PSA 1.3 — Stresses in a Pressurised Pipe: Hoop, Longitudinal, Radial
Cut a pressurised pipe three ways and balance forces on each cut:
(P = internal gauge pressure, D = outside diameter per code practice, t = wall thickness.)
Derivations in one breath — hoop: pressure on a diametral plane P·D·L is held by two wall strips 2·t·L → σ_H = PD/2t. Longitudinal: end thrust P·(πD²/4) carried by wall annulus π·D·t → σ_L = PD/4t. The factor 2 between them is geometry, not material.
See it live: every arrow animated on the half-pipe, with a live Barlow calculator — artifacts/psa-pressure-stress-3d.html
Barlow assumes uniform stress across the wall — good for D/t…
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