Power Generated by a Turbine – Rankers Physics
Topic: Work Energy and Power
Subtopic: Power

Power Generated by a Turbine

Water falls from a height of \(60\text{ m}\) at the rate of \(15\text{ kg/s}\) to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine (\(g = 10\text{ m/s}^2\)):
\(12.3\text{ kW}\)
\(7.0\text{ kW}\)
\(8.1\text{ kW}\)
\(10.2\text{ kW}\)

Solution:

The input power is \(P_{\text{in}} = \frac{dm}{dt} gh = 15 \times 10 \times 60 = 9000\text{ W} = 9\text{ kW}\). Frictional losses are 10%, meaning the output efficiency is 90%. Thus, generated power is \(0.90 \times 9\text{ kW} = 8.1\text{ kW}\).

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