Axisymmetric Motion of a Viscous Fluid Inside a Slender Surface of Revolution

[+] Author and Article Information
D. A. Caulk

Engineering Mechanics Department, General Motors Research Laboratories, Warren, Mich. 48090

P. M. Naghdi

Department of Mechanical Engineering, University of California, Berkeley, Calif. 94720

J. Appl. Mech 54(1), 190-196 (Mar 01, 1987) (7 pages) doi:10.1115/1.3172956 History: Received October 15, 1985; Revised April 07, 1986; Online July 21, 2009


Starting with the exact three-dimensional equations for an incompressible linear viscous fluid, an approximate system of one-dimensional nonlinear equations is derived for axisymmetric motion inside a slender surface of revolution. These equations are obtained by introducing an approximate velocity field into weighted integrals of the momentum equation over the circular cross-section of the fluid. The general equations may be specialized to reflect specific conditions on the lateral surface of the fluid, such as the presence of surface tension, a confining elastic membrane, or a rigid tube. Two specific examples are considered which involve flow in a rigid tube: (1) unsteady starting flow in a nonuniform tube, and (2) axisymmetric swirl superimposed on Poiseuille flow. In each case comparison is made with earlier, more restricted results derived by perturbation methods.

Copyright © 1987 by ASME
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