Frequency Analysis of Beams by Flexibility Method

A mathematical procedure is presented for the case of flow of a thin liquid film along the wall of a vertical cylinder. Surface tension forces are neglected. The velocity function is assumed to be a polynomial. The Navier-Stokes equation is combined with continuity and integrated to give an expression for film thickness as a function of position in the accelerated region of flow. In the limiting condition, an expression is given for the case of uniform flow along the walls of a vertical cylinder. The results are expressed in terms of a Reynolds number and a Froude number. A digital computer was used to indicate the variation of film thickness for several Reynolds number and Froude number combinations. The analysis provides a better understanding of the type of film flow that generally occurs in trickling filters and is often found in chemical process packing towers.