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?
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.