Are taxes,subsidies and social money transfers(i.e. welfare) accounted in money velocity? As far as I know, money velocity is an average amount of times a typical, say, dollar, gets spent on goods during 1 year. So if it's spend N times to pay for goods, then money velocity equals N.
But I wonder if it's all the truth or only part/simplification of it. Suppose an average dollar is spent, on average, 1 time to pay for goods, 2 time to pay taxes, 4 times to pay subsidies, 8 times to pay pensions. What money velocity would be?
Velocity of money is according to the Fed definition:

The velocity of money is the frequency at which one unit of currency is used to purchase domestically- produced goods and services within a given time period. In other words, it is the number of times one dollar is spent to buy goods and services per unit of time.

Hence paying taxes/transfers is not counted. In your example the velocity would be 1 assuming government does not spend the money from those taxes on goods and services, and assuming the money transferred through subsidies or pensions are not spent at all.
Also, as a side note velocity is rarely calculated directly due to the practical difficulties. Rather its often just inferred from other variables.  Furthermore, the example you give cannot occur in practice as 1 dollar cannot be simultaneously just spent once, taxed twice and transferred 12 times at the same time but I take it that the numbers are just randomly selected.