Caulk, D. A.; Naghdi, P. M. Axisymmetric motion of a viscous fluid inside a slender surface of revolution. (English) Zbl 0611.76051 J. Appl. Mech. 54, 190-196 (1987). 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. Cited in 3 Documents MSC: 76D10 Boundary-layer theory, separation and reattachment, higher-order effects 76U05 General theory of rotating fluids Keywords:exact three-dimensional equations; incompressible linear viscous fluid; one-dimensional nonlinear equations; axisymmetric motion; slender surface of revolution; weighted integrals; momentum equation; lateral surface; surface tension; elastic membrane; rigid tube; unsteady starting flow; axisymmetric swirl; Poiseuille flow PDFBibTeX XMLCite \textit{D. A. Caulk} and \textit{P. M. Naghdi}, J. Appl. Mech. 54, 190--196 (1987; Zbl 0611.76051) Full Text: DOI