Pressure Vessel Wall Thickness (Thin Cylinder)
Pressure Vessel Wall Thickness (Thin Cylinder)
Sizing a pressure vessel shell is fundamentally a rearrangement of the thin-wall hoop stress formula to solve for the minimum wall thickness that keeps stress within the material's allowable limit. Because most pressure vessel shells are fabricated from rolled plate joined by welds, the calculation also has to account for the fact that a weld seam is typically weaker than the surrounding parent plate, through a joint efficiency factor.Pressure vessel design is one of the more heavily code-regulated areas of mechanical engineering (ASME Section VIII, for instance) precisely because an under-designed vessel wall stores a large amount of energy that releases catastrophically if the shell ruptures — the joint efficiency factor exists specifically because uninspected or lower-quality welds have historically been implicated in vessel failures, so it directly rewards better weld inspection with a thinner allowable wall.
The minimum required wall thickness is t_req = p_i·d_c/(2·S_allow·E_j), the rearranged thin-wall hoop stress formula solved for thickness, including the joint efficiency factor. where p_i is the internal design pressure, d_c is the vessel diameter, S_allow is the allowable stress of the shell material, E_j is the weld joint efficiency factor, and t_req is the resulting minimum required wall thickness.
Inputs
p_i := 1.5 MPa=1.5 MPa
d_c := 800 mm=800 mm
S_allow := 140 MPa=140 MPa
E_j := 0.85=0.85
Rearranging the hoop stress formula to solve for thickness, and dividing the allowable stress by the joint efficiency factor, gives the minimum wall thickness needed so the weld seam — not just the parent plate — stays within its allowable stress.
t_req := p_i·d_c/(2·S_allow·E_j)=5.04 mm
Results
A required thickness of about 5 mm here would typically be rounded up to the next available standard plate thickness, and a corrosion allowance is usually added on top of this structural minimum for any vessel in service handling a corrosive or eroding medium. Notice that a lower joint efficiency (say, 0.70 for spot-radiographed welds instead of 0.85 for fully radiographed ones) directly increases the required thickness — this is why full radiographic weld inspection is often specified on higher-pressure vessels, since it can be more economical than the extra plate thickness a lower joint efficiency would demand. This thin-wall formula is valid only up to moderate diameter-to-thickness ratios; very thick or very high-pressure vessels need a full code-based (Lamé or ASME) thick-wall design instead.
Assumptions & limitations
- Thin-wall formula valid only for a sufficiently large diameter-to-thickness ratio; thick vessels need a different method.
- No corrosion allowance is included — this is the structural minimum thickness only.
- Joint efficiency reflects the specified level of weld inspection (e.g., full vs. spot radiography).
- Internal pressure only — external pressure (vacuum or buckling) design is a separate check.