Burst Pressure⚠ unverified
Mechanical / Pressure Vessels · Thin-wall burst pressure of a cylinder
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| r | r | m | 0.5 | Radius |
| t | t | m | 0.01 | Wall thickness |
| Sut | Sut | Pa | 400000000.0 | Ultimate strength |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| Pb | Pb | Pa | Burst pressure |
The science & history
Understanding the Parameters
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Ultimate strength $S_{ut}$ — the burst criterion uses ultimate (not yield) strength, since burst is a rupture, not first-yield, event.
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Thickness $t$ and radius $r$ — burst pressure scales with the $t/r$ ratio: thicker walls and smaller radii burst at higher pressure, exactly mirroring the hoop-stress dependence.
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Conservative estimate — this simple formula under-predicts the real burst pressure because it ignores strain hardening (the material strengthens as it stretches) and the thinning geometry. Real burst is typically higher; codes may use a flow stress (average of yield and ultimate) or empirical burst correlations for accuracy.
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Design use — compared against working pressure to set the burst safety factor; not a substitute for a proof/burst test on qualified designs.
Derivation (Approaching a Proof)
The hoop stress in a thin-walled cylinder is $\sigma_\theta = Pr/t$ (Thin-Wall Hoop Stress). Burst is modelled as the pressure at which this stress reaches the ultimate tensile strength:
$$\sigma_\theta = S_{ut} \;\Longrightarrow\; \frac{P_b\,r}{t} = S_{ut} \;\Longrightarrow\; P_b = \frac{S_{ut}\,t}{r}.$$
Because hoop stress (not longitudinal) governs, this is the correct failure mode — a longitudinal split. The model is first-order: it treats the material as perfectly plastic at $S_{ut}$ and the geometry as unchanging, both of which make it conservative relative to a real ductile burst.
Dimensional check. $P_b = \dfrac{S_{ut}\,t}{r} = \dfrac{\text{Pa}\cdot\text{m}}{\text{m}} = \text{Pa}$ — a pressure, as required.
History and Development
Burst-pressure estimation dates from the boiler era, when catastrophic explosions drove the demand for quantified safety margins and, ultimately, the ASME Boiler & Pressure Vessel Code (1914). The simple $S_{ut}\,t/r$ estimate is refined in modern practice by flow-stress and strain-hardening corrections (e.g. the Barlow and Faupel formulas) and by mandated hydrostatic burst testing, but it remains the quick back-of-envelope check that a design has adequate ultimate margin over its working pressure.
Related Concepts: Thin-Wall Hoop Stress, Required Thickness Thin, Hydrostatic Test Pressure, Factor Of Safety Ultimate, Pressure Vessel Design, Endurance Limit steel
Notes: Uses ultimate strength (rupture, not yield). Conservative — ignores strain hardening/geometry change (real burst higher). Hoop governs (longitudinal split). Compare to working pressure for the burst safety factor; not a substitute for a burst test.