FieldEngineersKitEngineering Reference & ASME Code Basis
1. Core Formula & Variable Definitions
ASME BPVC Section VIII Division 1 (head geometry / volume screening) · API 650 (Welded Tanks for Oil Storage — level–capacity practice) · ISO 7507 (Petroleum and liquid petroleum products — tank calibration)
Vshell = π r2 L · Vtotal = Vshell + 2 Vhead
2:1 SE: Vhead = π/24 · Di3 · Hemi: π/6 · Di3 · F&D/Klöpper ≈ 0.084766 · Di3
Horizontal shell liquid: L · (r2 acos((r−h)/r) − (r−h) √(2rh−h2))
ASME VIII Div 1 head geometry · API 650 / ISO 7507 level–capacity screening
Inside diameter Di and shell straight length L. Head volumes follow ASME VIII Div 1 screening (flat = 0; 2:1 SE; hemi; torispherical Klöpper / ASME F&D coefficient 0.084766). Horizontal partial fill uses circular segment on the shell plus head liquid ≈ 2·V_head·(segment area / πr²). Vertical fill stacks bottom-head cap, cylindrical shell, and top-head cap. Volumes reported in m³ / L / US gal / oil bbl. Screening only — no internals.
- Di (Inside Diameter) — Vessel inside diameter used for shell and head geometry (mm / in).
- L (Shell Straight Length) — Cylindrical shell length between head tangent lines (mm / in).
- h (Liquid Level) — Liquid height from vessel bottom. Horizontal: across diameter. Vertical: through bottom head + shell + top head.
- V_head (One-Head Full Volume) — ASME VIII Div 1 screening volume for one head (flat / 2:1 SE / hemi / F&D).
- V_liq (Partial Liquid Volume) — Screening liquid volume at level h (m³, L, US gal, bbl).
- Fill % (Percent of Total Capacity) — 100 · V_liq / V_total with V_total = V_shell + 2·V_head.
2. Allowances, Tolerances & Standards
Field screening geometry for level–capacity. Confirm stamped head drawings and certified strapping for design or custody transfer.
Common ASME F&D / Klöpper approximation with R=Di and r_knuckle=0.06·Di; head depth ≈ 0.169·Di.
Non-flat head liquid ≈ 2·V_head·f with f = circular segment area / (π r²) at the same liquid height.
Oil barrel based on 42 US gal. Liter = 1000 L/m³.
Quick Reference Lookup Table
| Orientation | Heads | Di | L | h | V_liq | Fill % | V_total |
|---|---|---|---|---|---|---|---|
| Horizontal | 2:1 SE | 2000 mm | 6000 mm | 1200 mm | 13.12 m³ (3466 gal) | 62.6 | 20.94 m³ |
| Vertical | Hemi | 3000 mm | 8000 mm | 5000 mm | 38.88 m³ (10270 gal) | 45.8 | 84.82 m³ |
| Horizontal | Flat | 96 in | 240 in | 48 in | 3760 US gal (14.23 m³) | 50.0 | 28.47 m³ |
| Vertical | 2:1 SE | 120 in | 360 in | 200 in | 9302 US gal (35.21 m³) | 47.5 | 74.13 m³ |
| Horizontal | Hemi | 1500 mm | 4000 mm | 750 mm | 5.30 m³ | 50.0 | 10.60 m³ |
| Vertical | F&D / Klöpper | 2500 mm | 5000 mm | 3000 mm | 13.98 m³ | 51.4 | 27.19 m³ |
| Horizontal | 2:1 SE | 72 in | 180 in | 36 in | 1798 US gal | 50.0 | 13.61 m³ |
| Vertical | Flat | 96 in | 300 in | 120 in | 3760 US gal | 40.0 | 35.58 m³ |
All rows are engine-computed from the FEK tank-vessel-volume solver (ASME VIII Div 1 head coefficients + circular-segment / vertical-cap screening). Not a certified API 650 / ISO 7507 strapping table — no internals.
3. Material & Code Limitations
Mass = V_liq · ρ. Presets are screening densities at ambient — override with custom ρ for process fluids.
| Material Group | Temperature Range | Allowable Stress / Limit | Engineering Notes |
|---|---|---|---|
| Water | — | 998 kg/m³ | Default ambient water density for mass screening. |
| Diesel / crude oil | — | 850 / 870 kg/m³ | Typical ambient screening densities — confirm assay. |
| H₂SO₄ (concentrated) | — | 1830 kg/m³ | Concentrated sulfuric acid screening density. |
4. Step-by-Step Worked Example
Field VerificationShowHide
Worked Example — Horizontal 2:1 SE · Di 2000 mm · L 6000 mm · h 1200 mm
Default metric duty: horizontal vessel, 2:1 ellipsoidal heads, water at ambient density.
Compute shell and head capacities
Partial fill on horizontal shell and heads
Fill percent of total capacity
Dipstick screening chart
5. Frequently Asked Questions & Technical References
ShowHide
ASME VIII Div 1 screening: flat = 0; 2:1 ellipsoidal = π/24·Di³; hemispherical = π/6·Di³; torispherical Klöpper / ASME F&D ≈ 0.084766·Di³ (R=Di, r_k=0.06·Di). Head depth: 2:1 SE = 0.25·Di; hemi = 0.5·Di; F&D ≈ 0.169·Di.
No. It is a geometric screening chart with no internals. Use API 650 / ISO 7507 certified strapping after fabrication for custody transfer.
Shell liquid uses the circular segment formula. Non-flat heads use 2·V_head·f where f is the filled-area fraction of the circular cross-section at height h.
Liquid stacks from the bottom head (cap formula) through the cylindrical shell, then into the top head. Level h is measured from the vessel bottom; max height is 2·headDepth + L.
Yes. V_total = V_shell + 2·V_head for both orientations. Fill % is liquid volume divided by that total capacity — so vertical hemi tanks often show lower fill % than shell-only rules of thumb.
Primary display follows metric/imperial preference (m³ or US gal), with liters and oil barrels (42 US gal) in badges. Conversion: 1 m³ = 1000 L = 264.172052 US gal = 6.28981 bbl.