Question

In Figure 4, a pump is required to raise 500 litres of fresh water a vertical distance
of 100 m.
a)
How much work will be done by the pump in raising the water?
b) If the pump has an efficiency of 50%, how much work must be done on the
pump to raise the water?

Answer 1

Given 500 L = 0.500 m^3 and ρwater ≈ 1000 kg/m^3, the mass m = 0.500×1000 = 500 kg.

a) Work to raise the water (gain in gravitational potential energy):
W = m g h = 500 kg × 9.8 m/s^2 × 100 m = 4.90×10^5 J (≈ 490 kJ).

b) If pump efficiency is 50%, the input work must be double:
Win = W / 0.50 = 4.90×10^5 J / 0.5 = 9.80×10^5 J (≈ 980 kJ).

(Using g = 9.81 m/s^2 gives W ≈ 4.905×10^5 J and Win ≈ 9.81×10^5 J.)