ASME B31.1 Power Piping Steam Pressure Relief

Calculate ASME B31.1 steam table properties from temperature and pressure.

Steam table values can be calculated for water and steam, saturated water, saturated steam, saturated water and steam, metastable water, and metastable steam. The calculations for water and steam are valid between 273.15 K and 1073.15 K (0 to 100 MPa), and between 1073.15 K and 2273.15 K (0 to 50 MPa).

The saturated water and steam calculations are valid between 273.15 K and 647.096 K.

The metastable calculation is valid between 273.15 K and 647.096 K, and for pressure from the saturated vapour line to the 5% equilibium moisture line (user defined).

Note : There is an anomaly in the steam calculation for region 3 between the saturated vapour line, the regions 2/3 boundary, and the critical pressure. Select either region 2 or region 3 for calculations in the anomaly zone.

Reference : IAPWS R7-97 Industrial Formulation for thermodynamic Properties of Water and Steam

Tool Input

• anomtype : Region 2/3 Anomaly Type
• proptype : Steam Phase
  • Pu : User Defined Pressure
  • Tu : User Defined Temperature
  • Xu : User Defined Saturated Steam Quality

Tool Output

• ρ : Density
• Cp : Specific Heat Constant Pressure
• Cp-Cv : Delta Specific Heat (Cp - Cv)
• Cp/Cv : Specific Heat Ratio
• Cv : Specific Heat Constant Volume
• P : Pressure
• T : Temperature
• Vc : Speed Of Sound
• Z : Compressibility Factor
• cvg : Convergence Check
• h : Enthalpy
• s : Entropy
• u : Internal Energy
• vg : Mole Specific Volume
• vm : Specific Volume
• wv : Specific Weight

Calculate ASME B31.1 steam density and compressibility factor from temperature and pressure.

The gas compressibility factor is calculated from the critical point temperature, critical point temperature, and the accentric factor using either the Peng Robinson, Soave, Redlich Kwong or Van Der Waals equations of state (EOS). The compressibility factor calculation is valid for vapour phase only. Use the Result Plot option to plot compressibility factor versus pressure and temperature, compressibility factor versus pressure and equation of state type, or compressibility factor versus temperature and equation of state type.

Tool Input

• eostype : Equation Of State Type
  • Zu : User Defined Gas Compressibility Factor
• P : Fluid Pressure
• T : Fluid Temperature

Tool Output

• ρ : Fluid Density
• ω : Accentric Factor
• Pc : Critical Point Pressure
• Rg : Specific Gas Constant
• SG : Gas Specific Gravity
• Tc : Critical Point Temperature
• Vm : Molar Volume
• Z : Compressibility Factor
• cvg : Convergence Check
• mmg : Gas Molar Mass

Calculate ASME B31.1 steam mass flow rate through a pressure relief vent for adiabatic and isothermal flow.

The pipeline or pressure vessel is assumed to be at stagnation conditions (M = 0), which is valid when the pipeline diameter is much greater than the vent diameter. Vent pressure losses are calculated from the vent pressure loss factor (fld = fL/D + K). At high pressure the vent exit flow is critical flow (Mc = 1 for adiabatic flow and Mc = √(1/γ) for isothermal flow). At lower pressures the vent exit flow is sub critical (M < Mc). The vent entry is sub critical at all conditions. Use the steam table to calculate a suitable value for the specific heat ratio γ, and the compressibility factor Z. For super heated steam γ = 1.334 can be used as an estimate.

Minor losses can be accounted for by using either the minor loss K factor, or the discharge coefficient Cd. Minor losses should include the vent entry, valves and bends etc. The vent exit should not be included (the fluid dynamic pressure is included in the calculation). The discharge coefficient can also be used as a design factor. API 520 recommends Cd = 0.9 for vents with a valve, or Cd = 0.62 for vents with a burst disk (with no K factor). For isothermal flow the inlet temperature should be set equal to the estimated isothermal temperature (eg ambient temperature). The stagnation temperature is constant for adiabatic flow, and varies with Mach number for isothermal flow.

The vent is assumed to be constant diameter. The flow is assumed to be fully turbulent. The Darcy friction factor is calculated using the rough pipe equation. The rough pipe equation is less accurate at low flow velocity. Phase changes are ignored. Use the Result Plot option to plot nozzle, vent inlet and exit pressure versus stagnation pressure, vent inlet and exit mach number versus stagnation pressure, or mass flow rate versus stagnation pressure and flow type.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

Tool Input

• schdtype : Vent Schedule Type
• diamtype : Vent Diameter Type
  • ODu : User Defined Vent Outside Diameter
  • IDu : User Defined Vent Inside Diameter
• wtntype : Wall Thickness Type
  • tnu : User Defined Vent Wall Thickness
• rfactype : Vent Internal Roughness Type
  • ru : User Defined Surface Roughness
  • rru : User Defined Relative Roughness
• fdtype : Darcy Friction Factor Type
  • fdu : User Defined Darcy Friction Factor
• leqtype : Minor Pressure Loss Type
  • ku : User Defined Minor Loss K Factor
  • lu : User Defined Minor Loss Length
  • lodu : User Defined Minor Loss Diameters (L/ID)
  • fL/Du : User Defined Pressure Loss Factor
• fluidtype : Specific Heat Ratio Type
  • γu : User Defined Specific Heat Ratio
• zfactype : Compressibility Factor Type
  • Zu : User Defined Compressibility Factor
• cdtype : Discharge Coefficient Type
  • Cdu : User Defined Discharge Coefficient
• flowtype : Flow Type
  • Tou : User Defined Adiabatic Stagnation Temperature
  • Tiu : User Defined Isothermal Vent Temperature
• Po : Stagnation Pressure
• Pa : Ambient Pressure (At Exit)
• L : Vent Length

Tool Output

• γ : Specific Heat Ratio
• ρe : Vent Exit Density
• ρi : Vent Inlet Density
• Cd : Discharge Coefficient
• Ce : Vent Exit Speed Of Sound
• Ci : Vent Inlet Speed Of Sound
• Fe : Vent Exit Reaction Force
• Ge : Vent Exit Mass Flux
• Gi : Vent Inlet Mass Flux
• ID : Vent Inside Diameter
• Le : Vent Eqivalent Length
• Mce : Vent Critical Exit Mach Number
• Mci : Vent Critical Inlet Mach Number
• Me : Vent Exit Mach Number
• Mi : Vent Inlet Mach Number
• Pe : Vent Exit Pressure
• Pi : Vent Inlet Pressure
• Rg : Specific Gas Constant
• SG : Gas Specific Gravity Relative To Air
• Te : Vent Exit Temperature
• Ti : Vent Inlet Temperature
• Toe : Vent Exit Stagnation Temperature
• Ve : Vent Exit Velocity
• Vi : Vent Inlet Velocity
• Z : Compressibility Factor
• cvg : Convergence Factor (≅ 1)
• fL/D : Pressure Loss Factor Including Minor Losses
• fL/Da : Added Friction Loss Factor
• fL/De : Effective Friction Loss Factor
• fd : Darcy Friction Factor
• m : Vent Mass Flowrate
• mmg : Gas Molar Mass
• n : Vent Mole Flow Rate
• rr : Surface Roughness Ratio

Calculate ASME B31.1 steam duct Fanno flow ratios and Fanno lines for adiabatic and isothermal critical flow with friction.

Fanno flow is calculated for critical flow conditions. Critical flow conditions occur when exit Mach number equals the critical Mach number and the critical exit pressure is greater than or equal to ambient pressure. For adiabatic flow the critical exit Mach number = 1 (eg sonic flow conditions). For isothermal flow the critical exit Mach number = √γ. Use the steam table to calculate a suitable value for the specific heat ratio γ. For super heated steam γ = 1.334 can be used as an estimate.

Use the Result Plot option to plot critical pressure loss factor versus inlet Mach number and either flow type or specific heat ratio; or Fanno lines for pressure ratio, temperature ratio, density ratio, speed of sound ratio, and velocity ratio, versus either Mach number or pressure loss factor, and versus either flow type or specific heat ratio. The plot range is set from the calculated value of either the inlet Mach number, or the pressure loss factor in the main calculation. Change the main calculation values to change the plot range.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

Tool Input

• fluidtype : Specific Heat Ratio Type
  • γu : User Defined Specific Heat Ratio
• fldtype : Pressure Loss Factor Type
  • Mciu : User Defined Inlet Mach Number
  • fL/Du : User Defined Pressure Loss Factor
• flowtype : Fluid Flow Type

Tool Output

• γ : Specific Heat Ratio
• ρi/ρ* : Inlet Density Over Critical Exit Density Ratio
• Ci/C* : Inlet Speed Of Sound Over Critical Exit Speed Of Sound Ratio
• M* : Critical Exit Mach Number
• Mi : Inlet Mach Number
• Pi/P* : Inlet Pressure Over Critical Exit Pressure Ratio
• Ti/T* : Inlet Temperature Over Critical Exit Temperature Ratio
• Vi/V* : Inlet Velocity Over Critical Velocity Ratio
• cvg : Convergence Factor (≅ 1)
• fL/D* : Critical Duct Pressure Loss factor

Calculate ASME B31.1 steam mass flow rate through a pressure relief header for adiabatic and isothermal flow conditions.

The pressure relief header is assumed to be part of a pressure relief system, and connected to the outlet of an upstream pressure relief valve, relief vent, or a smaller diameter relief header. The header inlet pressure should be set equal to exit pressure of the upstream device. The header should be sized so that the calculated header mass flowrate is greater than or equal to the upstream mass flowrate. For headers with more than one inlet, the header mass flowrate is divided by the number of inlets. The calculated header flowrate is the maximum possible value. The actual mass flowrate will always be equal to the upstream flowrate and the actual header inlet pressure will be less than or equal to the upstream exit pressure.

For adiabatic flow, the inlet temperature is calculated from the upstream stagnation temperature (the inlet temperature varies with the inlet Mach number). For isothermal flow the inlet temperature should be set equal to the estimated isothermal temperature (eg ambient temperature). The stagnation temperature is constant for adiabatic flow, and varies with Mach number for isothermal flow. Phase changes are ignored.

Header pressure losses are calculated from the pressure loss factor (fld = fL/D + K). The Darcy friction factor f is calculated for fully turbulent flow using the rough pipe equation. The header is assumed to be constant diameter. Minor losses can be included by the minor loss K factor or an equivalent length, and should include valves and bends etc. The header entry and exit losses should not be included (the fluid dynamic pressure loss is included in the calculation). The discharge coefficient can also be used for minor losses, and as a safety factor. If the ambient pressure is less than the critical exit pressure the header exit flow is critical (Mc = 1 for isentropic flow and Mc = √(1/γ ) for isothermal flow). If the ambient pressure is greater than the critical exit pressure, the header exit flow is sub critical (M < Mc). The header entry flow is assumed to be sub critical for all flow conditions. Use the steam table to calculate a suitable value for the specific heat ratio γ. For super heated steam γ = 1.334 can be used as an estimate.

Use the Result Plot option to plot inlet and exit pressure versus stagnation pressure, inlet and exit mach number versus stagnation pressure, or mass flow rate versus stagnation pressure and flow type.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

Tool Input

• schdtype : Header Schedule Type
• diamtype : Header Diameter Type
  • ODu : User Defined Header Outside Diameter
  • IDu : User Defined Header Inside Diameter
• wtntype : Wall Thickness Type
  • tnu : User Defined Header Wall Thickness
• rfactype : Header Internal Roughness Type
  • ru : User Defined Surface Roughness
  • rru : User Defined Relative Roughness
• fdtype : Darcy Friction Factor Type
  • fdu : User Defined Darcy Friction Factor
• leqtype : Minor Pressure Loss Type
  • ku : User Defined Minor Loss K Factor
  • lu : User Defined Minor Loss Length
  • lodu : User Defined Minor Loss Diameters (L/ID)
  • fL/Du : User Defined Pressure Loss Factor
• numtype : Number Of Inlets Type
  • Nu : User Defined Number Of Inlets
• fluidtype : Specific Heat Ratio Type
  • γu : User Defined Specific Heat Ratio
• zfactype : Compressibility Factor Type
  • Zu : User Defined Compressibility Factor
• cdtype : Discharge Coefficient Type
  • Cdu : User Defined Discharge Coefficient
• flowtype : Flow Type
  • Tou : User Defined Adiabatic Stagnation Temperature
  • Tiu : User Defined Isothermal Inlet Temperature
• Pi : Header Inlet Pressure
• Pa : Ambient Pressure (At Exit)
• L : Header Length

Tool Output

• γ : Specific Heat Ratio
• ρe : Header Exit Density
• ρi : Header Inlet Density
• Cd : Discharge Coefficient
• Ce : Header Exit Speed Of Sound
• Ci : Header Inlet Speed Of Sound
• Fe : Combined Exit Reaction Force (All PRVs)
• Ge : Header Exit Mass Flux
• Gi : Header Inlet Mass Flux
• ID : Header Inside Diameter
• Le : Header Eqivalent Length
• Mce : Header Critical Exit Mach Number
• Mci : Header Critical Inlet Mach Number
• Me : Header Exit Mach Number
• Mi : Header Inlet Mach Number
• N : Number Of PRV's Sharing The Header
• Pe : Header Exit Pressure
• Rg : Specific Gas Constant
• SG : Gas Specific Gravity Relative To Air
• Te : Header Exit Temperature
• Ti : Header Inlet Temperature
• Toe : Exit Stagnation Temperature
• Ve : Header Exit Velocity
• Vi : Header Inlet Velocity
• Z : Compressibility Factor
• cvg : Convergence Factor (≅ 1)
• fL/D : Pressure Loss Factor Including Minor Losses
• fL/Da : Added Friction Loss Factor
• fL/De : Effective Friction Loss Factor
• fd : Darcy Friction Factor
• mf : Mass Flowrate Per PRV
• mmg : Gas Molar Mass
• nf : Mole Flow Rate Per PRV
• rr : Surface Roughness Ratio

Calculate ASME B31.1 steam pipe Darcy friction factor from either the Moody diagram or the Von Karman rough pipe equation (API 520 Annex E).

At high Reynolds numbers the Moody diagram friction factor is fully turbulent and is dependent on the pipe roughness only. The pressure loss factor (fLe/ID) includes minor losses. Minor losses can be entered as either a K factor, an equivalent added length, or an equivalent added length over diameter ratio.

Tool Input

• schdtype : Pipe Schedule Type
• diamtype : Pipe Diameter Type
  • ODu : User Defined Outside Diameter
  • IDu : User Defined Inside Diameter
• wtntype : Wall Thickness Type
  • tnu : User Defined Wall Thickness
• rfactype : Pipe Internal Roughness Type
  • ru : User Defined Surface Roughness
  • rru : User Defined Relative Roughness
• fluidtype : Specific Heat Ratio Type
  • γu : User Defined Specific Heat Ratio
• zfactype : Factor Type
  • Zu : User Defined Compressibility Factor
• vctype : Speed Of Sound Type
  • Cu : User Defined Sound Velocity
• machtype : Flow Rate Type
  • Vu : User Defined Velocity
  • Mu : User Defined Mach Number
  • mfu : User Defined Mass Flow Rate
  • ngu : User Defined Mole Flow Rate
  • Reu : User Defined Reynolds Number
• visctype : Viscosity Type
  • μu : User Defined Dynamic Viscosity
  • νu : User Defined Kinematic Viscosity
• fdtype : Darcy Friction Factor Type
  • fdu : User Defined Darcy Friction Factor
• leqtype : Minor Pressure Loss Type
  • Ku : User Defined Minor Loss K Factor
  • lu : User Defined Minor Loss Length
  • lodu : User Defined Minor Loss Diameters (L/ID)
  • Leu : User Defined Equivalent Length
  • fL/Du : User Defined Pressure Loss Factor
• P : Fluid Pressure
• T : Fluid Temperature
• L : Pipe Length

Tool Output

• γ : Specific Heat Ratio
• μ : Dynamic Viscosity
• ρ : Fluid Density
• Ax : Nominal Cross Section Area
• C : Speed Of Sound
• ID : Inside Diameter
• Le : Pipe Eqivalent Length
• M : Flow Mach Number
• Qf : Volume Flowrate
• Re : Reynolds Number
• Rg : Specific Gas Constant
• SG : Gas Specific Gravity Relative To Air
• V : Velocity
• Z : Compressibility Factor
• cvg : Convergence Factor (≅ 1)
• fL/D : Pressure Loss Factor Including Minor Losses
• fd : Darcy Friction Factor
• mf : Mass Flowrate
• mmg : Gas Molar Mass
• ng : Mole Flow Rate
• rr : Surface Roughness Ratio
• vg : Mole Specific Volume