A pump draws water from a lower reservoir and delivers it to a nozzle located 15 m above the reservoir. The water is ejected from the nozzle at a speed of 20 m s ⁻¹ with a constant mass flow rate of 10 kg s ⁻¹ . What is the total mechanical power delivered by the pump to the water? (Take g = 10 m s ⁻² )

Step-by-step solution

The pump does work to both lift the water against gravity and impart kinetic energy to it. Rate of change of potential energy (Power for lifting): P_ PE = dm dt g h = 10 10 15 = 1500 W = 1.5 kW Rate of change of kinetic energy (Power for ejection): P_ KE = 1 2 dm dt v^2 = 1 2 10 (20)^2 = 5 400 = 2000 W = 2.0 kW Total mechanical power delivered by the pump: P_ total = P_ PE + P_ KE = 1.5 kW + 2.0 kW = 3.5 kW Answer: 3.5 kW