A squre hole of side length l is made at a depth of h and a circular hole is made at a depht of 4 h from the surface of water in a water tank kept on a horizontal surface (where l ltlt h). Find the radius r of the circular hole if equal amount of water comes out of the vessel through the holes per second.

Explanation

Refer to using equation of continuity at A and B, we have `A_1 upsilon_1 = A_2 upsilon_2`
`l^2 upsilon_1 = pi r^2 upsilon_2` …. (i)
Here, `upsilon_1 = sqrt(2gh) and upsilon_2 = sqrt(2g (4 h)` Putting values in (i) we have `l_2 sqrt(2gh) = pi r^2 xx sqrt(8gh) or r = l//(sqrt2pi)`