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The Barlow formula is a simplification of Lame's formula for thin walled pipes/ cylinders. The book by AP Moser (Buried Pipe Design) gives the derivation and arrives at S = PD/2t where D is infact the average diameter. This makes sense if you consider that there is a stress profile across the pipe wall with highest stress at the inside edge. So the average stress occurs in the material at the centre (ie. Do - t). The above book has a couple of good sketches illustrating this. Outer diameter is however quoted in the Barlow equation in some contexts - for example in ASME 31.8. This is apparently a simplification (infact nominal outside diameter is used which is actually a bit smaller than the real outer diameter). If using the formula to calculate wall thickness the answer will be slightly conservative but then you will generally look up a standard wall thickness (eg. from the table in ANSI B36.10) so you will likely arrive at the same answer anyway.

Q: Why does the Barlow formula use the outside diameter when the pressure relates to the inside diameter?

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