Poiseuille's Law: Conclusions

It seems remarkable that such a simple-looking algebraic formula, so much can be learned. In order to understand the mathematical origins of this formula using the velocity law, one only needs to know calculus. To get the velocity law from Newton's equations, one also needs to know about differential equations. But it can continue. In order to understand what happens when our basic assumptions are broken, one needs to understand the subtleties of the Navier-Stokes equations. These are usually too difficult to solve exactly, and so then one needs to be able to solve them numerically on a computer.

Further Explorations

Circulatory System Links
• American Heart Association
• The Heart: An Online Exploration
• Blood Supply to the Muscles (including how arterioles control flow)
• How Fats Affect Blood Flow
• How Cholesterol Affects Blood Flow

Derivations and Elements of Poiseuille's Law
• A derivation and solution using Newton's laws and calculus.
• A solution of the differential equation coming from Navier-Stokes.
• Viscosity: A definition as well as some values for assorted fluids.

References Used
For some references to the applicability of Poiseuille's law to blood flow, I looked at the following books:
• A. Burton, Physiology and Biophysics of the Circulation, Yearbook, 1965. See especially chapter 5.
• Caro, Pedley, Schroter and Seed, The mechanics of the circulation , Oxford, 1978. Again, the applicable material is in ch. 5.
• S. Middleman, Transport Phenomena in the Cardiovascular System , Wiley, 1972. Chapter 1.
For some information on the relative parameters of blood in the circulatory system, I got most information from
• R. L. Whitmore, Rheology of the Circulation, Pergamon, 1968. Chapter 7 is what I mostly used.

Feedback?

If you would like to let me know what you thought, or if you have other questions, feel free to send me your comments: walton@math.arizona.edu