Analytical solution to the problem of fluid outflow from an axisymmetric channel

The subject of the study is the outflow of fluid from a channel consisting of segments with different geometries used to improve thermal and hydraulic characteristics. Research methods are based on Newton's rheological law; the continuity equation and the Navier-Stokes equation, which are the basic equations of fluid flow; the method of mathematical modeling and the analytical method of its solutions. In the article, generalized formulas for determining the hydrodynamic characteristics of a fluid flow in axisymmetric channels are obtained. As an example, analytical expressions for the pressure and average flow velocity are obtained when fluid flows out of a cylindrical channel of a constant cross section and from a channel of a hyperbolic form. In perspective, by introducing an arbitrary arithmetic expression of the axisymmetric section of the channel, it is possible to determine the hydrodynamic characteristics of the flow.

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