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Pressure Vessel Quick Sizing

Estimate thin-wall stresses and required thickness for cylindrical or spherical pressure vessels. Built for fast sizing with clear limits on when to switch to thick-wall methods.

Tool Purpose & README

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Inputs

Expert Mode Show all parameters
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Safety Factor ? 2.0
1.0 (None) 4.0 (Conservative)

Advanced Inputs

Joint Efficiency E ? 1.00
0.70 (Low) 1.00 (Seamless)
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Key Results

Enter inputs and press Calculate to see results.

Required Thickness Derivation
1. Thin-wall thickness equation
$$ t = \frac{P r}{\sigma_{allow,eff}} + c $$
2. Substituted Values
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Hoop or Membrane Stress Derivation
1. Membrane stress equation
$$ \sigma_h = \frac{P r}{t} $$
2. Substituted Values
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Longitudinal Stress Derivation
1. Longitudinal stress equation
$$ \sigma_l = \frac{P r}{2 t} $$
2. Substituted Values
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Utilization Derivation
1. Von Mises stress
$$ \sigma_{vm} = \sqrt{\sigma_h^2 + \sigma_l^2 - \sigma_h \sigma_l} $$
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2. Utilization
$$ U = \frac{\sigma_{vm}}{\sigma_{allow,eff}} $$
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Contents
  1. Overview
  2. Key Equations
  3. Using Results
  4. Limitations
  5. References

1. Overview

This tool provides fast, thin-wall sizing for cylindrical and spherical pressure vessels. It reports membrane stresses, required thickness, and a thin-wall validity check. Use it for quick estimates and education, not code-compliant design.

Thin-wall reminder: The equations are valid when t/r <= 0.1. If the thin-wall check flags borderline or invalid results, switch to thick-wall methods.

2. Key Equations

Cylindrical Membrane Stresses $$ \sigma_h = \frac{P r}{t}, \quad \sigma_l = \frac{P r}{2 t} $$
  • P: internal pressure (MPa)
  • r: mean radius (mm)
  • t: wall thickness (mm)
  • sigma_h: hoop stress (MPa)
  • sigma_l: longitudinal stress (MPa)
Spherical Membrane Stress $$ \sigma_s = \frac{P r}{2 t} $$
  • sigma_s: membrane stress (MPa)
Required Thickness and Utilization $$ t_{req} = \frac{P r}{\sigma_{allow,eff}} + c, \quad U = \frac{\sigma_{vm}}{\sigma_{allow,eff}} $$
  • sigma_allow,eff: allowable with efficiency and safety factor (MPa)
  • c: corrosion allowance (mm)
  • sigma_vm: von Mises stress (MPa)
  • U: utilization ratio (dimensionless)

3. Interpreting Results

What to Look For

Utilization <= 1.0: Stress is below the effective allowable.
Thin-wall borderline: t/r > 0.1 suggests thicker walls may need Lame formulas.
Utilization > 1.0: Increase thickness or allowable stress.

4. Limitations

  • Thin-wall membrane theory only (t/r <= 0.1)
  • No external pressure, thermal gradients, or local discontinuities
  • Assumes closed ends for cylinders and uniform internal pressure
  • Not a code-compliant ASME Section VIII calculation

5. References

  • Shigley's Mechanical Engineering Design, 10th ed.
  • Roark's Formulas for Stress and Strain, 7th ed.
  • ASME Section VIII (code-based sizing - separate tool)