Question

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 (g=10 m/s²)

• A. 7.0 kW
• B. 10.2 kW
• C. 8.1 kW
• D. 12.3 kW

Answer 1

The Correct Option is C

To solve this problem, we need to calculate the power generated by the turbine using the potential energy of the falling water, accounting for energy losses due to friction.

First, we calculate the potential energy of the water falling from a height:

The potential energy (PE) of a mass \(m\) at height \(h\) is given by the formula:

\(PE = m \cdot g \cdot h\)

where:

• \(m = 15 \text{ kg/s}\) (mass flow rate of water)
• \(g = 10 \text{ m/s}^2\) (acceleration due to gravity)
• \(h = 60 \text{ m}\) (height from which water falls)

Substituting the given values, we find:

\(PE = 15 \times 10 \times 60 = 9000 \text{ J/s} = 9000 \text{ W}\)

Since 10% of the input energy is lost due to friction, only 90% of the potential energy is converted to useful power.

The useful power (P_useful) is calculated as:

\(P_{\text{useful}} = 0.9 \times 9000 = 8100 \text{ W}\)

Finally, convert watts to kilowatts:

\(P_{\text{useful}} = \frac{8100}{1000} = 8.1 \text{ kW}\)

Thus, the power generated by the turbine is 8.1 kW. The correct answer is:

8.1 kW