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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. –  Resonating Jun 25 '14 at 15:05
What blood volume can be normalized to is body volume. Since body volumes is slightly difficult to measure you can assume the density to be equal to that of water and calculate volume from body mass (bad approximation when comparing species with different bone and muscle densities). –  WYSIWYG Nov 21 '14 at 16:52

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