It depends, of course, on which velocity. Velocity is a ratio of some
measure of transactions value per unit time (usually per year) to some
measure of a money stock. In the nineteenth century, since there were
no national income statistics, monetary theorists seem mostly to have
thought of velocity as a transactions velocity ratio of the value
total transactions to either the quantity of money or of circulating
money. Total transactions include a lot of transactions that are not
income-generating, such as the sale of existing assets, particularly
financial assets. A glance at the clearing statistics for New York
banks suggests that this concept of velocity is not very meaningful,
since the volume of transactions is extremely high (many times
national income) and volatile.

Friedman's most coherent statement of the Quantity Theory maintained
that the "demand for money" was a "stable function" of a small number
of variables, including the price level, national income, and interest
rates. To make this operational you have to decide what stock of money
measure to use. A prediction of a velocity of money is implicit in any
such demand for money function, for that definition of "money".
(Typical measures are M0, M1, M2, M3, which include a wider and wider
spectrum of "near money" liquid assets.) The econometric tests of
Friedman's hypothesis weren't too unfavorable up to the 1970s, but the
data since then is less kind to it: whichever measure of money you
pick in order to get a good fit on historical data, the out-of-sample
explanatory power tends to be low.

Duncan Foley