Compressible Flow Pressure Relief Vent

Calculate the speed of sound and mach number for an ideal gas.

The speed of sound is calculated from the gas temperature, specific heat ratio and gas specific gravity. Either the Mach number can be calculated from a user defined velocity, or the velocity can be calculated from a user defined Mach number.

Tool Input

• fluidtype : Fluid Type
  • γu : User Defined Specific Heat Ratio
  • SGu : User Defined Gas Specific Gravity
• zfactype : Compressibility Factor Type
  • Zu : User Defined Compressibility Factor
• cctype : Speed Of Sound Type
  • Cu : User Defined Sound Velocity
• machtype : Mach Number Type
  • Vu : User Defined Fluid Velocity
  • Mu : User Defined Mach Number
• T : Fluid Temperature

Tool Output

• γ : Specific Heat Ratio
• C : Speed Of Sound
• M : Mach Number
• Rg : Specific Gas Constant
• SG : Gas Specific Gravity Relative To Air
• V : Fluid Velocity
• Z : Gas Compressibility Factor
• mmg : Gas Molar Mass

Calculate steam vent flow rate and pressure drop for critical and sub critical adiabatic and isothermal flow.

The pipeline is assumed to be at stagnation conditions (M = 0), which is valid when the pipeline diameter is much greater than the vent diameter. 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 subsonic (M < 1). The vent entry is sub critical for all conditions.

Minor losses can be accounted for using the minor loss K factor. 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 Cd can be used as a design or safety factor (API 520 recommends Cd = 0.9 for vents with a valve, or Cd = 0.62 for vents with a burst disk).

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. 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, mass flow rate versus stagnation pressure and flow type, or mass flow rate versus stagnation pressure and discharge coefficient.

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 gas compressibility factor and density from gas temperature and pressure for common gases: argon Ar, n-decane C10H22, ethylene C2H4, ethyl chloride C2H5Cl, ethane C2H6, propene C3H6, propane C3H8, iso-butane C4H10, n-butane C4H10, iso-pentane C5H12, n-pentane C5H12, n-hexane C6H14, n-heptane C7H16, n-octane C8H18, n-nonane C9H20, methyl chloride CH3Cl, methane CH4, chlorine Cl2, carbon monoxide CO, carbon dioxide CO2, hydrogen H2, steam H2O, hydrogen sulphide H2S, hydrogen chloride HCl, helium He, krypton Kr, nitrogen N2, air N2+O2, ammonia NH3, oxygen O2, sulphur dioxide SO2, xenon Xe.

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 gas 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

• fluidtype : Fluid Type
  • Pcu : User Defined Critical Point Pressure
  • Tcu : User Defined Critical Point Temperature
  • ωu : User Defined Accentric Factor
  • SGu : User Defined Gas Specific Gravity
• 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 duct, vent or header Darcy friction factor (fd) and pressure loss factor (fL/D) from the Von Karman rough pipe equation.

At high Reynolds numbers the flow is fully turbulent and the Darcy friction factor is dependent on the pipe roughness only. Minor losses can be included in the pressure loss factor, either as a K factor, an equivalent added length, or an equivalent added length over diameter ratio.

Tool Input

• schdtypea : Vent Schedule Type
• diamtypea : Vent Diameter Type
  • ODu : User Defined Vent Outside Diameter
  • IDu : User Defined Vent Inside Diameter
• wtntype : Vent 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
• Lv : Vent Length

Tool Output

• ID : Vent Inside Diameter
• Le : Vent Eqivalent Length
• fL/D : Pressure Loss Factor Including Minor Losses
• fd : Darcy Friction Factor
• rr : Surface Roughness Ratio

Calculate steam header frictional flow critical ratios for adiabatic (constant enthalpy) and isothermal (constant temperature) flow.

Critical flow conditions occur when the 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 Result Plot option to plot critical pressure loss factor versus inlet Mach number and either flow type or specific heat ratio; or 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 (Fanno lines). 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.

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.

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 steam header critical and subcritical flow ratios for adiabatic and isothermal flow with friction.

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. Sub critical duct flow occurs when the ambient pressure at exit is greater than the critical exit pressure. exit Mach number is less than the critical exit Mach number.

An equivalent pressure loss factor is calculated by adding a nominal extension to the duct. The inlet pressure of the extension equals ambient pressure. exit pressure of the duct plus extension equals exit pressure of the extension. exit Mach number of the original duct equals the inlet Mach number of the extension. 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 either inlet and exit Mach number versus pressure loss factor, or added and equivalent pressure loss factor versus pressure loss factor.

Tool Input

• fluidtype : Specific Heat Ratio Type
  • γu : User Defined Specific Heat Ratio
• flowtype : Fluid Flow Type
• Pi : Inlet Pressure
• Pa : Amient Pressure
• fL/D : Input Friction Loss Factor

Tool Output

• γ : Specific Heat Ratio
• ρi/ρe : Inlet Density Over Exit Density Ratio
• Ci/Ce : Inlet Speed Of Sound Over Exit Speed Of Sound Ratio
• Mce : Critical Exit Mach Number
• Mci : Critical Inlet Mach Number
• Me : Exit Mach Number
• Mi : Inlet Mach Number
• Pe : Exit Pressure
• Pi/Pe : Inlet Pressure Over Exit Pressure Ratio
• Ti/Te : Inlet Temperature Over Exit Temperature Ratio
• Vi/Ve : Inlet Velocity Over Exit Velocity Ratio
• cvg : Convergence Factor (≅ 1)
• fL/Da : Added Friction Loss Factor
• fL/De : Effective Friction Loss Factor

Calculate gas duct Fanno lines or flow ratios for adiabatic (constant enthalpy) and isothermal (constant temperature) flow.

Fanno lines or flow ratios are calculated for critical flow with friction loss. The inlet Mach number can be calculated from the friction loss factor (fLD), or the friction loss factor can be calculated from the inlet Mach number. Critical flow conditions occur when the 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.

Note : Fanno flow is normally calculated for adiabatic duct flow with friction. The calculator also calculates Fanno ratios for isothermal (constant temperature) flow.

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.

Tool Input

• fluidtype : Fluid 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