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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
Detailed Solution
Energy available per second to operate the turbine $= \dfrac{m}{t}\,g\,h$
$= 15 \times 10 \times 60 = 9000$ joule per second
Power supplied to the turbine = 9000 W
Power lost due to friction = 10 percent of 9000 = 900 W
Power generated by the turbine $= 9000 - 900 = 8100$ W
$= 8.1$ kW
Second approach: $P_{generated} = P_{input} \times \dfrac{90}{100} = \dfrac{mgh}{t} \times \dfrac{90}{100} = 15 \times 10 \times 60 \times \dfrac{90}{100} = 8.1$ kW
$= 15 \times 10 \times 60 = 9000$ joule per second
Power supplied to the turbine = 9000 W
Power lost due to friction = 10 percent of 9000 = 900 W
Power generated by the turbine $= 9000 - 900 = 8100$ W
$= 8.1$ kW
Second approach: $P_{generated} = P_{input} \times \dfrac{90}{100} = \dfrac{mgh}{t} \times \dfrac{90}{100} = 15 \times 10 \times 60 \times \dfrac{90}{100} = 8.1$ kW