Thin-Wall Vessel Max Allowable Working Pressure
The maximum allowable working pressure of a thin-wall cylinder from its wall, diameter, and allowable stress.
Example
You enter
- Wall thickness t (in) 0.25
- Diameter D (in, mean/inner) 12
- Allowable stress S (psi) 15000
You get
- Max allowable pressure (hoop-governed) 625 psi
- Longitudinal-limited pressure 1,250 psi (double the hoop; hoop governs)
Checked against published worked examples from: Pytel & Singer (via MATHalino).
Details, formula, and sources
ScopeP_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 or tableP_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).
Source and editionThe thin-wall pressure-vessel membrane-stress relation (Barlow / mechanics of materials) solved for the pressure, by name.
Free accessThe thin-wall hoop stress formula (Barlow's) is published free in any mechanics-of-materials reference. The ASME BPVC and the engineer of record govern.
What governsEstimate. AHJ and licensed professional govern.
API field namest_in, D_in, S_allow, p_max_psi, p_max_long_psi
- Membrane stress inverse P_max = 2 t S_allow / D from sigma_h = P D/(2 t); the longitudinal limit is double, so the hoop governsthin-wall / Barlow
- Thin-wall validity valid for D/t >= 20; below that use a Lame thick-wall checkmechanics of materials
- Not a code check no external pressure, discontinuity/nozzle stress, joint efficiency, or corrosion allowancescope of this tile