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

To illustrate this relationship empirically, assume that R1 = 5, R2 = 10 and
R3 = 20.
In this example, Rx = 2.86.
This demonstrates two important principles regarding the parallel arrangement
of blood vessels:
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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.
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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.
RK Revised
04/09/07
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