Mathematical Model of the Liquid Film Flow on the Flat Surface

摘要

A liquid film on surface of a body decreases frictional resistance and can be used as a boundary layer control element. This article contains a mathematical model of a film flow over a half-plane, directed at an angle to the horizon. Liquid flow depends on gravity and friction with the external air flow. A model of incompressible viscous liquid near the boundary layer is used as the flow model. Summands of motion equation are averaged over the film thickness by the Leibniz rule. The square low is assumed for distribution of longitudinal velocity in the cross-section of the film with regard to the friction at the film's surface. An approximate solution of the problem is received as power series in powers of small parameter. The results are presented in a form diagrams of the film thickness and the average longitudinal velocity over the length of the plate. The mathematical flow model can be used to define flat film flow performance.