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Compressible Flow

Calculate compressible flow ratios and gas properties for isentropic and isothermal flow (critical over stagnation ratios, flowing over stagnation ratios, and flowing over critical flow ratios).

For isentropic flow, critical flow occurs at M = 1. For isothermal flow, critical flow occurs at M = 1 / √k, where k is the specific heat ratio (Cp/Cv). For isothermal flow the isothermal temperature is assumed equal to the stagnation temperature. Phase changes are ignored.

For flow through a throat, the flow upstream from the throat is sub critical (M ≤ Mc). The flow downstream is super critical (M > Mc). The area ratio is inversely proportional to the mass flux ratio. At stagnation conditions, the area ratio is infinite.

Use the Result Plot option to plot flow ratios versus Mach number, or nozzle area ratio and diameter ratio versus Mach number.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR : Compressible Flow Critical Over Stagnation Flow Ratios [FREE]   ±

Calculate gas critical over stagnation flow ratios and gas properties for isentropic and isothermal flow.

The flow ratios are calculated as critical value over stagnation value, eg critical pressure over stagnation pressure. Critical properties are calculated at M = 1 for isentropic flow, and M = 1 / √k for isothermal flow, where k is the specific heat ratio (Cp/Cv). 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. For isothermal flow the critical temperature is assumed equal to the stagnation temperature at M = 0. The stagnation temperature is constant for isentropic flow, and varies with Mach number for isothermal flow. Phase changes 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 : Compressible Flow Flowing Over Stagnation Flow Ratios And Flowrate From Mach Number [FREE]   ±

Calculate gas flowing over stagnation flow ratios and gas properties from Mach number for isentropic and isothermal flow.

The flow ratios are calculated for flowing over stagnation values, eg flowing pressure over stagnation pressure. The stagnation properties are calculated at stationary conditions (M = 0). The temperature and pressure can be defined at either stagnation conditions, or at flowing conditions. Critical flow conditions occur at M = 1 for isentropic flow (sonic flow), and M = 1 / √k for isothermal flow, where k is the specific heat ratio (Cp/Cv). The mass flux is a maximum at critical flow conditions. For isothermal flow the flowing temperature is assumed equal to the stagnation temperature at M = 0. The stagnation temperature is constant for isentropic flow, and varies with Mach number for isothermal flow. Phase changes 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 : Flowing Pressure Type
    • Pou : User Defined Stagnation Pressure
    • Pfu : User Defined Flowing Pressure
    • Tou : User Defined Stagnation Temperature
    • Tfu : User Defined Flowing Temperature
  • flowtype : Fluid Flow Type
  • matype : Mach Number Type
    • Mu : User Defined Mach Number
  • ID : Inside Diameter

Tool Output

  • γ : Specific Heat Ratio
  • ρf : Flowing Density
  • ρf/ρo : Density Ratio
  • ρo : Stagnation Density
  • Cf : Flowing Speed Of Sound
  • Cf/Co : Speed Of Sound Ratio
  • Co : Stagnation Speed Of Sound
  • Gc : Critical Mass Flux (Mass Flow Rate Per Area)
  • Gf : Flowing Mass Flux (Mass Flow Rate Per Area)
  • Gf/Gc : Mass Flux Ratio
  • Mc : Critical Mach Number
  • Mf : Flowing Mach Number
  • Pf : Flowing Pressure
  • Pf/Po : Pressure Ratio
  • Po : Stagnation Pressure
  • Rg : Specific Gas Constant
  • SG : Gas Specific Gravity
  • Tf : Flowing Temperature
  • Tf/To : Temperature Ratio
  • To : Stagnation Temperature (M = 0)
  • Tof : Flowing Stagnation Temperature (M = Mf)
  • Vf : Flowing Fluid Velocity
  • Z : Compressibility Factor
  • mf : Flowing Mass Flow Rate
  • mmg : Gas Molar Mass
  • nf : Flowing Mole Flow Rate
CALCULATOR : Compressible Flow Flowing Over Critical Flow Ratios And Flowrate From Mach Number [FREE]   ±

Calculate flowing over critical flow ratios, area ratio and gas flowrate from Mach number for isentropic and isothermal choked flow through a throat.

The flow ratios are calculated for flowing over critical values, eg flowing pressure over critical pressure. Flow is assumed to be subsonic upstream of the throat (M < Mc), critical in the throat (M = Mc), and super critical downstream of the throat (M > Mc). Critical flow conditions occur at M = 1 for isentropic flow (sonic flow), and M = 1 / √k for isothermal flow, where k is the specific heat ratio (Cp/Cv). The temperature and pressure can be defined at either stagnation conditions, flowing conditions, or at critical conditions. The mass flux is a maximum at critical flow conditions. The mass flow rate and mole flow rate should be constant. The area ratio is the inverse of the mass flux ratio (A x G = constant). For isentropic flow the stagnation temperature is constant and the flowing temperature varies. For isothermal flow the flowing temperature is constant and the stagnation temperature varies (the flowing temperature is assumed equal to the stagnation temperature at M = 0). Phase changes 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 : Flowing Pressure Type
    • Pou : User Defined Stagnation Pressure
    • Pfu : User Defined Flowing Pressure
    • Pcu : User Defined Critical Pressure
    • Tou : User Defined Stagnation Temperature
    • Tfu : User Defined Flowing Temperature
    • Tcu : User Defined Critical Temperature
  • flowtype : Fluid Flow Type
  • M : Mach Number
  • IDc : Choke Diameter

Tool Output

  • γ : Specific Heat Ratio
  • ρc : Critical Density
  • ρf : Flowing Density
  • ρf/ρc : Density Ratio
  • Af/Ac : Area Ratio
  • Cc : Critical Speed Of Sound
  • Cf : Flowing Speed Of Sound
  • Cf/Cc : Speed Of Sound Ratio
  • Df/Dc : Diameter Ratio (Circular Duct)
  • Gc : Critical Mass Flux (Mass Flow Rate Per Area)
  • Gf : Flowing Mass Flux (Mass Flow Rate Per Area)
  • Gf/Gc : Mass Flux Ratio
  • IDf : Flow Diameter
  • Mc : Critical Mach Number
  • Pc : Critical Pressure
  • Pf : Flowing Pressure
  • Pf/Pc : Pressure Ratio
  • Po : Stagnation Pressure
  • Rg : Specific Gas Constant
  • SG : Gas Specific Gravity
  • Tc : Critical Temperature
  • Tf : Flowing Temperature
  • Tf/Tc : Temperature Ratio
  • To : Stagnation Temperature
  • Tof : Flowing Stagnation Temperature (M = Mf)
  • Vf : Flowing Fluid Velocity
  • Z : Compressibility Factor
  • mf : Fluid Mass Flow Rate
  • mmg : Gas Molar Mass
  • nf : Gas Mole Flow Rate
CALCULATOR : Compressible Flow Gas Density And Compressibility Factor [FREE]   ±

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

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