Flow Through Collapsible Tubes and Through in Situ Veins

Abstract

The flow of blood in veins differs from the flow of liquids in rigid, circular tubes in that veins are collapsible vessels. Studies in models employing thin-walled rubber tubes and in the intact animal have shown that the flow (ml/s) of liquid through such a collapsible tube, in which the pressure immediately downstream to the collapsed segment is less than the pressure surrounding the collapsed segment, is unaffected by changes in the downstream pressure. With changes in the downstream pressure the collapsed tube automatically adjusts its resistance so that flow remains constant. In the mammalian organism the flow of blood in veins above heart level, and at the points where veins enter the low pressure area of the thorax, is governed by the principles of flow through collapsible tubes. The importance of the collapse phenomena in the flow of blood through the lung and other organs is discussed. Flow through such tubes is a special case of Bernoulli's theorem for the flow of viscous liquids, and under certain circumstances it is described with a reasonable degree of accuracy by a modification of the Hagen-Poiseuille law for tubes of elliptical cross section.