Question

A rectangular vessel when full of water, takes 10 min 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 min
• B. 7 min
• C. 5 min
• D. 3 min

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}_{2}}}{{{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 $