A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m3 in 12 min. If the tank is 40 m above the ground, and the efficiency of the pump is 40%, how much electric power is consumed by the pump ?
Answers
Given info : A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m³ in 12 min. If the tank is 40 m above the ground, and the efficiency of the pump is 40%.
To find : how much electric power is consumed by the pump ?
solution : mass of water pumped up to fill the tank , m = volume × density of water
= 30 m³ × 1000 kg/m³
= 30,000 kg
height of the tank from the ground, h = 40 m
so potential energy of water, U = mgh
= 30,000 kg × 10 m/s² × 40 m
= 12 × 10⁶ J
power required to pump up water = (Energy/time)
= 12 × 10⁶/12 × 60 W
= (1/60) × 10⁶ W
but efficiency of motor is 40 % so, electric power consumed by motor = Power required to pump up water × 100/40
= (1/60) × 10⁶ × 100/40 W
= 41.67 kW
Therefore electric power consumed by the pump is 41.67 kW