Mean diameter
mm
Dm = Do − t, used by the thin-membrane model.
Fluid mechanics · Piping and pressure
Thin-wall pipe stresses under pressure
Estimate membrane stresses caused by internal pressure and compare their magnitude with an allowable stress.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
03
MetricResults
Circumferential stress
MPa
Also called hoop stress; it is usually the largest membrane stress.
Longitudinal stress
MPa
Axial membrane stress for a pipe with closed ends.
von Mises equivalent stress
MPa
Plane-stress state σθ–σz without shear.
Utilization
%
Ratio σVM/S.
Dm/t ratio
—
Geometric thinness indicator; a larger value better supports the thin-wall assumption.
View calculation detailsFormulas, SI conversion, numerical substitution and resultsOpen ↓
Calculation note
Full calculation details
Adopted range: ri/t > 10, with ri = Do/2 − t (inner radius). This limit is a conservative choice for the membrane model, not a code-compliance check. For a calculated thickness, both the theoretical thickness and the thickness including allowance are checked. Straight circular pipe with closed ends. Uniform positive internal gauge pressure. Wall sufficiently thin to neglect through-thickness stress variation. No local corrosion, ovality, weld, branch, bending, fatigue, shock, temperature or external pressure. This is an educational magnitude check, not a piping-code calculation.
01Formulas and symbols
Formulas used
Dm
Dm = Do − tMean wall diameterσθ
σθ = p·Dm/(2t)Circumferential membrane stressσz
σz = p·Dm/(4t)Longitudinal stress in a closed pipeσVM
σVM = √(σθ² − σθσz + σz²)Equivalent plane stress02Assumptions and limits
Scope of validity
- Straight circular pipe with closed ends.
- Uniform positive internal gauge pressure.
- Wall sufficiently thin to neglect through-thickness stress variation.
- No local corrosion, ovality, weld, branch, bending, fatigue, shock, temperature or external pressure.
- This is an educational magnitude check, not a piping-code calculation.
03Validation example
Reference numerical case
- p = 10 bar, Do = 114.3 mm, t = 4 mm and S = 120 MPa.
- Dm = 110.3 mm.
- σθ = 13.7875 MPa and σz = 6.89375 MPa.
- σVM = 11.940 MPa and utilization = 9.9503%.