A pump is required to lift 600 kg of water per minute from a well 25 m deep and to eject it with a speed of `50ms^(-1)` . Calculate the power required to perform the above task ? `(g=10 m " sec"^(-2))`

Explanation

Mass of water m = 600 kg , depth = h = 25 m
Speed of water `v=25m//s,g=10m//s^(2)`
time t = 1 min = 60 sec.
Power of motor P = Power to lift water `(p_(1))` + Kinetic energy of water (K.E) per second .
Power to lift water
`P_(1)=("mgh")/(t)=(.^(10)cancel(600)xx10xx25)/(cancel(60))=2500` watt
K.E of water per second = `(1)/(2)(mv^(2))/(t)`
`=(1)/(2)(.^(10)cancel(600)xx25xx25)/(cancel60)=(6250)/(2)`
3125 watt .
`therefore` Power of motor P = 2500+3125=5625
watt = 5.625 K.W