From Tubes and Catheters to the Basis of Hemodynamics: Viscosity and Hagen–Poiseuille Equation

Abstract

Because of viscosity, a real fluid flows through a tube only if there is a pressure difference between its two ends. In fact, it is necessary to do a work (and, hence, apply a net force) against the friction forces in order to maintain the fluid in motion (that’s why we need a heart!). In particular, Hagen–Poiseuille equation states that the volume flow rate of a viscous fluid which moves with laminar flow through a cylindrical conduit is directly proportional to the pressure difference between the two ends of the conduit and to the fourth power of its radius, and inversely proportional to the viscosity of the fluid and to the length of the conduit. Accustomed as we are, as anesthesiologists or intensivists, to deal with any type of “conduit” (tracheal tubes, venous catheters, extracorporeal membrane oxygenation cannulae, and so on), Hagen–Poiseuille equation is probably the physical law to which we are faced more often in our daily clinical practice; the choice of the gauge of a tracheotomy tube, or the decision to use either a central or a peripheral venous catheter, for example, rely also on this law. Moreover, the fundamental relationship between cardiac output and arterial pressure, on which we base hemodynamic monitoring and management, comes from Hagen–Poiseuille equation.