Pressure Vessels Wall Thickness

[PBX Ronin 23]

Are there any standards in terms the minimum thickness required of a meterial (ex. Aluminum 7 series) for certain pressure levels?

Is there an equation or a ratio that's generally accepted?

[Glickman]

im guessing your dealing with underwater, i doubt itll help much, but heres what you need to calculate the underwater pressure:

Presssure= 1+Depth/33

the pressure is in atmospheres, and the depth is in feet.

[PBX Ronin 23]

No. I'm talking about an air chamber. Fro example at 300psi, how thick does the wall on a chamber made of aluminum.

[J_Hoyt]

For a cylindrical pressure vessel:

sigma1 = pr/t
sigma2 = pr/2t

sigma1 - circumferential stress
sigma2 - longitudinal stress
p - pressure
r - inner radius
t - thickness of cylinder wall

Find out how much stress the material you want to use can handle and there ya go. Remember, different shapes will handle pressures better than others.

[PBX Ronin 23]

I'm assuming that a cylindrical vessel is the strongest or am I wrong?

[J_Hoyt]

No, a sphere would be the strongest. Totally uniform stress distribution (no corners where things will break). All I know about cylinders being used as pressure vessels is that they are the only shape discussed in my Mechanics of Materials course notes.

But you can think of a cylinder (as they would be used in pressure applications) as a sphere with a long section in it. Picture a sphere, cut it in half, seperate the halves, and join them. Just like a normal paintball HPA tank. So it will be close to the strongest shape.

[PBX Ronin 23]

Many thanks J.....

Additionally, is there a minimum requirement as far as DOT or other regulatory agencies would require the pressure/thickness ratio?

[J_Hoyt]

That's where I can't help ya. No DOT in my country.

[nippinout]

For a cylindrical pressure vessel:

sigma1 = pr/t
sigma2 = pr/2t

sigma1 - circumferential stress
sigma2 - longitudinal stress
p - pressure
r - inner radius
t - thickness of cylinder wall

Find out how much stress the material you want to use can handle and there ya go. Remember, different shapes will handle pressures better than others.

Here, Sigma1 is hoops stress, and Sigma2 is axial.

For design, you want to use Sigma1, as your control limit. This will give you a higher value of stress. You don't necessarily want to design the vessel to the stress limit of the material. A safety factor of 4 is reasonable.

[PBX Ronin 23]

When you say 4. Is that to the fourth power or 4 times. Forgive the non-engineer in me.

[J_Hoyt]

Safety factor is a multiplier. For safety purposes, assume that sigma1 = 4pr/t.

[nippinout]

Let's say our material yields at 16,000psi. We don't want our design strength to exceed a stress of 4,000psi. That's not the pressure in the vessel, that's the hoop stress due to the pressurized air.

Disclaimer: I've been designing a gun or two for a while now, but I'm only a student.

[PBX Ronin 23]

Very helpful stuff. Thanks guys.

[Cristobal]

It should be noted that the foregoing analysis applies to Thin-Walled cylinders where the internal, external and average radii are assumed to be approximately equal to each other. Typically this assumption would be used when the ratio of diameter to thickness is greater than 40. (d/t >40)

If d/t < 40, then you'll want to use a Thick-Walled analysis which is a bit more complicated because you also have a radial stress... but for most paintball applications, this won't apply.

nippinout is right on the money about a factor of safety -- you don't want to design anything without one. For a typical paintball application I would not use a factor of safety any lower than 4.