Steady, incompressible, inviscid flow through a finite collapsible tube under longitudinal tension

Steady, incompressible, inviscid flow through a collapsible tube under longitudinal tension held open at the ends is formulated as a two point boundary value problem for a nonlinear ordinary differential equation, describing the shape of the tube. Based on numerical calculations for various sets of values of total pressure Po and flow rate q, existence, uniqueness and multiplicity of solutions of the boundary value problem are discussed. When there is no flow, there is a unique solution for all tube lengths for Po 1; for Po 1 there is a unique solution for tube lengths up to that allowed, corresponding to the maximum inflation. For subcritical total pressures and negative inlet pressures there is a collapsed and a highly collapsed solution, which merge at the flow limitation flow rate value. For subcritical total pressures and positive inlet pressures, the occurrence of periodic solutions leads to multiplicity in the solution of the boundary value problem.