that's very interesting! but it's about angular momentum and I'm not confident that I can take the lesson over to linear momentum.
Here's my caveman f=ma thought experiment:
1. make it 2-d.
2. replace the fan with a person sitting on a chair on a frictionless surface.
3. instead of air it's an endless field cinder blocks ahead of him.
the person reaches out, and pulls in a cinder block. f=ma says they each move toward the other while the center of mass of the combination of them does not move.
Now, if he throws the cinderblock behind him, he moves further forward - this would be analogous to an airplane propeller. or a fan in an open pipe.
If he, um, splits the cinderblock in two and places each half directly off to his sides there is no net force exerted on him by this. This is the fan in a T-shaped pipe.
the fan+pipe grabs air from ahead, moves this mass backward and then sets it aside. it's not a jet-engine, but it is moving the air mass toward itself and must be moved equally and oppositely.
I don't think it's essential to worry about how the air/blocks rearrange themselves after this - but if the blocks surround and jostle, that's just another effect layered in super-position over this one, and if we don't agree so far then it will only make things more confusing
You have to look for the equal and opposite reaction. A normal jet creates a stream of fast air behind it. There's no such thing for a reverse jet that sucks air in.
With your concrete block example, as I start pulling the block towards me I experience an impulse forward. But when it approaches my body I slow it down to zero speed, creating an opposite impulse. So although I might have moved forward a few inches during the motion, my momentum is zero at the end. When you scale this up to large numbers of air molecules, the result is the same.
thanks for following up. I think this is one of those conversations that works better in front of a white board - it's surprisingly tricky to express in words.
if the demo was mainly to show that it's the jet of air expelled out the back that's providing thrust, then, fine it does that and its a valuable lesson. I guess I'm hung up on the technicality that there is actually a real movement of air mass even without that rearward jet and that has to be felt by the apparatus - I guess it's just unnoticeably small in the real world demo.
anyhow, my confidence in physics intuition has been shaken. thanks bunches.
Nah the demo was right. The impulse from the sucking (ie air molecules bouncing off the inside of the fan blade) is countered by the impulse from the air molecules bouncing off the inside off the back T-pipe. Different at a low Reynolds number with a reversible flow.
Reynolds number, compressibility, reversibility don't really matter for this - the principle under discussion is a simple momentum-balance. Find the force on the pipe by analyzing what is happening at the boundaries, you can ignore what happens inside. (in engineering this is called control-volume analysis).
The exiting flows out the sides neatly cancel. So what's happening from front-to-back? There is air flowing in at some velocity x cross-sectional area x air density. this momentum has to be balanced completely for the pipe to stay still - but there is no source of momentum in the other direction so the pipe will feel this force and move.
if the pipe was open at the back, there would be momentum exiting the pipe balancing the incoming momentum - or even over-balancing (as in a jet engine)
