Blood Flow in the Aorta

Abstract

Throughout this book, we treat blood as an incompressible fluid, that is, we consider that the blood density does not change. The equation of continuity asserts that if an incompressible fluid flows in a rigid tube with varying cross-sectional area along its length, the volume flow-rate Q(t),which is a function of the time t, takes the same value regardless of where it is measured. If the tube has a cross-sectional area A at a given section, the average longitudinal velocity u(t) at the same section is given by u(t) = Q(t)/A. Consider two sections, 1 and 2, of a rigid tube in which an incompressible fluid is flowing. Let u ₁, p ₁, and h _l be the average velocity, the static pressure, and the height of the tube axis above some fixed horizontal datum at section 1, and u ₂, p ₂, and h ₂, the corresponding quantities at section 2 (Fig. 1.1).