Power: Practice Problem & Solution
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 force are \(10%\) of the input energy. How much power is generated by the turbine? (\(g = 10\text{ m/s}^2\))
Solution Explained:
To solve this problem, we apply the core principles of Power. Understanding the underlying formula is key to arriving at the correct answer below:
The total input power is \(P_{\text{in}} = \frac{dm}{dt} gh = 15 \times 10 \times 60 = 9000\text{ W} = 9\text{ kW}\). Given that \(10%\) of energy is lost to friction, the efficiency is \(90%\), so the power generated is \(P_{\text{out}} = 0.9 \times 9\text{ kW} = 8.1\text{ kW}\).
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