Question

A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m³ in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30% how much electric power is consumed by the pump?

Answer 1

Here, the volume of water = 30 m³;

t = 15 min = 15 x 60 s = 900 sec

h = 40 m, η = 30%

As density of water, ρ = 10³ kg m^-3

Mass of water pumped, m = volume x density = 30 x 10³

Actual power consumed or output power,

P₀ = w/t = mgh/t = {30 x 10³ x 9.8 x 40}/{900}

= 13070 watt

If, P_i is the input power (required), then as

η = P₀/P₁

⇒ P_i = P₀/η = {13070}/{30/100} = 43567 W = 43.567 kW