Page 14, hemodynamics, Dr. D. Penney

Poiseuille Equation:

Early in the last century Jean Louis Marie Poiseuille collected data relevant to fluid flow. Several decades later Hagenbach and Neumann used his data to develop an empirical equation describing fluid flow. They generously gave Poiseuille's name to it. The equation states that flow is proportional to k, a constant of proportionality, which from this point on we will ignore.

In addition, flow is directly proportional to the perfusion pressure, inversely proportional to the fluid viscosity, directly proportional to radius raised to the 4th power, and inversely proportional to the vessel length. Thus, as perfusion pressure increases, flow increases directly. On the other hand, as viscosity rises, flow decreases directly. The most powerful factor determining fluid flow, and the one most significant to blood flow in tissue, is radius. This is true for two reasons:

  • Blood vessels are capable of changing their caliber by contraction and relaxation of smooth muscle.
  • Radius is raised to the fourth power.

    Thus, a tiny change in radius results in a very large change in flow. Doubling the radius increases flow 16-fold, while decreasing the radius by one-half decreases the flow to 1/16th, when all other factors remain constant. Thus change in radius is a very powerful influence on flow. Perfusion pressure is of secondary importance for determining flow in physiological systems. Although conduit length can potentially alter flow, blood vessels seldom change length. Change in viscosity is also of little importance, at least in the short-term, although viscosity could change greatly as in the polycythemia accompanying, for example, acclimation to life at high altitude.