As shown in Fig. P3.90, a liquid column of height h is confined in a vertical tube

Question:

As shown in Fig. P3.90, a liquid column of height h is confined in a vertical tube of cross-sectional area A by a stopper. At t = 0 the stopper is suddenly removed, exposing the bottom of the liquid to atmospheric pressure. Using a control volume analysis of mass and vertical momentum, derive the differential equation for the downward motion V(t) of the liquid. Assume one-dimensional, incompressible, frictionless flow.

As shown in Fig. P3.90, a liquid column