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A large open tank has two holes in the wall. One is a square hole of side L at a depth γ from the top and the other is a circular hole of radius R at a depth 4 γ 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) 2πL (c) L (d) L / 2π

A large open tank has two holes in the wall. One is a square hole of side L at a depth γ from the top and the other is a circular hole of radius R at a depth 4 γ 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) 2πL
(c) L
(d) L / 2π

Grade:upto college level

2 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
(a) Equating the rate of flow, we have √ (2gy) x L2 = √(2g x 4 y) πR2
[Flow = (area) x (velocity), velocity = √2gx]
Where x = height from top
⇒ L2 = 2 πR2 ⇒ R = L / √2π
Kushagra Madhukar
askIITians Faculty 629 Points
9 months ago
Dear student,
Please find the solution to your problem.
 
Equating the rate of flow, we have √ (2gy) x L2 = √(2g x 4 y) πR2
[Flow = (area) x (velocity), velocity = √2gx]
Where x = height from top
⇒ L2 = 2 πR2 ⇒ R = L / √2π
Hence option (a) is correct.
 
Thanks and regards,
Kushagra

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