# Calculation Methods - Relief Valve

There are two calculation methods available in FluidFlow for predicting the pressure loss through relief valves: API RP 520 & ISO 4126. API RP 520 caters to Newtonian liquids, steam, gas/vapors, and two-phase flow. ISO 4126 caters for liquid and gas flow only. API RP 520: For gas or vapor critical flow relief, the sizing equation used is: A = [w (T Z)0.5 / (C Kd P1 Kb Kc (M 0.5))] where:
A | is the effective discharge area.
w | is the mass flow (lb/hr).
T | is the absolute temperature of the gas.
Z | is the gas compressibility factor.
C | is a gas constant dependent on the specific heat ratio of the gas.
Kd | is the rated coefficient of discharge. For preliminary sizing estimation, a discharge coefficient of 0.975 may be used when a relief valve is installed with or without a bursting disk in combination.
P1 | is the upstream relieving pressure + overpressure + atmospheric pressure.
Kb | is the capacity correction factor due to back pressure.
Kc | is the combination correction factor for installations with a bursting disk upstream of the pressure relief valve. A value of 1.0 is occasionally used when a bursting disk is not installed and 0.9 is used when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value.
M | is the gas molecular weight.
API RP 520: For gas or vapor sub-critical flow relief, the sizing equation used is: A = [17.9 w (T Z)0.5 / (F2 Kd Kc (M P1 r P 0.5)) where:
A | is the effective discharge area.
w | is the mass flow (kg/h).
T | is the absolute temperature of the gas.
Z | is the gas compressibility factor.
F2 | is the coefficient for subcritical flow.
Kd | is the rated coefficient of discharge. For preliminary sizing estimation, a discharge coefficient of 0.975 may be used when a relief valve is installed with or without a bursting disk in combination.
Kc | is the combination correction factor for installations with a bursting disk upstream of the pressure relief valve. A value of 1.0 is occasionally used when a bursting disk is not installed and 0.9 is used when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value.
P1 | is the upstream relieving pressure + overpressure + atmospheric pressure.
Kb | is the capacity correction factor due to back pressure.
M | is the gas molecular weight.
API RP 520: For liquid flow relief, the sizing equation used is: A = [(Q (G0.5)) / (38 Kd Kw Kc Kv (r P 0.5))] where:
A | is the effective discharge area.
Q | is the mass flow rate.
G | is the specific gravity.
Kd | is the rated coefficient of discharge. For preliminary sizing estimation, a discharge coefficient of 0.975 may be used when a relief valve is installed with or without a bursting disk in combination.
Kw | is the correction factor due to back pressure. In systems where the back pressure is atmospheric, you can use a value of 1.0. This
| correction factor applies to balanced bellows valves only.
Kc | is the combination correction factor for installations with a bursting disk upstream of the pressure relief valve. A value of 1.0 is occasionally used when a bursting disk is not installed and 0.9 is used when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value.
Kv | is the correction factor due to viscosity. Note, that FluidFlow will determine this value as part of the calculation process.
API RP 520: For steam flow relief, the sizing equation used is: A = [w / (51.5 (P1 Kd Kb Kc KN KSH))] where:
A | is the effective discharge area.
w | is the mass flow rate.
P1 | is the upstream relieving pressure. This is the set pressure plus the allowable overpressure.
Kd | is the rated coefficient of discharge. For preliminary sizing estimation, a discharge coefficient of 0.975 may be used when a relief valve is installed with or without a bursting disk in combination.
Kb | is the back pressure correction factor for vapor. This correction factor applies | to balanced bellows valves only.
Kc | is the combination correction factor for installations with a bursting disk upstream of the pressure relief valve. A value of 1.0 is occasionally used when a bursting disk is not installed and 0.9 is used when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value.
KN | is the capacity correction factor for high-pressure dry saturated steam (set pressures above 1500 psi a). This correction factor is applied to account for the deviation between steam flow as determined by the Napier equation and the actual saturated steam flow rate at high pressures.
KSH | is the superheated steam correction factor. Note, that steam sizing equations are based on the flow of dry saturated steam When sizing a superheated steam application, this superheat correction factor is applied to correct the calculated saturated steam flow to superheated steam flow. For saturated steam at any pressure, KSH = 1.0. When the steam is superheated, FluidFlow will determine the value for KSH automatically.
API RP 520: For two-phase flashing or non-flashing flow relief through a pressure relief valve, the sizing equation used is: A = [(0.04 w) / (Kd Kb Kc G)] where:
A | is the effective discharge area.
w | is the mass flow rate.
Kd | is the rated discharge coefficient which should be obtained from the manufacturer. For preliminary sizing estimation, a discharge coefficient of 0.85 is occasionally used.
Kb | is the back pressure correction factor for vapor which should be obtained from the manufacturer. The back pressure correction factor applies to balanced bellows valves only.
Kc | is the combination correction factor for installations with a bursting disk upstream of the pressure relief valve. A value of 1.0 is occasionally used when a bursting disk is not installed and 0.9 is used when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value.
G | is the mass flux.
Note, for flashing flow, the two-phase system must consist of a saturated liquid and saturated vapor and contain no non-condensable gas. For non-flashing flow, the two-phase system must consist of a highly sub-cooled liquid and either a non-condensable gas, condensable vapor, or both. Fluids both above and below the thermodynamic critical point in condensing two-phase flow can also be handled. API RP 520: For two-phase sizing of sub-cooled liquid at the pressure relief valve inlet, the sizing equation used is: A = [(0.3208 Q ρ) / (Kd Kb Kc G)] where:
A | is the effective discharge area.
Q | is the volumetric flow rate.
ρ | is the liquid density.
Kd | is the rated discharge coefficient which should be obtained from the manufacturer. For preliminary sizing estimation, a discharge coefficient of 0.65 is occasionally used for subcooled liquids and 0.85 for saturated liquids.
Kb | is the back pressure correction factor for vapor which should be obtained from the manufacturer. The back pressure correction factor applies to balanced bellows valves only.
Kc | is the combination correction factor for installations with a bursting disk upstream of the pressure relief valve. A value of 1.0 is occasionally used when a bursting disk is not installed and 0.9 is used when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value.
G | is the mass flux.
This equation can be used for sizing pressure relief valves handling a sub-cooled liquid (including saturated) at the inlet. No condensable vapor or non-condensable gas should be present at the inlet. The sub-cooled liquid either flashes upstream or downstream of the pressure relief valve throat depending on which sub-cooling region the flow falls into. The following equation is only applicable to turbulent flow systems. Most two-phase relief scenarios will however be within the turbulent flow regime. API RP 520: For two-phase flashing flow relief with non-condensable gas according to API RP 520, the sizing equation used is: A = [(0.04 w) / (Kd Kb Kc G)] where:
A | is the effective discharge area.
w | is the mass flow rate.
Kd | is the rated discharge coefficient which should be obtained from the manufacturer. For preliminary sizing estimation, a discharge coefficient of 0.85 is occasionally used.
Kb | is the back pressure correction factor for vapor which should be obtained from the manufacturer. The back pressure correction factor applies to balanced bellows valves only.
Kc | is the combination correction factor for installations with a bursting disk upstream of the pressure relief valve. A value of 1.0 is occasionally used when a bursting disk is not installed and 0.9 is used when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value.
G | is the mass flux.
This equation can be used for sizing pressure relief valves handling two-phase flashing flow with a non-condensable gas or both a condensable vapor and non-condensable gas. ISO 4126: For gas or vapor critical flow relief, the sizing equation used is: A = [Qm (To Zo)0.5 / C α Po (M)0.5] where:
A | is the effective discharge area.
Qm | is the mass flow rate.
To | is the relieving temperature.
Zo | is the gas compressibility factor
C | is a gas constant dependent on the specific heat ratio of the gas.
α | is the discharge coefficient. - In the case of an internally protruding branch/nozzle, α = 0.68. - In the case of a flush branch/nozzle or a block flange whose inlets are not of hydrodynamic configuration, α = 0.73. - In the case of a branch/nozzle or a block flange of hydrodynamic configuration, e.g. with rounded or chamfered inlets, α = 0.8. Note, for further information and an explanation of the above terms, refer to ISO 4126.
Po | is the relieving pressure.
M | is the gas molecular weight.
ISO 4126: For gas or vapor sub-critical flow relief, the sizing equation used is: A = [Qm (To Zo)0.5 / C Kb α Po (M)0.5] where:
A | is the effective discharge area.
Qm | is the mass flow rate.
To | is the relieving temperature.
Zo | is the gas compressibility factor
C | is a gas constant dependent on the specific heat ratio of the gas.
α | is the discharge coefficient. - In the case of an internally protruding branch/nozzle, α = 0.68. - In the case of a flush branch/nozzle or a block flange whose inlets are not of hydrodynamic configuration, α = 0.73. - In the case of a branch/nozzle or a block flange of hydrodynamic configuration, e.g. with rounded or chamfered inlets, α = 0.8. Note, for further information and an explanation of the above terms, refer to ISO 4126.
Kb | is the capacity correction factor for subcritical flow.
Po | is the relieving pressure.
M | is the gas molecular weight.
ISO 4126: For liquid flow relief which does not flash to vapor, the sizing equation used is: A = [0.621 Qm / Kv α (ρ r P)0.5] where:
A | is the effective discharge area.
Qm | is the mass flow rate.
Kv | is the viscosity correction factor.
α | is the discharge coefficient. - In the case of an internally protruding branch/nozzle, α = 0.68. - In the case of a flush branch/nozzle or a block flange whose inlets are not of hydrodynamic configuration, α = 0.73. - In the case of a branch/nozzle or a block flange of hydrodynamic configuration, e.g. with rounded or chamfered inlets, α = 0.8. Note, for further information and an explanation of the above terms, refer to ISO 4126.
ρ | is the fluid density.
r P | is the differential pressure on venting across the safety relief device.
ISO 4126: For steam flow relief, the sizing equation used is: A = [3.469 Qm (Vo)0.5 / C α (Po)0.5] where:
A | is the effective discharge area.
Qm | is the mass flow rate.
Vo | is the specific volume at actual relieving pressure and temperature.
C | is a gas constant dependent on the specific heat ratio of the gas.
α | is the discharge coefficient. - In the case of an internally protruding branch/nozzle, α = 0.68. - In the case of a flush branch/nozzle or a block flange whose inlets are not of hydrodynamic configuration, α = 0.73. - In the case of a branch/nozzle or a block flange of hydrodynamic configuration, e.g. with rounded or chamfered inlets, α = 0.8. Note, for further information and an explanation of the above terms, refer to ISO 4126.
Po | is the relieving pressure.
ISO 4126: For two-phase flow relief systems, the ISO 4126 calculation method has not been implemented and as such, FluidFlow will revert to the API RP 520 solution procedure when this option is selected.