Poiseuille's Law of Laminar Flow
by Greg Crowther
This short song, written for Biology 220 at the University of Washington, covers the factors governing nonturbulent 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."
When you wanna thinka 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 deltaP,
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.
• MP3 (demo)
• sheet music (with melody playback)
• video
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 followup 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.
(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.)
