An Experimental Determination of the Propagation of Fluid Oscillations in a Tube with a Visco-elastic Wall; together with an Analysis of the Characteristics Required in an Electrical Analogue

Abstract

The work presented here has had two aims; first to determine experimentally the behaviour of oscillatory pressure waves in a rubber tube, when frequency, fluid density and viscosity were varied; and secondly to compare the findings with two theoretical treatments, first the highly simplified electrical transmission-line analogue, and second the more realistic hydrodynamic theory of Womersley. The experimental findings were that as regards longitudinal fluid impedance, the effective density of the fluid (inductance) increased with increasing frequency, as did the effective fluid resistance. The fluid inductance was closely related to its density, and the fluid resistance was in proportion to its viscosity, but had a rather smaller magnitude than expected. The properties of the wall of the tube were found to be determinable independently of the fluid; the dynamic elastic properties, determined in this way, were those of a visco-elastic solid, and varied with frequency in a manner concordant with other independent measurements. The phase velocity and transmission of the oscillations have been found to agree well with the behaviour predicted by Womersley for a visco-elastic, tethered tube. It is therefore suggested that this theoretical approach can be applied with some confidence in the prediction of phase velocity and transmission in studies of the arterial circulation, provided that the dynamic elastic properties of the wall be known. It has been shown that there can be no simple electrical analogue for the perfectly elastic tube, since it cannot take account of the coupling between the fluid- and wall-motion. If the tube has a visco-elastic wall, or is tethered, an analogue becomes in principle possible, but if it is to be faithful over a range of frequencies, its simple elements would have to be replaced by networks having specified frequency-characteristics. On the whole, therefore, it seems likely to be simpler to proceed directly with the hydraulic problem itself, rather than to seek its solution in terms of an analogue.