Question

A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water the quantities of water flowing out per second from both the holes are the same. Then R is equal to

• A.
• B.
• C. L
• D.

Answer 1

The correct option is B

Velocity of efflux when the hole is at depth h,
$v=\sqrt{2gh}Rateofflowofwaterfromsquarehole{Q}_1=a_1{v}_1=L^2\sqrt{2gy}Rateofflowofwaterfromcircularhole{Q}_2=a_2{v}_2=\pi R^2\sqrt{2g\left(4y\right)}andaccordingtoproblem{Q}_1=Q_2\Rightarrow L^2\sqrt{2gy}=\pi R^2\sqrt{2g\left(4y\right)}\Rightarrow R=\frac{L}{\sqrt{2\pi }}$