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 holes are the same. Then, R is equal to

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 holes are the same. Then, R is equal to (A)  (L/√2π )  (B)  2π L  (C)  L  (D)  (L/2π )

Tardigrade Admin · Accepted Answer

Velocity of efflux, v=√2 g h where, h denotes the depth of the hole. The quantities of water flowing put per second from both holes are given to be the same A1 v1=A2 v2 (L)2 √2 g y=(π R2) √2 g(4 y) (L)2=2 π R2 R=(L/√2 π)

$\frac{L}{2 π}$

$2 π L$

$L$

$\frac{L}{2 π}$

Velocity of efflux, $v = 2 g h$
where, $h$ denotes the depth of the hole.
The quantities of water flowing put per second from both holes are given to be the same
$A_{1} v_{1} = A_{2} v_{2}$
$(L)^{2} 2 g y = (π R^{2}) 2 g (4 y)$
$(L)^{2} = 2 π R^{2}$
$R = \frac{L}{2 π}$

2π​L​

2πL

L

2πL​

Velocity of efflux, v=2gh​ where, h denotes the depth of the hole. The quantities of water flowing put per second from both holes are given to be the same A1​v1​=A2​v2​ (L)22gy​=(πR2)2g(4y)​ (L)2=2πR2 R=2π​L​

$\frac{L}{2 π}$

$2 π L$

$L$

$\frac{L}{2 π}$

Velocity of efflux, $v = 2 g h$
where, $h$ denotes the depth of the hole.
The quantities of water flowing put per second from both holes are given to be the same
$A_{1} v_{1} = A_{2} v_{2}$
$(L)^{2} 2 g y = (π R^{2}) 2 g (4 y)$
$(L)^{2} = 2 π R^{2}$
$R = \frac{L}{2 π}$