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
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Velocity of efflux when the hole is at depth h, $v = \sqrt{2gh}$
Rate of flow of water from square hole
$Q_1 = \bar{a}_1 V_1$ = $L^{2} \sqrt{2gy}$
Rate of flow of water from circular hole
$Q_2 = a_2 V_2$ = $\pi R^{2} \sqrt{2g(4y)}$
According to problem $Q_1 = Q_2$
⇒ ⇒ $L^{2} \sqrt{2 g y} = \pi R^{2} \sqrt{2 g (4 y)}$ 
$R = \frac{L}{\sqrt{2 \pi}}$
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