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A large open tank has two holes in the w...

A large open tank has two holes in the wall. One is a square hole of side L at a depth h from the top and the other is a circular hole of radius R at a depth 4h from the top. When the tank is completely filled with water, quantities of water flowing out per second from both holes are the same. Then R is equal to

A

`L/(sqrt(2pi))`

B

`2piL`.

C

`sqrt(2/(pi)).L`

D

`L/(2pi)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `v_(1)` and `v_(2)` be the velocity of efflux from square and circular hole respectively. `S_(1)` and `S_(2)` be cross-section areas of square and circular holes.

`v_(1)=sqrt(8gy)` and `v_(2)=sqrt(2g(y))`
The volume of water coming out of square and circular hole per second is
`Q_(1)=v_(1)S_(1)=sqrt(8gy)L^(2) , Q_(2)=v_(2)S_(2)=sqrt(2gy) pi R^(2) :' Q_(1)=Q_(2)`
`:. R=sqrt(2/(pi)).L`
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