[xadhominemx]

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.

[vpribish]

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)

here's a video going through the math on a similar problem which is a little more complex in detail, but the same in principle: https://www.youtube.com/watch?v=hXApWf1r0Eo