Pa Pypr48hL

which is known as Poiseuille's law of flow through a single tube.

The circulation is much more complex than a single tube. Vascular anatomy is such that vessels are arranged both in series and in parallel. When vessels are in series, the total resistance is the sum of the individual resistances. However, when they are in parallel (such as in a capillary bed) there is a summation of their conducting capacities. The net conductance NK is the product of the individual conductances K and the number N of tubes or capillaries. As the resistance R is the inverse of NK, then as N increases so resistance decreases. For a given effective perfusion pressure, the greater is the cross-sectional area of the capillary bed the greater is the flow.

When total peripheral resistance or systemic vascular resistance (SVR) is considered, it is apparent that the circulation appears as a series of tubes of different caliber all connected in series. Overall resistance will be the sum of these resistances. For each reduction in radius there is a greater reduction in r4. As R = 8hL/pr4, resistance increases dramatically.

The reduction in size of the vessels from the level of the aorta to that of the arterioles results in an enormous increase in resistance so that the arterioles represent the major component in SVR. Capillaries are less important, despite their small radius, because they occur in huge numbers, are very short (0.5 mm), and are arranged in parallel. Also, they are subject to single-file rather than laminar flow.

Arterioles are effectively the regulators of organ blood flow. They contain smooth muscle in their walls which is densely innervated by the sympathetic system. Vasoconstriction results in a reduction in arteriolar radius, an increase in resistance, and therefore a reduction in organ blood flow.

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