Laminar Fluid Transients in Conduits of Arbitrary Cross Section
Publication: Journal of Engineering Mechanics
Volume 121, Issue 10
Abstract
Conduit cross sections of nonelementary shape are the rule in biological fluid systems. Because of mathematical and experimental difficulties, however, relatively little is known about the dynamics of flow in these vessels, particularly under time-varying conditions, although knowledge of the fluid motion therein in terms of properties such as driving head, velocity, and wall shear stress is clearly essential for proper diagnosis of a flow problem. This paper presents an analytical method for solving problems of unsteady laminar flow in long ducts of arbitrary cross section. The implied assumption of parallel flow renders the mathematical situation linear, but the proposed method is far from conventional because it allows consideration of almost any cross-sectional configuration conceivable. This novel approach is made possible by joining a steady-state superposition method for creating new conduits from known basic shapes with a regular perturbation scheme found suitable for dealing with fluid transients in circular pipes. The method is developed step by step, and the results are applied to an example with biomedical implications.
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References
1.
Clarion, C., and Pelissier, T.(1975). “A theoretical and experimental study of the velocity distribution and transition to turbulence in free oscillatory flow.”J. Fluid Mech., Cambridge, U.K., 70(1), 59–79.
2.
Fan, C., and Chao, B. T.(1965). “Unsteady, laminar, incompressible flow through rectangular ducts.”Zeitschrift fuer angewandte Mathematik und Physik (ZAMP), Basel, Switzerland, 16(3), 351–360.
3.
Hepworth, H. K., and Rice, W.(1970). “Laminar two-dimensional flow in conduits with arbitrary time-varying pressure gradient.”J. Appl. Mech., 37(3), 861–864.
4.
Letelier S., M. F. (1986). “Chapter 18: `Approaches to analyzing unsteady laminar flow in long pipes.”' Encyclopedia of Fluid Mechanics, Vol. 1, 560–588, Gulf Publishing Co., Houston, Tex.
5.
Letelier S., M. F., Gutiérres S., A., and Leutheusser, H. J. (1985). “Analysis of fluid transients in conduits of unconventional shape.”Proc., Forum on Unsteady Flow, ASME-FED, Vol. 27, 21–23.
6.
Letelier S., M. F., and Leutheusser, H. J.(1983). “Unified approach to the solution of problems of unsteady laminar flow in long pipes.”J. Appl. Mech., 50(1), 8–12.
7.
Letelier S., M. F., and Leutheusser, H. J.(1985). “Laminar flow in conduits of unconventional shape.”J. Engrg. Mech., ASCE, 111(6), 768–776.
8.
Leyton, D. (1986). “Flujo en uno estenosis,” Bachelor's thesis, University of Santiago, Santiago, Chile.
9.
Márquez Z., G. (1985). “Flujo laminar impermanente en ductos de secciones complejas,” Bachelor's thesis, University of Santiago, Santiago, Chile.
10.
Mueller, W.(1936). “Zum Problem der Anlaufstroemung einer Fluessigkeit im geraden Rohr mit Kreisring- und Kreisquerschnitt.”Zeitschrift fuer angewandte Mathematik und Mechanik (ZAMM), Potsdam, Germany, 16, 227–238.
11.
Schlichting, H. (1987). Boundary-layer theory, 7th Ed., McGraw-Hill Publishing Co., New York, N.Y.
12.
Sexl, Th.(1930). “Ueber den von E. G. Richardson entdeckten Annulareffekt.”Zeitschrift fuer Physik, Berlin, Germany, 61, 349–362.
13.
Szymanski, F. J.(1932). “Quelques solutions exactes des équations de l'hydrodynamique de fluide visqueux dans le cas d'un tube cylindrique.”J. Mathématiques Pures et Appliquées, Paris, France, 11(9), 67–107.
14.
Uchida, S.(1956). “The pulsating viscous flow superposed on steady laminar motion of incompressible fluid in a circular pipe.”Zeitschrift fuer angewandte Mathematik und Physik (ZAMP), Basel, Switzerland, 7(4), 413–422.
15.
Yih, C. S. (1969). Fluid mechanics . McGraw-Hill Book Co., New York, N.Y., 318–320.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 121 • Issue 10 • October 1995
Pages: 1069 - 1074
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Oct 1, 1995
Published in print: Oct 1995
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