Relief Valve Sizing in the Browser — API 520 Orifice Area, B31.1 App. II Reaction

Size the relief orifice per API 520 Part I — gas or vapor in critical or subcritical flow, steam with the Napier correction, liquid through a certified valve — then take the ASME B31.1 Appendix II open-discharge reaction force with the embedded steam-constant table, and route any of 26 API 521 contingencies to the paragraph that governs it. Everything computes in your browser on the Pro tier; the method write-up below is free to read.

Content last reviewed 2026-08-29 · page regenerated 2026-09-03 at build.

What it does

Four cards, in the order an overpressure problem actually moves:

API 521 scenario router

Pick the overpressure contingency — blocked outlet, control-valve failure, exterior fire, tube rupture, any of the 26 items in the standard's contingency list — and the router names the API 521 7th Edition section that governs it, so you establish the required relieving rate in your copy of the standard and come back with a number. It is deliberately a routing index and nothing more: relieving-rate guidance is copyrighted standard content, and the required relief load is your determination from the standard.

API 520 sizing

The published equation set from API 520 Part I, 10th Edition: Eq. 6 with the Eq. 12 coefficient C for critical gas flow, Eq. 16 with the Eq. 22 F₂ coefficient for subcritical, Eq. 25 with the Eq. 27/28 Napier correction for steam, Eq. 32 for liquid service with a certified valve. The card computes the critical-flow pressure P_cf from Eq. 5 and picks the gas regime itself — critical or subcritical is not a dropdown you can get wrong. Corrections K_d, K_b, K_c, K_w, K_v and K_SH are inputs with cited guidance, and the output is the required effective discharge area to five decimals.

B31.1 Appendix II reaction force

The open-discharge reaction at the elbow per ¶II-2.3.1.1: F₁ = ṁV₁/g_c + (P₁ − P_a)A₁, with the exit state solved from stagnation enthalpy per ¶II-2.2.1 and the mass flow taken at 1.11 × stamped capacity. The Table II-2.2.1-1 steam constants are embedded and applied through a picker that cites the table and row; the card multiplies F₁ by your dynamic load factor per ¶II-3.5.1.3 and reminds you that vent-pipe blowback (¶II-2.3.1.2) is a separate verification.

Section XIII device guide

A reference card mapping device types and capacity-certification paths (Part 9), with the honest note that set-pressure and accumulation limits belong to the referencing code — Section VIII or Section I rules for the equipment being protected.

What is embedded, and what stays in your copy of the standard

The same data firewall as every calculator on this site: published equations live in code; copyrighted table values do not — except for the reference tables named below.

• Embedded reference data: the B31.1-2024 Table II-2.2.1-1 steam constants (wet below 90% quality, saturated to 1,000 psia, superheated to 2,000 psia, each row carrying its applicability note).
• Yours to supply from API 520: fluid properties (k, MW, Z), the Table 11 coefficient C if you prefer the tabulated value to the computed one (an override field takes it directly), the Table 12/13 superheat correction K_SH, and the viscosity correction K_v. The card labels carry the standard defaults — K_d 0.975 valve / 0.62 rupture disk / 0.65 liquid — and warnings name every default that is silently doing work.
• Deliberately not embedded: API 521 relieving-rate methods (the router sends you to the governing section instead) and the API 526 orifice-letter table (see the FAQ).

That split is what makes the output auditable: every number in the report is either a published equation or a value you chose and can defend to a reviewer.

A typical run: contingency to reaction load

• 1 — Route the scenario. Pick the contingency in the API 521 router; it names the governing section. Establish the required relieving rate there, in your copy.
• 2 — Size the orifice. Enter the rate, relieving pressure and fluid properties in the API 520 card. The card computes P_cf, picks critical or subcritical itself, applies your corrections, and returns the required effective area.
• 3 — Select the valve. Pick the orifice letter that covers the area from API 526 and the vendor catalog — the one lookup this tool leaves in your copy.
• 4 — Take the reaction. Enter the stamped capacity and outlet geometry in the B31.1 Appendix II card: exit velocity, exit pressure, F₁, and F₁ × DLF as the design load for the discharge-elbow support.
• 5 — Capture the report. Add to report files each card into the Report Manager with a titleblock, printable output, and a .pcp project file that reopens with everything intact.

The sizing card's default state is the standard's own §5.6.3.2 worked example — 6.50573 in² — locked as a CI fixture and asserted by an end-to-end test on every deploy, so the first number you see is one you can check.

What it deliberately does not do

Stated plainly, the way the rest of this site states limits:

• No two-phase flow. Gas/vapor, steam and certified-liquid services only — DIERS-style two-phase methodology is outside the equation set and outside this tool.
• No fire heat-input calculation. The router will tell you exterior fire is §4.4.13's problem; computing the wetted-area heat input and the resulting rate is your work in API 521.
• No rupture-disk sizing. The K_c combination factor is applied where a disk sits upstream of the valve; sizing the disk itself is not attempted.
• No orifice-letter selection and no accumulation card yet. The output is required area; the letter is a lookup in your API 526. Set-pressure and accumulation limits per the referencing code (Section VIII, Section I) are a planned card that ships only after its per-code rules pass the verification gate.
• Not a flare-network solver. One device, one contingency at a time — header hydraulics and staged-relief interactions belong in process-simulation tools.

For the piping around the valve, the free calculators carry the adjacent checks: MAOP / MOP for the pressure ceiling the relief protects, water hammer / surge for the transient that may be your contingency, and B31.1 wall thickness for the discharge piping itself.

What's free and what needs Pro

This page — the method, the equations, the limits — is free to read, like every write-up on the site, and the 49 code calculators stay free permanently. The live PiperPSV tool is on the Pro tier — the entry paid tier, $2.99/month:

• Free — $0: every ASME code calculator (wall thickness, spans, SIFs, flexibility, occasional loads), each with a fixture-verified worked example.
• Pro — $2.99/month or $29/year: adds PiperPSV, PiperSIF (B31J-2023 and NM.1 factor catalogs), report capture, the Report Manager, .pcp project files, batch runs, and the cited code-table and pipe-size pickers.
• Pro Plus — $7.99/month or $79/year: adds PiperHGR spring sizing, PiperNOZ nozzle loading, PiperFLG bolted-flange analysis, and the UCS-66 MDMT tool. The monthly plan starts with 30 days free.
• Ultimate — $14.99/month or $149/year: adds PiperFEA nozzle/shell FEA (commissioning — validation status published), PiperSTR structural support design, the PiperISO premium export set, and the API 610/660/661/560 nozzle-load presets.

The full matrix and billing FAQ are at /pricing/.

Demo video

▶ Relief Valve Sizing in the Browser - PiperPSV API 520 Orifice Area and B31.1 Reaction Force (1:06) — The four-card run: route the contingency in the API 521 index, size the orifice per API 520 with the flow regime picked automatically from Pcf, and take the B31.1 App. II reaction force with the embedded steam-constant picker. Watch on YouTube.

Open the tool

Open PiperPSV — it loads in this tab on any paid account, defaults loaded with the standard's own worked example so you can verify before you trust it. If you are sizing against a contingency you have not routed yet, start with the API 521 router card and let the standard tell you where the rate comes from.

FAQ

Which API 520 sizing equations are implemented?

The published equation set from API 520 Part I, 10th Edition: Eq. 6 with the Eq. 12 coefficient C for gas or vapor in critical flow, Eq. 5 for the critical-flow pressure Pcf, Eq. 16 with the Eq. 22 F2 coefficient for subcritical flow, Eq. 25 for steam with the Eq. 27/28 Napier correction KN above 1,500 psia, and Eq. 32 for liquid service with a certified valve. The regime choice is not a dropdown you can get wrong: the card computes Pcf from k and the relieving pressure, compares the backpressure against it, and selects critical or subcritical automatically — if k is not supplied it assumes critical flow and says so in a warning rather than guessing silently. Every input the equations need beyond that — Kd, Kb, Kc, Kw, Kv, KSH, and the fluid properties — is yours to supply, because those values come from the standard's tables, not from equations it publishes.

Does it select the API 526 orifice letter for me?

No. The output is the required effective discharge area A in square inches, computed to five decimals — for the standard's own §5.6.3.2 example that is 6.50573 in², and that case is locked as a fixture and asserted by an end-to-end test on every deploy. Choosing the letter designation that covers A is a lookup in API 526's orifice-area table, which this tool does not embed; you read the table in your copy, pick the first orifice at or above the required area, and confirm it against the valve vendor's certified capacity. That is a one-line step, but it is deliberately your step: publishing the D-through-T areas would cross the same line the rest of this site is built to respect — equations live in code, copyrighted table values do not. If that table is ever embedded, letter selection is the first feature it unblocks.

Where do the fluid properties and correction factors come from?

From your copy of the standard, entered as inputs — that is the data firewall the whole site runs on. The card embeds the published equations; it does not embed Table 10 gas properties, the Table 11 C coefficients (though a computed C from k is standard and an override field accepts the table value directly), the Table 12/13 superheat-correction grid, or the viscosity chart behind Kv. The Kd field's own label carries the standard defaults — 0.975 for a valve, 0.62 for a bare rupture disk, 0.65 for liquid — and the card warns you wherever a default is doing work: KSH stays 1.0 until you supply the superheat value, and Kv 1.0 is only valid at or below 100 cP. The result is auditable rather than convenient: every number in the report is either a published equation or a value you chose and can defend.

How is the discharge reaction force calculated?

Per ASME B31.1-2024 Nonmandatory Appendix II, the open-discharge case: the exit velocity V1 and exit static pressure P1 come from the ¶II-2.2.1 energy balance on stagnation enthalpy h0 using the steam constants a and b, and the steady-state reaction at the discharge elbow is F1 = ṁ·V1/gc + (P1 − Pa)·A1 per ¶II-2.3.1.1, with the mass flow taken as 1.11 times stamped capacity — the code's built-in margin over the nameplate. The Table II-2.2.1-1 constants are embedded and applied through a cited picker: wet steam below 90 percent quality, saturated to 1,000 psia, superheated to 2,000 psia, each row carrying its applicability note. You then apply the dynamic load factor per ¶II-3.5.1.3 — the card multiplies F1 × DLF but leaves choosing the factor to you, and it reminds you that vent-pipe blowback under ¶II-2.3.1.2 is a separate verification.

What tier is PiperPSV on, and what exactly do I get?

PiperPSV is a Pro tool — $2.99/month or $29/year, the entry paid tier — alongside PiperSIF, the Report Manager, .pcp project files and the cited code-table pickers. Everything computes in your browser: inputs never leave the tab, there is no per-run cost, and the same inputs produce the same report forever. The card set is the API 520 sizing engine, the B31.1 Appendix II reaction card with the embedded steam-constant picker, the 26-contingency API 521 scenario router, and a Section XIII device-type guide; Add to report captures any card into the Report Manager with a titleblock, printable output and .pcp project files. The default state of the sizing card is the standard's own §5.6.3.2 worked example, so the first thing you see is a number you can check against your copy — 6.50573 square inches — before you trust it with your own relief case.