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What is the average speed of blood as it flows through the index finger on the right hand?
This reference gives about 10-20cm/s in the major arteries and 5 cm/s in the major veins of the index finger in 5 male subjects, though there was a lot of variation.
The answer is going to be highly dependent on the level of the vasculature you are talking: through the largest artery or capillaries you will get different results, and different results in veins as well, and it will depend on many other physiological parameters.
Because it will vary greatly, even within individual vessels, you can't use the speed to estimate volume per time because the vasculature does not maintain a constant diameter; in fact, changes in vessel diameter are the major contributors to changes in flow volume.