Friends,
We are being asked by our client to use bourdon effect on a long run buried pipeline. The line is 12" API 5L GR X52 (Design Condn. 95Deg. C and 95 Kg/cm^2 G).Is it really required to use bourdon effect?. Where I can get the stress equations involved?
Your response is highly appreciated.
regards
Suresh

Technically, I believe that the “Bourdon Effect” applies to the effect occurring when coils (or piping elbows) tend to open up or straighten under pressure, but this term has come to be synonymous with all pressure strain occurring in piping systems. Currently there are no explicit references to this effect in piping codes or technical papers. So we end up talking about a phenomenon that just about "everybody" knows how to use, how and when to apply, etc. but that isn’t really documented anywhere on paper.

Since piping codes explicitly tell us to simply add the pressure stress (PD/4t) to the other stresses “after the fact”, no displacements due to pressure get considered. The Bourdon calculation is an attempt to take into account that strain -- the strain that the piping undergoes when subjected to pressure. In reality the strain consists of the contributions of two components - the axial strain due to the pressure end cap effect (roughly PD/4tE) and then the Poisson effect (axial shrinkage due to radial and hoop expansion under pressure).

Virtually all pipe stress programs implement the Bourdon effect in the manner first developed for the MEC-21 pipe stress program, circa 1960. This method applies pressure elongation as a uniform strain to the entire piping system, in a way similar to thermal expansion (some codes, such as BS 7159, actually instruct the user to convert pressure strain to "equivalent temperature"). (Note that CAESAR II also provides the option of including the effect of the elbows opening under pressure.) The actual axial pressure strain calculation is done as:

e = P(Ri * Ri) / (Ro * Ro - Ri * Ri) / E - V P(Ri) / (Ro - Ri) / E , or,

Slightly more exact, but virtually identical for "thin" wall pipe:

e = [P(Ri * Ri) / (Ro * Ro - Ri * Ri) / E] (1 - 2 V)

Where:

e = uniform pressure strain
P = pressure
Ri = internal radius
Ro = outer radius
E = modulus of elasticity
V = Poisson's ratio

Without knowing exactly what your pipe sizes are (let’s try D = 914.4 mm and t = 25 mm):

Using the submitted parameters:

e = [P(Ri * Ri) / (Ro * Ro - Ri * Ri) / E] (1 - 2 V)

e = [95 Kg/cm^2 (864.4 * 864.4) / (914.4 * 914.4 - 864.4 * 864.4) / 2.1e6 Kg/cm^2] (1 - 2 * 0.3) = 0.00016 mm/mm

Is this important? Well, it depends on what you consider to be important. For example, the strain of the pipe due to thermal expansion at 95C is approximately 0.00085 mm/mm, or 5.3 times that of the pressure. So it is up to you to decide if that is significant.

One warning, however: be careful when applying pressure elongation as strain (as is done by all of these pipe stress applications). It is not correct in all (or maybe even most) circumstances, since end cap forces should really be applied as forces at bends and other closures, and the Poisson effect should be applied as uniform strain. Consider the example where a pipe runs straight between vessel nozzles. The Bourdon effect would apply uniform pressure extension to the pipe running between two anchors, and would therefore generate compression in the pipe and push on the nozzles. However, in reality, the end cap forces would be applied to the inside of the vessel opposite the nozzles, so the only strain in the pipe would be the Poisson effect, which would generate tension in the pipe and pull on the nozzles!

More brain surgery... on what basis????


If people would only take such care with the important details...

Ray,

Why did you use D values instead of R's in the formula?

Thanks

D = R * 2
R = D / 2