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? ($g = 10\text{ m/s}^2$) (2021, 2008)
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:
Input power is $P_{\text{in}} = \left(\frac{dm}{dt}\right)gh = 15 \times 10 \times 60 = 9000\text{ W} = 9\text{ kW}$. With $10\%$ frictional losses, efficiency is $90\%$. Power generated = $90\% \text{ of } 9\text{ kW} = 8.1\text{ kW}$.
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