Some calculations based on a mathematical model for fluid flow through a collapsible tube

The generation and stability of self excited oscillations in fluid flowing through an elastic tube subject to transmural pressure were studied using a mathematical model. The tube is modeled partly as an elastic membrane under longitudinal tension and partly having collapse resistance. Poisson's ratio for the elastic material is assumed to be zero. The fluid in the tube is incompressible and inviscid and in unsteady motion. All fluid variables are supposed to be uniform in any cross section normal to the axis of the tube. The coordinate system is attached to the wall of the tube. Solutions for fluid pressure, fluid velocity, distance along the axis, and longitudinal tension are presented. A boundary value problem is solved.