whatever the speed of sound is

well Bryan , since the air is limited to the
"speed of sound"

340.29 m/s

the tube size is not important as the tube can be any size
according to your reasoning it can never travel faster than
the speed of sound.

!!! air is not a ideal gas !!!

fine lets just use the slower speed of sound.

so lets open it up fully to 58 inch diameter.
removing the need for a tube or nozzle.
after all Im only looking for momentum as I have stated.

if I put 1000 cu ft of 1 atm air into the tank that
already has 1000 cu ft of 1 atm of air inside

the pressure doubles.

I now have 2000 cu ft of air inside the tank.
and the pressure is 14.7 * 2 = 29.4 psi

if I put in another 2000 cu ft of 1 atm air inside the
tank the pressure doubles again.

I now have 4000 cu ft of air inside the tank at 58.8 psi

if I put 4000 more cu ft of 1 atm air inside the tank
I now have 8000 cu ft of 1 atm air that has been squeezed into the 1000 cu ft tank.
and the air pressure is doubled again to 117.6 psi
air weights 0.0807 lb / cu ft
8000 cu ft * 0.0807 lb / cu ft = 645 lbs
645 pounds = 292.567079 kilograms

F = (m V) for force
P = (m x V) for momentum

P = 292.567 kg * 340.29 m/s = 99557.62443 kg-m/s

so the momentum is 99,557 kg-m/s

the tank is 54.5 ft long
its diameter is 58 inch

it takes apx 0.16 seconds for the mass of air to leave the tank...

if I use a large or small tube doesnt matter that much
according to your reasoning.

the air will only have a certain speed at that pressure.
and that speed is the speed of sound.

I can increase the time that I allow the air to escape from the tank by using a small orifice or tube.

and this will decrease the momentum that is felt by the pipe each second.

and the ONLY WAY you can counteract this momentum is to supply a force of 99,557 kg-m/s in the opposite direction of the momentum force to make the pipe not move at all.

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