An electric pump has an input power rating of 5 kW and operates with an efficiency of 80 % . It is used to lift water from a well of depth 20 m . What is the volume of water lifted by the pump per minute? (Take g = 10 m s ⁻² and density of water = 1000 kg m ⁻³ )

Step-by-step solution

Input power of the pump, P_ in = 5 kW = 5000 W Useful output power, P_ out = P_ in efficiency = 5000 80 100 = 4000 W Let the mass of water lifted per second be dm dt . Power used in lifting water, P_ out = dm dt g h 4000 = dm dt 10 20 dm dt = 4000 200 = 20 kg s ⁻¹ Mass of water lifted in one minute = 20 60 = 1200 kg Since the density of water is 1000 kg m ⁻³ (which is equivalent to 1 kg L ⁻¹ ), the volume of water lifted per minute is 1200 L . Answer: 1200 L