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Bernoulli's Equation

Calculate gas and liquid pressure using the Bernoulli equation.

The Bernoulli equation describes the conservation of energy in a static or moving fluid. For a frictionless fluid flow where no work is done by or to the system and the temperature is constant, energy is conserved. The Bernoulli equation can be expressed as conservation of energy, conservation of pressure or conservation of fluid head. The total pressure is referred to as the Bernoulli pressure (Pb) or the Energy Grade Line (EGL).

`Pb = Ps + Pd + Pz `
`Pg = Ps + Pd `
`Ph = Ps + Pz `

where :

Pb = Bernoulli pressure or total pressure or energy grade line (EGL) (= constant for frictionless flow)
Ps = static pressure
Pz = potential or pressure
Pd = dynamic pressure
Pg = stagnation pressure
Ph = hydraulic or piezometric pressure or hydraulic grade line (HGL)

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CALCULATOR : Bernoulli Equation For Liquid And General Flow [FREE]   ±

Calculate the Bernoulli equation pressure terms for flowing liquid and general fluid.

The total pressure equals the sum of the potential pressure, dynamic pressure and static pressure. The Bernoulli equation is also commonly expressed in terms of head, the equivalent height of a column of the fluid. The liquid flowrate can be defined by either velocity, volume flowrate, or mass flowrate.

This calculator can also be used for general flow of multiphase fluids. Calculate the fluid density and velocity using one of the multi phase flow calculators.

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
  • voltype : Flowrate Type
    • Qfu : User Defined Volume Flow Rate
    • Mfu : User Defined Mass Flow Rate
    • Vfu : User Defined Fluid Velocity
  • pltype : Local Pressure Type
    • Psu : User Defined Static Pressure
    • Pgu : User Defined Stagnation Pressure
  • ρ : Density
  • Z : Elevation Relative To Datum

Tool Output

  • ID : Inside Diameter
  • Mf : Mass Flowrate
  • Pb : Bernoulli Pressure (Ps + Pz + Pd)
  • Pd : Dynamic Pressure (From Velocity)
  • Pg : Stagnation Pressure (Ps + Pd)
  • Ph : Hydraulic Pressure (Ps + Pz)
  • Ps : Static Pressure
  • Pz : Potential Pressure (From Elevation)
  • Qf : Volume Flowrate
  • Vf : Velocity
CALCULATOR : Bernoulli Equation For Gas Flow [FREE]   ±

Calculate the Bernoulli equation pressure terms for flowing gas.

The total pressure or Bernoulli pressure equals the sum of the potential pressure, dynamic pressure and static pressure. The gas flowrate can be defined by either velocity, volume flowrate, mass flowrate, or mole flowrate.

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 : Fluid Type
    • SGu : User Defined Gas Specific Gravity
  • zfactype : Compressibility Factor Type
    • zu : User Defined Compressibility Factor
  • voltype : 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
  • Ps : Static Pressure
  • T : Fluid Temperature
  • Z : Elevation Relative To Datum

Tool Output

  • ρ : Density
  • ID : Inside Diameter
  • Mf : Mass Flowrate
  • Ng : Mole Flowrate
  • Pb : Bernoulli Pressure (Ps + Pz + Pd)
  • Pd : Dynamic Pressure (From Velocity)
  • Pg : Stagnation Pressure (Ps + Pd)
  • Ph : Hydraulic Pressure (Ps + Pz)
  • Pz : Potential Pressure (From Elevation)
  • Qf : Volume Flowrate
  • SG : Gas Specific Gravity
  • Vf : Velocity
  • z : Compressibility Factor
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 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)

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