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 forces are 10% of energy. How much power is generated by the turbine ? (g = 10 m/s$^2$)

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

Answer 1

The Correct Option is C

To calculate the power generated by the turbine, we need to determine the useful energy available for conversion into power after accounting for energy losses.

1. Calculate the Potential Energy (PE) of the water falling from a height:
   PE = m \cdot g \cdot h
   • where m = 15 \text{ kg/s} (mass flow rate),
   • g = 10 \text{ m/s}^2 (acceleration due to gravity),
   • h = 60 \text{ m} (height).
   PE = 15 \times 10 \times 60 = 9000 \text{ J/s or 9 kW}
2. Account for energy losses due to frictional forces:
   • Energy losses are 10% .
   • Therefore, the useful energy or net power input to the turbine is 90% of the potential energy.
   Net \ Power = 0.9 \times 9000 = 8100 \text{ J/s or 8.1 kW}
3. The power generated by the turbine:
   The power output of the turbine, considering the energy available, is 8.1 kW.

Thus, the correct answer is 8.1 kW.

• Ruling out other options:
  • 12.3 kW: This assumes zero losses, which is incorrect as there are frictional losses.
  • 7.0 kW: This does not match the calculation after accounting for the losses.
  • 10.2 kW: This is higher than the possible output considering the 10% loss.

Therefore, the correct option is 8.1 kW, accounting for the 10% energy loss due to friction.