Navier-Stokes Flow in Cylindrical Elastic Tubes

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University College London, Department of Physics & Astronomy, Gower Street, London, WC1E 6BT, UK

Abstract

Analytical expressions correlating the volumetric flow rate to the inlet and outlet pressures are derived for the time-independent flow of Newtonian fluids in cylindrically-shaped elastic tubes using a one-dimensional Navier-Stokes flow model with two pressure-area constitutive relations. These expressions for elastic tubes are the equivalent of Poiseuille and Poiseuille-type expressions for rigid tubes which were previously derived for the flow of Newtonian and non-Newtonian fluids under various flow conditions. Formulae and procedures for identifying the pressure field and tube geometric profile are also presented. The results are validated by a finite element method implementation. Sensible trends in the analytical and numerical results are observed and documented.

Keywords

Journal of Applied Fluid Mechanics
Volume 8, Issue 2
December 2014
Pages 181-188

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