How long should and electric motor of power 2 H.P. operate so as to pump 5m³ of water from a depth of 15m??
Answers
Here, mass of water = volume * density of water
As, volume of water = 5m³
density of water = 1000 kg/m³
=> mass of water = 5 * 1000
= 5000 kg
Power of electric motor = 2 HP
AS, 1 HP (HorsePower) = 750 W (approx)
=> Power of electric motor , P = 2 * 750
= 1500 W
Here, work done to operate electric motor = Power * time
= 1500 * t
Work done in taking water out = Potential energy stored in water
= mass * gravity * height
= 5000 * 10 * 15
= 750000 J
=> work done to operate electric motor = Work done in taking water out
=> 1500 * t = 750000 J
=> t = 750000/1500
= 500 sec
Thus, time for which electric motor of pump should operate = 500 sec
answer : 580.5 sec
explanation : power of electric motor , P = 2 H.P
we know, 1 horse power = 746 watt
so, power of electric motor, P = 2 × 746 = 1492 watt.
volume of water pumped by motor , V = 5m³
so, mass of water , m = V × density of water
= 5m³ × 1000 kg/m³ = 5000 kg
water is pumped from a depth , h = 15m
now, power = mgh/t
or, 1292 = 5000 × 10 × 15/t
or, t = 750000/1292 = 580.5 sec
hence , required time is 580.5 sec