Question

A water pump raises 50 litre of water through a height of 25 m in 5 sec. Calculate the power of the pump required.
(Take g = 10N/kg and density of water =1000 kg/m^3 )

Answer 1

rate of water flow = Q= volume/time = 50/5

Q = 5 ltr/sec

volume = 5 litre = 0.005 m^3

hence mass = vol. × density = 0.005 × 1000

mass = m = 5 kg

potential energy = mgh = 5× 10×25
= 1250 J

hence power = 1250 W

Answer 2

Height = 25m

Time = 5s

Volume = 50l

${ \blue{ \bf{ Let's \: convert \: volume \:to \:density: }}}$

density = mass / volume

So,

${ \blue{ \bf{ 1m² = 1000l }}}$

${ \blue{ \bf{ density = mass / volume }}}$

1000=mass/(1/1000×50)

mass=1000×50×1/1000

${ \blue{ \bf{ =50kg }}}$

${ \blue{ \bf{W=F=mg=50×10=500 }}}$

P=500×25/5

${ \blue{ \bf{P=2500W \: Ans }}}$