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# How to find the pressure capasity of a hollow metal cylinder Answered

I am tying to figure out how much air pressure a hollow metal cylinder could hold before it starts becoming dangerous. It will be for an air cannon I want to build so the cylinder itself would need to have an inside diameter of 4ft and about 6ft long.

## 5 Replies

trialex (author)2007-07-10

Yes! Aeronautical structural engineer to the rescue!!!! Finally, 4 years of uni pays off..

Pressure vessel analysis is EASY.

For a cylindrical section, the stress in the HOOP direction (i.e. in a circle around the wall) is

sigma = (p * r) / t

where

sigma = stress
p = internal pressure
r = internal radius
t = wall thickness

and for the AXIAL direction (i.e. pointing from one end to the other), the stress is

sigma = (p * r) / (2 * t)

So the hoop stress is always critical.

So now you can use these equations to design your vessel. PS 4ft x 6ft? That is MASSIVE. Like thousands of dollars of materials. Did you see the mythbusters chicken gun? It was SMALLER than this and was ridiculously over powerered.

So say you want to fire your gun at ROUGHLY 50psi, using mild steel with a strength of 30,000 psi. Firstly add a Margin of Safety of AT LEAST 2, lets choose 4. The inner radius is roughly 2x12 = 24 inches. The wall thickness you would therefore need would be...

30,000 = (50 x 4 x 24) / t

t = 50 x 4 x 24 / 30,000

= 0.16 inch

I didn't take into consideration the wall thickness in the inner radius, so it's a bit off, but close enough.

This is all assuming you have nice hemi-spheres on the ends. If you use flat plates, then they will be the critical component. Not hard to analyse those either.

I think you are going for overkill though. Unless you have some serious welding skills to attach a valve, barrel and inlet it's going to get dangerous quickly. Start off using a 2 inch diameter 20 inch long PVC pipe. You'd be suprised at what it can fire.

Sedgewick17 (author)2007-07-11

Thanks I would never been able to find this formula. I can weld pretty good I think but that is allot of pressure on the valve. I will do some tests like those that you suggested before I build anything-large scale.

Sedgewick17 (author)2007-07-10

I have a portable air compressor, but I do want to get a larger one. It would be over kill if I was aiming for 200ft, but the distance I want to get is 5,280ft.Thats right the O Holy mile. I have a devise that should inject all the air very quickly without wasting any compressed air

lemonie (author)2007-07-10

Have a look on the internet for industrial air compressors, which have hollow metal cylinders as reservoirs. They'll give you working pressures, and you're probably going to need one for your project anyway(?) L

Kiteman (author)2007-07-10

If you are buying the cylinder, the manufacturer should be able to tell you, but my first thought is that the size of your tank smacks of massive over-kill.

According to Backyard Ballistics, a foot-long section of 3-inch PVC pipe pressurised to 30psi (with a foot-pump) can loft a potato up to 200 yards. The PVC is rated at 40psi. Your tank should contain enough pressurised air for a hundred shots at only 30-40psi, enough to bore even the most avid potato-cannon enthusiast.