Flow through finite collapsible tubes: A branching problem
Abstract
Steady, incompressible, inviscid flow through a collapsible tube under longitudinal tension and held open at the ends was formulated as a twopoint boundary value problem for a nonlinear ordinary differential equation, describing the shape of the tube. Analytical solutions close to rho (Xi) identical with 1 are investigated for Po 1/4 P'. The nature of the solutions is explored using the method of harmonic balance. A possible branching from rho (Xi) identical with 1 of solutions with variation of lambda identical with q sq  Po is indicated and asymptotic expansions in lambda are calculated. The LyapunovSchmidt method is used to check calculations and branching behavior.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1984
 Bibcode:
 1984STIN...8528281R
 Keywords:

 Branching (Mathematics);
 Flow Equations;
 Pipe Flow;
 Boundary Value Problems;
 Harmonic Functions;
 Incompressible Flow;
 Steady Flow;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer