Unidirectional Flow in Rectilinear Vessels

Abstract

The equations governing fluid motion allow a mathematical solution in a few simple conditions only. The unidirectional flow in rectilinear geometry is one important group of such classes, where the exact solution for a cylindrical duct represents a reference for blood flow in straight vessels far enough from the entrance and in absence of other geometrical disturbances. The analysis is preceded by the introduction of the concept of the boundary layer, which describes the behavior of fluid motion in the vicinity of a wall where viscous adherence represents the dominant phenomenon. Then we derive the classical solution of the Navier–Stokes equations for steady flow in a cylindrical duct (Poiseuille flow); the analysis is then extended to pulsatile flows where a few important dimensionless numbers naturally appear for characterizing the possible behaviors of fluid motion.