I didnt botch it up , I worked it exactly as you posted it.
meaning that I need to check all of your formulas plus your math.

F=(10132kPa - 101kPa)* 0.00064516m^2

10132000Pa is still 1469.52 psi...

again you botched it up.
even after you aknowledged the initial mistake.
you still get 6471N
and that is wrong.

it really doesnt matter what the amount of thrust is anyway.

it can be fast or slow but faster is better in this case.

as I have stated before the thrust is not what MOVES the pipe.

the momentum of the mass moving inside the pipe is what moves
the pipe.

do you deny that the air mass moving inside the pipe would
move the pipe?

_________________________
3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.