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,
$t=,\frac{A}{A_0}\sqrt{\frac{2H}{g}}$
$\therefore \frac{t_1}{t_2}=\sqrt{\frac{H_1}{H_2}}$
$\Rightarrow \frac{t}{t_2}=\sqrt{\frac{H_1}{H_1/2}}$
$\Rightarrow \frac{t}{t_2}=\sqrt{2}$
$\therefore t_2=\frac{t}{\sqrt{2}}=\frac{10}{\sqrt{2}}=5\sqrt{2}$
$\approx 7min$