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Large-amplitude unsteady flow in liquid-filled elastic tubes

Published online by Cambridge University Press:  28 March 2006

John H. Olsen  and
Ascher H. Shapiro
John H. Olsen
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
Ascher H. Shapiro
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

Unsteady, large-amplitude motion of a viscous liquid in a long elastic tube is investigated theoretically and experimentally, in the context of physiological problems of blood flow in the larger arteries. Based on the assumptions of long wavelength and longitudinal tethering, a quasi-one-dimensional model is adopted, in which the tube wall moves only radially, and in which only longitudinal pressure gradients and fluid accelerations are important. The effects of fluid viscosity are treated for both laminar and turbulent flow. The governing non-linear equations are solved analytically in closed form by a perturbation expansion in the amplitude parameter, and, for comparison, by numerical integration of the characteristic curves. The two types of solution are compared with each other and with experimental data. Non-linear effects due to large amplitude motion are found to be not as large as those found in similar problems in gasdynamics and water waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 29 , Issue 3 , 6 September 1967 , pp. 513 - 538
Copyright
© 1967 Cambridge University Press

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References

Crandall, S. H. 1956 Engineering Analysis, ch. 6. New York: McGraw-Hill.
Lambert, J. W. 1958 On the nonlinearities of fluid flow in rigid tubes J. Franklin Inst. 266, 83–102.Google Scholar
Morgan, G. W. & Kiely, J. P. 1954 Wave propagation in a viscous liquid contained in a flexible tube JASA 26, 323–328.Google Scholar
Nicholson, H. 1966 Wave propagation in fluid filled elastic tubes, S.B. Thesis, M.I.T.
Olsen, J. H. 1966 Waves in fluid-filled elastic tubes. Doctoral Thesis, M.I.T.
Rohsenow, W. M. & Choi, H. Y. 1961 Heat, Mass, and Momentum Transfer. New Jersey: Prentice-Hall.
Rudinger, G. 1966 Review of current mathematical methods for the analysis of blood flow. Proc. Biomed. Fluid Mechs. Symposium, Amer. Soc. of Mech. Engrs, N.Y.
Schlichting, H. 1960 Boundary Layer Theory, p. 299, 4th ed. New York: McGraw-Hill.
Streeter, V. L., Keitzer, W. F. & Bohr, D. F. 1964 Energy dissipation in pulsatile flow through distensible tapered vessels, pp. 149–177, in Pulsatile Blood Flow, edited by E. O. Attinger. New York: McGraw-Hill.
Treloar, J. R. G. 1958 The Physics of Rubber Elasticity, p. 95. Oxford.
Womersley, J. R. 1957 An elastic tube theory of pulse transmission and oscillatory flow in mammalian arteries. WADC Tech. Rept. 56–614.Google Scholar