Blood flow

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Blood flow is the flow of blood in the cardiovascular system. The discovery that blood flows is attributed to William Harvey.

Mathematically, blood flow is described by the Darcy's law (the fluid equivalent of Ohm's law) and approximately by Hagen-Poiseuille's law (because it is accurate only for Newtonian fluids, while blood is not Newtonian and its flow can be described as laminar only in smaller vessels, elsewhere it is turbulent). The upper equation is Darcy's law, you get the Hagen-Poiseuille's law if you insert the lower in it (it is also written in its own article, see link above):

$F = \frac{\Delta P}{R}$

$R = (\frac{\nu L}{r^4})(\frac{8}{\pi})$

where:

F = blood flow

P = pressure

R = resistance

ν = fluid viscosity

L = length of tube

r = radius of tube

In the last equation it is important to note that blood flow changes with the fourth power with change of radius. This is important in angioplasty, as it enables the increase of blood flow with balloon catheter to the deprived organ significantly with only a small increase in radius of a vessel.