Any diffuser that creates a restriction to flow will cause a higher pressure to be created upstream of the diffuser.
Also a pitot tube will convert air flow to air pressure directly. The relationship of the pressure being proportional to the square of the velocity is a well documented physical property. They have been widely used in commercial, industrial and aviation applications for many decades.
az native: Look to the world of centrifugal pump design for discussion of the principles of efficient diffuser design. Air flow in conventional fans is for all practical purposes incompressible fluid flow. So the the same analytical techniques that apply to pumps (for incompressible liquids) apply to fans.
If this is getting too deep for non engineering types there are some simpler explanations that are a bit harder to frame in a few words. But try us.
Any CR-4 types out there who have a favorite internet reference link? ....... Ed Weldon
You have forgot the term 'all practical purposes' he has used. In centrifugal fans pressure rise is small, so change in density is almost negligible for practical purposes. But where pressure rise is in thousands of mmwc we can not ignore and we have to treat it like compressible.
__________________
"Did you get my e-mail?" - "The biggest problem in communication is the illusion that it has taken place" - George Bernard Shaw, 1856
Good Answers:
"Almost" Good Answers: