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, in-compressible, friction less flow.

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h(t)