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Dimensionless Number Calculation

Calculate dimensionless numbers for fluid flow and other physical systems. Dimensionless numbers are calculated from groups of variables so that the result is dimensionless. Dimensionless numbers can be calculated from any consistent set of units, and will have the same value. Dimensionless numbers can be a very powerful tool for analysing physical systems.

Modules :

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CALCULATOR : Dimensionless Angular Or Circular Wave Number k User Defined Frequency And Velocity   +

Calculate dimensionless circular or angular wavenumber from wave frequency and wave phase velocity.

The phase velocity is the travelling speed of the wave. The frequency is the inverse of thwe wave period. The frequency units may be set to wave period (s/rev seconds per revolution). The wavenumber is applicable to ocean waves and electromagentic waves.

Tool Input

  • c : Wave Celerity Or Propagation Speed
  • f : Wave Frequency

Tool Output

  • k : Angular Or Circular Wave Number

CALCULATOR : Dimensionless Angular Or Circular Wave Number k User Defined Wave Length   +

Calculate dimensionless circular or angular wavenumber from wavelength.

The wavenumber is applicable to ocean waves and electromagentic waves. The wave length is user defined.

Tool Input

  • L : Wave Length

Tool Output

  • k : Angular Or Circular Wave Number

CALCULATOR : Dimensionless Brinkman Number Br From Fluid Velocity (General Case)   +

Calculate dimensionless Brinkman number Br from fluid velocity (general case).

The dimensionless Brinkman number is the ratio of the fluid friction loss and the fluid thermal conduction. The Brinkman number is the product of the Eckert number and the Prandtl number (refer to Eckert number and the Prandtl number).

The fluid velocity is user defined.

Tool Input

  • Cp : Specific Heat Capacity Constant Pressure
  • ρ : Liquid Density
  • k : Fluid Heat Conductivity
  • T1 : Fluid Temperature 1
  • T2 : Fluid Temperature 2
  • V : Fluid Velocity
  • visctype : Viscosity Type
    • μu : User Defined Fluid Dynamic Viscosity
    • νu : User Defined Fluid Kinematic Viscosity

Tool Output

  • ΔT : Temperature Difference
  • α : Fluid Thermal Diffusivity
  • μ : Fluid Dynamic Viscosity
  • ν : Fluid Kinematic Viscosity
  • Br : B Value
  • Ec : E Value
  • Pr : P Value

CALCULATOR : Dimensionless Brinkman Number Br From Pipeline Liquid Volume Flow Rate   +

Calculate dimensionless Brinkman number Br from pipeline liquid volume flow rate.

The dimensionless Brinkman number is the ratio of the fluid friction loss and the fluid thermal conduction. The Brinkman number is the product of the Eckert number and the Prandtl number (refer to Eckert number and the Prandtl number).

The fluid velocity is calculated from the volume flow rate.

Tool Input

  • Cp : Specific Heat Capacity Constant Pressure
  • ρ : Fluid Density
  • Q : Liquid Volume Flowrate
  • ID : Nominal Inside Diameter
  • k : Fluid Heat Conductivity
  • T1 : Fluid Temperature 1
  • T2 : Fluid Temperature 2
  • visctype : Viscosity Type
    • μu : User Defined Fluid Dynamic Viscosity
    • νu : User Defined Fluid Kinematic Viscosity

Tool Output

  • ΔT : Temperature Difference
  • α : Fluid Thermal Diffusivity
  • μ : Fluid Dynamic Viscosity
  • ν : Fluid Kinematic Viscosity
  • Br : B Value
  • Ec : E Value
  • Pr : P Value
  • V : Fluid Velocity

CALCULATOR : Dimensionless Cavitation Number Ca From Fluid Velocity (General Case)   +

Calculate dimensionless cavitation number Ca from fluid velocity (general case).

The dimensionless cavitation number is the ratio of the difference between the fluid static pressure and the fluid vapour pressure over the fluid dynamic pressure. The cavitation number is used to determine the likelihood of cavitation occurring in a flow component (Ca should be > 1 to avoid cavitation). For flow components with complex geometry the maximum fluid velocity should be used rather than the fluid flowing velocity. For flow components with moving parts (eg an impellor), the maximum velocity of the moving part should be used rather than the fluid flowing velocity. The cavitation number is of similar form to the Euler number and the pressure loss factor or minor loss factor K (refer to Euler number and K factor).

The fluid velocity is user defined.

Tool Input

  • ρ : Liquid Density
  • P : Fluid Pressure
  • Pv : Vapour Pressure
  • V : Fluid Velocity

Tool Output

  • ΔP : Pressure Difference
  • Ca : C Value
  • Pd : Dynamic Pressure

CALCULATOR : Dimensionless Cavitation Number Ca From Pipeline Liquid Volume Flow Rate   +

Calculate dimensionless cavitation number Ca from pipeline liquid volume flow rate.

The dimensionless cavitation number is the ratio of the difference between the fluid static pressure and the fluid vapour pressure over the fluid dynamic pressure. The cavitation number is used to determine the likelihood of cavitation occurring in a flow component (Ca should be > 1 to avoid cavitation). For flow components with complex geometry the maximum fluid velocity should be used rather than the fluid flowing velocity. For flow components with moving parts (eg an impellor), the maximum velocity of the moving part should be used rather than the fluid flowing velocity. The cavitation number is of similar form to the Euler number and the pressure loss factor or minor loss factor K (refer to Euler number and K factor).

The fluid velocity is calculated from the volume flow rate.

Tool Input

  • ρ : Liquid Density
  • Q : Liquid Volume Flowrate
  • ID : Nominal Inside Diameter
  • P : Fluid Pressure
  • Pv : Vapour Pressure

Tool Output

  • ΔP : Pressure Difference
  • Ca : C Value
  • Pd : Dynamic Pressure
  • V : Fluid Velocity

CALCULATOR : Dimensionless Eckert Number Ec From Fluid Velocity (General Case)   +

Calculate dimensionless Eckert number Ec from fluid velocity (general case).

The dimensionless Eckert number is the ratio of the fluid kinetic energy to the fluid heat energy. For small Eckert numbers (Ec << 1), heat transfer is dominated by conduction and convection and kinetic effects may be ignored. The product of the Eckert number and the Prandtl number is equal to the Brinkman number (refer to Brinkman number).

The fluid velocity is user defined.

Tool Input

  • Cp : Specific Heat Capacity Constant Pressure
  • T1 : Fluid Temperature 1
  • T2 : Fluid Temperature 2
  • V : Fluid Velocity

Tool Output

  • ΔT : Temperature Difference
  • Ec : E Value

CALCULATOR : Dimensionless Eckert Number Ec From Pipeline Liquid Volume Flow Rate   +

Calculate dimensionless Eckert number Ec from pipeline liquid volume flow rate.

The dimensionless Eckert number is the ratio of the fluid kinetic energy to the fluid heat energy. For small Eckert numbers (Ec << 1), heat transfer is dominated by conduction and convection and kinetic effects may be ignored. The product of the Eckert number and the Prandtl number is equal to the Brinkman number (refer to Brinkman number).

The fluid velocity is calculated from the volume flow rate.

Tool Input

  • Cp : Specific Heat Capacity Constant Pressure
  • Q : Liquid Volume Flowrate
  • ID : Nominal Inside Diameter
  • T1 : Fluid Temperature 1
  • T2 : Fluid Temperature 2

Tool Output

  • ΔT : Temperature Difference
  • Ec : E Value
  • V : Fluid Velocity

CALCULATOR : Dimensionless Euler Number Eu From Fluid Velocity (General Case)   +

Calculate dimensionless Euler number Eu from fluid velocity (general case).

The dimensionless Euler number is the ratio of fluid pressure loss to fluid kinetic energy. The Euler number is typically used to characterise friction loss through components. The flow diameter and elevation are assumed to be constant. The inlet and outlet pressure may be measured as either guage pressure or absolute pressure provided that both pressures are measured in the same way. The cavitation number Ca is of similar form and is used to determine the susceptibility of the fluid to cavitation (refer to cavitation number).

The fluid velocity is user defined.

Tool Input

  • ρ : Liquid Density
  • P1 : Internal Pressure 1
  • P2 : Internal Pressure 2
  • V : Fluid Velocity

Tool Output

  • ΔP : Pressure Difference
  • Eu : E Value
  • K : K Value

CALCULATOR : Dimensionless Euler Number Eu From Pipeline Liquid Volume Flow Rate   +

Calculate dimensionless Euler number Eu from pipeline liquid volume flow rate.

The dimensionless Euler number is the ratio of fluid pressure loss to fluid kinetic energy. The Euler number is typically used to characterise friction loss through components. The flow diameter and elevation are assumed to be constant. The inlet and outlet pressure may be measured as either guage pressure or absolute pressure provided that both pressures are measured in the same way. The cavitation number Ca is of similar form and is used to determine the susceptibility of the fluid to cavitation (refer to cavitation number).

The fluid velocity is calculated from the volume flow rate.

Tool Input

  • ρ : Liquid Density
  • Q : Liquid Volume Flowrate
  • ID : Nominal Inside Diameter
  • P1 : Internal Pressure 1
  • P2 : Internal Pressure 2

Tool Output

  • ΔP : Pressure Difference
  • Eu : E Value
  • K : K Value
  • V : Fluid Velocity

CALCULATOR : Dimensionless Froude Number Fr For Open Channels And Shallow Water Waves   +

Calculate dimensionless Froude number Fr for open channels and shallow water waves.

The dimensionless Froude number is the ratio of inertia forces and gravity forces. It may be used to determine the resistance of a body moving through water, and also to determine the type of flow in open channels or shallow water waves. The Froude number was originally derived from the speed length ratio for ship resistance.

Tool Input

  • V : Fluid Velocity
  • d : Water Depth

Tool Output

  • Fr : Froude Number

CALCULATOR : Dimensionless Froude Number Fr For Ship Hydrodynamics   +

Calculate dimensionless Froude number Fr for ship hydrodynamics.

The dimensionless Froude number is the ratio of inertia forces and gravity forces. It may be used to determine the resistance of a body moving through water, and also to determine the type of flow in open channels or shallow water waves. The Froude number was originally derived from the speed length ratio for ship resistance. For ships the characteristic length is the waterline length.

Tool Input

  • L : Water Line Length
  • V : Fluid Velocity

Tool Output

  • Fr : Froude Number

CALCULATOR : Dimensionless Froude Number Fr From Wave Propagation Velocity (General Form)   +

Calculate dimensionless Froude number Fr from wave propagation velocity (general form).

The dimensionless Froude number is the ratio of inertia forces and gravity forces. It may be used to determine the resistance of a body moving through water, and also to determine the type of flow in open channels or shallow water waves. The Froude number was originally derived from the speed length ratio for ship resistance.

Tool Input

  • V : Fluid Velocity
  • c : Wave Celerity Or Propagation Speed

Tool Output

  • Fr : Froude Number

CALCULATOR : Dimensionless Grashof Number Gr (General Form)   +

Calculate dimensionless Grashof number Gr (general form).

The dimensionless Grashof number is the ratio of buoyancy forces and viscous forces acting on a heated fluid. The Grashof number may be used to determine the transition between laminar and turbulent boundary layer. The bulk fluid temperature should be used as the fluid temperature. The Rayleigh number is the product of the Grashof number and the Prandtl number (refer to Rayleigh number and Prandtl number).

Tool Input

  • L : Characteristic Length
  • To : Fluid Temperature
  • Ts : Surface Temperature
  • β : Fluid Volume Expansion Coefficient
  • ν : Fluid Kinematic Viscosity

Tool Output

  • ΔT : Temperature Difference
  • Gr : Grashof Number

CALCULATOR : Dimensionless Grashof Number Gr Ideal Gas   +

Calculate dimensionless Grashof number Gr for an ideal gas.

The dimensionless Grashof number is the ratio of buoyancy forces and viscous forces acting on a heated fluid. The Grashof number may be used to determine the transition between laminar and turbulent boundary layer. The bulk fluid temperature should be used as the fluid temperature. The Rayleigh number is the product of the Grashof number and the Prandtl number (refer to Rayleigh number and Prandtl number).

For an ideal gas the volume expansion coefficient may be calculated directly from the gas temperature. Select the temperature type for calculating the volume expansion coefficient: surface temperature, bulk fluid temperature or average temperature (average of the bulk fluid temperature and the surface temperature).

Tool Input

  • L : Characteristic Length
  • temptype : Temperature Type
  • To : Fluid Temperature
  • Ts : Surface Temperature
  • ν : Fluid Kinematic Viscosity

Tool Output

  • ΔT : Temperature Difference
  • β : Fluid Volume Expansion Coefficient
  • Gr : Grashof Number

CALCULATOR : Dimensionless Keulegan Carpenter Number Kc User Defined Velocity   +

Calculate dimensionless Keulegen-Carpenter number or period number is a measure of the ratio of drag forces to inertia forces in oscillating flow (typically wave flow). It may also be appliled to objects oscillating in a stationary fluid. For small Keulegen-Carpenter numbers inertia forces dominate. At large Keulegen-Carpenter numbers drag forces dominate.

The velocity amplitude is user defined. For oscillation motion other than wave motion, enter the oscillation period as the wave period.

Tool Input

  • Lc : Characteristic Length
  • Ua : Horizontal Wave Velocity
  • T : Wave Period

Tool Output

  • Kc : Dimensionless Keulegan Carpenter Number

CALCULATOR : Dimensionless Mach Number And Velocity   +

Calculate dimensionless Mach number from fluid velocity or fluid velocity from Mach number.

The dimensionless Mach number is the ratio of the velocity to the speed of sound in the fluid. It may be applied to a moving fluid, or to a moving body in a stationary fluid. The speed of sound can either be calculated for an ideal gas or be user defined.

Tool Input

  • fluidtype : Fluid Type
    • γu : User Defined Specific Heat Ratio
    • SGu : User Defined Gas Specific Gravity
  • machtype : Mach Number Type
    • Mu : User Defined Mach Number
    • Vu : User Defined Velocity
  • T : Fluid Temperature
  • vctype : Speed Of Sound Type
    • Cu : User Defined Sound Velocity
  • Z : Gas Compressibility Factor

Tool Output

  • γ : Specific Heat Ratio
  • C : Speed Of Sound
  • M : Mach Number
  • SG : Gas Specific Gravity Relative To Air
  • V : Velocity
  • mmg : Gas Molar Mass

CALCULATOR : Dimensionless Nusselt Number Nu (General Form)   +

Calculate dimensionless Nusselt number Nu (general form).

The dimensionless Nusselt number is the ratio of convective heat transfer and conductive heat transfer. For free convection the Nusselt number is often calculated from the Rayleigh number and the Prandtl number (refer to Rayleigh number and Prandtl number). For forced convection the Nusselt number is often calculated from the Reynolds number and the Prandtl number (refer to Reynolds number and Prandtl number).

Tool Input

  • L : Characteristic Length
  • h : Fluid Convective Heat Transfer
  • k : Fluid Heat Conductivity

Tool Output

  • Nu : Nusselt Number

CALCULATOR : Dimensionless Ocean Wave Numbers k f Ur HoD LoD H* d* (General Form)   +

Calculate dimensionless ocean wave number k, Ursell number Ur, wave frequency f, wave height over water depth ratio HoD, wave length over water depth ratio LoD, dimensionless wave height H*, and dimensionless water depth d*.

Tool Input

  • d : Water Depth
  • H : Wave Height
  • L : Wave Length
  • T : Wave Peak Period

Tool Output

  • H* : H Value
  • Ur : U Value
  • d* : D Value
  • f : Wave Frequency
  • hod : Wave Height Over Water Depth Ratio
  • k : Wave Number
  • lod : Wave Length Over Water Depth Ratio

CALCULATOR : Dimensionless Peclet Number Pe (Mass Diffusion Case)   +

Calculate dimensionless Peclet number Pe (mass diffusion case).

The dimensionless Peclet number is the ratio of advection and diffusion and is used in the analysis of fluid transport. For mass diffusion the Peclet number is equal to product of the Reynolds number and the Schmidt number (refer to Schmidt number and Reynolds number).

Tool Input

  • L : Characteristic Length
  • D : Fluid Thermal Diffusivity
  • V : Fluid Velocity
  • ν : Fluid Kinematic Viscosity

Tool Output

  • Pe : L Value
  • Re : Reynolds Number
  • Sc : S Value

CALCULATOR : Dimensionless Peclet Number Pe (Thermal Diffusion Case)   +

Calculate dimensionless Peclet number Pe (thermal diffusion case).

The dimensionless Peclet number is the ratio of advection and diffusion and is used in the analysis of fluid transport. For thermal diffusion the Peclet number is equal to product of the Reynolds number and the Prandtl number (refer to Prandtl number and Reynolds number).

Tool Input

  • L : Characteristic Length
  • Cp : Specific Heat Capacity Constant Pressure
  • ρ : Liquid Density
  • k : Fluid Heat Conductivity
  • V : Fluid Velocity
  • ν : Fluid Kinematic Viscosity

Tool Output

  • α : Fluid Thermal Diffusivity
  • Pe : L Value
  • Pr : P Value
  • Re : Reynolds Number

CALCULATOR : Dimensionless Prandtl Number Pr   +

Calculate dimensionless Prandtl number Pr.

The dimensionless Prandtl number is the ratio of the fluid viscosity to the thermal diffusivity. The product of the Eckert number and the Prandtl number is equal to the Brinkman number (refer to Brinkman number and Eckert Number). The product of the Grashof number and the Prandtl number is equal to the Rayleigh number (refer to Rayleigh number and Grashof number).

Tool Input

  • Cp : Specific Heat Capacity Constant Pressure
  • ρ : Fluid Density
  • k : Fluid Heat Conductivity
  • visctype : Viscosity Type
    • μu : User Defined Fluid Dynamic Viscosity
    • νu : User Defined Fluid Kinematic Viscosity

Tool Output

  • α : Fluid Thermal Diffusivity
  • μ : Fluid Dynamic Viscosity
  • ν : Fluid Kinematic Viscosity
  • Pr : P Value

CALCULATOR : Dimensionless Rayleigh Number Ra (General Form)   +

Calculate dimensionless Rayleigh number Ra (general form).

The dimensionless Rayleigh number is the ratio of buoyancy forces and viscous forces. The Rayleigh number is equal to the product of the Grashof number and the Prandtl number where the characteristic length equals the position (refer to Grashof number and Prandtl number).

Tool Input

  • L : Characteristic Length
  • Cp : Fluid Heat Capacity Constant Pressure
  • ρ : Fluid Density
  • k : Fluid Heat Conductivity
  • To : Fluid Temperature
  • Ts : Surface Temperature
  • β : Fluid Volume Expansion Coefficient
  • ν : Fluid Kinematic Viscosity

Tool Output

  • ΔT : Temperature Difference
  • α : Fluid Thermal Diffusivity
  • Gr : Grashof Number
  • Pr : Prandtl Number
  • Ra : Rayleigh Number

CALCULATOR : Dimensionless Rayleigh Number Ra Ideal Gas   +

Calculate dimensionless Rayleigh number Ra for an ideal gas.

The dimensionless Rayleigh number is the ratio of buoyancy forces and viscous forces.

The Rayleigh number is equal to the product of the Grashof number and the Prandtl number where the characteristic length equals the position (refer to Grashof number and Prandtl number).

For an ideal gas the volume expansion coefficient may be calculated directly from the gas temperature. Select the temperature type for calculating the volume expansion coefficient: surface temperature, bulk fluid temperature or average temperature (average of the bulk fluid temperature and the surface temperature).

Tool Input

  • L : Characteristic Length
  • Cp : Fluid Heat Capacity Constant Pressure
  • ρ : Fluid Density
  • k : Fluid Heat Conductivity
  • temptype : Temperature Type
  • To : Fluid Temperature
  • Ts : Surface Temperature
  • ν : Fluid Kinematic Viscosity

Tool Output

  • ΔT : Temperature Difference
  • α : Fluid Thermal Diffusivity
  • β : Fluid Volume Expansion Coefficient
  • Gr : Grashof Number
  • Pr : Prandtl Number
  • Ra : Rayleigh Number

CALCULATOR : Dimensionless Relative Roughness Number Rr From Roughness And Hydraulic Diameter For Rectangular Duct   +

Calculate dimensionless rectangular duct relative roughness from the internal roughness and the hydraulic diameter.

The duct relative roughness ratio is the ratio of the duct wall internal surface roughness to duct hydraulic diameter. The hydraulic diameter is equal to four times the cross section area divided by the perimeter.

Tool Input

  • H : Duct Height
  • roughtype : Internal Roughness Type
    • ru : User Defined Surface Roughness
  • W : Duct Width

Tool Output

  • D : Hydraulic Diameter
  • Rr : Dimensionless Surface Roughness Ratio
  • r : Surface Roughness

CALCULATOR : Dimensionless Relative Roughness Number Rr From Roughness And Internal Diameter For Pipeline   +

Calculate dimensionless pipeline relative roughness number from the internal roughness r and the pipeline internal diameter.

The pipe relative roughness ratio is the ratio of the pipe wall internal surface roughness to pipe internal diameter.

Tool Input

  • D : Inside Diameter
  • roughtype : Internal Roughness Type
    • ru : User Defined Surface Roughness

Tool Output

  • Rr : Dimensionless Surface Roughness Ratio
  • r : Surface Roughness

CALCULATOR : Dimensionless Reynolds Number Re From Characteristic Length And Velocity   +

Calculate dimensionless Reynolds number Re from fluid density, fluid viscosity, fluid velocity and characteristic length.

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

Tool Input

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

Tool Output

  • μ : Fluid Dynamic Viscosity
  • ν : Fluid Kinematic Viscosity
  • Re : Reynolds Number

CALCULATOR : Dimensionless Reynolds Number Re From Flow Rate For Three Phase Black Oil Pipeline   +

Calculate dimensionless Reynolds number from flow rate or velocity 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

  • diamtype : Pipe Diameter Type
    • IDu : User Defined Inside Diameter
    • ODu : User Defined Outside Diameter
  • ρo : Oil Density
  • ρw : Water Density
  • mvtype : Fluid Density Type
    • GORu : User Defined Gas Oil Ratio
    • ρu : User Defined Fluid Density
    • WCu : User Defined Water Cut
  • P : Fluid Pressure
  • schedtype : Pipe Schedule Type
  • SG : Gas Specific Gravity
  • T : Fluid Temperature
  • μg : Gas Dynamic Viscosity
  • μo : Oil Dynamic Viscosity
  • μw : Water Dynamic Viscosity
  • visctype : Viscosity Type
    • μu : User Defined Dynamic Viscosity
    • νu : User Defined Kinematic Viscosity
  • voltype : Fluid Volume Type
    • Ngu : User Defined Gas Mole Flow Rate
    • Mfu : User Defined Total Fluid Mass Flow Rate
    • Qlu : User Defined Liquid Volume Flow Rate
    • Qou : User Defined Oil Volume Flow Rate
    • Qfu : User Defined Total Fluid Volume Flow Rate
    • Reu : User Defined Reynolds Number
    • Vfu : User Defined Fluid Velocity
  • wtntype : Wall Thickness Schedule Type
    • tnu : User Defined Wall Thickness
  • Z : Gas Compressibility Factor

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
  • OD : Outside Diameter
  • 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
  • tn : Nominal Wall Thickness
  • vg : Gas Mole Volume (At T P)

CALCULATOR : Dimensionless Reynolds Number Re From Flow Rate For Two Phase Pipeline   +

Calculate Reynolds number from flow rate or velocity for single phase gas, single phase liquid, and two phase gas liquid pipelines.

The Reynolds number is the ratio of the fluid kinetic energy to the viscous energy loss. For pipelines the internal diameter is used as the characteristic length. For two phase flow the viscosity may be calculated from the gas mass fraction using either the mass average (Cichitti), reciprocal mass average (McAdams), or volume average (Dukler). The gas oil ratio is the ratio of gas moles to liquid volume. The gas mass fraction is the ratio of gas mass to total fluid mass. The gas volume fraction is the ratio of gas volume to total fluid volume.

Tool Input

  • diamtype : Pipe Diameter Type
    • IDu : User Defined Inside Diameter
    • ODu : User Defined Outside Diameter
  • ρl : Liquid Density
  • mvtype : Fluid Density Type
    • GORu : User Defined Gas Oil Ratio
    • Xmu : User Defined Gas Mass Fraction
    • ρu : User Defined Fluid Density
    • Xvu : User Defined Gas Volume Fraction
  • P : Fluid Pressure
  • schedtype : Pipe Schedule Type
  • SG : Gas Specific Gravity
  • T : Fluid Temperature
  • μg : Gas Dynamic Viscosity
  • μl : Liquid Dynamic Viscosity
  • visctype : Viscosity Type
    • μu : User Defined Dynamic Viscosity
    • νu : User Defined Kinematic Viscosity
  • voltype : Fluid Flow Rate Type
    • Ngu : User Defined Gas Mole Flow Rate
    • Mfu : User Defined Total Fluid Mass Flow Rate
    • Qlu : User Defined Liquid Volume Flow Rate
    • Qfu : User Defined Total Fluid Volume Flow Rate
    • Reu : User Defined Reynolds Number
    • Vfu : User Defined Fluid Velocity
  • wtntype : Wall Thickness Schedule Type
    • tnu : User Defined Wall Thickness
  • Z : Gas Compressibility Factor

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
  • OD : Outside Diameter
  • 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)
  • tn : Nominal Wall Thickness
  • vg : Gas Mole Volume (At T P)

CALCULATOR : Dimensionless Richardson Number Ri (General Form)   +

Calculate dimensionless Richardson number Ri (general form).

The dimensionless Richardson number is the ratio of potential energy and kinetic energy. The Richardson number may be used to determine the mixing and turbulence of stratified ocean and atmospheric flow. The characteristic length is a vertical length. The Richardson number may also be calculated as the ratio of potential buoyancy energy and kinetic energy, and in this case the Richardson number is equal to the Grashof number divided by the Reynolds number squared (refer to Grashof number and Reynolds number).

Tool Input

  • h : Characteristic Length
  • V : Fluid Velocity

Tool Output

  • Ri : Richardson Number

CALCULATOR : Dimensionless Richardson Number Ri (Thermal Convection Form)   +

Calculate dimensionless Richardson number Ri (thermal convection form).

The dimensionless Richardson number is the ratio of potential energy and kinetic energy. The Richardson number may be used to determine the mixing and turbulence of stratified ocean and atmospheric flow. The characteristic length is a vertical length. The Richardson number may also be calculated as the ratio of potential buoyancy energy and kinetic energy, and in this case the Richardson number is equal to the Grashof number divided by the Reynolds number squared (refer to Grashof number and Reynolds number).

Tool Input

  • L : Characteristic Length
  • To : Fluid Temperature
  • Ts : Surface Temperature
  • V : Fluid Velocity
  • β : Fluid Volume Expansion Coefficient

Tool Output

  • ΔT : Temperature Difference
  • Ri : Richardson Number

CALCULATOR : Dimensionless Richardson Number Ri (Thermal Convection Form) Ideal Gas   +

Calculate dimensionless Richardson number Ri (thermal convection form) for an ideal gas.

The Richardson number is calculated as the ratio of potential buoyancy energy and kinetic energy. For an ideal gas the volume expansion coefficient may be calculated directly from the gas temperature. Select the temperature type for calculating the volume expansion coefficient: surface temperature, bulk fluid temperature or average temperature (average of the bulk fluid temperature and the surface temperature).

Tool Input

  • L : Characteristic Length
  • temptype : Temperature Type
  • To : Fluid Temperature
  • Ts : Surface Temperature
  • V : Fluid Velocity

Tool Output

  • ΔT : Temperature Difference
  • β : Fluid Volume Expansion Coefficient
  • Ri : Richardson Number

CALCULATOR : Dimensionless Roshko Number Ro (General Form)   +

Calculate dimensionless Roshko number Ro (general form).

The dimensionless Roshko number is equal to the product of the Reynolds number and the Strouhal number (refer to Strouhal number and Reynolds number).

Tool Input

  • L : Characteristic Length
  • f : Vortex Shedding Frequency
  • ν : Fluid Kinematic Viscosity

Tool Output

  • Ro : R Value

CALCULATOR : Dimensionless Schmidt Number Sc   +

Calculate dimensionless Schmidt number Sc.

The dimensionless Schmidt number is the ratio of viscosity and mass diffusivity. The Peclet number is the mass diffusion equivalent of the Prandtl number for thermal diffusion (refer to Prandtl number). For mass diffusion the Peclet number is equal to product of the Reynolds number and the Schmidt number (refer to Peclet number and Reynolds number).

Tool Input

  • ρ : Fluid Density
  • D : Fluid Thermal Diffusivity
  • visctype : Viscosity Type
    • μu : User Defined Fluid Dynamic Viscosity
    • νu : User Defined Fluid Kinematic Viscosity

Tool Output

  • μ : Fluid Dynamic Viscosity
  • ν : Fluid Kinematic Viscosity
  • Sc : S Value

CALCULATOR : Dimensionless Sherwood Number Sh (General Form)   +

Calculate dimensionless Sherwood number Sh (general form).

The dimensionless Sherwood number is the ratio of convective mass transport and diffusive mass transport. The Sherwood number is the mass transfer equivalent of the Nusselt number (refer to Nusselt number), and may generally be calculated from the Reynolds number and the Schmidt number (refer to Schmidt number and Reynolds number).

Tool Input

  • L : Characteristic Length
  • D : Fluid Thermal Diffusivity
  • K : Fluid Heat Conductivity

Tool Output

  • Sh : S Value

CALCULATOR : Dimensionless Shields Number ϴ And Critical Fluid Velocity   +

Calculate the dimensionless Shields number or Shields parameter ϴ and the critical fluid velocity for initiation of sediment movement.

The Shields number is used to calculate the initiation of sediment movement in a fluid flow. For subsea waves and currents the critical Shields parameter is approximately 0.04. For laminar flow the critical Shields parameter is approximately 0.03.

Tool Input

  • facttype : Critical Shields Parameter Type
    • ϴcu : User Defined Critical Shields Number
  • ρb : Seawater Density
  • ρp : Particle Density
  • roughtype : Seabed Roughness Type
    • D50u : User Defined Particle Diameter
  • T : Wave Period
  • Uc : Current Velocity
  • Uw : Wave Horizontal Velocity
  • wavetype : Friction Factor Type

Tool Output

  • ϴ : Shields Parameter
  • ϴcr : Critical Shields Parameter
  • τ : Fluid Shear Stress
  • CVG : Convergence Factor
  • D50 : Mean Particle Diameter
  • Ss : Particle Relative Density
  • Ucr : Critical Fluid Velocity
  • fw : Friction Factor

CALCULATOR : Dimensionless Strouhal Number St (General Form)   +

Calculate dimensionless Strouhal number St (general form).

The dimensionless Strouhal number is used to determine the onset and type of vortex shedding in oscillating flow. The Roshko number is equal to the product of the Strouhal number and the Reynolds number (refer to Roshko number and Reynolds number).

Tool Input

  • L : Characteristic Length
  • f : Vortex Shedding Frequency
  • V : Fluid Velocity

Tool Output

  • St : Strouhal Number

CALCULATOR : Dimensionless Ursell Wave Number U (General Form)   +

Calculate dimensionless Ursell wave number.

The Ursell number is equal to the wave height over water depth ratio, multipled by the square of the wavlength over water depth ratio.

Tool Input

  • d : Water Depth
  • H : Wave Height
  • L : Wave Length

Tool Output

  • Ur : Ursell Number

CALCULATOR : Dimensionless Weber Number We (General Form)   +

Calculate dimensionless Weber number We.

The dimensionless Weber number is the ratio of inertia forces and surface tension forces. It may be used to analyse thin film flows and the formation of droplets and bubbles during impact of an object onto a fluid surface.

Tool Input

  • L : Characteristic Length
  • ρ : Fluid Density
  • σ : Surface Tension
  • V : Fluid Velocity

Tool Output

  • We : Weber Number
  • We* : Modified Weber Number