Torricelli's equation for efflux from a tank (Fig. 3B.14) a large uncovered tank is filled with a liquid to a height h. Near the bottom of the tank, there is a hole that allows the fluid to exit to the atmosphere. Apply Bernoulli's equation to a streamline that extends from the surface of the liquid at the top to a point in the exit stream just outside the vessel. Show that this leads to an efflux velocity V_efflux = ?2gh. This is known as Torricelli's equation. To get this result, one has to assume incompressibility (which is usually reasonable for most liquids), and that the height of the fluid surface is changing so slowly with time that the Bernoulli equation can be applied at any instant of time (the quasi-steady-state assumption)

h "1", Liquid surface at which v = 0 and p = Patm Typical streamline Fluid exit at which V = Vefflux and P= Patm