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API 520 Critical Flow Ratio

Calculate API 520 critical flow pressure ratios for an ideal gas using the copmpressible flow equations.

Critical properties are calculated at sonic flow conditions (M = 1). The stagnation properties are calculated at stationary conditions (M = 0). The temperature and pressure can be defined at either stagnation conditions, or at critical conditions. Flow is assumed to be adiabatic and isentropic. Changes in phase are ignored.

Reference : API 520 Sizing, Selection And Installation Of Pressure Relieving Devices (2014)

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CALCULATOR : API 520 Duct Pressure Loss Factor From The Von Karman Rough Pipe Equation [FREE]   ±

Calculate duct Darcy friction factor (fd) and pressure loss factor (fL/D) from the Von Karman rough pipe equation for gas, steam or liquid flow.

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
CALCULATOR : API 520 Section 5.6 Gas Pressure Relief Valve Critical Flow Ratio [FREE]   ±

Calculate sonic or critical flow ratios and properties for an ideal gas (API 520 Section 5.6).

Critical properties are calculated at sonic flow conditions (M = 1). The stagnation properties are calculated at stationary conditions (M = 0). The temperature and pressure can be defined at either stagnation conditions, or at critical conditions. Flow is assumed to be adiabatic and isentropic. Changes in phase are ignored.

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
  • presstype : Critical Pressure Type
    • Pou : User Defined Stagnation Pressure
    • Pcu : User Defined Critical Flowing Pressure
    • Tou : User Defined Stagnation Temperature
    • Tcu : User Defined Critical Flowing Temperature
  • flowtype : Fluid Flow Type
  • ID : Inside Diameter

Tool Output

  • γ : Specific Heat Ratio
  • ρc : Critical Density
  • ρc/ρo : Density Ratio
  • ρo : Stagnation Density
  • Cc : Critical Speed Of Sound
  • Cc/Co : Speed Of Sound Ratio
  • Co : Stagnation Speed Of Sound
  • Gc : Critical Mass Flux (Mass Flow Rate Per Area)
  • Mc : Critical Mach Number
  • Pc : Critical Pressure
  • Pc/Po : Pressure Ratio
  • Po : Stagnation Pressure
  • Rg : Specific Gas Constant
  • SG : Gas Specific Gravity
  • Tc : Critical Temperature
  • Tc/To : Temperature Ratio
  • To : Stagnation Temperature (M = 0)
  • Toc : Critical Stagnation Temperature (M = Mc)
  • Vc : Critical Fluid Velocity
  • Z : Compressibility Factor
  • mc : Critical Mass Flow Rate
  • mmg : Gas Molar Mass
  • nc : Critical Mole Flow Rate
CALCULATOR : API 520 Gas Header Flow Ratios For Critical Flow (Ideal Gas) [FREE]   ±

Calculate API 520 gas duct, vent or header critical flow ratios (or Fanno lines) for adiabatic (constant enthalpy) and isothermal (constant temperature) flow using ideal gas compressible flow equations.

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.

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
CALCULATOR : API 520 Steam Header Flow Ratios For Critical Flow (Ideal Gas) [FREE]   ±

Calculate API 520 steam duct, vent or header critical flow ratios (or Fanno lines) for adiabatic (constant enthalpy) and isothermal (constant temperature) flow using ideal gas compressible flow equations.

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
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