Question

A rectangular vessel when full of water, takes $10$ minutes to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water ?

• A. 9 minutes
• B. 7 minutes
• C. 5 minutes
• D. 3 minutes

Answer 1

Answer: (B)

If$ A_0$ is the area of orifice at the bottom below the free surface and A that of vessel, time t taken to be empited the tank,
$t =, \frac{A}{A_{0}} \sqrt{\frac{2H}{g} } $
$\therefore \frac{t_{1}}{t_{2}} =\sqrt{\frac{H_{1}}{H_{2}}} $
$\Rightarrow \frac{t}{t_{2}} =\sqrt{\frac{H_{1}}{H_{1} / 2}} $
$\Rightarrow \frac{t}{t_{2}}=\sqrt{2} $
$\therefore t_{2} =\frac{t}{\sqrt{2}}=\frac{10}{\sqrt{2}}=5 \sqrt{2} $
$ \approx 7\, min$