About Relief Valve Sizing Calculator — API 520 Orifice Area
The relief valve sizing calculator computes the required effective discharge area of a pressure relief valve using the API 520 Part I equations in their published US-customary form, then selects the next standard orifice from the API 526 letter series (D through T). For liquid service: A = Q/(38·Kd·Kw·Kc·Kv)·√(SG/ΔP) with the preliminary effective discharge coefficient Kd = 0.65. For gas or vapor in critical (choked) flow — the regime that covers most gas reliefs, where P₁ is more than roughly twice the absolute backpressure: A = W·√(T·Z/M)/(C·Kd·P₁·Kb·Kc) with Kd = 0.975 and the coefficient C = 520·√(k·(2/(k+1))^((k+1)/(k−1))), which reproduces API 520's tabulated C = 356 for air (k = 1.4).
This is preliminary sizing, and the tool says so on every output: it tells you which orifice letter class a relief duty lands in, so you can scope a valve, check a vendor proposal, or spot an undersized nozzle. It is not a substitute for API 520/521/526 engineering — subcritical gas flow, steam service with its superheat corrections, two-phase relief, the fire case, viscous liquids needing the Kv chart, and certified (as opposed to effective) discharge coefficients are all outside this simplification. Final selection and the relieving-scenario definition belong with the standard and the valve manufacturer's certified capacity data.
How It Works
- Pick the service. Liquid uses the certified-valve liquid equation; gas assumes critical (choked) flow — valid when the absolute relieving pressure is at least about twice the absolute backpressure, the common case for reliefs discharging to atmosphere or a low-pressure header.
- For liquid: enter the relieving flow in gpm, the specific gravity at flowing temperature, and the differential ΔP in psi — relieving pressure (set + overpressure) minus total backpressure, both absolute or both gauge, consistently.
- For gas: enter the mass flow in lb/hr, relieving temperature in °F (converted to °R internally), compressibility Z, molecular weight, specific-heat ratio k, and the absolute relieving pressure P₁ in psia — set pressure plus allowable overpressure plus atmospheric.
- Leave the correction factors at 1.0 unless you know otherwise: Kw derates balanced-bellows valves under backpressure (1.0 for conventional valves to atmosphere), Kc = 0.9 applies only with an upstream rupture disk, Kv < 1 only for viscous liquid service, Kb derates for backpressure approaching critical.
- Read the required effective area, the selected API 526 orifice letter, and the utilization — how much of the selected orifice the duty consumes. Utilization near 100% means the next scenario tweak bumps you a letter; treat it as a flag, not a comfort.
Worked Example
Scope a gas relief: 10,000 lb/hr of air (M = 28.97, k = 1.4, Z = 1) relieving at 60 °F (519.67 °R) and P₁ = 114.7 psia, conventional valve to atmosphere (Kb = Kc = 1). The coefficient C = 520·√(1.4 × (2/2.4)⁶) = 356.06 — the value API 520 tabulates as 356 for air. Required area: A = 10,000 × √(519.67 × 1 / 28.97) / (356.06 × 0.975 × 114.7 × 1 × 1) = 10,000 × 4.235 / 39,819 = 1.064 in². The next standard orifice is J (1.287 in²) at 83% utilization. A liquid check runs the same way: 100 gpm of water at ΔP = 25 psi needs A = 100/(38 × 0.65) × √(1/25) = 0.810 in² — also a J orifice.
Formulas
- Liquid service (certified valves)
A = Q / (38 · Kd · Kw · Kc · Kv) · √(SG / ΔP)- Gas/vapor, critical (choked) flow
A = W · √(T·Z / M) / (C · Kd · P₁ · Kb · Kc)- Gas-constant coefficient
C = 520 · √( k · (2/(k+1))^((k+1)/(k−1)) )- Orifice selection
API 526 letters: D 0.110 · E 0.196 · F 0.307 · G 0.503 · H 0.785 · J 1.287 · K 1.838 · L 2.853 · M 3.60 · N 4.34 · P 6.38 · Q 11.05 · R 16.0 · T 26.0 in²
Standards & References
- API Standard 520 Part I, Sizing and Selection of Pressure-Relieving Devices (9th ed.) — liquid (§5.8) and gas critical-flow (§5.6) effective-area equations with preliminary Kd = 0.65 / 0.975, as openly reproduced in the fluids library documentation, Technical Toolboxes, and the Emerson/Crosby Pressure Relief Valve Engineering Handbook
- API Standard 526, Flanged Steel Pressure-Relief Valves — standard effective orifice letter series D through T
- PRELIMINARY SIZING ONLY: subcritical gas flow, steam, two-phase, fire case (API 521), viscosity Kv charts, and certified discharge coefficients are outside this tool — final design per the standards and manufacturer capacity data
Frequently Asked Questions
What does "critical flow" mean, and does my gas relief qualify?
When the pressure ratio across the valve exceeds roughly 2:1 (exactly: backpressure below P₁ × (2/(k+1))^(k/(k−1)), about 0.53 × P₁ for air), the flow chokes at sonic velocity in the nozzle and the relieving rate stops depending on what is downstream. Most reliefs to atmosphere or a low-pressure flare header are comfortably critical. If your backpressure is higher than about half of P₁ absolute, this tool's equation over-predicts capacity — use the API 520 subcritical formula instead.
What is P₁, exactly?
The absolute upstream relieving pressure: set pressure plus the allowable overpressure (10% for a single non-fire valve per ASME VIII, 21% for fire case) plus atmospheric pressure. A 100 psig set valve at 10% accumulation relieves at P₁ = 100 × 1.10 + 14.7 = 124.7 psia. Feeding gauge pressure or bare set pressure into the equation undersizes A — the classic error this input ordering is designed to surface.
Why Kd = 0.65 and 0.975 — my valve's datasheet shows different coefficients?
These are API 520's "effective" coefficients for preliminary sizing against API 526 effective orifice areas — deliberately conservative pairings used before a valve is chosen. Once you select an actual valve, the manufacturer's ASME-certified (rated) coefficient with the actual orifice area governs, and the certified pair typically shows a few percent more capacity. Preliminary effective sizing then certified verification is exactly the two-step the standard intends.
Which correction factors do I actually need to touch?
Usually none — all default to 1.0. Set Kc = 0.9 only when a rupture disk is installed upstream of the valve. Kw derates balanced-bellows valves in liquid service as backpressure rises (vendor curves; conventional valves discharging to atmosphere keep 1.0). Kv drops below 1.0 only for genuinely viscous liquids (glycols, oils — check the Reynolds number). Kb derates gas capacity when backpressure approaches the critical ratio or for balanced valves per vendor curves.
The required area exceeds the T orifice — now what?
A T orifice (26 in²) is the largest single API 526 valve; beyond it the practice is multiple valves in parallel, each sized for its share of the relieving load with staggered set pressures per ASME VIII rules. The tool reports the required area and flags that no single letter covers it. That said, a requirement past T often signals the relieving scenario deserves scrutiny — fire-case loads especially are frequently over-estimated by shortcut methods.
Can I size steam, two-phase, or fire-case reliefs with this?
No. Steam has its own API 520 equation with superheat and Napier corrections; two-phase flow needs the DIERS/Appendix C methodology; and the fire case first requires the heat-input and relieving-load calculation of API 521 before any orifice math starts. This tool covers the two bread-and-butter equations — single-phase liquid and critical-flow gas — which is enough to class an orifice letter for scoping, and no more. The relieving scenario definition is the engineering; the area formula is the easy part.