How Often Should Steps Be Sized to Eliminate Expansion Loops in Sloped Pipework?

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The discussion centers on determining the appropriate sizing and frequency of steps in sloped pipework to eliminate the need for expansion loops. The user has found formulas for sizing loops but is confused about how to size steps effectively to negate expansion loops. They mention that a 90-degree step down a hill is less effective than a loop and express concern over the conservative nature of the Spirax Sarco formulas. The operating temperature range is from 15 to 300 degrees Celsius, with significant expansion noted. The user seeks more reliable references for pipework design and is grappling with the size of the loops calculated, which seem excessively large.
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I am working on a system that requires expansion loops. I have located formulae on engineering toolbox.com and the spirax sarco website for determining the size of the loops required. So a 2m wide loop needs to be 4m tall, and I need one every 17m, roughly.

What I struggling to get my head around is if I am stepping my pipe down a hill, what size and how often do I need a step to negate the requirement for expansion loops altogether. For some reason my mind can't piece this together. Does anybody have a view on the relationship?

My other question is, my aforementioned references, whilst useful, are hardly rock solid. Does anybody have a suggestion for references with a more defined foundation?

All ideas appreciated.
 
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The formulas in Spirax Sarco are useful but very conservative.

A 90 deg step down a hill will not be as affective as a loop of course.

I am fortunate I have access to the Caesar pipe stress software for these things.

What is your operating temperature.
 
From 15 to ca. 300 degC. I think there is about 30 com expansion in 50 m. The question is how many loops of what size do I need.

I keep getting a 4m high by 2m wide loop (twice), which intuitively seems massive to me, or a number of smaller ones.
 
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