Pressure reference and component elevation diagram

Section 01

What the calculator actually solves

The engine evaluates a schedule of pressure-boundary components. It does not apply one diameter and one formula to an abstract vessel.

A calculation begins with the selected route, pressure and temperature basis, fabrication coefficient, material properties and a component's corroded-condition geometry. The engine establishes the thickness remaining after deductions, runs the active internal-pressure, minimum-thickness and external-pressure procedures, and then inverts the route to rate each component. The lowest component rating governs vessel MAWP.

Pressure-thickness calculation flow

Route + pressure + temperature + fabrication + material + geometry
Effective pressure-resisting thickness
Internal / minimum / external checks
Component nominal requirement + utilization + rating
Vessel MAWP / MAP + hydrotest basis + report

Up to 12 components can be placed in one schedule. For each, the calculator reports the pressure-resisting requirement, route-specific minimum, corrosion allowance, mill undertolerance, required nominal thickness, available pressure thickness, utilization, component MAWP, MAP new/cold and, where entered, external-pressure results. The vessel summary adds governing MAWP/MAP and a sourced hydrotest basis. Calculations are canonical MPa, mm and °C; SI and US-customary display changes do not change the physical model. US pressure is displayed in psi, while stress uses the shared stress formatting.

Section 02

Five construction routes, five calculation contexts

Choose the route from the contract, jurisdiction and design basis. Route selection changes equations, applicability limits, material handling, external-pressure method and hydrotest logic—not merely the report label.

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Comparison of the five implemented pressure-vessel construction routes
Route	Source / edition	Jurisdiction cue	Internal pressure	External pressure	Material basis	Joint / examination	Hydrotest	Important qualification
ASME VIII-1	ASME BPVC Section VIII, Division 1 (2025)	United States flag card; project adoption must be confirmed	UG-27, UG-32, Mandatory Appendix 1 and UG-34	UG-28/UG-33 with II-D Table G and supported CS/HA curves	Curated 2021 II-D subset or user-entered properties	Joint efficiency $E$ ; convenience preset or user value	UG-99: $P_{T} = 1.3 MAWP (S_{T} / S_{D})$	VIII-1 source is 2025; curated II-D data are from the 2021 metric edition.
ASME VIII-2	ASME BPVC Section VIII, Division 2 (2025)	United States flag card; project adoption must be confirmed	Part 4.3 design by rule and 4.6.2 flat heads	Part 4.4 buckling with Annex 3-D tangent modulus	User-entered design/test and elastic-plastic properties	Entered joint efficiency $E$	Tables 4.1.3/8.2.1: $P_{T} = 1.25 MAWP (S_{T} / S_{D})$	Its equations and applicability checks are a distinct route, not VIII-1 with a changed safety factor.
AS 1210	AS 1210 (2010)	Australian flag card; legal adoption remains project-specific	§§3.7, 3.10, 3.12 and 3.15	§§3.9, 3.11 and 3.13	User-entered design/test strength and elastic properties	Entered joint efficiency $η$ plus fabrication/class metadata	§5.10 ordinary or Class 1H/2H basis	Classification, materials, fabrication, inspection and registration are not completed by the calculator.
CSA B51	CSA B51 (2014) jurisdiction wrapper	Canadian flag card; provincial/territorial adoption must be checked	Delegates pressure-thickness equations to ASME VIII-1	Delegates the implemented external-pressure route to VIII-1	Curated 2021 II-D subset or user-entered properties	ASME-style entered joint efficiency $E$	Delegated UG-99 basis	Selection does not perform design registration or satisfy local authority requirements.
EN 13445-3	EN 13445-3:2014, Issue 4 (2017)	European flag card; applicable conformity route must be established	§§7.4, 7.5, 7.6 and user-derived §10 flat-end factor	Clause 8 route with shape-deviation inputs	Nominal stress derived from user-entered class-specific properties	Testing group and joint coefficient $z$ under §5.6	PED Annex I 7.4: greater implemented pressure floor	PED essential requirements do not by themselves complete conformity assessment.

ASME BPVC Section VIII, Division 1 (2025)

UG-16 supplies minimum-thickness and undertolerance context; UG-27 covers cylindrical and spherical shells; UG-32 covers formed heads and conical sections; Mandatory Appendix 1 supplies the implemented thick-shell and nonstandard/thin formed-head branches; and UG-34 covers circular unstayed flat heads using the entered factor. UW-12 is the examination/joint-efficiency basis and UG-99 supplies the hydrostatic-test expression.

External cylinders and cones use UG-28 plus Section II-D Subpart 3 Table G and a supported material curve. Formed heads use UG-33. The implementation stores normative tabulated values and uses guarded interpolation; it does not digitize supplied chart images and does not extrapolate outside the stored domain. The VIII-1 source is 2025, but the curated Table 1A stresses and Table G/CS/HA data are from the 2021 metric II-D edition. An issued-design reviewer must verify that edition alignment.

ASME BPVC Section VIII, Division 2 (2025)

Part 4.3 provides its own design-by-rule internal-pressure equations for shells and formed heads; 4.6.2 covers the circular flat head. Part 4.4 supplies the external-pressure buckling route, with Annex 3-D tangent modulus behavior evaluated from the selected Section II-D external-pressure chart. Tables 4.1.3 and 8.2.1 support the implemented hydrotest pressure. Division 2 is not represented as Division 1 with a lower safety factor: its equations, geometry guards and external-pressure procedure are distinct.

AS 1210 (2010)

The module uses §3.4 minimum thickness; §3.7 internal cylindrical/spherical pressure; §3.9 external cylindrical and spherical pressure; §§3.10/3.11 conical internal and external pressure; §§3.12/3.13 formed ends; §3.15 flat ends; and §5.10 hydrotest logic. Fabrication inputs include manufacturing route, vessel class, lethal contents, steel Group F/G and an optional project minimum-thickness override. Those inputs do not complete all classification, material, fabrication, inspection or registration obligations.

CSA B51 (2014)

This is a Canadian jurisdiction wrapper, not an independent shell-formula family. It records CSA B51 context and delegates the implemented pressure-thickness procedures to ASME VIII-1. Provincial or territorial registration, adopted editions and local deviations remain with the engineer and authority having jurisdiction. Selecting the Canadian flag does not make a calculation registered or “CSA-certified.”

EN 13445-3:2014, Issue 4 (2017)

Clause 5.6 establishes the testing-group/joint-coefficient basis; Clause 6 derives nominal design stress from the selected material class and entered properties; §§7.4, 7.5 and 7.6 cover shells, dished ends and cones; Clause 8 is the external-pressure route; and Clause 10 supplies the basis for a user-derived flat-end factor. The implemented hydrostatic floor uses PED 2014/68/EU Annex I 7.4.

EN inputs expose non-austenitic, austenitic or cast class; tensile, yield/proof, test-temperature and elastic properties; rupture elongation; the Clause 6.3 alternative route; testing group; Poisson ratio; out-of-roundness; and maximum local radius where applicable. EN 13445 is not a Eurocode, and satisfying one PED pressure-test floor does not complete conformity assessment.

Section 03

Quick-start workflow for an engineering review

The reliable sequence is to establish the design basis first, model every pressure component second, and interpret numerical results only after scope and applicability messages are clean.

1
Confirm code, edition, jurisdiction and design basis
A familiar standard may not be the legally adopted route. Record the contractual edition and any jurisdictional qualification before entering geometry.
2
Enter project metadata and design-basis notes
Missing project, client, revision or basis notes make an otherwise correct calculation difficult to identify and review.
3
Enter pressure, heads and temperatures
Separate internal design pressure, component static head, external differential, design/test temperature and test-fluid head. Combining the two head inputs applies elevation at the wrong calculation stage.
4
Establish fabrication and joint coefficient
A convenience preset with the wrong weld category or examination basis can overstate allowable membrane stress.
5
Establish material properties and provenance
Wrong product form, thickness range, heat treatment, temperature or chart mapping can invalidate both strength and stability results.
6
Add every component that could govern
Omitting a thinner course, closure or reducer can overstate vessel MAWP because the engine can only rate components in the schedule.
7
Enter corroded-condition inside geometry
Using new geometry while also deducting corrosion allowance mixes reference conditions and can bias the result.
8
Enter corrosion allowance and mill undertolerance
Applying either deduction twice, or comparing a pressure thickness directly with nominal stock, distorts the schedule.
9
Enter external-pressure length and shape data
A guessed support spacing or idealized circularity can make a buckling capacity look more favorable than the real shell.
10
Resolve validation, indeterminate and warning states
A numerical-looking field is not defensible when a required property, chart range or geometry condition is invalid.
11
Review schedule, governing checks and ratings
Read required nominal, available thickness, utilization, MAWP/MAP and hydrotest together; no single headline value explains the design.
12
Open the complete report
All on-screen values are public and unblurred. Sign in only to generate/download the PDF or use the account project-saving workflow.

Section 04

Design-condition inputs: keep the pressure references separate

The calculator has two static-head inputs because design pressure and hydrotest pressure are evaluated at different stages and can have different fluids or reference elevations.

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Design-condition inputs and their implemented use
Input	Implemented use	Review question	Typical failure mode
Internal design pressure	Base pressure at the design reference point; local internal component pressure is this value plus entered design static head.	Is this design pressure, not normal operating pressure?	Using operating pressure understates thickness and overstates margin.
Static head at component	Added to internal design pressure for component thickness/rating. Subtracted from the lowest local component rating when vessel MAWP is returned to the reference point.	Does it match the component elevation and process-fluid density?	Omitting it understates local pressure at low components.
External pressure / vacuum	A positive differential acting on the outside/convex surface; it activates the route-specific stability check.	Does the differential include the governing atmospheric or process case?	Entering it as negative internal pressure bypasses the stability procedure.
Design temperature	Selects or supports design stress and external-pressure properties.	Is it the governing metal-temperature basis?	Using operating temperature without excursions can overstate allowable properties.
Test temperature	Supports the automatic stress ratio and fixed-geometry new/cold rating.	Are test-temperature properties verified?	Assuming ambient values without checking brittle-fracture or material limits.
Hydrotest-fluid head	Added after the reference-point hydrotest basis to report local component test pressure.	Does it use test-fluid density and gauge/component elevation?	Reusing process static head when the test fluid or elevation differs.
Hydrotest stress ratio	Automatic uses the selected material; manual records the lowest test/design ratio for a mixed-material vessel.	Does the automatic single-material ratio represent the whole boundary?	Using a favorable component ratio instead of the lowest vessel ratio.
UG-16 service	Selects general, compressed-air/steam/water or unfired-steam-boiler minimum thickness for VIII-1/CSA.	Does the service and material subsection match the project?	Treating the selector as a substitute for service classification.

Keep design head and test-fluid head on separate pressure paths

Design condition

Internal design pressure at referenceLocal component design pressure

Hydrotest condition

Route test basis at referenceLocal component test pressure

Section 05

Fabrication and material inputs

Pressure equations only become meaningful after allowable stress, joint coefficient and stability properties have a traceable product-form and temperature basis.

Joint efficiency and testing group

For non-EN routes the UI offers seamless and full-examination presets at 1.00, spot examination at 0.85 and no radiography at 0.70, plus a user-entered value. The schema verifies numeric consistency with a selected preset. It does not verify that the actual weld category, joint detail, material and examination extent qualify for that value. “Full,” “spot” and “none” are conveniences for input, not automatic UW-12 or project eligibility decisions.

EN testing groups 1 and 2 use the implemented design joint coefficient 1.00, group 3 uses 0.85, and group 4 uses 0.70 with the implemented 0.9 design-stress adjustment. The implemented test-condition coefficient is 1.00. Confirm every group restriction from the licensed edition.

AS 1210 fabrication metadata

The AS 1210 minimum-thickness path uses manufacturing route, vessel class, lethal-contents selection, steel Group F/G and an optional project-specific minimum. The default zero override applies the implemented Table 3.4.3 route. An override replaces that calculated minimum, so its project basis belongs in the report notes.

Curated ASME material subset

Curated mode is exposed only for VIII-1 and CSA. It contains exactly eight IDs. Design and test allowable stresses are linearly interpolated within the stored temperature row and are not extrapolated beyond it. The guide intentionally does not reproduce the stored stress or external-pressure tables.

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Curated ASME VIII-1/CSA material IDs and external-pressure chart mapping
Material ID	Product description	Chart
SA-516-70	SA-516 Grade 70 plate	CS-2
SA-106-B	SA-106 Grade B seamless pipe	CS-2
SA-333-6	SA-333 Grade 6 seamless pipe	CS-2
SA-105	SA-105 carbon-steel forging	CS-2
SA-240-304	SA-240 Type 304 plate	HA-1
SA-240-304L	SA-240 Type 304L plate	HA-3
SA-240-316	SA-240 Type 316 plate	HA-2
SA-240-316L	SA-240 Type 316L plate	HA-4

A stored ID still does not establish product-form eligibility, thickness range, heat treatment, impact properties or alignment with the project's adopted edition. VIII-2, AS 1210 and non-curated inputs use engineer-entered allowable/design and test stress. External pressure can also require yield or proof strength, elastic modulus and a correct chart assignment.

EN material fields

EN nominal stress is calculated from non-austenitic, austenitic or cast class and the currently exposed tensile, yield/proof, design/test-temperature, rupture-elongation and alternative-route inputs. Austenitic logic uses 1% proof properties and rupture elongation; the non-austenitic alternative route carries additional applicability conditions. External pressure adds design elastic modulus, Poisson ratio, out-of-roundness and, for spherical/formed parts, maximum local radius ratio. User-entered properties need a traceable material standard, product form, thickness, heat treatment and temperature basis.

Section 06

Geometry guide for all seven component types

Select the idealized pressure-boundary shape that matches the component, then enter its inside dimensions in the corroded calculation condition.

cylinder

Cylindrical shell

Represents: A straight, circular shell course.
Active geometry: Corroded-condition inside diameter; selected nominal thickness; corrosion and mill deductions. Add unsupported axial length for external pressure.
Symbol key: $D_{i}$ = corroded inside diameter; $L$ = unsupported axial length for external pressure.
Do not over-interpret: Head depth, crown/knuckle radii, cone angle and flat-head factor do not enter the cylinder equations.
Typical mistake: Using outside diameter, a new-condition diameter, or an unqualified stiffener pitch.
Availability / boundary: Internal and external pressure are implemented. Openings, local loads, supports and ring qualification remain separate.

sphere

Spherical shell

Represents: A complete spherical pressure boundary using spherical membrane geometry.
Active geometry: Corroded-condition inside diameter and component thickness deductions; EN external checks also use shape measurements.
Symbol key: $D_{i}$ = corroded inside diameter.
Do not over-interpret: Unsupported cylinder length, head depth, cone angle and attachment factor do not define the sphere.
Typical mistake: Treating a formed head as a complete sphere or overlooking as-built shape deviation.
Availability / boundary: Internal membrane and route-specific external stability are implemented; penetrations and attachments are not.

hemisphere

Hemispherical head

Represents: A hemispherical closure evaluated with spherical membrane geometry.
Active geometry: Corroded inside diameter and thickness deductions; EN external shape measurements where applicable.
Symbol key: $D_{i}$ = corroded inside diameter; the dashed chord is the head-to-shell junction.
Do not over-interpret: Ellipsoidal depth and torispherical crown/knuckle radii are not used.
Typical mistake: Assuming the head-to-shell junction is checked because the head membrane is checked.
Availability / boundary: Internal and external head checks are implemented. The head-to-shell junction is a separate assessment.

ellipsoidal-head

Ellipsoidal head

Represents: An ellipsoidal formed end, including—but not limited to—the nominal 2:1 form.
Active geometry: Corroded inside diameter and actual inside depth. A 2:1 head has $h_{i} = D_{i} /4$ .
Symbol key: $D_{i}$ = corroded inside diameter; $h_{i}$ = actual corroded inside depth.
Do not over-interpret: Entered torispherical crown and knuckle radii are not used for this selected type.
Typical mistake: Leaving $h_{i} = D_{i} /4$ for a nonstandard head, or using outside depth without conversion.
Availability / boundary: Internal and external formed-head checks are implemented within route-specific ratio limits; junction checks remain separate.

torispherical-head

Torispherical head

Represents: A formed end defined by a spherical crown joined through a knuckle.
Active geometry: Corroded inside diameter, inside crown radius $R$ (denoted $L$ in the VIII-1 expression) and inside knuckle radius $r$ .
Symbol key: $D_{i}$ = corroded inside diameter; $R$ or $L$ = inside crown radius; $r$ = inside knuckle radius.
Do not over-interpret: Ellipsoidal inside depth is not substituted when this type is selected.
Typical mistake: Using nominal style names instead of measured/design radii, or confusing inside and outside radii.
Availability / boundary: Internal crown/knuckle and route-specific external checks are implemented within geometry limits; the shell junction is separate.

conical-shell

Conical shell or reducer

Represents: An unknuckled circular cone segment using its large-end inside diameter.
Active geometry: Corroded large-end inside diameter, half-apex angle and, for external pressure, axial length between support lines.
Symbol key: $D_{i}$ = corroded large-end inside diameter; $L$ = axial length; $α$ = half-apex angle.
Do not over-interpret: Head depth, head radii and flat-end factor do not enter the cone membrane route.
Typical mistake: Entering included angle instead of half-apex angle, or modelling a knuckled transition as an unknuckled cone.
Availability / boundary: Internal and external cone procedures are implemented. Cone-to-cylinder reinforcement and transition stresses are separate.

flat-head

Circular unstayed flat head

Represents: A circular flat closure whose attachment detail is represented by a user-derived factor.
Active geometry: Corroded inside diameter, selected thickness and route-specific attachment factor $C$ , $K$ or $C_{e q}$ .
Symbol key: $d$ = calculation diameter; $C$ , $K$ or $C_{e q}$ = route-specific attachment factor.
Do not over-interpret: Unsupported shell length, formed-head depth/radii and cone angle do not define the flat end.
Typical mistake: Guessing the factor from a connection name or expecting the software to infer the edge detail.
Availability / boundary: Pressure bending is implemented for all five routes. Attachment stresses, welds and junction adequacy remain separate.

Section 07

Thickness bookkeeping: nominal is not pressure thickness

Keep the stock callout, deductions, remaining pressure metal and code requirements in separate columns. Most review errors in this step are category errors, not arithmetic errors.

Thickness-deduction stack

16.000 mm
Selected nominal
−2.000 mm
12.5% mill deduction
−1.500 mm
Corrosion allowance
12.500 mm
Available pressure thickness

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Meaning of each thickness quantity in the implemented calculation
Quantity	Meaning	How it is used
Selected nominal thickness	The entered plate, pipe, shell or head callout before deductions.	Starting point for available thickness and the value compared with reported required nominal.
Mill-undertolerance deduction	Entered percentage of nominal thickness.	The deduction is $m t_{n o m}$ , where $m$ is the entered mill-undertolerance fraction.
Corrosion allowance	Uniform thickness loss reserved for the entered service basis.	Deducted from remaining thickness; it does not enlarge entered inside geometry.
Available pressure thickness	$t_{a v ai l} = t_{n o m} (1 - m) - c$ , where $c$ is corrosion allowance.	Capacity thickness used for utilization and inverse rating.
Required pressure thickness	Route/geometry internal-pressure result.	Compared with code minimum and external-pressure requirement.
Route-specific code minimum	UG-16 or AS 1210 minimum where implemented; zero for routes without a separate module minimum.	Can govern even when pressure demand is small.
Required external thickness	Thickness found by the route-specific stability procedure for the entered external differential.	Included only when external pressure is entered.
Required nominal thickness	The governing pressure/minimum/external value with corrosion and mill deductions reversed.	Direct comparison target for a nominal material callout.

Section 08

Internal pressure: membrane mechanics routed through code rules

Pressure produces membrane force in curved shells and bending in flat closures, but each construction route controls the equation form, coefficients, geometry range and transition to other behavior.

Let $P$ be local internal pressure after static head; $S$ or $f$ design stress; $E$ , $η$ or $z$ the applicable joint coefficient; $D_{i}$ corroded inside diameter; and $R = D_{i} /2$ inside radius. Geometry factors such as ellipsoidal $K$ , torispherical $M$ , crown radius $L$ , knuckle radius $r$ , cone half-angle $α$ and flat-end factor $C$ come from entered geometry or the active standard route.

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Notation used in the pressure-thickness equations
Symbol	Engineering meaning	Typical SI unit
$t or e$	Required pressure-resisting thickness before corrosion and mill deductions are restored.	$mm$
$P$	Local calculation pressure, including the applicable static head.	$MPa$
$D_{i}, d, R$	Corroded-condition inside geometry for the selected component and equation.	$mm$
$S or f$	Allowable or nominal design stress for the route, material and temperature.	$MPa$
$E, η, z$	Applicable weld-joint, examination or testing-group coefficient.	Dimensionless
$K, M, C, C_{e q}$	Geometry or attachment factors defined by the active route.	Dimensionless

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Representative ASME VIII-1 formulas emitted by the active implementation
Geometry	Implemented formula presentation	Source / qualification
Cylinder	$t = \frac{P R}{S E - 0.6 P}$	UG-27 circumferential branch; longitudinal stress and Mandatory Appendix 1 thick branch are also evaluated.
Sphere / hemisphere	$t = \frac{P R}{2 S E - 0.2 P}$	UG-27 or UG-32; Mandatory Appendix 1 exponential branch is used when its trigger is met.
Ellipsoidal head	$t = \frac{P D _{i} K}{2 S E - 0.2 P}$	UG-32 / Mandatory Appendix 1 with entered inside depth and ratio guards.
Torispherical head	$t = \frac{P L M}{2 S E - 0.2 P}$	UG-32 / Mandatory Appendix 1 with entered $L / r$ and thin-head checks.
Unknuckled cone	$t = \frac{P D _{i}}{2 cos α ( S E - 0.6 P )}$	UG-32; this module limits the unknuckled half-apex angle to $3 0^{\circ}$ .
Circular flat head	$t = d \frac{C P}{S E}$	UG-34 with user-selected attachment factor $C$ .

These are not universal “pressure vessel equations.” Division 2 uses exponential shell forms—for example $t = \frac{D _{i}}{2} [exp (\frac{P}{S E}) - 1]$ for a cylinder—and its formed-head implementation checks elastic-plastic buckling. AS 1210 uses its own rational forms, such as $t = \frac{P D _{i}}{2 f η - P}$ for a cylinder. EN 13445 uses $e = \frac{P D _{i}}{2 f z - P}$ for a cylinder and evaluates formed ends as the maximum of spherical-crown, plastic-knuckle and elastic-knuckle requirements. A cross-code result cannot be reduced to a single safety-factor comparison.

Section 09

External pressure and vacuum are stability problems

A shell can be strong in membrane tension and still buckle under a modest external differential. Unsupported length, diameter-to-thickness ratio, material stiffness and imperfections can dominate.

The unsupported length is spacing between already code-qualified lines of support. A thicker shell is not a substitute for defining those boundaries correctly, and a proposed ring does not become qualified because its pitch was entered. The calculator does not size ring area or inertia, check ring or shell attachment welds, or verify junction reinforcement.

External pressure acts inward between qualified lines of support

↓ positive external differential ↓

Qualified supportQualified support

← entered unsupported length L →

The diagram explains the input model only. The calculator uses support spacing; it does not size or qualify the support sections and attachments.

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Route-specific external-pressure implementation
Route	Implemented approach	Key user data	Guardrail
ASME VIII-1 / CSA	UG-28/UG-33 with Table G geometric Factor A and supported CS-2/HA material Factor B data; log interpolation and stored flat tails.	Unsupported length, elastic modulus, design temperature, yield/stress data and correct chart assignment.	No material-chart extrapolation; Table G shell domain is guarded.
ASME VIII-2	Part 4.4 elastic/inelastic buckling with Annex 3-D tangent modulus derived from the selected II-D chart.	Length, elastic modulus, yield strength, stress and external chart.	Distinct Division 2 geometry and $D_{o} / t$ guards apply.
AS 1210	§3.9 cylinder/sphere, §3.11 cone and §3.13 formed-end collapse procedures.	Length, design-temperature elastic modulus, yield strength, design strength and geometry.	Stiffener adequacy and combined-loading requirements remain separate.
EN 13445-3	Clause 8 cylinder/cone/spherical/formed-end collapse with imperfection reductions.	Length, elastic modulus, yield/proof, Poisson ratio, radius deviation and local-radius ratio where shown.	Sphere/formed-head radius deviation above the implemented limit becomes indeterminate.

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Qualitative external-pressure sensitivity
Change	General tendency	Engineering interpretation
Longer unsupported length	Generally lowers allowable external pressure.	Longer shells have more freedom to form an unstable buckling mode.
Larger diameter-to-thickness ratio	Generally lowers stability.	A slender pressure boundary is more sensitive to geometric instability.
Lower elastic stiffness	Can lower external-pressure capacity.	Elastic buckling resistance depends on material stiffness.
Greater shape imperfection	Can reduce allowable pressure.	EN explicitly uses entered deviations in applicable checks; fabrication tolerances still need verification.
Closer qualified support spacing	Can improve capacity.	Only when each support line and its attachment are independently adequate.

These are tendencies, not replacement equations. Route transitions, inelastic behavior and geometry limits can make response non-linear; defer to the active procedure and its warnings.

Section 10

MAWP, MAP new/cold and hydrotest are different questions

Required thickness asks whether a selected component carries a specified pressure. Rating inverts the active route and asks what pressure the available thickness can carry.

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Relationship between design pressure, ratings and test pressure
Quantity	Implemented meaning	Reference condition
Design pressure	Entered internal pressure used as the vessel reference-point demand.	Project design condition; component calculation adds design static head.
Component MAWP	Inverse solution of the active internal-pressure route using available pressure thickness.	Local component, design temperature, corroded thickness.
Vessel MAWP	Lowest finite component MAWP less entered design static head.	Returned to the design-pressure reference point.
MAP new/cold	Inverse route with corrosion allowance restored and test-temperature properties, while entered inside geometry remains fixed.	Conservative fixed-geometry convention for uniform internal corrosion.
Hydrotest basis	Route-specific minimum pressure at the pressure reference point.	Execution, metal temperature, venting, brittle fracture, temporary support and procedure approval are separate.
Hydrotest at component	Hydrotest basis plus entered test-fluid head.	Local component elevation during the test.

The quantities answer different engineering questions

Specified demand

Design pressure

Reference-point input; static head is added locally.

Inverse design rating

Component MAWP

Available corroded thickness at design temperature.

Vessel envelope

Vessel MAWP

Lowest local component rating, returned to the reference point.

Alternate condition

MAP new/cold

Corrosion restored, test properties, fixed entered geometry.

Test basis

Hydrotest pressure

Route-specific factor and stress ratio, then test-fluid head locally.

MAP is not calculated by merely scaling required thickness. Corrosion allowance is restored to the available thickness, test-temperature properties are used, and the entered inside geometry stays fixed. This is conservative for uniform internal corrosion. An exact as-built or true new-condition rating requires a separate run with measured/as-built geometry.

Implemented reference-point hydrotest bases

ρ_{S} P_{T, VIII - 1/CSA} P_{T, VIII - 2} P_{T, EN} P_{T, AS 1210, ordinary} = (\frac{S _{T}}{S _{D}})_{m i n} = 1.3 MAWP ρ_{S} = 1.25 MAWP ρ_{S} = max (1.25 MAWP ρ_{S}, 1.43 MAWP) = 1.43 P_{design} ρ_{S}

Here $ρ_{S}$ is the selected test-to-design stress ratio; manual mode is intended for the lowest applicable ratio across a mixed-material boundary. AS 1210 Classes 1H/2H use the greater implemented floor. Local hydrotest pressure then adds the entered test-fluid head.

Section 11

Read results in the order a reviewer needs them

Do not begin with a green badge. Confirm that the input model is valid, the schematic matches the schedule, and every warning is understood before using a utilization or rating.

01
Input validation message
Resolve the first schema or preset inconsistency; results pause when required inputs are invalid.
02
Vessel schematic
Confirm route label, component count and intended pressure-boundary arrangement. It is a simplified model, not a fabrication drawing.
03
Overall pressure-thickness status
PASS means all represented implemented checks pass; FAIL means at least one demand/utilization exceeds its limit; INDETERMINATE means a necessary source range, input or applicability condition prevents a defensible result.
04
Warnings and scope flags
Treat material, chart, geometry, support-line, edition and hydrotest notes as part of the result.
05
Component schedule
Review required nominal, available pressure thickness, utilization, component MAWP and any external-pressure values for every component.
06
Governing checks and equations
Open the internal, minimum, MAWP, hydrotest and external check cards; confirm demand, capacity, source and governing mode.
07
Assumptions
Verify corroded geometry, uniform corrosion, mill tolerance, no-opening and component-junction assumptions against the project.
08
Report
Use the complete report to preserve metadata, input schedule, results, equations, warnings, assumptions and sources.

Principal outputs mean exactly what their labels state: required nominal restores corrosion/tolerance deductions; available pressure thickness is metal remaining for pressure; utilization compares the governing required thickness with that available thickness; MAWP/MAP are inverse ratings; required external thickness and allowable external pressure come from the stability route; external utilization compares entered external differential with allowable pressure; and governing mode/component identify what controls.

Fast engineering sanity checks

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Reasonableness checks before detailed clause review
Observation	What it may indicate	What to inspect
A tall liquid-filled vessel has zero static head	The pressure reference elevation may have been overlooked.	Process density, liquid level, component elevation and pressure-reference point.
Vessel MAWP exceeds every local component rating	The comparison is being made at inconsistent pressure references.	Remember that local component ratings include the entered static head; vessel MAWP is returned to the reference point.
MAP new/cold is treated as the exact nameplate/new rating	The fixed-geometry convention has been overlooked.	Corrosion restoration, test-temperature properties and whether actual as-built inside geometry needs a separate run.
External capacity hardly changes after a large length change	The selected geometry may not use unsupported length, or a route plateau/other mode may control.	Component type, active external equation, governing mode, support-line definition and warnings.
Several unlike components produce identical results	Inputs may have been duplicated without updating type-specific geometry.	Component type, inside depth/radii, cone angle, attachment factor and nominal thickness.
Required pressure thickness passes but required nominal fails the selected stock	Corrosion, mill tolerance, code minimum or external pressure governs the material callout.	Required nominal breakdown and governing component mode.

Section 12

Three engine-backed worked examples

Every value below is generated during the page build by calling runAllChecks with the stated SI input object. The data are illustrative only and are not an approved vessel design.

Example 1 — ASME VIII-1 shell and 2:1 ellipsoidal head

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Example 1 complete active input basis
Group	Input	Value
Route	Construction route	ASME VIII-1 (2025)
Pressure	Internal / design static head	1.500 / 0.080 MPa
Test	Test-fluid head / design / test temperature	0.120 MPa / 200 °C / 20 °C
Material	Mode / ID / design-test allowable	Curated / SA-516-70 / 138.000–138.000 MPa
Material	Yield (design/test) / E (design/test)	260/260 MPa / 190,000/200,000 MPa
Fabrication	Joint basis / E / service	Spot-radiography preset / 0.850 / general
Shell	Type / $D_{i}$ / nominal / CA / mill / $L$	Cylinder / 1,200 / 16 / 1.5 mm / 12.5% / 2,400 mm
Head	Type / $D_{i}$ / inside depth / nominal / CA / mill	Ellipsoidal / 1,200 / 300 / 14 / 1.5 mm / 12.5%
Hydro	Enabled / stress-ratio mode	Yes / automatic selected-material ratio

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Example 1 engine component schedule
Component	Pressure $t$ (mm)	Required nominal (mm)	Available $t$ (mm)	Utilization	Component MAWP (MPa)	Governing mode
Cylindrical shell	8.147690	11.025931	12.500000	65.182%	2.413580	circumferential stress
2:1 ellipsoidal head	8.092742	10.963134	10.750000	75.281%	2.097866	ellipsoidal crown

Vessel MAWP

2.017866 MPa

MAP new/cold

2.309995 MPa

Hydrotest basis

2.623226 MPa

Hydrotest at component

2.743226 MPa

The 2:1 ellipsoidal head governs overall internal-pressure utilization at 75.281% because its 14 mm nominal selection leaves 10.750 mm available, even though its calculated pressure requirement is slightly lower than the shell's. Vessel MAWP is the head's local 2.097866 MPa rating less 0.080 MPa static head. Source qualification: VIII-1 equations are from the supplied 2025 edition, while the curated II-D subset is 2021 metric.

Example 1 unrounded engine outputs

{
  "overallStatus": "pass",
  "governing": {
    "checkId": "PV_INTERNAL_PRESSURE_THICKNESS",
    "name": "Internal-pressure thickness — 2:1 ellipsoidal head",
    "status": "implemented",
    "demand": 8.092742142015673,
    "demandUnit": "mm",
    "capacity": 10.75,
    "capacityUnit": "mm",
    "utilization": 0.7528132225130859,
    "pass": true,
    "notes": [
      "Governing component mode: ellipsoidal crown."
    ],
    "equations": [
      {
        "tex": "t=\\frac{PDK}{2SE-0.2P}",
        "ref": "asme-viii-1"
      }
    ],
    "intermediates": {
      "D": 1200,
      "R": 600,
      "P": 1.58,
      "S": 138,
      "E": 0.85,
      "K": 1,
      "axis_ratio": 2
    },
    "sourceRefIds": [
      "ASME_VIII1_UG32",
      "ASME_VIII1_APP1",
      "ASME_VIII1_UG16",
      "ASME_II_D_1A"
    ],
    "assumptionIds": [
      "PRESSURE_THICKNESS_SCOPE",
      "INPUT_PROPERTIES",
      "DESIGN_GEOMETRY_BASIS",
      "MAP_GEOMETRY_BASIS",
      "JOINT_COEFFICIENT_USER",
      "CORROSION_UNIFORM",
      "MILL_TOLERANCE",
      "NO_OPENINGS",
      "COMPONENT_JUNCTION_SCOPE",
      "ASME_EDITION_ALIGNMENT"
    ]
  },
  "mawp_MPa": 2.017866322838248,
  "mapNewCold_MPa": 2.309995426005239,
  "hydrotestPressure_MPa": 2.6232262196897222,
  "hydrotestPressureAtComponent_MPa": 2.7432262196897224,
  "componentResults": [
    {
      "componentId": "shell",
      "label": "Cylindrical shell",
      "type": "cylinder",
      "status": "pass",
      "requiredPressureThickness_mm": 8.147689768976898,
      "requiredNominalThickness_mm": 11.025931164545026,
      "availablePressureThickness_mm": 12.5,
      "utilization": 0.6518151815181519,
      "mawp_MPa": 2.4135802469135803,
      "mapNewCold_MPa": 2.699211045364892,
      "minimumCodeThickness_mm": 1.5,
      "requiredExternalThickness_mm": 0,
      "externalUtilization": 0,
      "externalSourceRefIds": [],
      "externalWarnings": [],
      "externalIntermediates": {},
      "governingMode": "circumferential stress",
      "equation": "t=\\frac{PR}{SE-0.6P}",
      "sourceRefIds": [
        "ASME_VIII1_UG27",
        "ASME_VIII1_UG16",
        "ASME_II_D_1A"
      ],
      "warnings": [],
      "intermediates": {
        "D": 1200,
        "R": 600,
        "P": 1.58,
        "S": 138,
        "E": 0.85,
        "t_hoop": 8.147689768976898,
        "t_longitudinal": 4.030063936879336
      }
    },
    {
      "componentId": "head",
      "label": "2:1 ellipsoidal head",
      "type": "ellipsoidal-head",
      "status": "pass",
      "requiredPressureThickness_mm": 8.092742142015673,
      "requiredNominalThickness_mm": 10.96313387658934,
      "availablePressureThickness_mm": 10.75,
      "utilization": 0.7528132225130859,
      "mawp_MPa": 2.097866322838248,
      "mapNewCold_MPa": 2.389995426005239,
      "minimumCodeThickness_mm": 1.5,
      "requiredExternalThickness_mm": 0,
      "externalUtilization": 0,
      "externalSourceRefIds": [],
      "externalWarnings": [],
      "externalIntermediates": {},
      "governingMode": "ellipsoidal crown",
      "equation": "t=\\frac{PDK}{2SE-0.2P}",
      "sourceRefIds": [
        "ASME_VIII1_UG32",
        "ASME_VIII1_APP1",
        "ASME_VIII1_UG16",
        "ASME_II_D_1A"
      ],
      "warnings": [],
      "intermediates": {
        "D": 1200,
        "R": 600,
        "P": 1.58,
        "S": 138,
        "E": 0.85,
        "K": 1,
        "axis_ratio": 2
      }
    }
  ],
  "warnings": [
    "Minimum pressure at the reference point; add the entered 0.1200 MPa test-fluid head when checking the lowest component."
  ]
}

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Example 2 — external-pressure sensitivity to unsupported length

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Example 2 complete active input basis
Group	Input	Value
Route	Construction route	ASME VIII-1 (2025)
Pressure	Internal / static / external differential	0 / 0 / 0.100 MPa
Temperature	Design / test	150 °C / 20 °C
Material	Mode / ID / chart	Curated / SA-516-70 / CS-2
Material	Yield / elastic modulus	260 MPa / 190,000 MPa
Fabrication	Joint basis / $E$	Seamless preset / 1.000
Shell	$D_{i}$ / nominal / CA / mill	1,200 / 18 / 1.5 mm / 12.5%
Sensitivity	Unsupported length	600 mm, then 3,000 mm; all other inputs held fixed
Hydro	Report hydrotest	Disabled

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Example 2 engine external-pressure comparison
Unsupported L	Required external $t$	Required nominal	Allowable external $P$	External utilization	Component status
600 mm	2.868232 mm	4.992265 mm	1.775313 MPa	5.633%	PASS
3,000 mm	5.608693 mm	8.124221 mm	0.994019 MPa	10.060%	PASS

Increasing unsupported length from 600 to 3,000 mm increases the required external-pressure thickness from 2.868232 to 5.608693 mm and reduces allowable external pressure from 1.775313 to 0.994019 MPa. This comparison holds material, thickness, diameter, corrosion, tolerance and pressure fixed. It does not qualify a support line or design a stiffening ring.

Example 2 unrounded engine outputs

{
  "short": {
    "overallStatus": "pass",
    "governing": {
      "checkId": "PV_MINIMUM_THICKNESS",
      "name": "Minimum code thickness — Vacuum shell — L 600 mm",
      "status": "implemented",
      "demand": 1.5,
      "demandUnit": "mm",
      "capacity": 14.25,
      "capacityUnit": "mm",
      "utilization": 0.10526315789473684,
      "pass": true,
      "notes": [
        "External-pressure material chart: CS-2."
      ],
      "intermediates": {},
      "sourceRefIds": [
        "ASME_VIII1_UG27",
        "ASME_VIII1_UG28",
        "ASME_II_D_TABLE_G",
        "ASME_II_D_EXTERNAL_CHARTS",
        "ASME_VIII1_UG16",
        "ASME_II_D_1A"
      ],
      "assumptionIds": [
        "PRESSURE_THICKNESS_SCOPE",
        "INPUT_PROPERTIES",
        "DESIGN_GEOMETRY_BASIS",
        "MAP_GEOMETRY_BASIS",
        "JOINT_COEFFICIENT_USER",
        "CORROSION_UNIFORM",
        "MILL_TOLERANCE",
        "NO_OPENINGS",
        "COMPONENT_JUNCTION_SCOPE",
        "EXTERNAL_SUPPORT_SCOPE",
        "ASME_EDITION_ALIGNMENT"
      ]
    },
    "component": {
      "componentId": "vacuum-shell-600",
      "label": "Vacuum shell — L 600 mm",
      "type": "cylinder",
      "status": "pass",
      "requiredPressureThickness_mm": 0,
      "requiredNominalThickness_mm": 4.992265168745355,
      "availablePressureThickness_mm": 14.25,
      "utilization": 0.2012794401861183,
      "mawp_MPa": 3.23145181168351,
      "mapNewCold_MPa": 3.5663302978095,
      "minimumCodeThickness_mm": 1.5,
      "requiredExternalThickness_mm": 2.868232022652186,
      "allowableExternalPressure_MPa": 1.7753128198311594,
      "externalUtilization": 0.056328101100239045,
      "externalGoverningMode": "shell external-pressure stability",
      "externalEquation": "A\\ \\text{from Table G},\\qquad P_a=\\frac{4B}{3\\left(\\frac{D_o}{t}\\right)}",
      "externalSourceRefIds": [
        "ASME_VIII1_UG28",
        "ASME_II_D_TABLE_G",
        "ASME_II_D_EXTERNAL_CHARTS"
      ],
      "externalWarnings": [
        "External-pressure material chart: CS-2."
      ],
      "externalIntermediates": {
        "unsupported_length_mm": 600,
        "elastic_modulus_MPa": 190000
      },
      "governingMode": "shell external-pressure stability",
      "equation": "t=\\frac{PR}{SE-0.6P}",
      "sourceRefIds": [
        "ASME_VIII1_UG27",
        "ASME_VIII1_UG28",
        "ASME_II_D_TABLE_G",
        "ASME_II_D_EXTERNAL_CHARTS",
        "ASME_VIII1_UG16",
        "ASME_II_D_1A"
      ],
      "warnings": [
        "External-pressure material chart: CS-2."
      ],
      "intermediates": {
        "D": 1200,
        "R": 600,
        "P": 0,
        "S": 138,
        "E": 1,
        "t_hoop": 0,
        "t_longitudinal": 0
      }
    },
    "warnings": [
      "Vacuum shell — L 600 mm: External-pressure material chart: CS-2.",
      "Hydrotest output is disabled."
    ]
  },
  "long": {
    "overallStatus": "pass",
    "governing": {
      "checkId": "PV_MINIMUM_THICKNESS",
      "name": "Minimum code thickness — Vacuum shell — L 3000 mm",
      "status": "implemented",
      "demand": 1.5,
      "demandUnit": "mm",
      "capacity": 14.25,
      "capacityUnit": "mm",
      "utilization": 0.10526315789473684,
      "pass": true,
      "notes": [
        "External-pressure material chart: CS-2."
      ],
      "intermediates": {},
      "sourceRefIds": [
        "ASME_VIII1_UG27",
        "ASME_VIII1_UG28",
        "ASME_II_D_TABLE_G",
        "ASME_II_D_EXTERNAL_CHARTS",
        "ASME_VIII1_UG16",
        "ASME_II_D_1A"
      ],
      "assumptionIds": [
        "PRESSURE_THICKNESS_SCOPE",
        "INPUT_PROPERTIES",
        "DESIGN_GEOMETRY_BASIS",
        "MAP_GEOMETRY_BASIS",
        "JOINT_COEFFICIENT_USER",
        "CORROSION_UNIFORM",
        "MILL_TOLERANCE",
        "NO_OPENINGS",
        "COMPONENT_JUNCTION_SCOPE",
        "EXTERNAL_SUPPORT_SCOPE",
        "ASME_EDITION_ALIGNMENT"
      ]
    },
    "component": {
      "componentId": "vacuum-shell-3000",
      "label": "Vacuum shell — L 3000 mm",
      "type": "cylinder",
      "status": "pass",
      "requiredPressureThickness_mm": 0,
      "requiredNominalThickness_mm": 8.124220547841809,
      "availablePressureThickness_mm": 14.25,
      "utilization": 0.3935924897797602,
      "mawp_MPa": 3.23145181168351,
      "mapNewCold_MPa": 3.5663302978095,
      "minimumCodeThickness_mm": 1.5,
      "requiredExternalThickness_mm": 5.6086929793615825,
      "allowableExternalPressure_MPa": 0.9940188771486296,
      "externalUtilization": 0.10060171119370766,
      "externalGoverningMode": "shell external-pressure stability",
      "externalEquation": "A\\ \\text{from Table G},\\qquad P_a=\\frac{4B}{3\\left(\\frac{D_o}{t}\\right)}",
      "externalSourceRefIds": [
        "ASME_VIII1_UG28",
        "ASME_II_D_TABLE_G",
        "ASME_II_D_EXTERNAL_CHARTS"
      ],
      "externalWarnings": [
        "External-pressure material chart: CS-2."
      ],
      "externalIntermediates": {
        "unsupported_length_mm": 3000,
        "elastic_modulus_MPa": 190000
      },
      "governingMode": "shell external-pressure stability",
      "equation": "t=\\frac{PR}{SE-0.6P}",
      "sourceRefIds": [
        "ASME_VIII1_UG27",
        "ASME_VIII1_UG28",
        "ASME_II_D_TABLE_G",
        "ASME_II_D_EXTERNAL_CHARTS",
        "ASME_VIII1_UG16",
        "ASME_II_D_1A"
      ],
      "warnings": [
        "External-pressure material chart: CS-2."
      ],
      "intermediates": {
        "D": 1200,
        "R": 600,
        "P": 0,
        "S": 138,
        "E": 1,
        "t_hoop": 0,
        "t_longitudinal": 0
      }
    },
    "warnings": [
      "Vacuum shell — L 3000 mm: External-pressure material chart: CS-2.",
      "Hydrotest output is disabled."
    ]
  }
}

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Example 3 — actual ellipsoidal-head depth changes the result

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Example 3 complete active input basis
Group	Input	Value
Route	Construction route	ASME VIII-1 (2025)
Pressure	Internal / static head	2.000 / 0.050 MPa
Temperature	Design / test	200 °C / 20 °C
Material	Mode / ID / allowable stress	Curated / SA-516-70 / 138 MPa
Fabrication	Joint basis / $E$	Full-radiography preset / 1.000
Head	$D_{i}$ / nominal / CA / mill	1,200 / 16 / 1.5 mm / 12.5%
Geometry comparison	Inside depth	300 mm (2:1), then 350 mm; all other inputs fixed
Hydro	Report hydrotest	Disabled

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Example 3 engine formed-head comparison
Inside depth	Axis ratio $D_{i} / (2 h_{i})$	$K$	Pressure $t$	Required nominal	Component MAWP	Utilization
300 mm	2.000000	1.000000	8.926304 mm	11.915776 mm	2.869023 MPa	71.410%
350 mm	1.714286	0.823129	7.347502 mm	10.111430 mm	3.483951 MPa	58.780%

The deeper 350 mm head gives the implemented axis ratio 1.714286 and factor 0.823129, reducing required pressure thickness relative to the 2:1 geometry. This is not a recommendation to change head shape: formed-head procurement, tolerances, junction behavior, fabrication and route limits still need project review. It demonstrates why actual inside depth must replace a nominal 2:1 assumption when the head is not 2:1.

Example 3 unrounded engine outputs

{
  "depth300": {
    "overallStatus": "pass",
    "governing": {
      "checkId": "PV_INTERNAL_PRESSURE_THICKNESS",
      "name": "Internal-pressure thickness — Ellipsoidal head — h 300 mm",
      "status": "implemented",
      "demand": 8.926303566892848,
      "demandUnit": "mm",
      "capacity": 12.5,
      "capacityUnit": "mm",
      "utilization": 0.7141042853514279,
      "pass": true,
      "notes": [
        "Governing component mode: ellipsoidal crown."
      ],
      "equations": [
        {
          "tex": "t=\\frac{PDK}{2SE-0.2P}",
          "ref": "asme-viii-1"
        }
      ],
      "intermediates": {
        "D": 1200,
        "R": 600,
        "P": 2.05,
        "S": 138,
        "E": 1,
        "K": 1,
        "axis_ratio": 2
      },
      "sourceRefIds": [
        "ASME_VIII1_UG32",
        "ASME_VIII1_APP1",
        "ASME_VIII1_UG16",
        "ASME_II_D_1A"
      ],
      "assumptionIds": [
        "PRESSURE_THICKNESS_SCOPE",
        "INPUT_PROPERTIES",
        "DESIGN_GEOMETRY_BASIS",
        "MAP_GEOMETRY_BASIS",
        "JOINT_COEFFICIENT_USER",
        "CORROSION_UNIFORM",
        "MILL_TOLERANCE",
        "NO_OPENINGS",
        "COMPONENT_JUNCTION_SCOPE",
        "ASME_EDITION_ALIGNMENT"
      ]
    },
    "component": {
      "componentId": "ellipsoidal-head-300",
      "label": "Ellipsoidal head — h 300 mm",
      "type": "ellipsoidal-head",
      "status": "pass",
      "requiredPressureThickness_mm": 8.926303566892848,
      "requiredNominalThickness_mm": 11.915775505020397,
      "availablePressureThickness_mm": 12.5,
      "utilization": 0.7141042853514279,
      "mawp_MPa": 2.869022869022869,
      "mapNewCold_MPa": 3.212504156967077,
      "minimumCodeThickness_mm": 1.5,
      "requiredExternalThickness_mm": 0,
      "externalUtilization": 0,
      "externalSourceRefIds": [],
      "externalWarnings": [],
      "externalIntermediates": {},
      "governingMode": "ellipsoidal crown",
      "equation": "t=\\frac{PDK}{2SE-0.2P}",
      "sourceRefIds": [
        "ASME_VIII1_UG32",
        "ASME_VIII1_APP1",
        "ASME_VIII1_UG16",
        "ASME_II_D_1A"
      ],
      "warnings": [],
      "intermediates": {
        "D": 1200,
        "R": 600,
        "P": 2.05,
        "S": 138,
        "E": 1,
        "K": 1,
        "axis_ratio": 2
      }
    },
    "warnings": [
      "Hydrotest output is disabled."
    ]
  },
  "depth350": {
    "overallStatus": "pass",
    "governing": {
      "checkId": "PV_INTERNAL_PRESSURE_THICKNESS",
      "name": "Internal-pressure thickness — Ellipsoidal head — h 350 mm",
      "status": "implemented",
      "demand": 7.347501575469623,
      "demandUnit": "mm",
      "capacity": 12.5,
      "capacityUnit": "mm",
      "utilization": 0.5878001260375698,
      "pass": true,
      "notes": [
        "Governing component mode: ellipsoidal crown."
      ],
      "equations": [
        {
          "tex": "t=\\frac{PDK}{2SE-0.2P}",
          "ref": "asme-viii-1"
        }
      ],
      "intermediates": {
        "D": 1200,
        "R": 600,
        "P": 2.05,
        "S": 138,
        "E": 1,
        "K": 0.8231292517006802,
        "axis_ratio": 1.7142857142857142
      },
      "sourceRefIds": [
        "ASME_VIII1_UG32",
        "ASME_VIII1_APP1",
        "ASME_VIII1_UG16",
        "ASME_II_D_1A"
      ],
      "assumptionIds": [
        "PRESSURE_THICKNESS_SCOPE",
        "INPUT_PROPERTIES",
        "DESIGN_GEOMETRY_BASIS",
        "MAP_GEOMETRY_BASIS",
        "JOINT_COEFFICIENT_USER",
        "CORROSION_UNIFORM",
        "MILL_TOLERANCE",
        "NO_OPENINGS",
        "COMPONENT_JUNCTION_SCOPE",
        "ASME_EDITION_ALIGNMENT"
      ]
    },
    "component": {
      "componentId": "ellipsoidal-head-350",
      "label": "Ellipsoidal head — h 350 mm",
      "type": "ellipsoidal-head",
      "status": "pass",
      "requiredPressureThickness_mm": 7.347501575469623,
      "requiredNominalThickness_mm": 10.111430371965284,
      "availablePressureThickness_mm": 12.5,
      "utilization": 0.5878001260375698,
      "mawp_MPa": 3.4839507444999747,
      "mapNewCold_MPa": 3.9008430647008896,
      "minimumCodeThickness_mm": 1.5,
      "requiredExternalThickness_mm": 0,
      "externalUtilization": 0,
      "externalSourceRefIds": [],
      "externalWarnings": [],
      "externalIntermediates": {},
      "governingMode": "ellipsoidal crown",
      "equation": "t=\\frac{PDK}{2SE-0.2P}",
      "sourceRefIds": [
        "ASME_VIII1_UG32",
        "ASME_VIII1_APP1",
        "ASME_VIII1_UG16",
        "ASME_II_D_1A"
      ],
      "warnings": [],
      "intermediates": {
        "D": 1200,
        "R": 600,
        "P": 2.05,
        "S": 138,
        "E": 1,
        "K": 0.8231292517006802,
        "axis_ratio": 1.7142857142857142
      }
    },
    "warnings": [
      "Hydrotest output is disabled."
    ]
  }
}

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Section 13

Common mistakes and troubleshooting

Use the consequence column to understand why a field matters, then correct the design basis rather than changing an input only to improve the result.

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High-value pressure-vessel thickness troubleshooting table
Mistake	Likely consequence	Corrective action
Choosing a familiar code instead of the adopted route/edition	Equations, factors, material basis and hydrotest logic may be inapplicable.	Confirm contract, authority and edition; record them in notes.
Entering operating pressure instead of design pressure	Required thickness is understated.	Use the project design pressure at the stated reference point.
Omitting design static head	Low components are checked at too little pressure and vessel MAWP can be overstated.	Calculate head from process-fluid density and elevation, then enter it separately.
Treating external pressure as negative internal pressure	Buckling/stability checks are bypassed.	Enter a positive external differential in its own field.
Entering new geometry while treating it as corroded geometry	Thickness and geometry reference conditions become inconsistent.	Enter inside calculation geometry at the corroded condition.
Applying corrosion allowance twice	Required nominal is overstated or available thickness understated.	Enter CA once; let the engine deduct and restore it.
Comparing pressure t directly with nominal stock	Mill undertolerance and corrosion allowance are missed.	Compare nominal stock with reported required nominal thickness.
Selecting joint efficiency from examination wording alone	Membrane capacity may be overstated.	Verify weld category, detail, material and examination table.
Using curated material outside its applicability	Allowable stress or chart data may not match the actual product.	Verify product form, thickness, heat treatment, temperature and edition.
Selecting the wrong external-pressure chart	Factor B/tangent-modulus behavior can be wrong.	Trace the chart to specification, grade, condition and temperature.
Treating entered stiffener spacing as qualified	External capacity relies on a support line that may be inadequate.	Design/qualify ring inertia, area, welds and junction separately.
Using nominal 2:1 geometry for a nonstandard head	Head factor and applicability checks are wrong.	Enter actual corroded-condition inside depth or radii.
Guessing the flat-head factor	Required flat-head thickness can be materially wrong.	Derive $C$ , $K$ or $C_{e q}$ from the actual licensed-standard detail.
Treating fixed-geometry MAP as exact as-built MAP	New-condition rating can be mischaracterized.	Run actual as-built geometry for an exact as-built rating.
Treating hydrotest basis as a complete test procedure	Execution hazards and temporary conditions remain unchecked.	Prepare and approve a separate test procedure and condition assessment.
Treating PASS as whole-vessel certification	Unmodeled limit states and regulatory steps are overlooked.	Complete and review the whole-vessel assessment package.

Section 14

Whole-vessel design boundaries

These are legitimate boundaries between a component pressure-thickness schedule and a complete pressure-equipment design—not hidden formulas waiting behind the result.

Nozzle and opening reinforcement
Flanges, gasketed and bolted joints
Cone-to-cylinder, head-to-shell and flat-end junction stresses or reinforcement
Local loads, clips, lugs and other attachments
Piping reactions and thermal interaction
Supports, saddles, skirts, legs, lifting points, wind and seismic
Stiffening-ring area, inertia, welds and line-of-support qualification
Fatigue and cyclic service
Creep and time-dependent material behavior
Impact-test and brittle-fracture requirements
Non-circular, jacketed and expansion-joint behavior
Fabrication tolerances, forming and NDE
Pressure-test procedure and temporary test condition
Relief protection and operating safeguards
Registration, conformity assessment, inspection and certification

Local vessel attachments and lifting can demand their own design path. Where a project includes lifting trunnions, the lifting trunnion calculator can support that separate check, but it does not close the pressure-vessel scope above.

Section 15

Report and review workflow

The full pressure-vessel calculation and complete on-screen report are public and unblurred. Authentication is used only when the user generates/downloads the PDF or saves through the account workflow.

The report records project metadata, route and edition, material basis, design/test conditions, component input schedule, component results, equations, warnings, assumptions and source references. There is no pressure-vessel report watermark or subscription requirement for the PDF: sign in to generate/download it. Saving a project/report also uses the account workflow.

Before issue, assign a calculation revision, have a competent reviewer verify the input/source basis, and combine this report with the remaining whole-vessel calculations. A report is a traceable record, not a substitute for review.

Pre-issue review checklist

Route, edition and jurisdiction confirmed
Material properties traced to product form and temperature
Design and test temperatures confirmed
Pressure reference elevations confirmed
Joint efficiency/testing group basis confirmed
Every pressure-boundary component that could govern modeled
Corroded inside-geometry convention confirmed
Corrosion allowance and mill tolerance treatment confirmed
External support spacing and support lines qualified
All warnings and indeterminate states resolved
MAWP and fixed-geometry MAP meanings understood
Hydrotest basis independently checked
Separate whole-vessel assessments attached
Reviewer, revision and issue status recorded

Open complete example report Review methodology

Section 16

Frequently asked questions

Short answers to the distinctions that most often determine whether a thickness result is being interpreted correctly.

Is this an ASME pressure vessel certification tool?

No. It implements pressure-thickness checks for the entered component model. It does not certify, register, inspect, stamp or approve a vessel, and it does not complete the many whole-vessel assessments outside this calculator.

What is the difference between required thickness and required nominal thickness?

Required pressure, code-minimum and external thicknesses are pressure-resisting values. Required nominal thickness is the governing one of those values increased to restore corrosion allowance and percentage mill undertolerance, so it can be compared with a nominal plate, pipe or head callout.

Does corrosion allowance increase vessel diameter in the calculator?

No. Entered inside diameter, depth and radii are already the calculation geometry in the corroded condition. Corrosion allowance is deducted from thickness; it is not automatically added to a dimension.

Which component controls vessel MAWP?

The component with the lowest calculated local pressure rating controls. The calculator subtracts entered static head from that lowest local rating to report vessel MAWP at the design-pressure reference point.

Why can a vacuum case govern a relatively thick vessel?

External pressure is a buckling problem. Diameter-to-thickness ratio, unsupported length, elastic stiffness, yield behavior and imperfections can control stability even when internal-pressure membrane stress is modest.

What unsupported length should I enter?

Enter spacing between lines of support that are already qualified under the selected route, including any route-required head contribution. Do not enter a proposed stiffener pitch and treat the calculation as qualification of that stiffener.

Does the calculator design stiffening rings?

No. It does not size ring area or inertia, check attachment welds, or qualify a ring or junction as a line of support.

Can I use a custom ellipsoidal or torispherical head?

Yes. Enter actual ellipsoidal inside depth or actual torispherical inside crown and knuckle radii. The route can still return indeterminate when the geometry is outside its implemented applicability limits.

How is joint efficiency selected?

The interface offers seamless/full-examination 1.00, spot-examination 0.85 and no-radiography 0.70 convenience presets plus a user value. Eligibility still has to be established from the actual weld category, joint detail, material and examination provisions.

Are ASME allowable stresses automatic?

Only for the eight curated VIII-1/CSA material IDs and only within their stored 2021 Table 1A temperature ranges. Other ASME inputs and all VIII-2 properties shown in the UI remain user-entered and must be verified.

Why does EN 13445 require additional material properties?

The implemented Clause 6 nominal-stress route depends on material class, tensile and yield/proof properties, temperature, rupture elongation and alternative-route selection. External pressure also needs elastic modulus, Poisson ratio and shape information.

What is the difference between MAWP and MAP new/cold?

MAWP uses design-temperature properties and corroded available thickness. The implemented MAP restores corrosion allowance to thickness, uses test-temperature properties and keeps entered geometry fixed. Exact as-built new geometry requires a separate run.

Does the hydrotest result include liquid head?

The reported hydrotest basis is at the pressure reference point. The separate hydrotest-fluid head input is then added to report local pressure at the entered component elevation.

Can I use the CSA route without provincial registration?

The calculator cannot answer that jurisdictional question. The CSA selection records context and delegates pressure equations to VIII-1; the engineer must confirm registration, adopted edition and authority requirements.

Why did the calculator return indeterminate?

A necessary property, chart range, denominator, thickness ratio, head proportion, cone angle, shape limit or other applicability condition did not support a defensible numerical result. Read the validation message and warnings; do not tune an input merely to force PASS.

Are the full results free?

Yes. Pressure-vessel calculation values and the complete on-screen report are public and unblurred for this calculator.

Do I need a subscription to download the pressure-vessel PDF?

No subscription is required. You sign in to generate or download the PDF.

Can the report be used without checking nozzles, fatigue and local loads?

No. The report can document this pressure-thickness calculation, but it must be combined with the remaining applicable vessel assessments before issue.

Section 17

Source and edition map

Xarpis stores clause metadata and implementation-derived equations. It does not republish licensed standard text or the full material/external-pressure tables.

Scroll table horizontally →

Principal sources used by the five construction routes
Source	Edition	Implemented topics
ASME BPVC VIII-1	2025	UG-16, UG-27, UG-28, UG-32, UG-33, UG-34, UG-99, UW-12 and Mandatory Appendix 1.
ASME BPVC VIII-2	2025	Parts 4.3, 4.4, 4.6.2, Annex 3-D and Tables 4.1.3/8.2.1.
ASME BPVC II-D	2021 metric	Curated Table 1A allowables, Subpart 3 Table G and CS-2/HA-1 through HA-4 data.
AS 1210	2010	§§3.4, 3.7, 3.9–3.13, 3.15 and 5.10.
CSA B51	2014	Canadian context and delegation to the ASME construction rules.
EN 13445-3	2014, Issue 4 (2017)	§§5.6, 6, 7.4–7.6, 8 and 10.
PED 2014/68/EU	2014	Annex I 7.4 hydrostatic-test floor for the implemented EN route.

Ready to calculate

Build the full component schedule, then keep every assumption visible.

Start with the adopted route and traceable material basis, model each pressure boundary in its corroded condition, and review warnings, ratings and source references before issue.

Begin a pressure-vessel calculation Review methodology Example report

What the calculator actually solves

Five construction routes, five calculation contexts

ASME BPVC Section VIII, Division 1 (2025)

ASME BPVC Section VIII, Division 2 (2025)

AS 1210 (2010)

CSA B51 (2014)

EN 13445-3:2014, Issue 4 (2017)

Quick-start workflow for an engineering review

Confirm code, edition, jurisdiction and design basis

Enter project metadata and design-basis notes

Enter pressure, heads and temperatures

Establish fabrication and joint coefficient

Establish material properties and provenance

Add every component that could govern

Enter corroded-condition inside geometry

Enter corrosion allowance and mill undertolerance

Enter external-pressure length and shape data

Resolve validation, indeterminate and warning states

Review schedule, governing checks and ratings

Open the complete report

Design-condition inputs: keep the pressure references separate

Fabrication and material inputs

Joint efficiency and testing group

AS 1210 fabrication metadata

Curated ASME material subset

EN material fields

Geometry guide for all seven component types

Cylindrical shell

Spherical shell

Hemispherical head

Ellipsoidal head

Torispherical head

Conical shell or reducer

Circular unstayed flat head

Thickness bookkeeping: nominal is not pressure thickness

Internal pressure: membrane mechanics routed through code rules

External pressure and vacuum are stability problems

MAWP, MAP new/cold and hydrotest are different questions

Implemented reference-point hydrotest bases

Read results in the order a reviewer needs them

Input validation message

Vessel schematic

Overall pressure-thickness status

Warnings and scope flags

Component schedule

Governing checks and equations

Assumptions

Report

Fast engineering sanity checks

Three engine-backed worked examples

Example 1 — ASME VIII-1 shell and 2:1 ellipsoidal head

Example 2 — external-pressure sensitivity to unsupported length

Example 3 — actual ellipsoidal-head depth changes the result

Common mistakes and troubleshooting

Whole-vessel design boundaries

Report and review workflow

Pre-issue review checklist

Frequently asked questions

Source and edition map

Build the full component schedule, then keep every assumption visible.