Drainage of liquids (see Fig. 2D.2) how much liquid clings to the inside surface of a large vessel when it is drained? As shown in the figure there is a thin film of liquid left behind on the wall as the liquid level in the vessel falls. The local film thickness is a function of both z (the distance down from the initial liquid level) and t (the elapsed time).  

(a) Make an unsteady-state mass balance on a portion of the film between z and z + ∆_z to get

(b) Use Eq. 2.2-18 and a quasi-steady-assumption to obtain the following first-order partial differential equation for δ(z, t);

(c) Solve this equation to get what restrictions have to be placed on this result?

Transcribed Image Text:

Initial level of liquid 8(z, t) = thickness of film A: Liquid level moving downward with speed s Wall of containing vessel Part (a) (v;)8 = az at Part (b) Pg at dz Part (c) 8(z, t) = Pg t