Time to Empty a Tank with Water Flowing at 2h kg/s

[Manshah]

a tank is filled with water up to its brim a hole was made at the bottom of tank find time taken to empty tank if water flows at rate of 2h kg/s where h is height of liquid column and is equal to 20m radius is equal to h/2

[Moderator's note: moved from a technical forum.]

 

[anuttarasammyak]

Differential equation for change of mass in the tank for infinitesimal time change dt is
$$\rho dV=\rho Adh =-2h c dt$$
where $\rho$ is density of water $1000 kg/m^3$, A is horizontal cross section area $2*20*\pi$m^2, c is constant to adjust physical dimension c = 1 kg /(sec meter). h=40 m when t=0.