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 Cubic Feet per Minute (CFM) ensures a given air speed at a given distance.
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$\begingroup$ I expect you're dealing with turbulence in your fan example. Unfortunately, turbulence is one of the BIG physics problems that no one has yet been able to mathematically model. $\endgroup$– David WhiteSep 2, 2021 at 23:50
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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.
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$\begingroup$ It seems that they assume that the same CFM travels in the cone so the velocity is proportional to the cross section. By this rule the velocity will not go down in a tube. This doesn't sound accurate to me. I guess that in a room some kinetic energy is wasted in moving air molecules in amany directions so the air slows much faster. $\endgroup$– OMGshApr 25, 2018 at 12:47
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$\begingroup$ @OMGsh In a steady state, CFM has to be the same. $\endgroup$– V.F.Apr 25, 2018 at 13:27
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$\begingroup$ @OMGsh ...or rather, close enough to use this method. So, I agree that this is an approximation, but, considering many other uncertainties associated with measuring air speed at a distance from a fan, it does not seem to be unreasonable. $\endgroup$– V.F.Apr 25, 2018 at 15:03