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Bernoulli's Equation Fluid Flowrate And Velocity

Calculate pipeline fluid density and flow rate using the Bernoulli equation.

Fluid density and flowrate can be calculated for liquid pipelines, gas pipelines, two phase gas liquid pipelines, and three phase gas oil and water (black oil) pipelines.

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CALCULATOR : Bernoulli Equation Fresh Water Density From Temperature [FREE]   ±

Calculate Bernoulli equation fresh water density from temperature at atmospheric pressure (IAPWS R7-97 steam table).

The calculation is valid from the freezing point (0 C) to the boiling point (100 C). Use the Result Plot option to plot density versus temperature.

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

Tool Input

  • T : Temperature

Tool Output

  • ρ : Density

CALCULATOR : Bernoulli Equation Salt Water Density From Temperature And Salinity [FREE]   ±

Calculate Bernoulli equation salt water density from temperature and practical salinity at atmospheric pressure (TEOS-10 seawater).

Practical salinity = parts per thousand of dissolved solids (mainly salt). The absolute salinity is taken as 35.16504 / 35 times the practical salinity. The absolute salinity anomaly δSA is ignored. Use the Result Plot option to plot density versus temperature.

Reference : TEOS-10 Thermodynamic Equation Of Seawater (2010)

Tool Input

  • T : Seawater Temperature

Tool Output

  • ρ : Seawater Density

CALCULATOR : Bernoulli Equation Gas Density And Compressibility Factor [FREE]   ±

Calculate Bernoulli equation gas density and compressibility factor from the fluid pressure, temperature and critical point constants for selected gases.

The compressibility factor can be calculated from either the Peng Robinson, Soave, Redlich Kwong, or van der Waals equation 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
    • SGu : User Defined Gas Specific Gravity
    • ωu : User Defined Acentric Factor
    • Pcu : User Defined Critical Pressure
    • Tcu : User Defined Critical Temperature
  • eostype : Equation Of State
    • Zu : User Defined Compressibility Factor
  • P : Fluid Pressure
  • T : Fluid Temperature

Tool Output

  • ρ : Fluid Density
  • ω : Accentric Factor
  • Pc : Critical Point Pressure
  • Pr : Reduced Pressure
  • SG : Gas Specific Gravity Relative To Air
  • Tc : Critical Point Temperature
  • Tr : Reduced Temperature
  • Vm : Molar Volume
  • Z : Compressibility Factor
  • cvg : Convergence Check
  • mw : Fluid Molar Mass

CALCULATOR : Bernoulli Equation Liquid Density And Specific Gravity [FREE]   ±

Calculate Bernoulli equation liquid density and specific gravity, degrees Baume, degrees Twaddell, and degrees API.

For liquids lighter than or equal to water the density can be defined as degrees API, or degrees Baume (Be-). For liquids heavier than water the density can be defined by degrees Baume (Be+), or degrees Twaddell.

Tool Input

  • sgtype : Density Type
    • SGu : User Defined Specific Gravity
    • Be+u : User Defined Degrees Baume SG > 1
    • Be-u : User Defined Degrees Baume SG <= 1
    • Twu : User Defined Degrees Twaddell SG > 1
    • APIu : User Defined Degrees API SG <= 1
    • ρu : User Defined Liquid Density

Tool Output

  • ρ : Fluid Density
  • API : Degrees API SG ≤ 1
  • Be+ : Degrees Baume SG > 1
  • Be- : Degrees Baume SG ≤ 1
  • SG : Specific Gravity
  • Tw : Degrees Twaddell SG > 1

CALCULATOR : Bernoulli Equation Liquid Velocity And Flowrate [FREE]   ±

Calculate Bernoulli equation liquid velocity and flowrate.

Liquid density can be calculated from specific gravity, degrees Baume, degrees Twaddell, or degrees API. For liquids lighter than or equal to water the density can be defined as degrees API, or degrees Baume (Be-). For liquids heavier than water the density can be defined by degrees Baume (Be+), or degrees Twaddell.

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
  • sgtype : Density Type
    • SGu : User Defined Specific Gravity
    • Be+u : User Defined Degrees Baume SG > 1
    • Be-u : User Defined Degrees Baume SG <= 1
    • Twu : User Defined Degrees Twaddell SG > 1
    • APIu : User Defined Degrees API SG <= 1
    • ρu : User Defined Liquid Density
  • voltype : Fluid Flowrate Type
    • Qfu : User Defined Volume Flow Rate
    • Mfu : User Defined Mass Flow Rate
    • Vfu : User Defined Fluid Velocity

Tool Output

  • ρ : Fluid Density
  • API : Degrees API SG ≤ 1
  • Be+ : Degrees Baume SG > 1
  • Be- : Degrees Baume SG ≤ 1
  • ID : Inside Diameter
  • Mf : Liquid Mass Flowrate
  • Qf : Liquid Volume Flowrate
  • SG : Specific Gravity
  • Tw : Degrees Twaddell SG > 1
  • Vf : Fluid Velocity

CALCULATOR : Bernoulli Equation Gas Velocity And Flowrate [FREE]   ±

Calculate Bernoulli equation gas velocity and flowrate from temperature, pressure and specific gravity.

Gas molar mass is approximately equal to the molar mass of dry air times the gas specific gravity at standard conditions (for most gases the compressibility factor Z is approximately equal to 1 at standard conditions). The molar mass of dry air is taken as 28.964 kg/kg-mole. For gas mixtures, gas specific gravity is easier to measure than the molar mass. Gas flowrate can be defined by gas volume flowrate, gas mass flowrate, gas mole flowrate, or gas velocity.

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
  • fluidtype : Gas Type
    • SGu : User Defined Gas Specific Gravity
  • voltype : Gas Flowrate Type
    • Qfu : User Defined Gas Volume Flow Rate
    • Mfu : User Defined Gas Mass Flow Rate
    • Ngu : User Defined Gas Mole Flow Rate
    • Vfu : User Defined Gas Velocity
  • P : Gas Pressure
  • T : Gas Temperature
  • Z : Gas Compressibility Factor

Tool Output

  • ρ : Gas Density
  • ID : Inside Diameter
  • M : Gas Molar Mass
  • Mf : Gas Mass Flowrate
  • Ng : Gas Mole Flowrate
  • Qf : Gas Volume Flowrate (At T P)
  • R : Gas Constant
  • SG : Gas Specific Gravity
  • Vf : Gas Velocity
  • vg : Gas Mole Volume (At T P)

CALCULATOR : Bernoulli Equation Two Phase Gas Liquid Velocity And Flowrate [FREE]   ±

Calculate Bernoulli equation two phase gas liquid velocity and flowrate.

Gas oil ratio (GOR) is the ratio of gas moles over oil volume. Gas moles are commonly measured as gas volume at standard conditions (eg SCF or SCM). Fluid density and flow rate can be calculated for single phase fluid, single phase gas, and two phase gas liquid.

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
  • mvtype : Fluid Density Type
    • GORu : User Defined Gas Oil Ratio
    • Xmu : User Defined Gas Mass Fraction
    • Xvu : User Defined Gas Volume Fraction
    • ρu : User Defined Fluid Density
  • voltype : Fluid Flowrate Type
    • Qlu : User Defined Liquid Volume Flow Rate
    • Ngu : User Defined Gas Mole Flow Rate
    • Qfu : User Defined Total Fluid Volume Flow Rate
    • Mfu : User Defined Total Fluid Mass Flow Rate
    • Vfu : User Defined Fluid Velocity
  • ρl : Liquid Density
  • P : Fluid Pressure
  • T : Fluid Temperature
  • Z : Gas Compressibility Factor
  • SG : Gas Specific Gravity

Tool Output

  • ρf : Average Fluid Density
  • ρg : Gas Density (At T P)
  • GOR : Gas Oil Ratio
  • ID : Inside Diameter
  • Mf : Total Fluid Mass Flowrate
  • Mg : Gas Mass Flowrate
  • Ml : Liquid Mass Flowrate
  • Ng : Gas Mole Flowrate
  • Qf : Total Fluid Volume Flowrate
  • Qg : Gas Volume Flowrate (At T P )
  • Ql : Liquid Volume Flowrate
  • Vf : Average Fluid Velocity
  • Vg : Superficial Gas Velocity
  • Vl : Superficial Liquid Velocity
  • Xm : Gas Mass Fraction
  • Xv : Gas Volume Fraction (At T P)
  • vg : Gas Mole Volume (At T P)

CALCULATOR : Bernoulli Equation Three Phase Water Oil And Gas Velocity And Flowrate [PLUS]   ±

Calculate Bernoulli equation three phase water oil and gas (black oil) velocity and flowrate.

Black oil is a three phase mixture of oil, water and gas. Gas oil ratio (GOR) is the ratio of gas moles over oil volume. Gas moles are commonly measured as gas volume at standard conditions (eg SCF or SCM). Water cut is measured relative to the total liquid volume (gas volume is ignored). Gas oil ratio (GOR) is measured relative to the oil volume at standard conditions (water volume is ignored).

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
  • mvtype : Fluid Density Type
    • GORu : User Defined Gas Oil Ratio
    • WCu : User Defined Water Cut
    • ρu : User Defined Fluid Density
  • voltype : Fluid Volume Type
    • Qou : User Defined Oil Volume Flow Rate
    • Qlu : User Defined Liquid Volume Flow Rate
    • Ngu : User Defined Gas Mole Flow Rate
    • Qfu : User Defined Total Fluid Volume Flow Rate
    • Mfu : User Defined Total Fluid Mass Flow Rate
    • Vfu : User Defined Fluid Velocity
  • ρo : Oil Density
  • ρw : Water Density
  • P : Fluid Pressure
  • T : Fluid Temperature
  • Z : Gas Compressibility Factor
  • SG : Gas Specific Gravity

Tool Output

  • ρf : Average Fluid Density
  • ρg : Gas Density
  • ρl : Liquid Density
  • GOR : Gas Oil Ratio
  • ID : Inside Diameter
  • Mf : Total Fluid Mass Flowrate
  • Mg : Gas Mass Flowrate
  • Ml : Liquid Mass Flowrate
  • Mo : Oil Mass Flowrate
  • Mw : Water Mass Flowrate
  • Ng : Gas Mole Flowrate
  • Qf : Total Fluid Volume Flowrate
  • Qg : Gas Volume Flowrate
  • Ql : Liquid Volume Flowrate
  • Qo : Oil Volume Flowrate
  • Qw : Water Volume Flowrate
  • Vf : Average Fluid Velocity
  • Vg : Gas Superficial Velocity
  • Vl : Liquid Superficial Velocity
  • Vo : Oil Superficial Velocity
  • Vw : Water Superficial Velocity
  • WC : Water Cut
  • Xmg : Gas Mass Fraction
  • Xml : Liquid Mass Fraction
  • Xmo : Oil Mass Fraction
  • Xmw : Water Mass Fraction
  • Xvg : Gas Volume Fraction
  • Xvl : Liquid Volume Fraction
  • Xvo : Oil Volume Fraction
  • Xvw : Water Volume Fraction
  • vg : Gas Mole Volume (At T P)