longitudinal stress in pipeline

[mrmojo]

The longitudinal strain of a pipeline due to internal pressure only is given by:

longitudinal strain = longitudinal stress/young’s modulus poisson’s ratio*(hoop stress/young’s modulus)
where

longitudinal stress = outer radius *pressure/(2*wall thickness)

hoop stress = internal radius*pressure/wall thickness

The definition for longitudinal stress assumes a pipeline closed at it ends, which allows the pressure of the fluid to push against the end, creating a longitudinal stress due to pressure. My question is: how realistic is this? I mean fluids (gas, oil) flow freely through pipelines; hence they don’t push up against anything, and hence don’t create a longitudinal stress as described by the above equations.
So what do I have wrong here?

 

[BigInch]

You didn't understand them.

Yes there is a closed end effect in an infinitely long pipeline. In a flowing pipeline the longitudinal stress is equal to the internal pressure at any point x cross-sectional area of flow / area of steel. You can prove this to yourself by making a free body diagram of a length of pipe with flow. The resistance to flow that causes the pressure drop along a flowing pipeline's length places friction forces distributed around the inside of the pipe wall, the friction acting equally and opposite to the direction of flow. Sum the friction forces and subtract them from the "end cap force", P₁ x A at the inlet to the pipe segment and subtract P₂ x A at the outlet to the segment and the forces balance. Or maybe easier to see when considering a long pipe with closed ends and a tee allowing flow in near one end with another tee near the other end allowing flow out. Include end cap forces equal to the inlet pressure x A, the outlet pressure x A at the other end, now balance those with the frictional forces on the pipe wall from fluid flow. Equals zero, right.

From "BigInch's Extremely simple theory of everything."

 

[mrmojo]

So you're saying a significant component of the longitudinal; stress is due to friction loss between the flowing medium and the pipe wall -- do you have a reference for this?

The formula I see for longitudinal strain in a buried pipeline has 3 terms:

longitudinal strain=strain due to temperature expansion-strain due to hoop strain*poisson's ratio+strain due to longitudinal stress.

The first 2 terms in that equation I understand, what the origin of the longitudinal stress term (last term) is gets me -- soil friction and temperature have already been taken into account and the formula for the last term in the above equation (long. stress) is outer radius *pressure/(2*wall thickness). to derive this formula using a free body diagram requires you to assume closed ends on the pipe, which doesn't seem realistic to me.

Nowhere in this derivation is friction related to the pressure loss of the flowing fluid mentioned as the cause of longitudinal stress.

 

[mrmojo]

There was the same thread here which never answered the question:

http://www.eng-tips.com/viewthread.cfm?qid=107971

 

[BigInch]

That formula considers no flowing fluid, just contained fluid at constant pressure, variable temperature. Reference? You're looking at the formula arn't you. Its you that doesn't want to believe it.

From "BigInch's Extremely simple theory of everything."