I'ts always puzzled me why we always talk about the prop producing thrust by pushing the air back
The considerations and explanations relate to one's vantage point.
If that be
(a) a substantial distance, then the "gross" effects are obvious - air gets thrown/pushed/shoved/whatever this way or that and there is a reaction (which is the thing we are after). This viewpoint is simple and appeals to me as a pilot as it gives me most of what I need to know to point an aeroplane in a desired direction etc ...
.. ranging through to ... being
(b) right up, close and personal, where we find ourselves looking at what is happening at/near the lifting surfaces which are actually performing the magic things. Then the mathematicians come into their own ... This viewpoint appeals to me as an engineer as I can use the mathematics to predict loads, etc., which provide useful information for doing engineering stuff.
but when we get to the wing we tie ourselves up in knots with Bernoulli, circulation, coanda and other exotica
knots - that was a pun, right ?
Bernoulli - useful for getting a feel about fluid flow and pressures - good pilot stuff
circulation - engineer stuff and not of much interest to the pilot except for handwaving whilst talking about trailing vortices at the bar on Saturday night in the presence of adoring neophytes
(Henri) Coanda useful for handwaving explanations of a number of attractive party tricks at the bar on Saturday night in the presence of adoring advanced neophytes (but not of much interest to the pilot).