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Axisymmetric motion of a viscous fluid inside a slender surface of revolution. (English) Zbl 0611.76051

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.

MSC:

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76U05 General theory of rotating fluids
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