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Comments from the question How is the blood volume of a living organism measured without killing it? by @Nico discussed that the time of blood recirculation scales with the size of the organism. I was curious if there were a series of dimensionless numbers that characterize blood flow, blood volume, and time of blood recirculation?

Such dimensionless numbers exists for stride length and drug penetration.

Edit I like @Nico's comment so much it's going to part of the question. Any description of the circulatory system doesn't necessarily have to be dimensionless. However, I would imagine that one could develop a characteristic time (lets call it Tau) based on blood flow (L/t), cross-sectional area (L^2), and circulation time (t). From that characteristic time Tau, interesting observations and appropriate comparisons about the various ratios and how they vary amongst species.

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Why would it need to be dimensionless? Blood flow is a speed (mm/s), blood volume is a volume (ml) time of blood recirculation is a time (s). –  nico Apr 16 '12 at 6:29
By the way, to further expand my comment, I was considering that the ratio between cardiac output and the volume of the circulatory system would vary between species. I wasn't necessarily implying that it would be higher in smaller animals, although re-reading my comment it looks like I was saying exaclty that!! :) –  nico Apr 16 '12 at 6:32
It is perfectly valid to make normalized comparisons that have dimensions. I think the stride length being dimensionless was coincidental (body length/stride length). An example measurement that normalizes body parameters is the Body Mass Index (BMI) which scales mass:height^2, or the fuel economy of cars express as miles per gallon. –  leonardo Apr 16 '12 at 7:08
The trouble with miles/gallon is that it has square-cube problems. Motorcycles get far more miles/gallon despite being less aerodynamic, because they are smaller. So if you wanted a measure of how efficient motorcycles as a design independent of their size were, a dimensionless measure would resist scaling problems. It's especially important in biology because nothing is the same size as anything else. –  Jeremy Kemball Jun 25 at 15:05

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