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

For an orifice under gravity, discharge speed varies with the square root of head. The time to drain between two levels is proportional to the difference of square roots of those heads (Torricelli’s law).

Time from height H to 0: T = k √H

Time from height H₁ to 0: t = k √H₁

Given

When full (height = H): T = 10 min → k = 10 / √H.

Half-Full Case

Initial head = H/2. Time to empty from H/2 to 0:

t = k √(H/2) = (10 / √H) × √(H/2) = 10 × (1/√2) ≈ 7.07 min

Answer: 7 minutes