Flow of Liquids Through "Collapsible" Tubes

Liquid flowing through a thin-walled "collapsible" tube similar to a vein, inclined to any angle between vertical and slightly above horizontal, differs from the flow in rigid tubes in that: a "collapsible" tube accepts any flow presented to it without affecting the rate of flow through the system; the lateral pressure at all cross sections throughout the tube is zero and does not change as the flow changes; the cross section of the tube and the mean velocity of flow increase as the flow increases; for any particular flow, the cross section increases and the mean velocity of flow diminishes as the potential energy difference between the upper and lower ends of the tube is decreased; for any given flow and potential energy difference, an increase in the length of the tube causes an increase in the cross section and a decrease in the mean velocity; also, an increase in the perimeter of the tube causes an increase in cross section and a decrease in mean velocity, and an increase in the viscosity of the liquid causes an increase in cross section and a reduction in mean velocity. In such tubes there is no lateral pressure gradient between any two cross sections as there is in rigid tubes; instead there is a potential energy gradient which is proportional to the energy loss along the tube. Under certain conditions the flow of liquid through a collapsible tube is described with a reasonable degree of accuracy by a modification of Poiseuille's law for tubes of elliptical cross section.