Question

A rectangular vessel when full of water, takes $10\text{min}$ to be emptied through an orifice at its bottom. How much time will it take to be emptied when it is half filled ?

• A. $9\text{min}$
• B. $7\text{min}$
• C. $5\text{min}$
• D. $3\text{min}$

Answer 1

The correct option is B $7\text{min}$

Given, time taken to empty fully filled vessel, $t_1=10\text{min}$
To find: Time taken to empty half filled vessel, $t_2=?$

We know, time taken to empty a tank is given by -
$T=\frac{A}{a}\sqrt{\frac{2h}{g}}$, where
$A\to$ area of cross-section of tank
$a\to$ area of cross-section of hole
$h\to$ height of water in the tank

$\Rightarrow T\propto \sqrt{h}$
So,
$\frac{T_1}{T_2}=\frac{\sqrt{h_1}}{\sqrt{h_2}}$
$\Rightarrow \frac{10\text{min}}{T_2}=\frac{\sqrt{h}}{\sqrt{\frac{h}{2}}}$
$[$ assumed, height of fully filled water to be $h]$
$\Rightarrow T_2=\frac{10}{\sqrt{2}}=7\text{min}$