Is it determined completely by the air pressure and the temperature? Do I need to take into account also the geometry of the "air cone" of the fan or is it determined by the speed of the air when it leaves the fan? Practically I would like to solve questions e.g. which CFM ensures a given air speed at a given distance.
A general approach of finding a required CFM based on a desired air speed at a given distance from a fan comes down to knowing the shape of the cone, which is a function of the fan construction. Presumably, you can get this information from a manufacturer or from some other sources.
If you know the shape of the cone, you can calculate the cone area at the distance of interest and from there the CFM of the fan as a product of that area and the desired air speed.
This method is concisely described in this fan application guide from Greenheck.