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Dimensionless Reynolds Number

Calculate the dimensionless Reynolds number for pipes, rectangular ducts and general flow.

The Reynolds number approximates the ratio of kinetic energy over viscous drag loss.

`Re = ρ V L / μ = V L / ν `

where :

Re = Reynolds number
ρ = fluid density
V = fluid velocity
L = characteristic length
μ = dynamic viscosity
ν = kinematic viscosity = μ / ρ

At low reynolds numbers the flow is laminar. At high Reynolds numbers the flow is turbulent. The characteristic length is a defining length dimension. For pipelines the inside diameter is used as the characteristic length. For rectangular ducts the hydraulic diameter is used as the characteristic length.

`ID = 2 w h / (w + h) `

where :

ID = hydraulic diameter
w = duct width
h = duct height

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Links : ±
CALCULATOR : Dimensionless Reynolds Number Re General Pipeline [FREE]   ±

Calculate dimensionless Reynolds number from velocity for general pipelines.

The Reynolds number is the ratio of the fluid kinetic energy to the viscous energy loss.

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
  • visctype : Viscosity Type
    • μu : User Defined Dynamic Viscosity
    • νu : User Defined Kinematic Viscosity
    • ρu : User Defined Density
  • V : Fluid Velocity

Tool Output

  • ν : Fluid Kinematic Viscosity
  • ID : Inside Diameter
  • Re : Reynolds Number
CALCULATOR : Dimensionless Reynolds Number Re General Rectangular Duct [FREE]   ±

Calculate dimensionless Reynolds number from velocity for rectangular ducts.

The Reynolds number is the ratio of the fluid kinetic energy to the viscous energy loss. For rectangular ducts the hydraulic diameter is equal to four times the cross section area divided by the perimeter.

Tool Input

  • visctype : Viscosity Type
    • μu : User Defined Dynamic Viscosity
    • νu : User Defined Kinematic Viscosity
    • ρu : User Defined Density
  • V : Fluid Velocity
  • W : Duct Inside Width
  • H : Duct Inside Height

Tool Output

  • ν : Fluid Kinematic Viscosity
  • D : Hydraulic Diameter
  • Re : Reynolds Number
CALCULATOR : Dimensionless Reynolds Number Re (General Form) [FREE]   ±

Calculate dimensionless Reynolds number Re from velocity for general characteristic length.

The Reynolds number is the ratio of the fluid kinetic energy to the viscous energy loss. The characteristic length is a defining dimension for the flow, eg for flow across a surface (aerofoil), the characteristic length is the length of the surface (ie the width of the aerofoil).

Tool Input

  • visctype : Viscosity Type
    • μu : User Defined Dynamic Viscosity
    • νu : User Defined Kinematic Viscosity
    • ρu : User Defined Density
  • V : Fluid Velocity
  • L : Characteristic Length

Tool Output

  • ν : Fluid Kinematic Viscosity
  • Re : Reynolds Number
CALCULATOR : Dimensionless Reynolds Number Re Three Phase Black Oil Pipeline [PLUS]   ±

Calculate dimensionless Reynolds number from flow rate for three phase black oil pipelines (oil water and gas phases).

Black oil is a three phase mixture of oil, water and gas. 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
    • Reu : User Defined Reynolds Number
  • visctype : Viscosity Type (Must Be User Defined For User Defined Density)
    • μu : User Defined Dynamic Viscosity
    • νu : User Defined Kinematic Viscosity
  • ρo : Oil Density
  • ρw : Water Density
  • P : Fluid Pressure
  • T : Fluid Temperature
  • Z : Gas Compressibility Factor
  • SG : Gas Specific Gravity
  • μo : Oil Dynamic Viscosity
  • μw : Water Dynamic Viscosity
  • μg : Gas Dynamic Viscosity

Tool Output

  • μf : Fluid Dynamic Viscosity
  • νf : Fluid Kinematic Viscosity
  • 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
  • Re : Reynolds Number
  • 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)

CALCULATOR : Dimensionless Reynolds Number Re Two Phase Oil And Gas Pipeline [PLUS]   ±

Calculate dimensionless Reynolds number from flow rate for two phase gas liquid pipelines.

The Reynolds number is the ratio of the fluid kinetic energy to the viscous energy loss. The gas oil ratio is the ratio of gas moles to liquid volume. Gas oil ratio (GOR) is measured relative to the oil volume at standard conditions.

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 Flow Rate 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
    • Reu : User Defined Reynolds Number
  • visctype : Viscosity Type
    • μu : User Defined Dynamic Viscosity
    • νu : User Defined Kinematic Viscosity
  • μl : Liquid Dynamic Viscosity
  • μg : Gas Dynamic Viscosity
  • ρl : Liquid Density
  • P : Fluid Pressure
  • T : Fluid Temperature
  • Z : Gas Compressibility Factor
  • SG : Gas Specific Gravity

Tool Output

  • μf : Fluid Dynamic Viscosity
  • νf : Fluid Kinematic Viscosity
  • ρf : Average Fluid Density
  • ρg : Gas Density (At T P)
  • GOR : Gas Oil Ratio
  • ID : Inside Diameter
  • Mf : Total Mass Flowrate
  • Mg : Gas Mass Flowrate
  • Ml : Liquid Mass Flowrate
  • Ng : Gas Mole Flowrate
  • Qf : Total Volume Flowrate
  • Qg : Gas Volume Flowrate
  • Ql : Liquid Volume Flowrate
  • Re : Reynolds Number
  • Vf : Total 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 : Dimensionless Reynolds Number Re Single Phase Liquid Pipeline [FREE]   ±

Calculate dimensionless Reynolds number from flowrate for single phase liquid pipelines.

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
    • Reu : User Defined Reynolds Number
  • visctype : Viscosity Type
    • μu : User Defined Dynamic Viscosity
    • νu : User Defined Kinematic Viscosity

Tool Output

  • μ : Fluid Dynamic Viscosity
  • ν : Fluid Kinematic Viscosity
  • ρ : Fluid Density
  • ID : Inside Diameter
  • M : Fluid Mass Flowrate
  • Q : Fluid Volume Flowrate
  • Re : Fluid Reynolds Number
  • SG : Specific Gravity
  • V : Fluid Velocity
CALCULATOR : Dimensionless Reynolds Number Re Single Phase Gas Pipeline [FREE]   ±

Calculate dimensionless Reynolds number from flowrate for single phase gas pipelines.

The gas density is calculated from the temperature, pressure and gas constant.

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
    • Reu : User Defined Reynolds Number
  • visctype : Viscosity Type
    • μu : User Defined Dynamic Viscosity
    • νu : User Defined Kinematic Viscosity
  • P : Gas Pressure
  • T : Gas Temperature
  • Z : Gas Compressibility Factor

Tool Output

  • μ : Fluid Dynamic Viscosity
  • ν : Fluid Kinematic Viscosity
  • ρ : Gas Density
  • ID : Inside Diameter
  • M : Gas Mass Flowrate
  • N : Gas Mole Flowrate
  • Q : Gas Volume Flowrate (At T P)
  • R : Gas Constant
  • Re : Fluid Reynolds Number
  • SG : Gas Specific Gravity
  • V : Gas Velocity
  • mm : Gas Molar Mass
  • vg : Gas Molar Volume (At T P)
CALCULATOR : Dimensionless Reynolds Number Re Fresh Water Pipeline [FREE]   ±

Calculate dimensionless Reynolds number from flowrate and temperature for fresh water pipelines (IAPWS R12-08 and IAPWS R7-97 steam table).

The calculation is valid from 0 to 100 degrees C. Use the Result Plot option to plot viscosity versus temperature.

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 : Fluid Flowrate Type
    • Qu : User Defined Volume Flow Rate
    • Mu : User Defined Mass Flow Rate
    • Vu : User Defined Fluid Velocity
    • Reu : User Defined Reynolds Number
  • T : Temperature

Tool Output

  • μ : Dynamic Viscosity
  • ν : Kinematic Viscosity
  • ρ : Fluid Density
  • ID : Inside Diameter
  • M : Liquid Mass Flowrate
  • Q : Liquid Volume Flowrate
  • Re : Reynolds Number
  • V : Fluid Velocity
CALCULATOR : Dimensionless Reynolds Number Re Salt Water Pipeline [FREE]   ±

Calculate dimensionless Reynolds number from flowrate, temperature and salinity for salt water pipelines (TEOS10, IAPWS R12-08 and IAPWS R7-97 steam table).

The calculation is valid from 0 to 100 degrees C. Use the Result Plot option to plot viscosity versus temperature.

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 : Fluid Flowrate Type
    • Qu : User Defined Volume Flow Rate
    • Mu : User Defined Mass Flow Rate
    • Vu : User Defined Fluid Velocity
    • Reu : User Defined Reynolds Number
  • T : Temperature

Tool Output

  • μ : Dynamic Viscosity
  • ν : Kinematic Viscosity
  • ρ : Fluid Density
  • ID : Inside Diameter
  • M : Liquid Mass Flowrate
  • Q : Liquid Volume Flowrate
  • Re : Reynolds Number
  • V : Fluid Velocity
CALCULATOR : Dimensionless Number Liquid Density [FREE]   ±

Calculate dimensionless number liquid density 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

  • 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 : Dimensionless Number Gas Density And Compressibility Factor [FREE]   ±

Calculate dimensionless number gas density and compressibility factor from temperature, pressure and critical point constants.

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 : Dimensionless Number Fresh Water Density From Temperature [FREE]   ±

Calculate dimensionless number 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.

Tool Input

  • T : Temperature

Tool Output

  • ρ : Density
CALCULATOR : Dimensionless Number Salt Water Density From Temperature And Salinity [FREE]   ±

Calculate dimensionless number salt water density at atmospheric pressure from temperature and salinity (TEOS-10).

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.

Tool Input

  • T : Seawater Temperature

Tool Output

  • ρ : Seawater Density
CALCULATOR : Dimensionless Number Liquid Pipeline Density And Flowrate [FREE]   ±

Calculate dimensionless number liquid pipeline flowrate.

Liquid density can be defined by either 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. Flowrate can be defined by volume flowrate, mass flowrate, or fluid 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
  • 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
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