Pipe axial expansion due to internal pressure 1

[NewENG102]

I would like to calculate the change in axial length in a pipe full of water when the pipe is pressurized.
Could anybody provide the formulas or advise where I can find them? I assume this number would be very small in a 100' run of pipe.

Ratio r/t>5 --- Longitudinal Stress = Pr/2t

Thanks,

 

[TGS4]

[rant]
I'm not going to give you the equation, but I am going to point you in the direction of figuring it out yourself.
[/rant]

First, you start with something simple:
F=kx (Standard spring equation)

You want to solve for x (your change in axial length). So, rearrange the equation.

Next, you know F, because you have the internal pressure and the internal cross-sectional area of the pipe.

The spring-yness of a length of anything, due to axial loading, is E*A/l. I'll leave it to you to figure out that this A is different from the internal cross-sectional area of the pipe above. L is the length of pipe. Hopefully E is obvious.

Voila. Now, you have figured out how to do this all by yourself.

 

[LittleInch]

Change in axial length is from a number of forces / elements

For unrestrained pipe, you have end cap force (P x internal area) as a force. Extension is then as TGS4

The poissons ratio means that as you pressure up, there is a stress / force in a negative (compresisve)axial direction

normally biggest element is thermal expansion or contraction which is delta T x temperature co-efficient.

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

 

[NewENG102]

Thank you both for your responding.

@TGS4 - The "A" in the spring formula is the cross-sectional area of the pipe wall.
The "E" is the modulus of elasticity (steel pipe).

I was taking the approach Δ = PL/AE this is a relationship between load and deflection.
where: P= thrust force , L= Length of pipe, A= cross-sectional area of the pipe wall & E= modulus of elasticity
I get the same result using both formula.

 

[TGS4]

 

[rconner]

It sounds like what you are talking about is referred to as "Bourdon" movement, i.e. increase in length of the pipeline segment if the section is bullheaded to contain pressure with no external restraint on the end caps. [There is, on the other hand a phenomenon of "Poisson" movement, i.e. actual contraction in length if the section is instead sleeved or unrestrained expansion sleeve-joined within a longer straight pipeline with no pressure-induced thrust focus(foci) present.]

As to your question, it thus makes a whole lot of difference exactly what piping material you are talking about, how/if you are constraining its ends, and how long pressure will be held on same. If you are talking about e.g. meaningful thickness of welded steel with a very high elastic modulus, low Poisson's ratio, and little tendency towards creep, I believe the change in length in either case is indeed miniscule. If you are on the other hand talking about various polymers or plastics, with very low moduli of elasticity the expansion or contraction can be much greater [I think took a look at a model several years ago with a couple thousand feet of 24" polyethylene pipe with end caps, no external restraint to caps, roller supports/assumed frictionless, and at "rated" pressure, and came up with an expansion of an incredible couple feet in that extreme case!]If anyone wants to really understand such behavior, take a cylindrical balloon (like the kind used to tie balloon poodles), blow it up and watch what happens.

 

[rconner]

[Oops, I meant to say some plastics have very low long-term modulus of elasticity and very high, long-term Poisson's ratios (compared to initial values more often published) that increase or amplify such behaviors.]