Relationship between pressure, vessel diameter, length, blood viscosity, and blood flow.
The primary function of the cardiovascular system is to distribute and collect blood in all parts of the body. It consists of a pump (i.e., the heart) and a network of viscoelastic tubes (i.e., the aorta, arterioles, capillaries, venules, veins, and the superior and inferior vena cavae) (Detweiler, 1979, p. 3 3). In order to maintain adequate perfusion of the body's many organs and tissues, both blood pressure and blood flow must be intricately controlled. In general, all blood flowing through the aorta must also flow through the capillaries and veins. Although such flow is, hence, governed by the law of equality, the hydrostatic pressure in each of the three types of vessels is markedly different. For example, blood pressure is typically highest in the aorta, intermediate in the arteries, and low in the capillaries and veins. Thus, as blood flows throughout the body, the hydraulic energy provided by the heart is gradually dissipated via friction and heat (Detweiler, 1979, p. 3 3). The rate at which this loss occurs depends on vessels' resistance to blood flow. These relationships can be written as follows:
Volume flow (V) = Pressure gradient (P) / Resistance (R)
This formula is equivalent to Ohm's law of electrical circuits, i.e., I = E/R. Although it may be extremely useful for describing the direct relationship between blood pressure and blood flow, it fails to account for either the pulsatile nature of the flow or the complex branching which occurs within the cardiovascular system.
Another formula relevant to these processes is the equation of "continuity of flow." These relations can be written as follows: v(a) x A(a) = v(b) x A(b), where "v" is the velocity of flow and "A" is the cross sectional area. Thus, the linear velocity of blood flow is inversely proportional to the total cross sectional area at any given poin...