Propagation of Pressure Waves in Inviscid Fluid Contained in Thin Elastic Tube

Abstract

In this study, the artery is treated as an isotropic, incompressible, thin-walled elastic tube while the blood is assumed as an incompressible inviscid fluid. Inviscid fluid refers to the nonviscous fluid, that is the viscosity of the fluid is equal to zero. Under the assumption of long wave approximation, the reductive perturbation method is adopted to obtain a set of nonlinear differential equations with various orders. By solving these various orders of differential equations, they are reduced to a nonlinear evolution equation which is called Korteweg-de Vries (KdV) equation. Next, the KdV equation is solved analytically. The graphical outputs have been presented and discussed. It is found that the solution of the KdV equation is in the form of an envelope traveling solitary waves which propagate to the right along the tube. This study is restricted to the propagation of harmonic waves in the inviscid fluid. Therefore, the fluid velocity and fluid pressure maintained the shape of the wave without deformation when the harmonic waves propagated along the tube.