Show complete solution:A vessel of volume V, with a constant cross-sectional area of A and a height of H, is initially (t = 0) filled with a fluid having a density of ρ. At a certain time (t > 0), a...

Show complete solution: A vessel of volume V, with a constant cross-sectional area of A and a height of H, is initially (t = 0) filled with a fluid having a density of ρ. At a certain time (t > 0), a drain was opened at the bottom of the vessel for the fluid to flow through by gravity. The velocity coming out of the drain is expressed as vout = C0 (gh)1/2 where C0 is a constant, g is the acceleration due to gravity, and h is the height of the fluid inside the tank. Develop an equation for the height h as a function of time t.