How much water a pump of 5 kW can raise in two minutes to a height of 20 m ? (take $g=10 \mathrm{~m}

Question

How much water a pump of 5 kW can raise in two minutes to a height of 20 m ? (take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

Professor PC Thomas Classes · Answer

(a) : Power $P = 5 \mathrm{~kW} = 5000 \mathrm{~W}$. Time $t = 2 	ext{ minutes} = 120 \mathrm{~s}$. Height $h = 20 \mathrm{~m}$. Work done by the pump $W = P 	imes t = 5000 	imes 120 = 600000 \mathrm{~J}$. Potential energy $mgh = W \Rightarrow m 	imes 10 	imes 20 = 600000 \Rightarrow 200m = 600000 \Rightarrow m = 3000 \mathrm{~kg}$. Since the density of water is $1 \mathrm{~kg/litre}$, the volume is 3000 litres.