^3\,s^{-1}}, \; h = 400\,\mathrm{m}, \; g = 10\,\mathrm{m\,s^{-2}} \)
\( P_{\mathrm{in}} = \rho Q g h = 1000 \times 100 \times 10 \times 400 = 4\times10^{8}\,\mathrm{W} = 400\,\mathrm{MW} \)
\( P_{\mathrm{electric}} = 0.70 \times 400\,\mathrm{MW} = 280\,\mathrm{MW} \)