Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? [2021]

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Solution

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 force are 10% of the input energy. How much power is generated by the turbine [2021, 2008]

1 7.0 kW

2 10.2 kW

3 8.1 kW

4 12.3 kW

Ans.
(3)

Given, $h = 60$ $m$

Now, water falls at the rate of 15 kg is

i.e., $\frac{m}{t} = 15 kg/s$

$g = 10 {m/s}^{2}$

As loss due to friction is 10%, therefore only 90% of input energy is used to generate power.

$∴$ $P = g h \frac{m}{t} \times \frac{90}{100}$

$P = 10 \times 60 \times 15 \times \frac{90}{100} = 8100 W \Rightarrow P = 8.1 kW$

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