FLOW IN A NARROWING CHANNEL OF AN INCOMPRESSIBLE FLUID
Keywords:
The differential equation of the boundary layer written with respect to the current function; hyperbolic and inverse hyperbolic functions; current functions, incompressible fluidAbstract
A nonlinear partial differential equation of the third order with respect to the current function describing the boundary layer of a steady plane-parallel incompressible fluid flow is considered. An exact analytical solution describing the plane-parallel flow of an incompressible fluid in a narrowing channel has been found. Expressions for the current function, the longitudinal u and transverse v component of the velocity and the equation of the current line are determined. Self-similar solutions of the equation of a stationary laminar hydrodynamic boundary layer on a flat plate are found. In this case, the solution is expressed in terms of (tangent) trigonometric functions, the functions determining the distribution of the velocity field are established. The solution of the equation corresponding to the more general case of integration is expressed in terms of cylindrical and Bessel functions of the first and second kind.
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