Answer to Question #303211 in Chemical Engineering for seshu

Question

In a gas absorption experiment a viscous fluid flows upward through a small circular tube and then downward in laminar flow on the outside. Set up a momentum balance over a shell of thickness r in the film, as shown in figure 1 (Appendix A). Note that the “momentum in” and “momentum out” arrows are always taken in the positive coordinate direction, even though in this problem the momentum is flowing through the cylindrical surfaces in the negative r direction. i. Show that the velocity distribution in the falling film (neglecting end effects) is 2 2 2 1 2 ln 4 z gR r r v a R R         = − +               ii. Show that the mass rate of flow in the film is given by 2 4 2 4 4 1 4 3 4 ln 8 gR w a a a a   = − + − +     iii. Show that the result in (b) simplifies to the following equation, if the film thickness is very small ( Use a = +  1 , 1   ) 2 3 cos 3 gW w     = , Where W R = 2 and   = R .

Answer 1

Answer is given below