Figure 2B.6 Velocity distribution and momentum balance in the t-direction for the flow of a film down the outside of a circular tube.

small circular tube and then down in laminar flow around the outside of the tube. Perform a momentum balance over an envelope of thickness Ar on the film, as shown in Figure 2B.6. Note that the "momentum input" and "momentum output" arrows are always taken in the positive coordinate direction, even though in this problem the momentum flows across the cylindrical surfaces in the positive direction. negative r.

a) Show that the velocity distribution in the falling film (ignoring end effects) is

b) Obtain an expression for the velocity of mass flow in the film. C) Show that the result of part b) simplifies to equation 2.2-21 if the thickness of

the film is very small.

vz=4gR2[1(Rr)2+2a2ln(Rr)]