A problem in the mathematical biophysics of blood circulation: II. Relation between pressure and flow of a viscous fluid in an elastic distensible tube

Abstract

In an elastic distensible tube, like a blood vessel, the radius is determined by the equality of the hydrostatic pressure and the elastic forces. If a viscous fluid flows through such a tube, there is a pressure drop along the line of flow. This results in a variation of the radius of the tube along the axis. An approximate expression, valid within a limited range of values, is derived for the radius of the tube as a function of the distance along the axis. Another approximate expression is derived for the relation between pressure drop and total flow in such a case. For sufficiently high rates of flow the pressure drop does not vary linearly with the flow, as in the usual poiseuille's law, but more rapidly.