Didactic Muse
Page 8
TMS
Going with the flow: Poiseuille's Law
By Dennis McMahon.
Learning Objectives: Poiseuille’s Law Blood Flow
In this article you will:
Be able to describe Poiseuille’s Law.
Be able to describe how it is proportional to the viscosity of the blood
flow within the human body.
The name Jean Louis Marie Poiseuille may not ring a bell with your average person on the street, but his accomplishments in France over 150
years ago have a direct bearing on us as medical equipment technologists. Poiseuille (pronounced ―pwa-ZWER‖) was educated in mathematics and physics, and was a pioneer physiologist who studied the physics
of blood flow. What resulted was the theory and laws of fluid mechanics:
the relationships between the flow, viscosity, and dimensions of the tube
(or vessel) conducting a fluid. Working with another scientist, Gotthilf
Hagen, the result is a law that applies to any fluid that flows with little or
no turbulence. Although intended to apply to non-compressible fluids (i.e.
liquids), it also applies to gas flows.
Fig 2. Poiseuille Law and formula. Where
Q is the flow
r is the radius of the tubing
ΔP is the pressure difference
(P1 – P2)
η is the coefficient of viscosity
L is the length of tubing.
Simply stated, Poiseuille’s Law (fig. 1) says that for fluid flowing in a
tube, the flow is inversely proportional to the viscosity of the fluid and
length of the tube, but directly proportional to the difference in pressure
across that length and the radius of the tubing (fig. 2). The coefficient of
viscosity is a measure of the resistance of a fluid to being deformed by
motion in a carrier. In other words, the "thickness‖ of a liquid. Viscosity is
measured in a unit honoring Poiseuille, the ―Poise‖. Coefficients of viscosity are usually expressed in centiPoise (cP). The value for water at
room temperature is about 1cP, while that for blood at body temperature
is about 4cP. (It’s true: Blood is thicker than water!) For contrast, the
value for glycerin is ~1500cP, and for air, ~0.02 cP.
What makes Poiseuille’s equation so unique is that the value for the
radius is raised to the power of 4. The significance of this is that the
slightest change in the radius has a dramatic effect on the flow. If we increase the radius by only 10% (and all other variables are unchanged),
we increase the flow by 46%. If we double the radius, the flow increases
by a factor of 16. Conversely, any decrease in the radius decreases the
flow significantly. The implications for flows in the body are obvious.
(fig.3) The accumulation of plaque in arteries decreases blood flow to tissues (especially to the heart). Constriction of bronchioles decreases the
movement of inspired and exhaled gases in the lungs (ask anyone suffering an episode of asthma!).
…(Continued on next page)
Fig 1. Poiseuille Law