Vessel Weight⚠ unverified
Mechanical / Pressure Vessels · Compute the approximate wall weight of a cylindrical pressure vessel
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| P | P | Pa | 1.0 | Internal pressure |
| r | r | m | 1.0 | Cylinder radius |
| L | L | m | 1.0 | Cylinder length |
| rho | ρ | kg/m**3 | 1.0 | Material density |
| S | S | Pa | 1.0 | Allowable stress of the material |
| SF | SF | — | 1.0 | Safety factor applied to the allowable stress, dimensionless. Default is 1.0 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | t | kg | Approximate vessel wall mass, in kilograms (kg). Returns 0.0 for the thickness term when ``S`` is not positive |
The science & history
Understanding the Parameters
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Thickness $t = Pr/(S/SF)$ — the pressure-required wall (a simplified hoop-stress sizing without the $0.6P$ correction of Required Thickness Thin). Higher pressure or a lower allowable → thicker wall → heavier vessel.
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Shell surface area $2\pi r L$ — the lateral area of the cylinder; multiplied by thickness it gives the metal volume, and by density the mass.
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Density $\rho$ — carbon steel $\approx 7850\ \text{kg/m}^3$; the direct multiplier to mass. Lighter alloys reduce weight but usually cost more per kg.
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Approximate — this counts only the cylindrical shell: it omits the heads, nozzles, flanges, supports, and any corrosion allowance, all of which add real weight. It is a first-order estimate for cost and handling, not a fabrication weight.
Derivation (Approaching a Proof)
Two steps. First, size the wall for pressure using the (simplified) hoop-stress relation $\sigma_\theta = Pr/t$ with the effective allowable $S/SF$:
$$\frac{P r}{t} = \frac{S}{SF} \;\Longrightarrow\; t = \frac{P r}{S/SF}.$$
Second, compute the shell's metal volume as its lateral surface area times thickness, and multiply by density for mass. For a thin wall the lateral area is $2\pi r L$, so the material volume is $2\pi r L\,t$ and
$$m = \rho\,(2\pi r L)\,t.$$
Substituting $t$ gives $m$ directly in terms of the inputs. The registry stops the displayed formula at the thickness step, so the equation box shows $t$ while the returned value is $m$.
Dimensional check. $m = \rho\,(2\pi r L)\,t = \dfrac{\text{kg}}{\text{m}^3}\cdot\text{m}\cdot\text{m}\cdot \text{m} = \text{kg}$ — a mass, as the output label states.
History and Development
Estimating vessel weight from the pressure-required thickness is a standard early-design step in process and plant engineering, where weight drives cost (fabricated steel is priced largely by mass) and dictates crane, transport, and foundation requirements. Detailed estimates add heads, nozzles, flanges, internals, and supports; rules of thumb (e.g. a shell-plus-heads factor) bridge this first-order shell mass to a full fabricated weight.
Related Concepts: Vessel Volume Cylinder, Required Thickness Thin, Thin-Wall Hoop Stress, Pressure Vessel Design, Specific Strength
Notes: Output is the shell mass in kg ($m = \rho\,2\pi r L\,t$) — registry mislabels the symbol $t$ and shows only the thickness step. Cylindrical shell only (no heads/nozzles/flanges/supports/corrosion allowance). Thickness form here omits the $0.6P$ correction of Required Thickness Thin.