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Seawater Or Salt 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 : DNVGL RP O501 Water Cut Ratio   ±
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 : 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 )   ±
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