Question

When water falls from a height of 80 m at the rate of 20 kg s$^{-1}$ to operate a turbine the losses due to frictional force are 20% of input energy. How much power is generated by the turbine?

• A. 12.8 KW
• B. 62.5 KW
• C. 25.6 KW
• D. 21.6 KW

Hint:

To calculate power generated in turbines, first find the potential energy from the falling water and account for energy losses due to friction. The energy available for work is the remaining 80\% of input energy.

Answer 1

The Correct Option is A

The input energy is given by the potential energy of the falling water, which is: \[ E_{\text{input}} = mgh \] Where: - \( m = 20 \, \text{kg/s} \) is the rate of flow of water, - \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity, - \( h = 80 \, \text{m} \) is the height of fall. Substitute the values: \[ E_{\text{input}} = 20 \times 9.8 \times 80 = 15680 \, \text{J/s} = 15.68 \, \text{kW} \] Now, 20% of the input energy is lost, so the energy available to the turbine is: \[ E_{\text{output}} = (1 - 0.20) \times E_{\text{input}} = 0.80 \times 15.68 = 12.8 \, \text{kW} \]
Thus, the power generated by the turbine is \( 12.8 \, \text{kW} \).