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Fluid Density Modules

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CALCULATOR MODULE : Line Pipe Fluid Mass And Volume   ±
CALCULATOR MODULE : Liquid Pipeline Pressure Loss From The Darcy Weisbach Equation   ±

Calculate single phase liquid pipeline pressure loss using the Darcy Weisbach equation.

`Po = P - (fd L / (ID) + K) 1/2 ρ V^2 + ρ g (zi - zo) `

where :

Po = outlet pressure
P = inlet pressure
fd = Darcy friction factor
L = piping length
ID = piping inside diameter
K = total friction loss factor for fittings
ρ = fluid density
V = fluid velocity
g = gravity constant
zi = inlet elevation
zo = outlet elevation

The Darcy friction factor can be calculated for

  • Hagen-Poiseuille laminar flow equation
  • original Colebrook White equation
  • modified Colebrook White equation
  • Prandtl Nikuradse smooth pipe equation
  • Blasius smooth pipe equation
  • Colebrook smooth pipe equation
  • Miller smooth pipe equation
  • Konakov smooth pipe equation
  • Von Karman rough pipe equation

For low Reynolds numbers Re < 2000, the fluid flow is laminar and the Darcy friction factor should be calculated using the Hagen-Poiseuille laminar flow equation. For high Reynolds numbers Re > 4000, the fluid flow is turbulent and the Darcy friction factor should be calculated using one of the turbulent flow equations. In the transition region 2000 < Re < 4000, the flow is unstable and the friction loss cannot be reliably calculated. The minor loss K factor is used to account for pipeline fittings such as bends, tees, valves etc..

The calculators use the Darcy-Weisbach pressure loss equation. The Fanning friction factor is used with the Fanning pressure loss equation. The transmission factors are commonly used for gas flow. The results for the Darcy and Fanning equations are identical provided that the correct friction factor is used.

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CALCULATOR MODULE : Liquid Pipeline Fluid Density Viscosity And Specific Gravity   ±
CALCULATOR MODULE : Gas Pipeline Pressure Loss From The Darcy Weisbach Equation   ±

Calculate single phase gas pipeline pressure loss using the Darcy Weisbach equation.

`Po = √(P^2 - m^2(fd.L / D + K) ls (16mma.SG.ZRoT)/(pi^2D^4) ) / (es) `
`ss = (z2 - z2) SG.mma.g / (Ro T Z) `
`es = e^(ss) `
`ls = (es^2 - 1) / (ss) `

where :

Po = outlet pressure
P = inlet pressure
fd = Darcy friction factor
L = piping length
D = piping inside diameter
K = total friction loss factor for fittings
m = gas mole flowrategas
mma = air molar mass
SG = gas specific gravity
Z = gas compressibility factor
Ro = universal gas constant
T = gas temperature
g = gravity constant
zi = inlet elevation
zo = outlet elevation
ss = elevation exponent
es = elevation pressure factor
ls = elevation length factor

For low Reynolds numbers Re < 2000, the fluid flow is laminar and the Darcy friction factor should be calculated using the Hagen-Poiseuille laminar flow equation. For high Reynolds numbers Re > 4000, the fluid flow is turbulent and the Darcy friction factor should be calculated using one of the turbulent flow equations. In the transition region 2000 < Re < 4000, the flow is unstable and the friction loss cannot be reliably calculated. The minor loss K factor is used to account for pipeline fittings such as bends, tees, valves etc..

The calculators use the Darcy-Weisbach pressure loss equation with the Darcy friction factor. The Fanning transmission factor combined with the Fanning equation is commonly used for gas flow. The results for the Darcy and Fanning equations are identical provided that the correct friction factor is used.

The gas specific gravity is the ratio of gas density over the density of dry air at base temperature and pressure. The compressibility factor is assumed to equal 1 at the base conditions. The gas specific gravity is proportional to the gas molar mass.

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CALCULATOR MODULE : Gas Pipeline Fluid Density And Specific Gravity   ±
CALCULATOR MODULE : API RP 14E Fluid Density   ±
CALCULATOR MODULE : Compressible Flow Speed Of Sound   ±

Calculate gas and liquid speed of sound and Mach number.

The Mach number is the ratio of the flow velocity to the speed of sound. It applies to either a moving fluid or to a moving object passing through stationary fluid. For a Mach number greater than one, the flow is supersonic. For a Mach number less than one, the flow is subsonic.

For an ideal gas, the speed of sound or sonic velocity can be calculated from the gas temperature, gas specific heat ratio and the gas specific gravity. For liquids the speed of sound can be calculated from the liquid bulk modulus and the liquid density.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR MODULE : Compressible Flow Gas Property   ±

Calculate compressible flow gas properties.

Calculate gas specific heat constant pressure, specific heat constant volume, specific heat ratio, molar mass, gas constant, gas specific gravity, gas compressibility factor and density from gas temperature and pressure. 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 equation of state (EOS).

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR MODULE : DNVGL RP O501 Fluid Density And Viscosity   ±
CALCULATOR MODULE : API 520 Fluid Property   ±

Calculate API 520 gas and steam properties.

Properties include density, specific heat constant pressure, specific heat constant volume, specific heat ratio, molar mass, gas constant, gas specific gravity, and gas compressibility factor. 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).Steam properties are calculated from IAPWS R7-97, industrial properties of steam.

Gas specific gravity at standard conditions is approximately equal to the gas molar mass divided by the molar mass of dry air. The molar mass of dry air is taken as 28.964 kg/kg-mole.

Reference : API 520 Sizing, Selection And Installation Of Pressure Relieving Devices (2014)

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CALCULATOR MODULE : Fresh Water Bulk Modulus   ±

Calculate fresh water density and bulk modulus from temperature using Kell's equations (1975).

Kells equations are valid for temperatures from 0 to 100 C, at atmospheric pressure. The calculations are based on the 1968 international temperature scale (IPTS-68).

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CALCULATOR MODULE : Pump Liquid Vapour Pressure Viscosity And Density   ±
CALCULATOR MODULE : Fluid Density And Volume   ±

Calculate fluid density for single phase fluid (oil, water, or gas), two phase fluid (oil and gas, or oil and water), and three phase black oil (oil, water and gas).

The gas oil ratio is the ratio of gas moles to oil volume. Gas oil ratio is often measured as gas standard volume (scf or scm) per oil volume (barrels, gallons, cubic feet or cubic meters). 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. Water cut is the ratio of water volume over total liquid volume (equals the water volume fraction in the liquid). Gas volume is dependent on fluid temperature and pressure.

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CALCULATOR MODULE : Two Phase Gas Liquid Density   ±

Calculate fluid density for two phase fluid (oil and gas, or gas and water).

The gas oil ratio is the ratio of gas moles to oil 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. Gas volume is dependent on fluid temperature and pressure. Gas oil ratio is often measured as gas standard volume (scf or scm) per oil volume (barrels, gallons, cubic feet or cubic meters).

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CALCULATOR MODULE : Three Phase Gas Oil Water (Black Oil) Density   ±

Calculate fluid density for three phase black oil (oil, water and gas).

The gas oil ratio is the ratio of gas moles to oil 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. Water cut is the ratio of water volume over total liquid volume (equals the water volume fraction in the liquid). Gas volume is dependent on fluid temperature and pressure. Gas oil ratio is often measured as gas standard volume (scf or scm) per oil volume (barrels, gallons, cubic feet or cubic meters).

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CALCULATOR MODULE : Single Phase Gas Specific Gravity   ±
CALCULATOR MODULE : Single Phase Liquid Specific Gravity   ±

Calculate liquid specific gravity for single phase liquid.

Liquid specific gravity is calculated relative to the density of water (1000 kg/m^3). Liquid density can also be defined as degrees API (liquids lighter than water), degrees Baume (liquids lighter than water or liquids heavier than water), or degrees Twaddell (liquids heavier than water).

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CALCULATOR MODULE : Fluid Dosing Rate And Density   ±
CALCULATOR MODULE : Water And Steam Density   ±
CALCULATOR MODULE : Single Phase Gas Density   ±
CALCULATOR MODULE : Gas Compressibility Factor   ±

Calculate gas compressibility factor or Z factor.

The compressibility factor is used to account for the non ideal behaviour of real gases. The non ideal gas law is expressed as

` P V = Z Ro T `

where :

P = gas pressure `
`T = gas temperature `
`V = gas mole volume `
`Z = gas compressibility factor `
`Ro = universal gas constant

The compressibility factor canbe calculated using either the Peng Robinson, Soave, Redlich Kwong or Van Der Waals cubic equations of state (EOS), or using the virial equation.

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CALCULATOR MODULE : Gas Compressibility Factor From The Virial Equation   ±

Calculate gas compressibility factor or Z factor from the virial equation.

The compressibility factor is calculated using the second order virial equation

`Z = (P.vm) / (Ro .T) = 1 + B / (vm) `
`B = a - b.e^(c / T) `

where :

Z = the compressibility factor
P = gas pressure
T = gas temperature
vm = gas mole volume
Ro = the universal gas constant
B = the second order virial coefficient
a, b, c are Virial constants

The gas mole volume is calculated by solving the quadratic equation, and the compressibility factor is calculated from the mole volume.

Reference : Kaye And Laby : Tables Of Physical And Chemical Constants

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CALCULATOR MODULE : Fluid Mixture From Kay's Rule   ±

Calculate pseudo-critical properties (temperature, pressure, accentric factor, molar mass) of a fluid mixture using the simple form of Kay's rule with no interaction parameters.

The mole fraction of component one is automatically adjusted so that the sum of the mole fractions equals one. The mixture properties are approximate.

    Related Modules :

    CALCULATOR MODULE : IAPWS R7-97 Fresh Water Density At Atmospheric Pressure   ±

    Calculate IAPWS R7-97 fresh water density from temperature at atmospheric pressure.

    The calculation is valid between the melting point (273.15 K), and the boiling point (373.15 K).

    Note : There is an anomaly in the steam calculation for region 3 between the saturated vapour line, the region 2/3 boundary, and the critical pressure. Refer to the region 3 anomaly help page for more details (click the utility button on the data bar). IAPWS R7-97 is intended for industrial use, and is a simplified version of IAPWS R6-95 for scientific use. IAPWS R7-97 was developed as an improvement of the IFC-67 model.

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

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    CALCULATOR MODULE : TEOS-10 Seawater Density   ±

    Calculate TEOS-10 seawater density from temperature, pressure and practical salinity.

    The hydrostatic pressure used in TEOS-10 can be calculated from water depth or relative elevation. The water density is assumed constant. Changes in water density with water depth, salinity and temperature are ignored. Elevation is measured relative to an arbitrary datum (+ve up -ve down). Mean sea level (MSL) is often used as a datum.

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

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    CALCULATOR MODULE : TEOS-10 Seawater Dynamic And Kinematic Viscosity   ±

    Calculate TEOS-10 seawater dynamic and kinematic viscosity from temperature, pressure, and practical salinity.

    Seawater viscosity is calculated from fresh water viscosity using the equation from Sharqawy (2010). The fresh water viscosity is calculated from temperature and density using the IAPWS R12-08 industrial equations. Practical salinity = parts per thousand of dissolved solids (mainly salt). The absolute salinity is taken as 35.16504 / 35 times the practical salinity (absolute salinity equals reference salinity). The absolute salinity anomaly δSA is ignored.

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

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    CALCULATOR MODULE : IAPWS R12-08 Fresh Water Dynamic And Kinematic Viscosity   ±

    Calculate the dynamic viscosity and kinematic viscosity of water and steam using the IAPWS R12-08 industrial equation (u2 = 1).

    The viscosity can be either calculated directly from temperature and density, or from temperature and pressure using IAPWS R7-97 to calculate the density.

    Note : There is an anomaly in the calculated density and viscosity close to the critical point. Refer to the help pages for more details (click the utility button on the data bar).

    References :

    IAPWS R12-08 Industrial Formulation 2008 for the Viscosity of Ordinary Water Substance
    IAPWS R7-97 Industrial Formulation for thermodynamic Properties of Water and Steam

      Related Modules :

      CALCULATOR MODULE : Yaws Gas Density From Critical Point   ±

      Calculate gas density from critical pressure, critical temperature and acentric factor data for organic and inorganic fluids (Yaws).

      The compressibility factor can be calculated from either the Peng Robinson, Soave, Redlich Kwong, or van der Waals cubic equation. The compressibility factor calculation is valid for gas phase only. The gas specific gravity is approximately equal to the ratio of the gas molar mass over the molar mass of air (28.964 g/mol).

      Reference : Yaws Chemical Properties Handbook, McGraw Hill

      DATA MODULE : Fluid Density And Specific Gravity ( Open In Popup Workbook )   ±
      DATA MODULE : Fluid Dynamic And Kinematic Viscosity ( Open In Popup Workbook )   ±