Shock Waves in Fluid-Filled Distensible Tubes

Abstract

Flow of a liquid through distensible tubes is of interest primarily in biological systems, and some properties of shock waves in such tubes are discussed. In shock-fixed coordinates, these flows are steady, and the shock is associated with an increase of pressure and cross-sectional area. Shock transition is analyzed for two flow models, namely, immediate flow separation, when the flow enters the shock zone, and no separation. Shock properties are expressed in terms of the speed index (ratio of the velocity of the shock to that of a small-amplitude wave) and dissipation (loss of total pressure). Examples are worked out for the thoracic aorta of an anesthetized dog, a perfectly elastic tube, and a partially collapsed tube. Appreciable differences in shock velocity and dissipation result if either flow separation or no separation is assumed.