Design Formulas & Engineering Reference
| Quantity | Equation | Reference |
|---|---|---|
| Vessel volume | V = π/4·D²·L + 2·Vhead | Geometry |
| Shell thickness | t = P·R / (S·E − 0.6P) | UG-27 |
| 2:1 head thickness | t = P·D / (2S·E − 0.2P) | UG-32(d) |
| Torispherical head | t = 0.885·P·L / (S·E − 0.1P) | UG-32(e) |
| Hemispherical head | t = P·R / (2S·E − 0.2P) | UG-32(f) |
| Hydrotest pressure | Pt = 1.3·MAWP·(Stest/Sdesign) | UG-99(b) |
| Fire heat input | Q = 43 200·Awet0.82 [W] | API 521 |
| Vapor pressure | log₁₀P = A − B/(T + C) | Antoine (NIST) |
P = design pressure, R/D = inside radius/diameter in the corroded condition, S = allowable stress at design temperature (ASME II-D), E = joint efficiency (UW-12), L = crown radius, Awet = fire-wetted surface. The corrosion allowance is added to each required thickness before rounding up to the next standard plate.
Why the design pressure follows the vapor pressure
An LPG vessel has no pump holding its pressure — the liquid itself does. At any temperature the liquid boils until the vapor above it reaches the mixture's vapor pressure. So the design pressure must cover the vapor pressure at the hottest credible day, not at the filling temperature. Propane at 50 °C sits near 17 barg; that single fact sizes every propane bullet in a tropical climate.
Why the filling ratio exists
LPG liquid expands roughly 15× more than water per degree. A vessel filled liquid-full on a cool morning becomes hydraulically locked as the sun heats it, and pressure then rises almost vertically — far past any relief valve's ability to help. The ~85% limit guarantees a vapor cushion that lets pressure follow the (much gentler) vapor-pressure curve instead.
Why hydrotest is higher than design
The 1.3× factor proves the vessel with margin, catching gross material and welding defects at a controlled overstress while the vessel is full of incompressible water — which stores almost no energy, so even a failure during test is a leak, not an explosion. Testing with gas at the same pressure would be lethal.
Why the head is a different thickness
A doubly-curved head carries pressure in two directions, so a hemisphere needs only half the shell's thickness. Shallower heads (2:1 ellipsoidal, torispherical) are cheaper to form but structurally less efficient — the torispherical knuckle in particular concentrates bending, which is why its formula carries the 0.885 factor and why it gets uneconomical at LPG pressures.
Why L/D matters
For a fixed volume, a fatter vessel has less shell area but its larger diameter demands thicker plate (t ∝ D); a slimmer one uses thinner plate but more of it, more welds, and a longer foundation. The economic optimum for pressure storage usually lands at L/D of 3–5. Outside that range you are paying either for plate thickness or for real estate.
- Preliminary design only — a code vessel also needs nozzle reinforcement (UG-37), external pressure, saddle stress (Zick analysis), wind/seismic, and fabrication drawings.
- Liquid densities at 15 °C; mixture density by mass-weighted specific volume; vapor pressure by Raoult blend of NIST Antoine correlations.
- Weights on nominal plate with +6% head forming and +10% attachments allowance.
- Hydrotest stress ratio taken as 1.0 — correct it when test and design temperatures differ significantly.
- Fire relief per API 521 with prompt firefighting and drainage; use the PSV calculator to size the orifice.
- Nozzle schedule is a rule-of-thumb band by capacity — confirm against actual process flowrates.
Vapor pressure at the maximum design temperature governs. At 50 °C propane sits near 17 barg, so 17.5–18 barg is the common design pressure. Check your local code's required design temperature.
At 17+ barg a torispherical head becomes very thick (0.885 factor), while a hemisphere is thin but expensive to form. The 2:1 ellipsoidal is the economic middle: reasonable thickness, one-piece pressing, shallow enough to keep overall length down.
Mounding or burial removes the fire case (lower relief load) and improves safety distances, but adds cathodic protection and inspection burden. This calculator covers the above-ground pressure design; the mechanical sizing is the same for mounded vessels.
No. It produces a complete, traceable preliminary design — geometry, thickness, loads, relief basis — that a vessel fabricator's code calculation then confirms. Nozzle reinforcement, saddle stresses, and seismic remain to be checked.