Formula(s) for wall thickness of a pressure vessel?
I realize that there are a ton of variables involved, but I'm looking for some math and science instead of just copying prior art. The project(s) is a high powered air rifle, and I need to be able to determine what tubing wall thickness will allow how much pressure. I realize that alloy is important, if it makes it simpler, assume 4130. And tube diameter most likely around 1", and will certainly NOT exceed 2". My goal is a working pressure of 3000 PSI, as that's pretty much a standard in the airgun world. End treatments will be threaded, which I'm aware will also have an impact on wall thickness required. Any help would be much appreciated.
Sounds like... Danger.
Why not buy an off the shelf tank? I bet some air guns use separate tanks that you could buy as a replacement part. Or maybe something like a tiny hydraulic accumulator.
I mean you do realise that should this tank burst while you are looking down the sight you might need a new face?
Can't say I have ever seen any 3000psi tanks with threaded end caps either. Usually they are drawn/rolled out of one solid chunk of steel.
Alternatively, why not feed it directly from bulk 3000psi air gun tank via 'remote' hose? (Bulk as in, those 2~3" by 8 to 10" tanks)
If all else fails try Googling. For example this one:
It even has a calculator!
What you're looking for is barlow's formula. http://en.wikipedia.org/wiki/Barlow%27s_formula For safety's sake, don't work at the limits of the material. Use a safety factor of say, 4.
To apply this, take 4130 (annealed, since it isn't specified) at a yeild strength of 52,200 psi.
MAWP of 3000 psi, multiplied by 4 for safety factor gives us 12000 psi
OD of 1"
Barlow's formula is Pressure = 2*Strength*Wall thickness / OD therefore:
12000 = 2*52200*Wall thickness / 1
12000*1 = 2*52200*Wall / 1 * 1
12000 = 2*52200*Wall
12000/2 = 2*52200*Wall/2
6000 = 52200*Wall
6000/52200 = 52200*Wall/52200
0.1149 = Wall
So, if you use 1" of 0.120" wall 4130 annealed tubing you should be just fine for the tubing. Next comes a bunch of calculations for fastener strength (Hint: heads in shear are much stronger than threads in shear) etc.
If you're looking for a real education when it comes to planning an airgun build, look at the canadian airgun forum (http://airgunforum.ca) for posts by rsterne especially, but also Voltar1, jezX, supersundance, and more who have forgotten more than I know on the subject.
oh btw, you should also consider that standard tube is welded and not nearly as strong as 'DOM' or 'drawn over mandrel' tube
DOM is also insanely expensive compared to regular tube. I am no expert, but while tanks under 300psi I have often seen welded, every 3000psi tank I have seen has been one peace with no evidence of welding.
It would be better to specify SEAMLESS DOM, as some mills also make welded tubing that is subsequently drawn over a mandrel.
Originally Posted by Black_Moons