Different choice of coordinates for the falling film problem, Re-derive the velocity profile and the average velocity in S2.2, by replacing x by a coordinate x measured away from the wall; that is, x = 0 is the wall surface, and x = 8 is the liquid-gas interface. Show that the velocity distribution is then given by and then use this to get the average velocity. Show how one can get Eq. 2B.1-1 from Eq. 2.2-18 by making a change of variable.

v. (pg8/)[(x/8) - (x/8)] cos B =