The central aim of this paper is to contribute to the understanding of the effect of vessel tapering on the propagation of pressure and velocity wave forms. It presents new analytic solutions for the temporal and spatial variation of these two variables that account for weak fluid compressibility. It extends previous work of the author in which only the effect of wall deformation (i.e. vessel distensibility) was taken into account. The solutions are derived in the frequency domain and can account for the steady solution component (d.c. component) obtained by taking the asymptotic value for very low frequencies. It is shown that the effect of compressibility makes the equations more complex but it is still possible to derive closed form analytic solutions in terms of Bessel functions of orders 1/3 and 4/3. The analytical solutions are compared with 3D FSI simulations for the case of propagation of a step pressure variation at the inlet of a tapered vessel. Good agreement is observed between the 1D analytical and 3D numerical solutions.

This content is only available via PDF.
You do not currently have access to this content.