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Poiseuille's Law of Laminar Flow

by Greg Crowther


Lyrics

When you wanna think-a like Poiseuille,
There's a formula you employ.
When the blood flows around and around and around,
The flow rate through a given vessel can be found

As r times r times r times r
(That's r to the fourth)
Times delta-P,
And that's all divided by
Eight over pi
Times the length of the vessel
Times viscosity.

r times r times r times r
(That's r to the fourth)
Times delta P,
And that's all divided by
Eight over pi
Times the length of the vessel
Times viscosity.


Comments

A short song, written for Biology 220 at the University of Washington, about the factors governing blood flow. Ideally, it should be performed with a peppy zydeco feel. In this formulation of Poiseuille's Law, r stands for radius and delta P is the difference in pressure. (Alternatively, the law can be written simply as delta P over resistance. Resistance may also be abbreviated R, so be careful!)

The repetition of “r times r times r times r” emphasizes that blood flow rate is highly sensitive to vessel radius (r). In addition, the rhyme with “employ” helps students pronounce the French surname “Poiseuille."

Questions: (1) How does vessel radius (the “r” in the song) relate to resistance to blood flow? (2) What is delta P here? Is this the same delta P that is in Fick’s Law of Diffusion? (3) Can you rearrange the equation so that pi is in the numerator?Answers: (1) Resistance to flow (often abbreviated with a capital R) is proportional to radius to the 4th power. (2) Here delta P refers to a difference in hydrostatic pressure over the length of the vessel. It is not the same as the delta P in Fick’s Law of Diffusion. (3) The equation can be rewritten as: Flow = (pi*r4*(delta-P))/(8*length*viscosity).


Other Files

MP3 (demo)

score (with melody play-back)

video