A study on the low Reynolds number flow in a valved vessel

Abstract

The understanding of the fluid flow in valved vessels is of importance pertaining to its application to the problem of fluid transport in valved vessels of the living body, such as veins and lymphatic ducts. In order to have a quantitative understanding of fluid flow through valved vessels, the Newtonian fluid flow through a rigid circular cylindrical tube involving a series of uniformly spaced plate orifices of axisymmetric geometry is studied at low Reynolds number. The solution of the above problem is posed as a series solution of the Stokes equation and the equation of continuity, satisfying the appropriate boundary conditions. The velocity distributions and the average rate of the mean pressure change along the tube axis are computed for a number of different combinations of the orifice-tube radius ratio and the ratio of the inter-orifice distance to the tube radius. The results of the analysis are discussed for possible application to certain physiological systems.