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?

Answer

[`L//sqrt(2pi)`]

Explanation

`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))`