Poiseuille's Law of Laminar Flow
by Greg Crowther
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.
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*r^{4}*(deltaP))/(8*length*viscosity).
• MP3 (demo)
• score (with melody playback)
• video
