Pressure relief valve sizing
A relief valve is the last barrier on a vessel, so the sizing is done to a standard rather than to a rule of thumb. The gas equation is a choked nozzle whose capacity depends on upstream pressure and a gas constant that is a function of k alone; the liquid equation is a square root of differential pressure. Both produce an effective area, which is then rounded up to the next API 526 orifice letter.
| Term | Value | Note |
|---|---|---|
| Set pressure | 150 psig | as entered |
| Relieving pressure P1 | 179.7 psia | 110% of set plus atmosphere |
| Back pressure | 14.7 psia | 0 psig |
| Required flow | 20,000 lb/hr | from the relieving case |
| Gas constant C | 347.0 | k = 1.30 |
| Critical ratio | 0.546 | below this the flow is choked |
| Temperature | 660 °R | absolute |
| Molecular weight | 44.0 | lb/lbmol |
| Discharge coefficient Kd | 0.975 | gas and vapour |
| Required area | 1.274 in² | effective orifice |
| Selected orifice | J — 1.287 in² | API 526 letter |
| Rated capacity | 20,207 lb/hr | at the selected area |
A J orifice (1.287 in²) passes 20207 lb/hr at these conditions, 99% of its rated capacity. The flow is choked, so the capacity depends on upstream pressure only.
A = W √(TZ/M) / (C Kd P1 Kb Kc) · API 520 Part I, Eq. 1.
C = 520 √(k (2/(k+1))^((k+1)/(k−1))) · A function of k only.
A = Q √(G/ΔP) / (38 Kd Kw Kc Kv) · API 520 Part I, Eq. 5.
next API 526 letter ≥ A · D through T.
A clear path from inputs to results.
A relief valve is the last barrier on a vessel, so the sizing is done to a standard rather than to a rule of thumb. The gas equation is a choked nozzle whose capacity depends on upstream pressure and a gas constant that is a function of k alone; the liquid equation is a square root of differential pressure.
How to use
- Choose gas or liquid service.
- Set the set pressure, back pressure and required flow.
- Add the gas properties, or the liquid specific gravity.
- Read the required area and the API 526 orifice that covers it.
The formula
Reference: API 520 Part I, Sizing, Selection and Installation of Pressure-Relieving Devices; orifice letters from API 526.
Worked example
20,000 lb/hr of gas at a 150 psig set pressure
- 150 psig set, atmospheric back pressure.
- 20,000 lb/hr, molecular weight 44, k = 1.3.
- 200 °F relieving temperature, Z = 1.
- 1
The relieving pressure is 110% of set plus atmosphere: 179.7 psia.
- 2
The gas constant C is 347.0 for k = 1.3.
- 3
The required area is (20,000 / (347 × 0.975 × 179.7)) × √(659.7/44) = 1.274 in².
- 4
The next API 526 orifice is J at 1.287 in².
- 5
At atmospheric back pressure the flow is choked, so capacity depends on upstream pressure only.
1.274 in² required · J orifice · choked flow.
Interpreting the result
Choked flow is the normal case for a gas relief valve discharging to atmosphere, and it means the back pressure has no effect on capacity. Once the back pressure rises above about 10% of set, a conventional valve’s capacity starts to fall and a balanced bellows valve is needed — which is why the back-pressure correction is the term most often mishandled.
Assumptions & limitations
- A conventional valve with 10% overpressure, Kb = 1 and Kc = 1.
- Gas service uses Kd = 0.975 and liquid service 0.65.
- The relief case is the governing one; fire and thermal relief are separate cases.
- Two-phase and flashing flow are not modelled.
Frequently asked questions
What is the gas constant C?
A function of the specific-heat ratio only: C = 520 √(k(2/(k+1))^((k+1)/(k−1))). It is about 356 for air and 347 for k = 1.3.
Why is Kd different for gas and liquid?
Because the two are calibrated against different test fluids and the discharge behaviour differs. Gas and vapour use 0.975; liquid uses 0.65.
How do I pick between a conventional and a balanced valve?
By back pressure. Above about 10% of set, a conventional valve’s capacity falls and a balanced bellows valve is required to keep it predictable.
What does choked mean?
The flow has reached the speed of sound at the orifice throat, so lowering the downstream pressure further does not increase the flow. Capacity then depends only on upstream conditions.
What is the 10% overpressure?
The allowance above set pressure at which the valve is rated to reach full lift. It is 10% for most cases and 21% for fire exposure.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.