Two-phase relief sizing
A relief valve on a liquid-filled vessel does not relieve liquid: as the pressure drops through the seat the liquid flashes, and the flow becomes two-phase. The mixture is far bulkier than the liquid, so the valve that would be right for liquid service is far too small — often by a factor of four.
| Term | Value | Note |
|---|---|---|
| Set pressure | 150 psig | as entered |
| Relieving pressure | 179.7 psia | 110% of set plus atmosphere |
| Relieving pressure | 1239 kPa | for the mass-flux expression |
| Inlet specific volume | 0.001000 m³/kg | saturated liquid |
| Omega | 9.10 | the flashing value, 9.1 |
| Critical mass flux | 7,701 kg/m²·s | G = 0.66 √(P₁/v₀ω) |
| Required flow | 5,000 kg/h | as entered |
| Required area | 0.280 in² | effective orifice |
| Liquid-only area | 0.069 in² | the wrong answer |
| Selected orifice | F — 0.307 in² | API 526 |
The two-phase area is 4.0 times the liquid-only answer. Sizing this service as a liquid is the classic error: the valve would be undersized by that factor and would not protect the vessel.
ω = 9.1 · Saturated liquid that flashes.
G = 0.66 √(P₁/(v₀ ω)) · Critical (choked) flow.
A = W/G · Effective orifice.
A = Q/(38 K_d √ΔP) · What not to use.
A clear path from inputs to results.
A relief valve on a liquid-filled vessel does not relieve liquid: as the pressure drops through the seat the liquid flashes, and the flow becomes two-phase. The mixture is far bulkier than the liquid, so the valve that would be right for liquid service is far too small.
How to use
- Set the pressure and the required relieving rate.
- Choose the inlet condition — saturated liquid is the common case.
- Enter the discharge coefficient.
- Read the required area and the API 526 orifice.
The formula
Reference: API 520 Part I Appendix C, the omega method for flashing service.
Worked example
5,000 kg/h of saturated water at a 150 psig set pressure
- 150 psig set, 5,000 kg/h.
- Saturated liquid inlet, discharge coefficient 0.65.
- 1
The relieving pressure is 110% of set plus atmosphere: 179.7 psia, or 1,239 kPa.
- 2
With ω = 9.1 and v₀ = 0.001 m³/kg, the critical mass flux is 7,700 kg/m²·s.
- 3
The required flow of 1.39 kg/s therefore needs 1.8 cm², or 0.28 in².
- 4
The liquid-only equation would have given 0.07 in² — four times too small.
- 5
The next API 526 orifice is F at 0.307 in².
0.28 in² · F orifice · 4× the liquid answer.
Interpreting the result
Sizing a flashing service with the liquid equation is the classic error: the valve looks adequate on paper and is undersized by a factor of four in service, which is exactly when it matters. The omega method exists because the flashing cannot be ignored.
Assumptions & limitations
- A saturated liquid inlet that flashes through the seat.
- Critical (choked) flow, which applies for ω above about 4.
- A conventional valve with a 0.65 discharge coefficient.
- No inlet or outlet piping loss.
Frequently asked questions
Why does the liquid flash?
Because the pressure at the valve seat is below the vapour pressure at the inlet temperature, so the liquid boils as it accelerates through the orifice.
Why is the two-phase area so much larger?
Because the mass flux is far lower — the mixture occupies much more volume than the liquid, so the same mass flow needs a much bigger hole.
Does the same apply to a steam trap?
Yes — a trap discharging condensate flashes in exactly the same way, which is why a trap is sized on the flash steam volume rather than the condensate flow.
What is omega?
A single dimensionless parameter that captures the flashing behaviour. It is 9.1 for saturated water, and larger means more flashing and a lower mass flux.
Is the flow always choked?
For a flashing service, usually. If ω is below about 4 the flow may be subcritical and a different expression applies.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.