Water flows from a lake into a turbine that is a vertical distance of 90 m below the lake, as shown.

Question 36

Water flows from a lake into a turbine that is a vertical distance of 90 m below the lake, as shown.

The mass flow rate of the water is 2400 kg min^-1. The turbine has an efficiency of 75%.

What is the output power of the turbine?

A 26 kW                      B 35 kW                      C 1.6 MW                    D 2.1 MW

Reference: Past Exam Paper – June 2017 Paper 11 Q19

Solution:

Answer: A.

Power = energy / time

Water in the lake (at top) has gravitational potential energy.

Power = GPE / time

Power = mgh / t = (m/t) gh

The mass flow rate of the water is 2400 kg min^-1. This represents the quantity (m/t).

m/t = 2400 kg min^-1

To be used in the above formula for the power of water, it should be converted into SI units.

2400 kg min^-1 means that 2400 kg of water flows in 1 min.

1 min - - > 2400 kg

60 s - - > 2400 kg

1 s - - > 2400/60 = 40 kg

The mass flow rate is 40 kg s^-1.

Power of water = (m/t) gh = 40 × 9.8 × 90 = 35 280 W

This is the power available from the water. But the turbine has an efficiency of only 75%.

Power output of turbine = (75/100) × 35 280 = 26 460 = 26 kW