Analytical Solutions of Viscous Flow in Constricted or Widened Tubes

[+] Author and Article Information
R. Van Dooren

Department of Analytical Mechanics, Vrije Universiteit Brussel, Brussels, Belgium

J. Appl. Mech 45(2), 241-245 (Jun 01, 1978) (5 pages) doi:10.1115/1.3424281 History: Received February 01, 1976; Revised November 01, 1977; Online July 12, 2010


The steady laminar axisymmetric flow of a Newtonian viscous homogeneous incompressible fluid through constricted or widened circular tubes is studied. Assuming that the tube wall is slightly curved with the axial distance as described by an exponential function, an analytical method is presented based on the perturbation method in connection with a transformation that maps the curved tube domain into a rectangular region. The results for the velocity, the pressure, and the wall shear stress for various values of the Reynolds number and of the parameters specifying the exponentially curved wall, are represented and discussed in detail. The necessity of the assumption that the flow is two dimensional is justified.

Copyright © 1978 by ASME
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