Pressure Vessel Calculator & Simulator

by

🚀 Pressure Vessel Calculator & Simulator

PRESSURE VESSEL

Pressure Vessel Stress Calculator & Real-Time 2D Burst Simulator
VESSEL CORE ACTIVE

Simulation Control Variables

Tank Gas Pressure (0.0 to 10.0 MPa)
MPa
Inner Diameter (100 to 2000 mm)
mm
Vessel Plate Thickness (2 to 100 mm)
mm
Plate Yield Strength Limit (100 to 600 MPa)
MPa

Vessel Expansion Behavior & High-Pressure Burst Virtual Simulation

✅ Thin-walled Vessel Condition Satisfied (Thin-walled active)
Hoop Stress (σh): 0.0 MPa
Thickness-to-Diameter Ratio (t/D)
0.020
Axial-to-Hoop Stress Ratio
2 : 1
Current Wall Factor of Safety (F.S.)
2.45
Elastic Behavior State
Circumferential / Hoop Stress (σh) 0.0 MPa
Axial Stress (σl) 0.0 MPa
Maximum Shear Stress (τmax) 0.0 MPa

Thin-Walled Theory Stress Equations

σh = p × D / (2 × t)
σl = p × D / (4 × t)
Disclaimer: The calculation results of this simulator are provided for educational and reference purposes only. For actual product design or fabrication, please verify with the latest engineering standards and official design codes. The integrity of the calculated values is not guaranteed, and the developer and this blog assume no liability for any direct or indirect damages arising from their use.
💡 💡 Quick User Guide
  1. Select Vessel Type: Choose either a Cylindrical Vessel (commonly used for gas cylinders) or a Spherical Vessel (used for storage tanks) from the top tab.
  2. Input Vessel Dimensions and Pressure: Use the sliders to enter the inner diameter (D), wall thickness (t), and internal gas/liquid pressure (p).
  3. Adjust Material Limits: Configure the yield strength (Sy), which is the inherent strength limit of the pressure vessel material.
  4. Check Safety Assessment & High-Pressure Burst Simulation: Verify the vessel thickness condition (t/D < 0.1 for thin-walled theory limit) and observe the localized burst and high-pressure gas jet particle animation when the internal pressure exceeds the material strength limit.
📚 Explore Thin-Walled Pressure Vessel Engineering Theory & Formulas ▼

1. Prerequisites of a Thin-Walled Pressure Vessel

A vessel that stores high-pressure gas or liquid internally is called a pressure vessel. Among these, vessels where the wall thickness t is extremely thin compared to the inner radius r or inner diameter D are defined as thin-walled pressure vessels.

Generally, thin-walled theory can be safely applied when the ratio of wall thickness to inner diameter meets the following condition:

t / D ≤ 0.1  (or  t / r ≤ 0.1)

Under this condition, the stress distribution across the wall thickness is assumed to be highly uniform, allowing for precise calculation of the plane stress (normal stress) induced on the wall using simple algebraic equations.

2. Hoop Stress and Longitudinal Stress

When a vessel expands due to internal pressure, the primary stresses induced on the inner walls are as follows.

① Cylindrical Pressure Vessel:

  • Hoop Stress (σ_h): The stress acting circumferentially around the cylinder, trying to tear it apart. It directly acts on longitudinal welds.
    σ_h = (p × D) / (2 × t)  [MPa]
  • Longitudinal Stress (σ_l): The stress acting along the axial direction of the cylinder.
    σ_l = (p × D) / (4 × t)  [MPa]

σ_h is exactly twice as large as σ_l. Therefore, a cylindrical gas vessel will always fail by splitting open longitudinally (along its length) when it bursts.

② Spherical Pressure Vessel:

Due to perfect symmetry in all directions, all tangential stresses are identical to the longitudinal stress formula:

σ_h = σ_l = (p × D) / (4 × t)  [MPa]

Consequently, spherical vessels can be designed with half the wall thickness of a cylindrical vessel under the same diameter and pressure conditions while maintaining the same safety margin, making it a highly economical shape for large, high-pressure storage systems.

3. Structural Failure and Max Shear Stress Calculation

The maximum shear stress (τ_max), which causes out-of-plane plastic flow via a 45-degree slip within the pressure vessel plate, is defined through Mohr's circle mechanics as follows:

Maximum Shear Stress for a Cylindrical Vessel:

τ_max = σ_h / 2 = (p × D) / (4 × t)

When the stress reaches the allowable stress or yield strength (Sy), localized areas of the vessel shell wall will reach their tensile fracture limit, resulting in a burst. Therefore, strict valve protection and non-destructive testing/processing control must be maintained.

Leave a Comment