A theoretical investigation of non-uniform film flow
McKee, Robert Lowry
Master of Science
The description of steady non-uniform laminar flow was attempted. The model used was that of a thin incompressible, isothermal liquid film flowing down an infinitely wide plate. Solutions predicting the film thickness and velocity profiles as a function of distance down the plate were obtained for various initial conditions. The solutions were obtained by using a form of the Mechanical Energy Equation and an approximated form of the equation of motion. The Mechanical Energy Equation was an ordinary differential equation, and as such it was solved numerically by the Modified-modified Euler method. The equation of motion was finally reduced to a linear partial differential equation and also solved numerically. From the results, a correlation for the development of velocity profiles as a function of the Reynold's number was obtained. It was found to be linear with the initial film thickness as a parameter. The velocity profiles obtained were similar in shape to those measured experimentally by Nedderman; however, it was impossible to duplicate film thickness profiles obtained experimentally by Ryan-Bell. Film thickness profiles calculated by the Mechanical Energy Equation should be good approximations for a physical situation once flow has become "similar”, but no experimental data was available for comparison.