Abstract
A system of Navier-Stokes equations for two-dimensional unsteady flows of a viscous incompressible fluid in a boundary layer is considered. The physical quantities of the longitudinal and transverse components of velocity, pressure are decomposed into an asymptotic series by degrees of the small parameter ε. The estimation of the individual terms of the equations from the point of order of their magnitude has been preliminarily performed. Output to a recurrent system of partial differential equations of the second order with respect to the first approximation of physical quantities, a system of Prandtl equations is obtained, which is the main one in the study of incompressible fluid flows in the boundary layer, the following approximations are linear partial differential equations of the second order with variable coefficients. Precisely asymptotic solutions of the equation of hydrodynamic boundary layer on a flat plate have been found. Integrate a nonlinear ordinary third-order differential equation with certain current functions distributed by current speeds. The conditions for the separation of the boundary layer and the friction resistance have been established.
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