I would like to open this topic back up regarding the proper method of perfmorming a "static analysis" on relief valve discharge piping. We have an ongoing discussion at work on how to do it. My opinion is that, when dealing with a discharge pipe that has multiple turns before it discharges either to atmosphere or to a larger relief header, all the vector forces should NOT be applied at the same time but instead as different vectors AT different points in time (i.e F1 at t1, F2 at t2, etc.). Of course, assuming F1 = F2 = F3 if cross sectional area stays constant throughout.

So let's say you have Miyamoto's piping but relief being passed is gas. I agree the fluid will be traveling at extremely high velocities, but unless the spools are very short, the metal will NOT feel these at the same time (even if it's only miliseconds). But yet I see everyone's standard practice is to apply them all at once at every turn in direction as one single vector force (F1 at t1, t2, t3, etc.).

There is one post in particular from Loren Brown that I believe backs my reasoning up, see below:

"For an open system, if you have more than one bend in your vent stack then apply this force at each bend under a separate load vector.

For a closed system you would apply this force on bends on each “long” leg of pipe. The only way to truly figure out which pipe leg is short enough to ignore the PSV force is to run the force/time profile through Caesar II's DLF generator in the dynamics module, but then you might as well perform this analysis dynamically. For short pipes the duration of the unbalanced PSV force is small and this shifts the DLF peak to the right (higher frequency) which at some point is past the majority of your piping system natural frequencies of interest. But if you are going to do this statically you might simply take the nine longest pipe legs and apply your force to each bend corresponding to these longest legs. This would be the "brute force" approach, not really an approach based on physics.

You have 9 different force vectors to choose from so apply your PSV force under a different force vector for each bend because we want to only examine the effect on one bend at a time. Then set up separate OPE cases that include your different force vectors."

Ignoring the calculation method of the actual thrust loads (which I calculate based on Process Engineering's computer modeled fluid conditions at discharge of PSV and at downstream points and also applying a conservative DLF of 2.0), what do the experts think is the correct way of doing this static analysis? Shouldn't it be like this (in Miyamoto's example):

L1 = W+P1+T1 (OPE)
L2 = W+P1+T1+F1 (OPE)
L3 = W+P1+T1+F2 (OPE)
L4 = W+P1+T1+F3 (OPE)
L5 = W+P1+T1+F4 (OPE)
L6 = W+P1 (SUS)
L7 = L1-L6 (EXP)
L8 = L2-L1 (OCC) segregated effect of F1
L9 = L3-L1 (OCC) segregated effect of F2
L10 = L4-L1 (OCC) segregated effect of F3
L11 = L5-L1 (OCC) segregated effect of F4
L12= L6+L8 (OCC) use Scalar Combination Method
L13= L6+L9 (OCC) scalar combination
L14= L6+L10 (OCC) scalar combination
L15= L6+L11 (OCC) scalar combination

Thanks.

The forces in question should be considered as the maximum imbalanced force within an element, rather than F∞ at the elbows. If the force at each elbow is simplified as a linear ramp between 0 and F∞, but displaced at a time equal to the length between elbows divided by the speed of sound, then the force on each element between bends is F=min(F∞,F∞*L/Lcrit) where Lcrit = valve opening time/speed of sound.

The question then becomes why does LC Peng advise to apply loads to all elements simultaneously in a static analysis?

Imagine a pipe system with just elbows and elements that connect them. Element 1 connects the PSV (which effectively counts as an elbow in this thought experiement) to elbow 1. Element 2 connects elbows 1 and 2, etc.

Assuming relatively short elements, F1 = F∞*L/Lcrit, where L is the length of the element itself. You can apply this force to the elbow upstream, downstream, or even place a node in the middle of the element and place the force there. Force is always in the opposite direction of flow.

Once flow reaches elbow 2, the force is merely cancelled. The fluid does not push element 1 back into place. The only force to push the pipe back into place is the stiffness of the pipe itself. However, the fluid does not care about this fact, and proceeds to impart load onto element 2 at the same time. While imparting load onto element 2, yes, the stiffness of the pipe starts pushing element 1 back towards its original configuration, but the assumption here is that it can't keep up with the fluid at that pace. I.E. speed of sound >> speed of pipe.

The assumption that the loads all apply simultaneously assumes that the speed of sound is ∞ and the speed of pipe is 0, but only for purposes of inter-element load interaction.

My counter-argument, though, is that there exists a piping configuration where these combined loads may not necessarily be more conservative than application of a single load at a time in a static analysis. While I can't contrive one off the top of my head, I imagine if you supply enough non-linear supports with enough springs, you can probably manage it.