Summary
An analytical method of solution of some problems of laminar, oscillatory flow in elastic porous tubes is given. The mathematical model is based on an one-dimensional approach to the liquid motion. The derived formulae describe the main flow characteristics: pressure, velocity, local and surface outflow of fluid. Influence of geometric dimensions, mechanical properties of elastic tubes, local outflow and filtration through the porous wall, on liquid motion durability is analysed. A simple method of experimental determination of functional parameters is shown.
Similar content being viewed by others
References
Anliker, M., Histand, M. B., Ogden, E.: Dispersion and attenuation of small artificial pressure waves in the canine aorta. Circ. Res.23, 539–551 (1968).
Bergel, D. H.: The dynamic elastic properties of arterial wall. J. Physiol.156, 458–469 (1961).
Donovan, F. M., Taylor, B. C., Su, M.C.: One-dimensional computer analysis of oscillatory flow in rigid tubes. ASME J. Biomech. Eng.113, 476–484 (1991).
Ferry, J. D.: Viscoelastic properties of polymers. New York: Wiley 1980.
Franke, P. G., Seyler, F.: Computation of unsteady pipe flow with respect to visco-elastic material properties. J. Hydraulic Res.21, 345–353 (1983).
Histand, M. B., Anliker, M.: Influence of flow and pressure on wave propagation in the canine aorta. Circ. Res.32, 524–529 (1973).
Kavity, Y., Collins, R.: Steady state fluid flow in viscoelastic tubes. Application to blood flow in human arteries. Arch. Mech.26, 921–931 (1974).
Limmer, J.: Druckstoßberechnung in elastischen Rohrleitungen mit Berücksichtigung der radialen Dehnung. Dissertation, Technische Universität München 1974.
Lishen, S., Wylie, E. B.: Complex wavespeed and hydraulic transients in viscoelastic pipes. J. Fluid Eng.112, 496–500 (1990).
McDonald, D. A.: Blood flow in arteries. London: Arnold 1974.
Mitosek, M.: Steady liquid and gas flow in elastic tubes. Prace Naukowe PW 71, Warsaw 19–45 (1981).
Mitosek, M.:The chosen problems of fluid flow in elastic tubes. Typescript 1991.
Ohmi, M., Iguchi, M.: Critical Reynolds number in an oscillating pipe flow. Bull. JSME25, 165–172 (1982).
Olsen, J. H., Shapiro, A. H.: Large amplitude unsteady flow in liquid-filled elastic tubes. J. Fluid Mech.29, 513–538 (1967).
Pedley, T. J.: The fluid mechanics of large blood vessels. Cambridge: University Press 1980.
Petrov, V. G., Edissonov, I.: Nonlinear dynamic model with concentrated parameters of flow and pressure in an elastic porous reservoir of the type of aorta. Acta Mech.83, 39–49 (1990).
Porenta, G., Young, D. F., Rogge, T. R.: A finite-element model of blood flow in arteries including taper, branches and obstruction. ASME J. Biomech. Eng.108, 161–167 (1986).
Rath, H. J.: Unsteady pressure waves and shock waves in elastic tubes containing bubble air-water mixture. Acta Mech.38, 1–17 (1981).
Streeter, V. L., Weitzer, W. F., Bohr, D. F.: Pulsatile blood flow. New York: McGraw-Hill 1964.
Streeter, V. L., Wylie, E. B.: Fluid mechanics. Tokyo: McGraw-Hill-Kogakusha 1975.
Teipel, I.: Nichtlineare Wellenausbreitungsvorgänge in elastischen Leitungen. Acta Mech.16, 93–106 (1973).
Traczyk, W. Z., Trzebski, A.: Fizjologia czlowieka z elementami fizjologii stosowanej i klinicznej. Warszawa: PZWL 1990.
Treylor, L. R. G.: The physics of elasticity. Oxford: OUP 1958.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mitosek, M. Oscillatory liquid flow in elastic porous tubes. Acta Mechanica 101, 139–153 (1993). https://doi.org/10.1007/BF01175602
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01175602