How to determine air velocity in open ended tube?

Question

I am an electrical engineer but was tasked with something a little different this time around and was hoping you guys could help. I would like to determine if my dry air system is sufficient for my purposes and I would like to accomplish that by determining flow rate in CFM. I have been doing my own research but have been having trouble relating Bernoulli's principle to my situation. If I start with a 50 foot long 0.5in diameter (inner diameter) nylon tube pressurized at 85PSI that is sealed on both ends, and then suddenly opens on one end, how would i determine the velocity of air leaving the tube? I understand as the air begins to leave the tube the velocity would start to decrease so I am interested in the initial, maximum velocity. In actuality, the 50ft long tube is fed by a larger system that is fed by a regulator with a 200 scfm maximum flow rate so I believe that assumption is sufficient.

Follow up questions: Looking at the problem, I would assume it is a turbulent flow but from what I can tell, without a air velocity I cannot calculate a Reynolds number. Do we know what the Reynolds number for nylon tube is?

I believe air should be compressed in this scenario but how does the problem change if we assume it is incompressible?

Answer 1

This is a pretty difficult problem to predict, and depends on the precise nature of how you open the tube. If it is a truly "sudden" opening, which you would most likely need a bursting diaphragm to achieve, I believe your maximum possible velocity would be based on the normal shockwave generated:

$$\frac{p_0}{p} = \frac {(85+15) ~\rm {psia}}{15 ~\rm {psia}} = 6.67$$

Using Normal Shock tables, this pressure ratio gives you a Mach number of about 2.45, or 2756 $~\rm{ft/s}$.

This is a theoretical maximum, but if you are opening this with a valve or lid, the real behavior will be quite a bit less than this, and depends on the details of the valve and how it is opened.

There is also an Engineering Stack Exchange that may be more appropriate for advice on this.

(As a footnote, the actual behavior in the case of a sudden diaphragm burst may be more like a rocket nozzle exhaust, a series of oblique shocks, whose flow speed requires a more detailed calculation https://www.reddit.com/r/Damnthatsinteresting/comments/17j5sne/a_soda_bottle_filled_with_water_and_pressurized/?rdt=62495)