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 $\frac{L}{\sqrt{nπ}}$ then n is

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Detailed Solution

$Velocity of efflux from the first hole is \sqrt{2 gy}$

$and rate of flow of water = \sqrt{2 gy} {[L]}^{2}$

$Velocity of efflux from the s e c o n d hole is \sqrt{2 g (4 y)}$

$and the rate of flow of water = \sqrt{2 g (4 y)} {πR}^{2}$

$given \sqrt{2 g (4 y)} {πR}^{2} = \sqrt{2 gy} {[L]}^{2}$

$R = \frac{L}{\sqrt{2 π}}$

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