Parallel Resistance Calculations

Assume that a small artery is giving rise to three smaller arterioles, each parallel to the other. The total resistance (R_x) for the three parallel arterioles comprising the segment would be:

 or solving for R_x, 

To illustrate this relationship empirically, assume that R₁ = 5, R₂ = 10 and R₃ = 20.

In this example, R_x = 2.86.

This demonstrates two important principles regarding the parallel arrangement of blood vessels:

1. The total resistance of a network of parallel vessels is less than the resistance of the vessel having the lowest resistance. Therefore, a parallel arrangement of vessels greatly reduces resistance to blood flow. That is why capillaries, which have the highest resistance of individual vessels because of their small diameter, constitute only a small portion of the total vascular resistance of an organ or microvascular network.
2. When there are many parallel vessels, changing the resistance of a small number of these vessels will have little effect on total resistance for the segment.

Revised 04/09/07