Suppose that a liquid is pumped upward at constant volume flow rate Q through a tube of outer radius R, as shown in Fig. P7.9. The liquid overflows the top and runs down the outside. At a certain distance from the top the air–liquid interface reaches a constant radius λR and the flow becomes fully developed. The liquid film is not necessarily thin relative to R.

(a) Assuming for the moment that λ is known, determine the velocity profile in the film.

(b) Derive an expression that would allow you to calculate λ, assuming that Q, R, and the liquid properties are given.

Transcribed Image Text:

Gas Po |• g Liquid R λR Figure P7.9 Liquid overflowing a vertical tube and flowing down the outside.