The Dynamic Characteristics of Tapered Fluid Lines with Viscoelastic Pipe Walls

Analytical Solutions of Transient Responses

Abstract

Transient responses are theoretically given for laminar flows in tapered viscoelastic circular fluid transmission lines. The basic equations for the analysis are transfer matrices, which were derived based on a fluid line model in which the frequency-dependent effect of viscosity was taken into consideration. In the matrices, a modified version of the Voigt mechanical model is applied to the viscoelastic pipe wall model. The responses to stepwise changes in pressure or flow rate are theoretically obtained under open-end and closed-end conditions. It is confirmed that the theoretical results agree well with simulated ones, when the rate of divergence (or convergence) of the pipeline is very small.