Blood flow? (Physics Q)?

Question

When the body requires an increased blood flow rate in a particular organ or muscle it can accomplish this by increasing the diameter of arterioles in that area. This is referred to as vasodilation. What percentage increase in the diamter of an arteriole is required to double the volume flow rate of blood, all other factors remaining the same?

Answer 1

Volume = Area * length

Area = pi * r^2 = (PI/4) * D^2

Vc = Volume of blood normally carried by the arteriole
Vd = Volume of blood carried by the dilated arteriole
Ac = cross-sectional area of un-dilated arteriole
Ad = " " " dilated "
Dc = diameter of the arteriole under normal conditions
Dd = " " " after vasolidation/dilation

For a given length of a blood vessel,

(Vd/Vc) = (Ad/Ac) = (Dd/Dc)^2

If the volume of blood needs to double, then Vd/Vc = 2

Based upon the above relationship, this means that...

(Dd/Dc)^2 = 2 -----------> Dd = 2^0.5 * Dc ~ 1.4142 Dc

The diameter of the arteriole has to increase by ~ 41.42% in order to handle twice the normal volume of blood