Hi Joe,

You have asked a question which is more difficult to answer than perhaps
you realize. First, before reading the rest of the post, the question(s)
I have for you are... "How important is the relief system? How large are
the forces involved? What flow regime is the flow in?"

Easy, least accurate/reliable (perhaps)approach...
1) Determine the discharge force for an open relief system. This can be
done with the CAESAR II relief synthesizer or some of the other
tools my colleague John Breen has mentioned.

2) Take this force, multiply by the dynamic load factor* of your choice
and apply it along elbow pairs in the correct vector one at a time
(you'll need multiple models).

*The use of a DLF in static structural analysis of a dynamically applied
impact load is widely published in various engineering texts. The value
commonly used is X 2. I have found that in some cases this is woefully
inadequate.

Harder, but a bit more
realistic...
Using the force number in 2 above use one of two methods to perform a
dynamic analysis. The two types of dynamic analysis possible were
described in an article written in COADE's newsletter. I believe that
this is available on this web site.

Hardest, most reliable answer
1) Get a copy of the DIERHS handbook from the AIChE organization.

2) Pour through the book and look over some very interesting math!

3) Realize that you may need some help go find a qualified, sympathetic,
Chem E

4) Chem E will then develop time-based data for momentum/ pressure loads
at elbows throughout the system.

5) Summate the data to form dynamic time/force data sets in Excel.

6) Use this data in a detailed system model of the system in CAESAR II. This model should incorporate large masses and structural K rates. Analyze and design using this data. **(See
Illustration)

7) Collect fee from owner at the end, and rest comfortably knowing that you did the best you could.

Some facts:
The unbalanced loads are applied on short lengths of pipe for a short time, conversely the long lengths have these unbalanced force applied longer. This means you need restraints on the longer runs.

Ironically everybody likes to clamp down the piping at the relief valve
and ignore the long runs!

Structural participation of even a few milliseconds load can be great or small and depends on the relative stiffnesses of the piping and the structure as well as large masses. An imposed load can be magnified much more the x2! I have had to resort to sping loaded sway struts to cut these enormous types of load down to size.

That's it, the questions you have to answer are the hardest. I have found on a critical relief system, when the owner has great concerns, that the best answers are readily paid for.

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Best Regards,

John C. Luf