Find the time taken for height of water level to fall from 'h' to 'h'in a vessel, if water comes out from a small hole at the bottom

Explanation

From equation of continity for an incompressible liquid `Av^(1)=asqrt(2gh)` (or) `v^(1)=((a)/(A))sqrt(2gh)`
where `v^(1)` is the rate of descendence of the level of free surface. So, `v^(1)` can be written as: `V^(1)=(-dh)/(dt)`
`therefore (-dh)/(dt)=((a)/(A))sqrt(2gh)` (or) `overset(h^(1))underset(h)int(dh)/(sqrt(h))=-((a)/(A))sqrt(2g)overset(t)underset(t=0)intdt`
`therefore 2(sqrt(h^(1)-sqrt(h))) =-((a)/(A))(sqrt(2g))t` (or)`t=(2A)/(asqrt(2g))(sqrt(h^(1))-sqrt(h))prop t`