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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 `4 h` from the top. Whwn the tank is completely filled with water, the quantity of water flowing out per second from both the holes are the same. What is the value of r?

Text Solution

Verified by Experts

The correct Answer is:
[`L//sqrt(2pi)`]
`V_(1)=a_(1)v_(1)=L^(2)xxsqrt(2gh)`
`V_(2)=a_(2)v_(2)=(pi r^(2))xxsqrt(2gxx4h)`
As, `V_(1)=V_(2)`
So, `L^(2)sqrt(2gh)=pi r^(2)sqrt(8gh)` or `r=(L)/(sqrt(2pi))`
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Knowledge Check

  • 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 or water flowing out per second from the two holes are the same. Then, the value of R is

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    B
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