Question

a lift pump of 5hp pumps water in an overhead tank 4m x 3m x 2m size and situated at a height of 15m from the ground level. The efficiency of pump is 75%. What is the time required to completely fill the overhead tank.

Answer 1

volume of water = 4m × 3m × 2m = 24 m³
we know, density of water = 1000 kg/m³
so, mass of water = volume of water × density of water = 24 m³ × 1000 kg/m³ = 24000 kg

now, energy of water at height 15m from the ground level = mgh
here, m is the mass of water ,
g is the acceleration due to gravity
h is the height from the ground level

hence, energy of water , E = 24000 × 10 × 15J
so, power by water consume in t time = 24 × 10⁴ × 15 J/t { Because power = energy/time }

now, efficiency of pumps = 75% of 5Hp
= 75/100 × 5 × 746 watt { 1Hp = 746 watt}
= 15 × 746/4 watt

now, efficiency of pumps = power consume by water in time t
15 × 746 = 24 × 10⁴ × 15/t
t = 24 × 10⁴/746 sec = 5.36 minutes