Pipeng Toolbox : Nozzle Flow Rate Calculators Blank User
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Compressible Flow Nozzle Flow Rate

Calculate compressible flow mass flow rate and mole flow rate through a nozzle for isentropic and isothermal flow.

At high pressure the nozzle flow is critical (the critical exit pressure is ≥ the ambient pressure). The critical Mach number Mc = 1 for adiabatic low and Mc = 1 / √γ for isothermal flow (γ = the gas specific heat ratio). At lower pressures the nozzle flow is sub critical (M < Mc) (the critical exit pressure is < the ambient pressure). For isothermal flow the stagnation temperature should be close to or equal to the ambient temperature (eg gas transmission pipeline). The discharge coefficient can be used to account for friction losses, and as a design factor.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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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

CALCULATOR : Compressible Flow Nozzle Flowrate [PLUS]   ±

Calculate nozzle mass flowrate and mole flowrate for isentropic and isothermal flow.

The upstream fluid is assumed to be stationary (stagnation conditions). If the ambient pressure is less than the critical pressure the flow is critical (Mc = 1 for isentropic flow and Mc = √(1/γ) for isothermal flow). If the ambient pressure is greater than the critical nozzle pressure, the flow is sub critical (M < Mc).

The discharge coefficient is used to account for friction losses in the nozzle, and as a safety factor. Phase changes are ignored. For isothermal flow the inlet temperature should be set equal to the estimated isothermal temperature (eg ambient temperature). The stagnation temperature is constant for isentropic flow, and varies with Mach number for isothermal flow.

Use the Result Plot option to plot nozzle pressure versus stagnation pressure and flowtype, nozzle mach number versus stagnation pressure and flow type, mass flow rate versus stagnation pressure and flow type, mass flowrate versus nozzle area and discharge coefficient, or mass flowrate versus nozzle diameter and discharge coefficient.

Tool Input

  • fluidtype : Fluid Type
    • γu : User Defined Specific Heat Ratio
    • SGu : User Defined Gas Specific Gravity
  • zfactype : Factor Type
    • Zu : User Defined Compressibility Factor
  • antype : Nozzle Area Type
    • Dnu : User Defined Nozzle Diameter
    • Anu : User Defined Nozzle Area
  • cdtype : Discharge Coefficient Type
    • Cdu : User Defined Discharge Coefficient
  • flowtype : Fluid Flow Type
    • Tou : User Defined Isentropic Stagnation Temperature
    • Tiu : User Defined Isothermal Inlet Temperature
  • Po : Stagnation Pressure
  • Pa : Ambient Pressure

Tool Output

  • γ : Specific Heat Ratio
  • ρn : Nozzle Fluid Density
  • An : Nozzle Cross Section Area
  • Cd : Nozzle Discharge Coefficient
  • Cn : Nozzle Speed Of Sound
  • Dn : Nozzle Diameter
  • Fn : Nozzle Reaction Force
  • Gn : Nozzle Mass Flux
  • Mcn : Critical Nozzle Mach Number
  • Mn : Nozzle Mach Number
  • Pn : Nozzle Pressure
  • Rg : Specific Gas Constant
  • SG : Gas Specific Gravity
  • Tn : Nozzle Temperature
  • Ton : Nozzle Stagnation Temperature
  • Vn : Nozzle Fluid Velocity
  • Z : Fluid Compressibility Factor
  • cvg : Convergence Factor (≅ 1)
  • mf : Mass Flowrate
  • mmg : Gas Molar Mass
  • ng : Mole Flowrate