Pressure in a cylinder

[nitro]

Hello,

Given a copper tube with capped ends, of 150mm in length, 28mm i/d and a wall thickness of 1.5 mm, can anybody give me the formulae for calculating the pressure that it will withstand prior to rupture at an amb. temp. of +20 deg.C. at ground level? Any answers would be appreciated.

Kind Regards, nitro

[swansont]

AFAIK it depends on the copper properties (e.g. composition, whether it's been annealed) or if it's a copper alloy.

 

http://www.roymech.co.uk/Useful_Tables/Matter/Copper_Alloys.html

 

"Copper alloys do not have a sharply defined yield point"

 

that's the point where you transition from elastic to plastic deformation.

 

They also list tensile strength as being between 200 and 400 MPa, so that's probably your pressure range.

 

What's the application? "capped at both ends" makes it sound like a pipe bomb.

[insane_alien]

They also list tensile strength as being between 200 and 400 MPa, so that's probably your pressure range.

 

no, no its not. thats the maximum amount of stress it can handle. i guarantee if you put 100MPa in that pipe it would explode. also, if that were the way it worked if you had kilometer thick walls the maximum you could put in it would be 400MPa, something dodgy there.

 

What's the application? "capped at both ends" makes it sound like a pipe bomb.

 

thats what i'm thinking too.

 

annyway, copper is not an ideal pressure vessel.

 

you may want to lookup stresses in a cylinder to find a way to calculate it. though i think the caps would give out long before the pipe(depends on the way they are attached i suppose)

[YT2095]

I thought Pipe bomb too, but figured I`d give the benefit of the doubt 1`st in case it was just a bad idea for pressure vessel, I decided to wait and see how the thread develops 1`st.

[nitro]

Thank you both for your comments. I can assure you that I have no intentions of making a bomb !!!, I am a retired 68 year old Electronic eng. and my Nephew has just purchased one of these new 88 gm. CO2 powered air rifles. He wants a silencer for it, and that I can design, and copper is readily to hand ( domestic heating pipes) in my garage, but I cannot remember or locate the formula for the calculations in lbs/sq.in. for a given pipe size and length - hence the question. I believe the pressure output of such a bottle is in the order of 1000 psi. but should things go wrong, I need to know that the pipe can take that sort of pressure - quite an innocent question really !!.

Kind Regards, nitro

[insane_alien]

well, if you mentioned that in the first place... n/m

 

the cylinder will not have to withstand the full pressure. it should be fine but i'd test it first before giving it to anyone.

 

also, what is the legality for silencers on air rifles?

[nitro]

In the UK it is fine, I do hold a FAC licence as well. I have found my answer I think using Lame equations.

Kind Regards, nitro

[swansont]

no, no its not. thats the maximum amount of stress it can handle. i guarantee if you put 100MPa in that pipe it would explode. also, if that were the way it worked if you had kilometer thick walls the maximum you could put in it would be 400MPa, something dodgy there.

 

Yeah, and I should have kept reading, too

 

"yield strength of annealed material is approximately one-third the tensile strength." and "Yield strength of a hard-temper copper is approximately two-thirds of tensile strength."

 

And obviously a monolayer of copper won't withstand the same pressure as a micron, which can't withstand the same pressure as a millimeter, etc.

[YT2095]

yeah, you Really should have stated your intentions 1`st, copper tubing will work perfectly without rupture for a CO2 pellet gun, I`v made them myself for shooting rat nests less than 5 metres away.

 

and also used them on an 80cc 4 stroke petrol generator to keep the noise right down (using a coffee can as the baffles).

 

 

go for it

[nitro]

Thanks for all your replies. I apologise if I have caused some of you to think that my intentions were less than honourable, but it was a "Physics question" and that is why It was posted in the manner it was. So, as any design IMO must be "Fail safe", given that the rifle in question is a bolt action breech loading (thats one end of the barrel capped off), and should the open end of the silencer become blocked with whatever, (thats the other end capped off)are you saying that 1.1 cubic inches of CO2 at 1000 psi for a period of say 300mS. will not rupture the chamber?. This is not a 28mm i/d void, as a 8mm i/d tube passes through it, with holes of 5mm dia. dilled into it, and then baffles sealed to the inside of the 28mm tube, there a 5 of these, so in essence there will momentarily be 5 separate chambers varying in length from 10mm to 48mm, each receiving an exponential deceleration of pressure.

Kind Regards, nitro

[thedarkshade]

You know, you'll probably will laugh at this, but one of my thoughts (weird ones) came to my mind as I read the title of this thread. Here's what I'm thinking.

 

The formula for pressure is [math]p=\frac{F}{S}[/math], and as the formula in this case is circular then S is actually [math]S=\pi r^2[/math].

So the formula would now look like this:

 

[math]p=\frac{F}{\pi r^2}[/math]

[insane_alien]

who the hell uses S for area?

 

and that only works for the end caps.

[thedarkshade]

who the hell uses S for area?

 

and that only works for the end caps.

What do you mean S for area? If you don't mind explaining a little more.

[5614]

In your equation you said P=F/S, where P is pressure, F is force and S is the area over which the force is applied. What he was saying was that using S for area is an unusual notation... normally people use A for area, so P=F/A is what people expect to see.

[swansont]

[math]A=\pi r^2[/math]

 

is the formula for area of a circle. You used S rather than A, which is more commonly used. Not really a big deal.

[nitro]

Thanks for all your replies. I apologise if I have caused some of you to think that my intentions were less than honourable, but it was a "Physics question" and that is why It was posted in the manner it was. So, as any design IMO must be "Fail safe", given that the rifle in question is a bolt action breech loading (thats one end of the barrel capped off), and should the open end of the silencer become blocked with whatever, (thats the other end capped off)are you saying that 1.1 cubic inches of CO2 at 1000 psi for a period of say 300mS. will not rupture the chamber?. This is not a 28mm i/d void, as a 8mm i/d tube passes through it, with holes of 5mm dia. dilled into it, and then baffles sealed to the inside of the 28mm tube, there a 5 of these, so in essence there will momentarily be 5 separate chambers varying in length from 10mm to 48mm, each receiving an exponential deceleration of pressure.

Kind Regards, nitro

The answers above are very useful but should they also include the tensile strength of the copper ?, Thank you very much, however, after all that, will it be safe ?

Kind Regards, nitro

[thedarkshade]

[math]A=\pi r^2[/math]

 

is the formula for area of a circle. You used S rather than A, which is more commonly used. Not really a big deal.

Oh, OK! Didn't know that! That is the kind of stuff we do at my place.

Thanks for letting me know swansont!

[John Cuthber]

IIRC the usual failure mode for pipes is to split along the length rather than to blow the end off.

If the ends are stuck on properly then you need to look at the force trying to split the pipe.

Imagine the pipe just before it bursts.

The force acting on it to split it is the pressure times the area, but the area in this case is the product of the pipe's diameter to it's length.

 

The force holding it together is the the force needed to tear the walls and that's twice the thickness times the length.

From that you can work out the stress on the copper and, provided you keep that well below the yeild sress for the copper you should be OK.