Streamline Motion of a Viscous, Incompressible Fluid in a Curved Pipe with an Elliptical Cross Section

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Abstract : This study concerns the laminar flow of an incompressible fluid through a curved pipe with an elliptical cross section. The governing equations are derived by applying the Navier-Stokes and continuity equations in cylindrical coordinates and the method of successive approximations to get the five partial differential equations. These equations are solved by the perturbation method, and twenty numerical examples are presented. For each example, arbitrary numerical parameters are assumed for input into an IBM 7094 Computer to obtain solutions for the simultaneous algebraic equations. For an eccentricity of one, the ellipse degenerates to a circle and Dean's solution for the streamline flow of an incompressible fluid through a curved pipe with a circular cross section is obtained.

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