Help with this formula for the Thermal Expansion of a pipe please

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SUMMARY

The discussion centers on the derivation of the formula for thermal expansion of pipes, specifically in relation to a loop configuration involving two vertical legs and standard 90° pipe elbows. The reference source from Corzan provides a "loop" diagram that illustrates the necessary dimensions and ratios, including a length ratio of 2L/5 and a leg-to-leg spacing ratio of L/5. A counterpoint is presented with a link to Engineers Edge, which offers an alternative perspective on pipe expansion calculations. Understanding these configurations is crucial for accurate thermal expansion assessments in piping systems.

PREREQUISITES
  • Understanding of thermal expansion principles in engineering
  • Familiarity with piping systems and configurations
  • Knowledge of standard pipe fittings, specifically 90° elbows
  • Ability to interpret engineering diagrams and specifications
NEXT STEPS
  • Review the Corzan reference for detailed loop configuration diagrams
  • Study the Engineers Edge calculator for alternative thermal expansion formulas
  • Explore the impact of different materials on thermal expansion in piping
  • Investigate best practices for designing thermal expansion loops in piping systems
USEFUL FOR

Mechanical engineers, piping designers, and anyone involved in the design and analysis of thermal expansion in piping systems will benefit from this discussion.

dirk_mec1
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I do not understand how this formula is derived:

1572634191689.png


Can somebody help me?

Source:

https://www.corzan.com/en-us/piping-systems/specification/thermal-expansion
 
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Note: Important information needed is missing from the above thread post.
It is necessary to go to the reference source and view its "loop" diagram consisting of two vertical legs' with a length ratio = 2L/5 of the calculated L requirement with two standard 90° pipe ells at the top connecting a horizontal pipe section with a leg to leg spacing ratio = L/5 requirement to understand what apparently results in the above formula.
As a result the above appears to be a formula based upon all of the above loop configuration requirements.
 
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