Thin-Wall Vessel Max Allowable Working Pressure
The inverse of the hoop-stress-thin-wall tile: the maximum allowable working pressure of a thin-wall cylinder from its wall, diameter, and allowable stress, P_max = 2 t S_allow/D (hoop-governed; the longitudinal limit is double). A 12 in vessel with a 0.25 in wall at 15,000 psi allowable holds 625 psi. To size the wall for a known design pressure instead, rearrange to t_min = P D/(2 S_allow). Valid for D/t >= 20. Not a substitute for the ASME BPVC or the engineer of record.
Formula and source
P_max = 2 t S_allow / D (hoop-governed); P_max_long = 4 t S_allow / D = double; the inverse of sigma_h = P D / (2 t).
The thin-wall pressure-vessel membrane-stress relation (Barlow / mechanics of materials) solved for the pressure, by name.
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