Filling and emptying a tank of liquid

Abstract

A right cylindrical tank open to the atmosphere is being filled by a laminar jet of incompressible inviscid liquid falling onto its free surface. At the same time, fluid is escaping through a hole centered in the bottom of the tank. Newton's second law for variable mass and the unsteady Bernoulli equation are combined to find the time dependence of the liquid height in the tank. The level of analysis is suitable for an introductory undergraduate course in fluid dynamics.