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Poiseuille's Law of Laminar Flow

by Greg Crowther


Context

This short song, written for Biology 220 at the University of Washington, covers the factors governing non-turbulent 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."


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.


Other Files

MP3 (demo)

sheet music (with melody play-back)

video


Lesson Plan

Songs like this one can be used during class meetings and/or in homework assignments. Either way, the song will be most impactful if students DO something with it, as opposed to just listening.

An initial, simple follow-up activity could be to answer the study questions below. A more extensive interaction with the song might entail (A) learning to sing it, using the audio file and/or sheet music as a guide, or (B) designing kinesthetic movements ("dance moves") to embody it. The latter activity should begin with students identifying the most important or most challenging content of the song, and deciding how to illustrate that particular content.


Study 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 may be found on the answers page.)