Question:
Water is falling on the blades of a turbine at a rate of 100 kg/s. If the height of the fall is 100 m, the power transferred to the turbine will be approximately:
Water is falling on the blades of a turbine at a rate of 100 kg/s. If the height of the fall is 100 m, the power transferred to the turbine will be approximately:
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To calculate the power from falling water, use the formula \( P = mgh/t \), where \( m \) is the mass flow rate, \( g \) is the acceleration due to gravity, and \( h \) is the height of the fall.
Updated On: Apr 22, 2026
- 100 kW
- 10 kW
- 1 kW
- 100 W
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The Correct Option is A
Solution and Explanation
Step 1: Use the power formula.
The power \( P \) transferred to the turbine is the rate of change of potential energy, given by: \[ P = \frac{mgh}{t} \] where \( m = 100 \, \text{kg/s} \), \( g = 9.8 \, \text{m/s}^2 \), \( h = 100 \, \text{m} \).
Step 2: Substitute the values.
Substituting the known values into the formula: \[ P = 100 \times 9.8 \times 100 = 98000 \, \text{W} = 100 \, \text{kW} \]
Step 3: Conclusion.
The power transferred to the turbine is 100 kW, which is option (1).
The power \( P \) transferred to the turbine is the rate of change of potential energy, given by: \[ P = \frac{mgh}{t} \] where \( m = 100 \, \text{kg/s} \), \( g = 9.8 \, \text{m/s}^2 \), \( h = 100 \, \text{m} \).
Step 2: Substitute the values.
Substituting the known values into the formula: \[ P = 100 \times 9.8 \times 100 = 98000 \, \text{W} = 100 \, \text{kW} \]
Step 3: Conclusion.
The power transferred to the turbine is 100 kW, which is option (1).
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