Question

A tank with a diameter of 18 m and a height of 27 m is filled with a liquid of density 62.4 kg/m${}^3$ by a pump in a well that has a diameter of 10 m and a liquid level 30 m below ground level. [There is no recharge (refilling) of the well during pumping].

In order to fill the tank, the liquid shall be lifted by a distance of (in m):

• A. $43.54$
• B. $165.26$
• C. $9.8$
• D. $87.24$

Answer 1

The correct option is D $87.24$

To fill tank, the pump must lift $\pi \left(9{)}^2\right(27)=6867m^3$ of liquid from well.
As the liquid is pumped, liquid level in well drops by a distance $a$
$\Rightarrow \pi (5{)}^{2}a=6867$
$\Rightarrow$ $a=87.48m$
$\therefore$ $h$ = $\frac{a}{2}+30+\frac{27}{2}=87.24$ m