Self-similar solutions of navier-stokes equations for rotational flow of incompressible fluid in a round pipe

Abstract

Self-similar solutions of Navier—Stokes equations are obtained for rotational and laminar flows in a round pipe with porous and impermeable walls. Longitudinal and circular velocity components are assumed to be linear functions of the longitudinal coordinate. The obtained system of ordinary differential equations is numerically integrated. Solutions for laminar flows are not unique in the investigated here range of parameter variation that defines the intensity of suction and injection of fluid. Solutions for rotational and laminar flows in pipes with porous walls, which are characteristic of the boundary value problem, are treated separately. Curves of radial distribution of velocity components of rotational and laminar flows are presented for several intensities of sucking and injection. Curves and tables of integral characteristics of flow are also presented.