I can buy a Vane Anemometer cheaply but a Air Flow meter (with a cone) costs a lot more.
Can I just make my own cone?
What issues should I expect if I add a cone to a Vane Anemometer?
How do I convert the readings into liters per second?
Damnit ... the one formula that we had to use for every problem in fluid dynamics, and our professor made us derive everything from it ...
Effectively, for your problem, volume of air flow is going to be
I say 'sum of', but it's really an integral as the speed's not going to be constant across the whole opening. The cone just forces the air to a smaller area so there's not as much variance, and it's of a fixed area to make the calculations easier.
I'd estimate it by looking at the opening as a 4x4 grid, and taking 16 air speeds, one for each grid cell, average them, then multiply by the opening size, and converting to dm^3/s (as a liter is a cube 0.1m per side). Or convert to m^3/s, then multiply by 1000.