Question

Calculate the time for which a motor pump of 10 HP and efficiency 80% must be switched on, so as to pump 20 m³ of water through a vertical height of 20 m.

[Density of water = 1000 kg m⁻³; g = 10 ms⁻²; 1 HP = 750 W]

Answer 1

Mass of water = density × volume

= 1000 × 20

= 20,000 kg

Useful work needed to lift the water = mgh

= 20,000 × 10 × 20

= 4,000,000 J

Input power of the pump = 10 × 750 = 7500 W

Useful power = 80% of 7500

= 0.80 × 7500

= 6000 W

\[ \text{Using}\ \ \text{Power} = \frac{\text{Work}}{\text{Time}} \]

\[ \text{Time} = \frac{\text{Work}}{\text{Useful power}} \]

\[ \text{Time} = \frac{4{,}000{,}000}{6000} \]

Time = 666.67 s.

Therefore, the pump must be switched on for about 666.67 s.