The friction factor and velocity profile data are internally consistent, as evidenced by treatment with an extension of the von KArm An correlating equation. NOTATION c D = pipe diameter, ft. = empirical correction term, Equation (2) r w, friction factorReynolds number DVP u w radial position, ft. pipe radius, ft. mean point velocity in pipe, ft./sec. u/u*, dimensionless velocity v'rwgc/p, friction velocity, ft./sec. center-line velocity, ft./sec. mean velocity, ft./sec. distance from wall, ft.
LITERATURE CITED= shear stress at the wall, Ib.r/sq. ft. = shear stress in general, Ib.r/sq. ft.Theoretical analyses based upon film theory and penetration theory models of the interphase mass transfer process have contributed greatly to the understanding of the effect of a simultaneous chemical reaction upon the rate of mass transfer. For a review of these and other models and their use in predicting the effect of a chemical reaction upon the mass transfer rate the reader is referred to references 2, 3, 4, 5, 6, 7, 19, and 22. An especially interesting aspect of these theoretical studies has been the surprising agreement of film theory predictions with penetration theory predictions except when diffusivity ratios depart greatly from unity (3, 6).Most of the theoretical treatments of simultaneous mass transfer and chemical reaction have been based on the as-sumption that the various diffusing and reacting species were uncharged molecules, although in most commercially important examples of simultaneous mass transfer and chemical reaction ionic species are involved. Furthermore it has long been known (14, 15, 17, 18) that ions, since they are electrically charged, obey a different law of diffusion than that for molecular species. This lead Shenvood and Wei (21) and later Sherwood and Ryan ( 2 0 ) to a study of ion diffusion effects upon the film theory solution for mass transfer accompanied by an infinitely rapid irreversible chemical reaction. Shenvood and Wei showed that ion diffusion effects were large in the systems they studied and also that their diffusion cell data for these systems supported their ionic theory.