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Fresh Water Modules

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CALCULATOR MODULE : Dimensionless Number   ±

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.

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CALCULATOR MODULE : Dimensionless Keulegan Carpenter Number   ±

Calculate the dimensionless Keulegen Carpenter number or period number.

The Keulegen Carpenter number approximates the ratio of drag forces to inertia forces acting on a structure in oscillating flow (typically wave flow).

`Kc = V T / (OOD) = V^2 / (A* OOD) `
`A* = V / T `

where :

Kc = Keulegan Carpenter number
V = velocity amplitude
T = oscillation period
OOD = structure outer diameter or characteristic length
A* = approximate acceleration amplitude

For small Keulegen Carpenter numbers inertia forces dominate. At large Keulegen Carpenter numbers drag forces dominate. The Keulegen Carpenter number can also be applied to structures oscillating in a stationary fluid.

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CALCULATOR MODULE : Dimensionless Wave Number   ±

Calculate common dimensionless and dimensional ocean wave numbers.

Ocean wave numbers include :

`kw = (2 pi) / L = 2 pi(fw) / c `
`fw = 1 / T `
`Ur = h l^2 / d^3 = (h/d)^3 / (l/d)^2 `
`H* = H / (g t^2) `
`d* = d / (g t^2) `

where :

kw = wave number (dimesion 1/length)
fw = wave frequency (dimension 1/time)
Ur = dimensionless Ursell number
H* = dimensionless wave height
d* = dimensionless water depth
L = wave length
f = wave frequency
c = wave celerity or propagation speed

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CALCULATOR MODULE : Dimensionless Ursell Number   ±

Calculate the dimensionless Ursell number.

The Ursell number is a measure of the non linearity of ocean waves.

`Ur = h L^2 / d^3 = (h/d)^3 / (L/d)^2 `

where :

Ur = Ursell number
h = wave height
L = wave length
d = water depth

The Airy wave is suitable for Ur < 1. Stokes wave should be used for Ur < 40. Cnoidal wave should be used for Ur > 40.

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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 Pressure Loss From The Moody Diagram   ±

Calculate pressure loss for single phase liquid pipelines and ducts using the Darcy Weisbach version of the Moody Diagram.

`fdl = 64/(Re) `
`1/(√fdo) = -2 log10(r/3.7 + 2.51 / (Re √(fdo))) `
`1/(√fdm) = -2 log10(r/3.7 + 2.825 / (Re √(fdm))) `

where :

fdl = Hagen-Poiseuille laminar flow equation Darcy friction factor
fdo = original Colebrook White equation Darcy friction factor
fdm = modified Colebrook White equation Darcy friction factor
Re = Reynolds number
r = relative roughness

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..

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CALCULATOR MODULE : Water Pipeline Pressure Loss From The Hazen Williams Equation   ±

Calculate pressure loss for single phase liquid pipelines using the Hazen Williams equation. For SI units

`Q = 0.85 c.A.rh^0.63 s^0.54 `
`rh = ID/4 `

where :

Q = flow rate
A = cross section area
ID = inside diameter
rh = hydraulic radius
s = channel slope
c = Hazen Williams friction factor

The Hazen Williams equation was developed for water pipes. Pipe roughness is accounted for using the Hazen Williams friction factor. The hydraulic radius is the ratio of pipe cross section area over pipe circumference (r/2 = ID/4). Valves, tees and other pipe fittings should be included by adding a minor loss equivalent length to the pipeline length.

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CALCULATOR MODULE : Water Open Channel Or Culvert Flow Rate From The Manning Equation   ±

Calculate flowrate in circular or rectangular water channels using the Manning equation.

`Q = A (rh^2)/3 s^(1/2) / n `
`rh = A/P `

where :

Q = flow rate
A = cross section area
P = wetted perimeter
rh = hydraulic radius
s = channel slope
n = Manning friction factor

The channel is assumed to be either open, or partly full and at ambient pressure. The head loss equals the change in elevation. Channel roughness is accounted for using the Manning friction factor. The hydraulic radius is the ratio of channel cross section area over the wetted perimeter. Valves, tees and other pipe fittings should be included by adding a minor loss equivalent length to the pipeline length.

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CALCULATOR MODULE : API RP 14E Maximum Erosional Velocity   ±

Calculate API RP 14E maximum allowable erosional velocity for platform piping systems.

The fluid density can be calculated for single phase gas, single phase liquid, two phase gas liquid, or three phase black oil (gas oil and water). The erosional velocity is calculated from the fluid density and the C Factor. Equation 2.14 in API RP 14E uses FPS units. The API RP 14E calculators have been factored to use SI units.

For fluids with no entrained solids a maximum C value of 100 for continuous service, or 125 for intermittent service can be used. For fluids treated with corrosion inhibitor, or for corrosion resistant materials a maximum C value of 150 to 200 may be used for continuous service, and upto 250 for intermittent service. For fluids with solids, the C value should be significantly reduced.

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 the volume ratio of water in liquid (oil and water).

Reference : API 14E Recommended Practice For Design and Installation of Offshore Production Platform Piping Systems

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CALCULATOR MODULE : DNVGL RP O501 Water Cut Ratio   ±
CALCULATOR MODULE : Water Hammer Transient Pressure   ±

Calculate water hammer transient pressure and pressure wave velocity.

Water hammer is caused by a sudden reduction of flow rate in liquid pipelines. Water hammer commonly occurs in water pipes, but it can occur in any liquid piping system. The transient pressure is reduced if gas is present in the liquid, or if the effective shut off time is greater than the maximum shut off time. The maximum shut off time is the time taken for the pressure transient to travel to the pipe inlet, and back again.

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CALCULATOR MODULE : Transient Pressure Wave Velocity   ±

Calculate water hammer transient pressure wave velocity.

A sudden reduction of velocity in a liquid pipeline initiates a pressure wave which travels to the pipe inlet, and then back. The wave velocity increases with pipe stiffness. Any gas present in the liquid reduces the pressure wave velocity. The maximum shut off time is the time taken for the pressure transient to travel to the pipe inlet, and back again.

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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 : Sound Velocity In Water   ±
CALCULATOR MODULE : Water Hammer Pipe Diameter Schedule   ±

Calculate transient flow pipe inside diameter and internal cross section area from pipe diameter and wall thickness.

Use the Result Table option to display a table of the inside diameter and cross section area versus either outside diameter or wall thickness.

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

Calculate dynamic and kinematic viscosity for three phase black oil (gas oil and water).

Kinematic viscosity is equal to the dynamic viscosity divided by the density of the fluid. The viscosity of two phase fluids and mixtures can be calculated from the dynamic viscosity and the volume fraction.

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 : Water And Steam Viscosity   ±

Calculate dynamic and kinematic viscosity of water and steam from temperature and pressure.

The viscosity is calculated from temperature and density using the IAPWS R12-08 industrial equation (u2 = 1). The density can be calculated from temperature and pressure using IAPWS R7-97.

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

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CALCULATOR MODULE : Two Phase Liquid Water Cut Ratio   ±
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 : Water And Steam Density   ±
CALCULATOR MODULE : Three Phase Gas Oil Water (Black Oil) Heat Capacity   ±

Calculate three phase gas oil water (black oil) heat capacity.

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). Gas oil ratio (GOR) is the ratio of gas moles over liquid volume. Gas moles are commonly measured by standard cubic feet (scf), and stand cubic meters (scm). 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 : Water And Steam Heat Capacity   ±

Calculate water and steam heat capacity from temperature and pressure (IAPWS R7-97).

Heat capacity and thermodynamic properties can be calculated for water and steam, saturated water, saturated steam, saturated water and steam, metastable water, and metastable steam. The calculations for water and steam are valid between 273.15 K and 1073.15 K (0 to 100 MPa), and between 1073.15 K and 2273.15 K (0 to 50 MPa).

The saturated water and steam calculations are valid between 273.15 K and 647.096 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 : 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 : Fluid Vapour Pressure   ±
CALCULATOR MODULE : IAPWS R7-97 Steam Vapour Pressure   ±

Calculate IAPWS R7-97 saturated vapour pressure and temperature.

The saturation point can be calculated from either the saturation temperature, or the saturation pressure.

Steam properties can be calculated for saturated liquid, saturated vapour, and mixed saturated liquid and vapour from quality factor. The enthalpy and internal energy are calculated from the mass. Use the Result Plot option to plot the steam pressure and steam properties versus temperature.

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 : 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 Conductivity   ±

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

Practical salinity is measured by comparing the sea water conductivity with a reference conductivity.

To convert pressure: 1 MPa = 100 dbar (deci bars) or 1 dbar = 1e4 Pa. To convert conductivity 1 S/m = 10 mS/cm.

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

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CALCULATOR MODULE : TEOS-10 Seawater Salinity   ±

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

Practical salinity is measured by comparing the sea water conductivity with a reference conductivity.

To convert pressure: 1 MPa = 100 dbar (deci bars) or 1 dbar = 1e4 Pa. To convert conductivity 1 S/m = 10 mS/cm.

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 : TEOS-10 Seawater Vapour Pressure   ±

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

Seawater vapour pressure is calculated from fresh water vapour pressure using the equation from Sharqawy (2010). The fresh water vapour pressure is calculated from temperature using the IAPWS R7-97 steam 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

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    CALCULATOR MODULE : Airy Linear Gravity Wave   ±

    Calculate Airy wave velocity, acceleration and surface profile. The Airy linear gravity wave theory is a first order model of freshwater and seawater gravity waves. The Airy wave is assumed to have a simple sinusoidal (first order harmonic) profile which is a reasonable approximation for small amplitude deep water waves. As the wave amplitude increases and or the water depth decreases the waves tend to become more peaky and are no longer a simple sinusoidal shape. The Airy wave model is then less accurate for analysing water particle motions. For large amplitude waves, or shallow water waves other wave models such as Stokes wave or Cnoidal wave should be used. The recommended wave type is displayed below the calc bar.

    Check that the convergence is close to or equal to one. The wave period should be measured at zero current velocity to avoid Doppler effects.

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      CALCULATOR MODULE : Stokes Fifth Order Wave   ±

      Calculate Stokes wave velocity, acceleration and surface profile using Skjelbria and Hendrickson's fifth order wave method.

      Stokes wave model is suitable for waves with short wavelength or small amplitude. The calculators include the correction to the sign of the c 8 term in the C2 coefficient (changed from + to -2592 c 8 ). Check that the convergence is close to or equal to one. The wave period should be measured at zero current velocity to avoid Doppler effects.

      Note : The Stokes wave theory uses a truncated infinite series. The truncated series is only valid for certain conditions. For shallow water waves the cnoidal wave is recommended. The recommended wave type is displayed below the calc bar.

      Reference : Lars Skjelbria and James Hendrickson, Fifth Order Gravity Wave Theory

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        CALCULATOR MODULE : Cnoidal Fifth Order Wave   ±

        Calculate Cnoidal wave velocity, acceleration and surface profile using Fentons 1999 fifth order wave method.

        The Cnoidal wave is defined by the elliptic modulus m, the wave trough depth w, and the wave alpha parameter α. The Cnoidal wave model is a truncated series and is only valid within certain ranges. The Cnoidal wave theory is not recommended where the wavelength over water depth ratio (Lod) is less than 8. The recommended wave type is displayed below the calc bar.

        Note : The cnoidal wave theory uses a truncated infinite series. The truncated series is only valid for conditions where the series converges (m > 0.8). For deep water waves with small m, the series does not converge (use the Stokes wave instead).

        Check that the convergence is close to or equal to one. The wave period should be measured at zero current velocity to avoid Doppler effects.

        Reference : J D Fenton, The Cnoidal Theory Of Water Waves, Developments in Offshore Engineering, Gulf, Houston, chapter 2, 1999

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          CALCULATOR MODULE : Ocean Current   ±

          Calculate current velocity versus water depth using either the logarithmic profile or the 1/7th power law profile.

          The current velocity is calculated relative to a measured reference velocity at a reference elevation. For best results the reference velocity should be measured at an elevation close to the target elevation. Current flow can be stratified with different layers moving at different speeds and directions. The current velocity can be calculated at a single point or averaged over a range. The logarithmic and power law profiles are only valid in the current boundary layer near the seabed.

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            CALCULATOR MODULE : Ocean Wave Shoaling And Wave Height   ±

            Calculate ocean wave shoaling wave height from water depth.

            Shoaling occurs as the water depth decreases or becomes more shallow. the wave length and celerity decrease (the wave becomes slower), and the wave height increases. The wave energy flux is assumed to be constant. For Airy waves the wave energy flux is proportional to c H^2 (the wave celerity times the wave height squared). The same relationship is assumed to also apply to Stokes and cnoidal waves. Use the Result Plot option to compare the initial wave and shoaling wave profiles, or the wave height versus water depth for Airy, Stokes and cnoidal waves. The recommended wave type is displayed below the calc bar.

            Note : The Stokes wave is the most suitable for a transtion from deep water to shallow water waves. The cnoidal wave is not suitable for deep water waves. The Airy wave is not suitable for shallow water waves.

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            CALCULATOR MODULE : DNVGL RP F109 Shields Number   ±

            Calculate DNVGL RP-F109 Shields number and critical velocity.

            Shields number is the ratio of shear force to weight force and is used to estimate the onset of seabed movement for non cohesive soils. The critical velocity corresponds to to the onset of seabed movement.

            Reference : DNVGL-RP-F109 : On-Bottom Stability Design Of Submarine Pipelines (Download from the DNVGL website)

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