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

Find the time taken for height of water level to fall from 'h' to 'h'i

1.	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
Answer» SOLUTION :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`