Question

An engine can pump 30,000 L of water to a vertical height of 45 m in 10 min. Calculate the work done by the machine and its power. (density of water = ${10}^{3}kg/m^3$)

Answer 1

Given,

Volume of water $V=30000L=30000\times {10}^{-3}{m}^3=30m^3$

Height = $h=45m$

Time = $t=10min=600s$

Density of water $\rho =1000kg/m^3$

Mass of water $m=\rho \times V=1000\times 30=30000kg$

We know that, work done = $W=mgh$

$\therefore W=mgh=30000\times 10\times 45=1.35\times {10}^{7}J$

We know that, Power = $P=\frac{W}{t}$

$\therefore P=\frac{W}{t}=\frac{1.35\times {10}^7}{600}=22500W$.