A flow of a thin layer of liquid is simulated on a flat surface of a body located in a stream of\nair. Liquid film on the surface of the body reduces frictional resistance and can be used as a boundary\nlayer control element. The paper presents a mathematical model of the film flow on a half-plane,\nlocated at an angle to the horizon. The fluid flow is determined by the force of gravity and friction\nfrom the external air current. A model of an incompressible viscous fluid is used in the boundary-layer\napproximation. The terms of the motion equation are averaged over the film thickness according to\nthe Leibniz rule. In the cross section of the film, a quadratic law is adopted for the distribution of\nthe longitudinal velocity, taking into account friction on the film surface. An analytical solution of\nthe problem is obtained in the form of series in powers of the small parameter for determining the\nfilm thickness and the average longitudinal velocity along the length of the plate. It is shown that the\nfriction decreases with flow around a half-plane with a film of liquid on the surface.
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