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.
• D.

Answer 1

The correct option is B

Velocity of efflux when the hole is at depth h, $v=\sqrt{2gh}$
Rate of flow of water from square hole
$Q_1=a_1{v}_1=L^2\sqrt{2gy}$
$Q_2=a_2{v}_2=\pi R^2\sqrt{2g\left(4y\right)}$
According to problem $Q_1=Q_2$
$\Rightarrow$ $L^2\sqrt{2gy}=\pi R^2\sqrt{2g\left(4y\right)}\Rightarrow =\frac{L}{\sqrt{2\pi }}$