Question

A 10 H.P. motor pumps out water from a well of depth 20m and fills a water tank of volume 22380 litres at a height of 10m from the ground. The running time of the motor to fill the empty water tank is ($g=10m{s}^{-2}$)

• A. 5 minutes
• B. 10 minutes
• C. 15 minutes
• D. 20 minutes

Answer 1

Answer: (C)

. 15 minutes.

Volume of water to raise = $V=22380l=22380\times {10}^{-3}{m}^3$

Depth below the ground = $d=20m$

Height above the ground = $h=10m$

Therefore the total change in height = $△h=h_2-h_1=h-d=10-(-20)=30m$.

Power = $P=10HP=7460W$

The work done to raise a mass $m$ at a height $h$ near the surface of the earth is given by, $W=△U=mg△h$.

The power required is given by, $P=\frac{Workdone}{Timetaken}=\frac{W}{t}$

$\Rightarrow P=\frac{mgh}{t}=\frac{V\rho gh}{t}$

($\because m=V\rho$)

$\Rightarrow t=\frac{V\rho gh}{P}$

$\therefore t=\frac{22380\times {10}^{-3}\times {10}^3\times 10\times 30}{10\times 746}=900sec=15min$.

Thus the running time of the motor to fill the empty water tank is 15 minutes.