Question

A water pump pump out 2400 kg of water per minute if water is coming out with a velocity of 3 metre per second what is the power of the pump???
my way of thinking:
F=∆p/∆t
F=v ∆m/∆t we get force as 120 N
now considering the displacement as 3 metre from velocity we get work done and hence the power as 360 watt why I am incorrect????

Answer 1

Solution:
2400 kg of water per minute is pumped. initially water is at rest. the change in energy is the work done.
speed of water = 3 meters/second = v
So 2400 kg of water comes out in 1 min. Hence 40 kg per second.
let t = time. so mass/time = m/t = 40 kg/sec.

The kinetic energy = work done = 1/2 m v²
Power = work done / time = 1/2 (m / t) v²
= 1/2 * 40 kg/sec * 3² m²/sec² = 180 kg-m/sec²-m = 180 W

IN your case,
you took delta m = 40/sec, that's ok
but the velocity(3 m/sec) given in the question is average veloctiy, hence if you take the distance, you have to take average of it.
average distance will be (3-0)/2 = 3/2
work done now = 120* 3/2 = 180 ans