t along the cardiovascular tree (Detweiler, 1979, p. 3 4).
Cross sectional area can be described in terms of vessel radius (i.e., one half the vessel diameter) and length. As radii increase, resistance decreases. In addition, as the length of a given vessel decreases, resistance also decreases.
These principles can be used to characterize different blood vessels with respect to blood pressure and blood flow. For example, any widening of the vascular bed as occurs when blood flows through the capillaries not only decreases vascular resistance, but results in slower blood flow as well (Detweiler, 1979, p. 3 5).
The Poiseuille relationship is yet another hemodynamic equation. It describes blood flow as a function of several different variables: V = P (pi) r4 / 8 L (eta), where pi can be approximated as 3.1416. Accordingly, in addition to such factors as the applied pressure gradient (P), vessel radius (r), and vessel length (L), fluid flow per unit time (V) may also be affected by fluid viscosity (eta). Thus, for Newtonian fluids (i.e., fluids which maintain constant viscosity regardless of velocity), flow is not only directly proportional to the pressure gradient and inversely proportional to vessel length, but is also inversely proportional to liquid viscosity. Poiseuille's formula also states, however, that flow is most affected by vessel radius. For example, increasing a vessel's radius by a factor of 2 will increase its fluid flow by 24, or 16, times.
Fluid viscosity is probably best described as the "thickness" of a particular liquid. This property depends upon the internal resistance developed within the liquid itself (i.e., the degree to which its own molecules cohere).
Blood is typically about five times more viscous than water (Detweiler, 1979, p. 3 191). With greater viscosity, liquids require greater pressures to propel them along. Conversely, when pressure gradients remain constant, greate...