Relief area calculation for a rupture disc according to API 520

Short answer: the relief area of a rupture disc is calculated with the equations of API 520 Part I (equivalent to those of ASME) for the worst-case flow rate. If the disc discharges directly to atmosphere and meets the "8 and 5 diameter" rule, the discharge coefficient method is used with K_D = 0.62. In any other case the flow resistance method is used, in which the disc is just another pipe fitting with its certified K_R factor.

By the P&V Control Devices technical team · Published October 4, 2026 · Reading time: 9 min

Before calculating: the relief flow rate

Direct answer: the area depends on the flow that has to be discharged, and that flow comes from the scenario analysis, not from the size of the line.

API 521 helps identify overpressure scenarios: external fire, cooling water failure, outlet blockage, control valve failure, heat exchanger tube rupture, runaway reaction, among others. For each one the relief flow is estimated and the sizing is done with the most demanding. In runaway reactions and deflagrations the flow can be two-phase and requires specific methodologies (for example, those of DIERS) that are outside the scope of this guide.

The two sizing methods

"8 and 5" rule: the disc discharges directly to atmosphere, is installed no more than 8 pipe diameters from the vessel, the discharge piping does not exceed 5 diameters, and the nominal diameter of the inlet and outlet piping is not smaller than that of the disc.

Equation for gas or vapor in critical flow

When the back pressure is below the critical pressure (for air, approximately 53 % of the absolute relieving pressure), the flow is critical and API 520 Part I gives, in English units:

A = W / (C · K_D · P₁ · K_b · K_c) · √(T · Z / M)

• A: required effective discharge area, in².
• W: mass relief flow rate, lb/h.
• C: coefficient that depends on the specific heat ratio k: C = 520 · √[k · (2/(k+1))^(k+1)/(k-1)]. For k = 1.4, C ≈ 356.
• K_D: discharge coefficient; 0.62 for a rupture disc under the "8 and 5" rule.
• P₁: upstream relieving pressure, psia = burst pressure + allowable overpressure + atmospheric pressure.
• K_b: back pressure correction factor (1.0 in critical flow for a rupture disc).
• K_c: combination factor; 1.0 if there is no disc upstream of a valve.
• T: relieving temperature, °R; Z: compressibility factor; M: molecular mass.

API 520 includes the equivalent version in SI units. If the back pressure exceeds the critical pressure, the flow is subcritical and a different equation is used.

Worked example (indicative)

A compressed air vessel with an MAWP of 100 psig must relieve 10,000 lb/h at 100 °F. The disc, marked at 100 psig, discharges directly to atmosphere and meets the "8 and 5" rule. There is a single device, so a 10 % accumulation is allowed.

1. P₁ = 100 + 10 + 14.7 = 124.7 psia.
2. T = 100 + 460 = 560 °R; Z ≈ 1; M = 28.97; k = 1.4, so C ≈ 356.
3. A = 10 000 / (356 × 0,62 × 124,7) × √(560 / 28,97).
4. 356 × 0,62 × 124,7 ≈ 27 524; 10 000 / 27 524 ≈ 0,363; √19,33 ≈ 4,40.
5. A ≈ 1.60 in², equivalent to a flow diameter of about 1.43 in.

With this result, a 2 in disc usually has ample area, but the final check is made with the minimum net flow area published by the manufacturer for that model and size, which may be smaller than the pipe's inner area because of the petals or supports.

Liquid service

For liquids, API 520 relates the volumetric flow rate to the square root of the pressure drop and the specific gravity; in US customary units it takes the form A = Q / (38 · K_D · K_w · K_c · K_v) · √(G / (P₁ − P₂)), with Q in gpm and pressures in psig. For a rupture disc under the "8 and 5" rule, K_D = 0.62 is used, and K_v corrects for viscous liquids. In addition, you should confirm that the disc model is suitable for liquid service (some reverse-acting discs need gas under the dome to open fully).

Flow resistance method (K_R)

Short answer: instead of calculating an area, you verify that the entire relief system (inlet nozzle, disc, piping, elbows and outlet) can pass the required flow with the available pressure.

1. The resistances of each section are added: pipe friction (fL/D), fittings, entrance, exit and the disc's certified K_R.
2. With that total resistance, the system flow rate is calculated using compressible (gas) or incompressible (liquid) flow equations.
3. A safety factor of 0.9 is applied to the calculated capacity, as the codes require for this method.
4. Verify that the resulting capacity exceeds the required flow rate.

K_R is obtained by testing for each model and size. If the certified value is not available, a conservative value is usually used (for example, K_R = 2.4 per ASME practice for uncertified discs), which penalizes capacity. More detail in the glossary.

Disc upstream of a valve

In a disc + valve combination, the valve defines the area. Its capacity is multiplied by the combination factor K_c: 0.9 if no certified factor exists for that pairing, or the certified value if one exists. In addition, the disc must not have a flow area smaller than the valve inlet. See rupture disc vs pressure relief valve.

Common mistakes

• Applying K_D = 0.62 with a long discharge pipe or one connected to a header.
• Using gauge pressure instead of absolute in P₁.
• Forgetting the allowable accumulation (or using the fire accumulation when the scenario is not a fire).
• Compare the calculated area with the inside area of the pipe and not with the minimum net flow area of the disc.
• Not checking the inlet pressure drop when the disc protects a valve.

Note: educational guide. Equations and factors must be taken from the current edition of API 520 and the code applicable to the equipment.

Related guides: How to select a disc · Standards · Installation