enclosed pipe volumes at various pressures

[someguy79]

I'm looking for a relationship between pressure and change in the enclosed volume of a pipe. I have the equations to generate radial, tangential, and longitudinal stresses. I had planned to use these values to get strains and convert that into a change in volume.

I am concerned that the radial and tangential components of stress will not be valid in common forms of Hooke's law (xyz coordinates). Consequently, I don't trust that I'll get accurate estimates of volume change.

The system uses various NPS 2 and smaller Sch 160 pipes.
Operating pressures range from 500 to 1500 psig.
All cases are assumed to be static (non-flowing, steady state).
Pipes have closed ends.

Is there a relatively simple relationship I might use to estimate enclosed volume at several different pressures?

 

[zdas04]

At 1500 psig the pipe volume of 2-inch Sched 160 is absolutely identical to the pipe volume at 500 psig to about 4 decimal places. The MAWP of that pipe is 4800 psig.

I think you'll have to share what you are trying to test before any working engineer will take this question seriously.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[someguy79]

zdas04,

Where did you find a volume-pressure relationship on 2" Sch 160 pipe? that's exactly the type of information I'm looking for.

 

[LittleInch]

To my mind, at any point around the circumference you have hoop stress (well known equation), axial (compressive) stress from poissons ratio and for a short section of pipe end cap forces.

That's all assuming your temperature doesn't change.

What's your issue?

As dave say though for a relatively short section of small diameter pipe, your volume change will be nearly impossible to measure or see. Therefore the application of this seems to be irrelevant.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[MortenA]

@someguy:
I read you question as concerning the possible expansion of the pipe segment itself (the steel) as caused by increasing pressure? BUT you may also be asking for an equation the correlated pressure change with temperature change in an enclosed volume?

Best regards, Morten

 

[someguy79]

I'm not concerned with temperature change here. Correlations between temperature change and volume are easy enough to find, as are the relevant data for coefficients of thermal expansion.

I expect the change in volume to be very small. If I could find the relationships myself, I suspect I could rule this out. However, I only have a half solved problem and anecdotes. Statements of assumption and the authoritative words of others on an internet forum will not suffice.

As mentioned above, I already know how to solve the stress states for a thick walled pressure vessel (pipe with closed ends, internal pressure, no other external forces). Such relationships are easy to find in several references. These do not give quantitative information about volume change.

 

[LittleInch]

Try these two papers / chapters

http://www.ewp.rpi.edu/hartford/use...ect/4. Supporting_Material/Books/19206_06.pdf

http://www.ewp.rpi.edu/hartford/use...ect/4. Supporting_Material/Books/32658_09.pdf

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[rconner]

Am curious once you obtain this theoretical "volume" change, what do you intend to do with that number or relationship (or how will it be used)?

 

[dicksewerrat]

If you know the volume at atmospheric pressure including internal measurements and can calculate to change in radius of the pipe, what is the issue? volume of a 1 unit section of pipe is area of inside of pipe times the number of unit lengths. volume 1 minus volume 2 = change in volume. If you are actually looking for the weight of the material(gas) in the pressurized pipe that would be a bit different.

Richard A. Cornelius, P.E.

http://WWW.amlinereast.com