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

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.

active| newest | oldestPressure 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.

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.