A pump lifts 200L of water per minute through a height of 5m , and ejects it through an orifice 2 cm in diameter. Find the velocity of efflux of water and the power of the pump.

Explanation

Volume of water lifted by the pump in 1s
`=(200)/(60) =(10)/(3) L =(10^4)/(3) cm^3`.
Mass of this volume of water =` (10^4)/(3) g=(10)/(3) kg`
`therefore` Increase in potential energy in 1 second
`=(10)/(3) xx9.8xx5 J*s^(-1)= 163 .33J`
`therefore` Power of the pump to raise water up to the height of 5 m = 163.33 W.
If the velocity of efflux is v, then `pi r^2 xxv=(10^4)/(3)`
`or, v=(10^4xx7)/(3xx22xx(1)^2)=1061 cm*s^(-1) =10.61 m*s^(-1)`.
Kinetic energy of the amount of water thrown out per second
`=1/2 xx(10)/(3) xx(10.61)^2 J =187.62 J`.
`therefore` Power of efflux = 187 .62W
`therefore` Total power of the pump = 163.33+187.62 =350.95 W.