Dimensionless number for blood volume
Blood volume is not a dimensionless number - it's a volume. Historically we used to measure this in patients or volunteers by giving a large carbohydrate molecule like a starch that is not digestible or harmful to the body. Just like every other body fluid compartment volume (i.e. plasma, interstitial fluid, intracellular and extracellular) that we have, blood volume is estimated by intravenously injecting a known concentration of a particular compound. Once that compound equilibrates you take a blood sample and measure the compound's concentration again.

Initial Concentration * Initial Volume = Final Concentration * Final Volume

When you inject a known volume of a known concentration that only fills the "blood" component, and then you measure a final concentration - you can then solve for the "Final Volume" for "blood volume".