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Periodic flow of a viscous liquid in a thick-walled elastic tube

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Abstract

Arterial blood flow is analyzed on the basis of a realistic model consisting of a viscous liquid contained in a thick-walled viscoelastic tube. Approximate forms of the Navier-Stokes and continuity equations are derived for this model and solved in conjunction with the equations of motion of an elastic solid. Expressions are found for the displacement of the tube wall, velocity distribution, volume flow rate and phase velocity of the pressure wave. Changes in the shape of the pressure wave caused by damping and dispersion are determined, and the effect of viscoelasticity is assessed. Numerical results are presented which correspond to observed parameters of the circulatory systems of living animals.

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Literature

  • Love, A. E. H. 1944.A Treatise on The Mathematical Theory of Elasticity. New York: Dover Publications.

    MATH  Google Scholar 

  • McDonald, D. A. 1960.Blood Flow in Arteries. Baltimore, Maryland: Williams and Wilkins Co.

    Google Scholar 

  • Morgan, G. W. and W. R. Ferrante. 1955. “Wave Propagation in Elastic Tubes Filled with Streaming Liquid.”Journal of the Acoustical Society of America,27, 715–725.

    Article  MathSciNet  Google Scholar 

  • Morgan, G. W. and J. Kiely. 1954. “Wave Propagation in a Viscous Liquid Contained in a Flexible Tube.”Journal of the Acoustical Society of America,26, 323–328.

    Article  MathSciNet  Google Scholar 

  • Whirlow, D. K. 1963.A Study of the Haemodynamics of the Mammalian Circulatory System. Ph.D. Thesis, Carnegie Institute of Technology, Pittsburgh, Pennsylvania.

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  • Womersley, J. R. 1957.An Elastic Tube Theory of Pulse Transmission and Oscillatory Flow in Mammalian Arteries. Wright Air Development Center Technical Report TR 56-614.

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Authors and Affiliations

  1. U.S. Army, Fort Belvoir, Virginia

    D. K. Whirlow (Lieutenant)

  2. Carnegie Institute of Technology, Pittsburgh, Pennsylvania

    W. T. Rouleau (Associate Professor Mechanical Engineering)

Authors
  1. D. K. Whirlow
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  2. W. T. Rouleau
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Additional information

This research was partially supported by the National Science Foundation; it was done in part by D. K. Whirlow in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Carnegie Institute of Technology.

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Whirlow, D.K., Rouleau, W.T. Periodic flow of a viscous liquid in a thick-walled elastic tube. Bulletin of Mathematical Biophysics 27, 355–370 (1965). https://doi.org/10.1007/BF02478411

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  • DOI: https://doi.org/10.1007/BF02478411

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