What relief sizing is really asking
A pressure relief valve is the last line of defence: when everything else has failed, it must pass enough mass fast enough to stop the vessel exceeding its design pressure. Sizing therefore starts not with the valve but with the relief case — blocked outlet, external fire, control valve failure, thermal expansion, tube rupture. Determining the worst credible load is process engineering work, and it dominates the answer far more than the equations below.
The API 520 equations
with A in mm², W in kg/h, Q in L/min, and P₁ the absolute relieving pressure. The coefficient C depends only on the specific heat ratio: C = 0.03948 × √[k·(2/(k+1))(k+1)/(k−1)], which works out to 0.02703 for air at k = 1.4.
Worked example
10,000 kg/h of air relief, set at 1,000 kPa gauge with 10% overpressure, at 127 °C:
- Relieving pressure = 1,000 × 1.10 + 101.325 = 1,201 kPa abs
- C = 0.02703 for k = 1.4, Kd = 0.975
- A = 10,000 ÷ (0.02703 × 0.975 × 1,201) × √(400 × 1 ÷ 29)
- A = 316 × 3.713 = 1,173 mm² → select API orifice K (1,186 mm²)
Standard API orifice areas
| Letter | mm² | in² | Letter | mm² | in² |
|---|---|---|---|---|---|
| D | 71 | 0.110 | L | 1841 | 2.853 |
| E | 126 | 0.196 | M | 2323 | 3.600 |
| F | 198 | 0.307 | N | 2800 | 4.340 |
| G | 325 | 0.503 | P | 4116 | 6.380 |
| H | 506 | 0.785 | Q | 7129 | 11.05 |
| J | 830 | 1.287 | R | 10323 | 16.00 |
| K | 1186 | 1.838 | T | 16774 | 26.00 |
Field notes
- Always round up to the next letter. The standard areas exist so that valves are interchangeable; selecting the nearest letter rather than the next larger one can leave the relief undersized for its case.
- Oversizing is a real failure mode too. A grossly oversized PSV chatters — opening and slamming shut rapidly — which destroys the seat and can damage the inlet piping. It is not the safe direction it appears to be.
- The 3% inlet pressure drop rule governs inlet piping: exceed it and the valve chatters regardless of correct area. Check it with the pipe pressure drop calculator.
- Back pressure changes everything. Superimposed and built-up back pressure reduce capacity through Kb, and above roughly 10% of set pressure a conventional valve needs replacing with a balanced bellows or pilot-operated type.
- Two-phase and flashing relief are outside these equations and need the API 520 Appendix D or DIERS methods.
- This is preliminary sizing. Certified Kd values, actual relief loads and the full standard govern the real design.
Frequently asked questions
How do I calculate relief valve orifice area?
For gas in critical flow, A = W ÷ (C·Kd·P1·Kb·Kc) × √(TZ/M), giving area in mm² with flow in kg/h and absolute inlet pressure in kPa. Steam and liquid use their own API 520 forms. The computed area is then rounded up to the next standard API orifice letter.
What are the API orifice letters?
A standard series from D through T, each a fixed area from 71 mm² up to 26,000 mm². Sizing always selects the next letter larger than the calculated requirement — never the nearest, and never smaller.
What is the difference between set pressure and relieving pressure?
Set pressure is where the valve begins to open. Relieving pressure is set pressure plus the allowable overpressure, typically 10 percent for a single valve on a non-fire case, plus atmospheric to make it absolute. The sizing equations use relieving pressure.
What discharge coefficient should I use?
For preliminary sizing, 0.975 for gas and steam and 0.65 for liquid are the conventional API values. Final sizing must use the certified Kd from the manufacturer for the specific valve, which is usually slightly different.
Preliminary sizing for reference and education only. Pressure relief design is safety-critical and must be performed to the full API 520 / 521 methodology by a competent engineer using certified valve data. See our disclaimer.