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CALCULATOR MODULE : ASME B31.3 Process Piping Fluid Velocity And Flow Rate   ±

Calculate ASME B31.3 process piping fluid velocity and flow rate for two phase gas liquid piping, and three phase black oil piping (gas water and oil).

The two phase fluid calculator can be used for single phase gas, single phase liquid, or two phase gas and liquid. The three phase black oil calculator can be used for single phase oil, single phase water, two phase oil and water, and three phase oil, water and gas. Water cut is the volume fraction of water in the liquid phase (ignoring the gas phase). Gas oil ratio (GOR) is the ratio of gas moles to liquid volume (ignoring the water phase). Gas moles are commonly measured as gas volume at standard conditions, eg SCM (Standard Conditions Meter) or SCF (Standard Conditions Feet).

Reference : ANSI/ASME B31.3 : Process Piping (2018)

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CALCULATOR MODULE : ASME B31.4 Liquid Pipeline Fluid Velocity And Flow Rate   ±

Calculate ASME B31.4 liquid pipeline fluid velocity and flow rate for two phase gas liquid piping, and three phase black oil piping (gas water and oil).

The two phase fluid calculator can be used for single phase gas, single phase liquid, or two phase gas and liquid. The three phase black oil calculator can be used for single phase oil, single phase water, two phase oil and water, and three phase oil, water and gas. Water cut is the volume fraction of water in the liquid phase (ignoring the gas phase). Gas oil ratio (GOR) is the ratio of gas moles to liquid volume (ignoring the water phase). Gas moles are commonly measured as gas volume at standard conditions, eg SCM (Standard Conditions Meter) or SCF (Standard Conditions Feet).

Reference : ANSI/ASME B31.4 : Pipeline Transportation Systems For Liquids And Slurries (2012)

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CALCULATOR MODULE : ASME B31.8 Gas Pipeline Fluid Velocity And Flow Rate   ±

Calculate ASME ASME B31.8 gas pipeline fluid velocity and flow rate for two phase gas liquid piping, and three phase black oil piping (gas water and oil).

The two phase fluid calculator can be used for single phase gas, single phase liquid, or two phase gas and liquid. The three phase black oil calculator can be used for single phase oil, single phase water, two phase oil and water, and three phase oil, water and gas. Water cut is the volume fraction of water in the liquid phase (ignoring the gas phase). Gas oil ratio (GOR) is the ratio of gas moles to liquid volume (ignoring the water phase). Gas moles are commonly measured as gas volume at standard conditions, eg SCM (Standard Conditions Meter) or SCF (Standard Conditions Feet).

Reference : ANSI/ASME B31.8 : Gas Transmission And Distribution Piping Systems (2018)

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CALCULATOR MODULE : ASME B31.1 Power Piping Steam Mass And Flow Rate   ±

Calculate ASME B31.1 power piping steam mass, velocity and flow rate from the steam table (IAPWS R7-97 Steam Table).

Steam mass and volume can be calculated from steam temperature and pressure, and either steam mass, steam volume, or piping length. Steam flow rate and velocity can be calculated from steam temperature and pressure, and either steam mass flow rate, steam volume flow rate, or steam velocity.

Steam 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.

The metastable calculation is valid between 273.15 K and 647.096 K, and for pressure from the saturated vapour line to the 5% equilibium moisture line (user defined).

Note : There is an anomaly in the steam calculation for region 3 between the saturated vapour line, the regions 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).

Reference : ANSI/ASME B31.1 : Power Piping (2014)

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CALCULATOR MODULE : ASME B31.5 Refrigeration Piping Fluid Velocity And Flow Rate   ±

Calculate ASME B31.5 refrigeration piping fluid velocity and flow rate for two phase gas and liquid.

The two phase gas liquid calculator can be used for single phase gas, single phase liquid, or two phase gas and liquid. Gas oil ratio (GOR) is the ratio of gas moles to liquid volume (ignoring the water phase). Gas moles are commonly measured as gas volume at standard conditions, eg SCM (Standard Conditions Meter) or SCF (Standard Conditions Feet).

Reference : ANSI/ASME B31.5 : Refrigeration Piping And Heat Transfer Components (2013)

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CALCULATOR MODULE : Pipeline Fluid Velocity And Flowrate   ±

Calculate pipeline fluid velocity, density and flowrate for two phase gas liquid, three phase gas oil and water (black oil), single phase gas, and single phase liquid.

Two phase gas liquid density is calculated from the gas oil ratio (GOR). Three phase black oil density is calculated from the gas oil ratio (GOR), and water cut (WC). Single phase gas density is calculated from temperature, pressure, specific gravity (relative to air), and compressibility factor. Single phase liquid density can be calcuated from specific gravity, degrees Baume (Be+), degrees Baume (Be-), degrees API, or degrees Twaddell.

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CALCULATOR MODULE : DNVGL ST F101 Submarine Pipeline Fluid Velocity And Flowrate   ±

Calculate DNVGL-ST-F101 subsea pipeline fluid velocity and flowrate for two phase gas and liquid, and three phase oil, water and gas (black oil).

The two phase fluid calculator can be used for single phase gas, single phase liquid, or two phase gas and liquid. The three phase black oil calculator can be used for single phase oil, single phase water, two phase oil and water, and three phase oil, water and gas. Water cut is the volume fraction of water in the liquid phase (ignoring the gas phase). Gas oil ratio (GOR) is the ratio of gas moles to liquid volume (ignoring the water phase). Gas moles are commonly measured as gas volume at standard conditions, eg SCM (Standard Conditions Meter) or SCF (Standard Conditions Feet).

Reference : DNVGL-ST-F101 : Submarine Pipeline Systems (Download from the DNVGL website)

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CALCULATOR MODULE : API RP 1111 Pipeline Fluid Velocity And Flow Rate   ±

Calculate API RP 1111 limit state pipeline fluid velocity and flow rate for two phase gas liquid piping, and three phase black oil piping (gas water and oil).

The two phase fluid calculator can be used for single phase gas, single phase liquid, or two phase gas and liquid. The three phase black oil calculator can be used for single phase oil, single phase water, two phase oil and water, and three phase oil, water and gas. Water cut is the volume fraction of water in the liquid phase (ignoring the gas phase). Gas oil ratio (GOR) is the ratio of gas moles to liquid volume (ignoring the water phase). Gas moles are commonly measured as gas volume at standard conditions, eg SCM (Standard Conditions Meter) or SCF (Standard Conditions Feet).

Reference : API RP 1111 : Design, Construction, Operation, and Maintenance of Offshore Hydrocarbon Pipelines (Limit State Design) (2011)

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CALCULATOR MODULE : AS 2885.1 Pipeline Maximum Velocity   ±

Calculate AS 2885.1 pipeline maximum allowable velocity for fluids subject to erosion.

The erosional velocity is calculated from the fluid density and the C Factor (API RP 14E). The fluid density can be calculated for single phase, two phase, or three phase fluids. DNVGL RP-O501 can be used for erosion rate calculations. Transmission pipelines which are transporting clean fluids are not normally subject to erosion.

Reference : Australian Standard AS 2885.1 : Pipelines - Gas And Liquid Petroleum Part 1 : Design And Construction (2015)

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CALCULATOR MODULE : AS 2885.1 Pipeline Fluid Velocity And Flow Rate   ±

Calculate AS 2885.1 pipeline fluid velocity and flow rate for two phase gas liquid piping, and three phase black oil piping (gas water and oil).

The two phase fluid calculator can be used for single phase gas, single phase liquid, or two phase gas and liquid. The three phase black oil calculator can be used for single phase oil, single phase water, two phase oil and water, and three phase oil, water and gas. Water cut is the volume fraction of water in the liquid phase (ignoring the gas phase). Gas oil ratio (GOR) is the ratio of gas moles to liquid volume (ignoring the water phase). Gas moles are commonly measured as gas volume at standard conditions, eg SCM (Standard Conditions Meter) or SCF (Standard Conditions Feet).

Reference : Australian Standard AS 2885.1 : Pipelines - Gas And Liquid Petroleum Part 1 : Design And Construction (2015)

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CALCULATOR MODULE : Piping Check Valve Minor Loss Factor   ±

Calculate typical gas and liquid pipe check valve minimum velocity and minor loss factors (K, Cd, Cv*, Av, Cv-uk, Cv-us, Cv-met and Kv).

The minimum flowrate is the flowrate required to keep the check valve fully open. For full port valves the valve port cross section area equals the nominal internal cross section area. For reduced port valves the valve port cross section area is less than the nominal internal cross section area. For circular valve ports the diameter ratio is equal to the valve port diameter over the nominal inside diameter. For non circular valve ports, use the square root of the internal area ratio (the square root of the valve port area over the nominal internal area).

Minor loss factors are calculated for:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

The calculated values are typical. Manufacturers data should be used if it is available.

Reference : Crane Technical Paper 410M Metric Version : Flow Of Fluids Through Valves, Fittings And Pipe

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CALCULATOR MODULE : Bernoulli's Equation Fluid Flowrate And Velocity   ±
CALCULATOR MODULE : Bernoulli's Equation Prandtl Tube   ±

Calculate fluid velocity from the pressure difference across a Pitot-Static or Prandtl tube using the Bernoulli equation.

Prandtl tubes or Pitot-Static tubes are used to measure the fluid static pressure, and the fluid stagnation pressure (the sum of the static pressure and the dynamic pressure). The fluid velocity can be calculated from the dynamic pressure. The dynamic pressure is equal to the stagnation pressure minus the static pressure.

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CALCULATOR MODULE : Bernoulli's Equation Pitot Tube   ±

Calculate fluid velocity from the Pitot tube pressure measurement using the Bernoulli equation.

Pitot tubes are used to measure the fluid stagnation pressure (the sum of the static pressure and the dynamic pressure). The fluid velocity can be calculated from the Pitot tube pressure for cases where the static pressure is negligible. For example in shallow water where the stagnation pressure is measured by gauge pressure.

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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 : Liquid Pipeline Fluid Velocity And Flow Rate   ±
CALCULATOR MODULE : Gas Pipeline Fluid Velocity And Flow Rate   ±
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 : API RP 14E Fluid Velocity   ±

Calculate API RP 14E fluid velocity and flowrate for single phase gas, single phase liquid, two phase gas liquid, and three phase gas, oil and water (black oil).

Flow rate can be calculated for mass flow rate, volume flow rate, mole flow rate and velocity. Gas density is calculated from temperature and pressure, and either specific gravity or molar mass. Liquid density can be calculated from specific gravity, degrees Baume, degrees Twaddell, or degrees API. 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).

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

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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 : DNVGL RP O501 Erosion Rate   ±
CALCULATOR MODULE : DNVGL RP O501 Pipeline Fluid Velocity   ±

Calculate DNVGL RP O501 pipeline fluid velocity for single phase gas, single phase liquid, two phase gas liquid, or three phase black oil (gas, oil and water).

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 measured relative to the total liquid volume (gas volume is ignored).

Liquid density can be calculated from 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.

Gas density can be calculated from gas specific gravity, or gas molar mass. Gas molar mass is approximately equal to the molar mass of dry air times the gas specific gravity at standard conditions (for most gases the compressibility factor Z is approximately equal to 1 at standard conditions). The molar mass of dry air is taken as 28.964 kg/kg-mole. For gas mixtures, gas specific gravity is easier to measure than the molar mass.

Reference : DNVGL-RP-O501 Managing Sand Production And Erosion : formerly DNV-RP-O501 (Download from the DNVGL website)

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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 : Pump Specific Speed   ±

Calculate pump specific speed from pump rotational speed, flowrate and delta pressure.

The pump specific speed is calculated at the best efficiency point (BEP), the point on the pump curve with the greatest efficiency.

`Ns = n Q^(1/2) (ρ/(ΔP))^(3/4) = n (Q^(1/2)) / (g.ΔH)^(3/4) `

where :

Ns = pump specific speed
n = pump rotational speed
Q = flow rate at BEP
ρ = fluid density
ΔP = delta pressure at BEP
ΔH = delta head at BEP
g = gravity constant
BEP = best efficiency point

The pump specific speed can be used to determine the type of pump which should be used (multi stage, centrifugal, mixed flow or axial). The pump size and speed can then be determined from the pump coefficients using the affinity or similarity laws. Usually, a known pump is scaled to operate at the BEP with the required design flow rate and delta pressure.

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

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CALCULATOR MODULE : Pump Hydraulic And Input Power   ±

Calculate pump hydraulic power and input power or motive power from flowrate and delta pressure.

`Wh = Q ΔP `
`Wi = (Wh) / E `

where :

Wh = hydraulic power
Wi = input power or motive power
Q = volume flowrate
ΔP = delta stagnation pressure
E = efficiency factor

The pump efficiency accounts for energy losses in the pump such as friction etc. The input power is the motive power required to drive the pump (the size of motor). To calculate the energy required (eg electrical energy) the efficiency factor should equal the pump efficiency times the motor efficiency.

`E = Ep.Ee `

where :

Ep = pump efficiency factor
Ee = electric motor efficiency factor

Pump efficiency varies with flowrate. The flowrate with maximum efficiency is referred to as the best efficiency point (BEP).

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

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CALCULATOR MODULE : Pump Variable Frequency Drive (VFD) Design Speed   ±

Calculate pump variable frequency drive (VFD) speed to match pump design pressure and design flowrate for viscous and non viscous fluids.

The design pump speed is calculated using the affinity or similarity laws.

`(ΔP2)/(ΔP1) = (ρ2)/(ρ1) (n2)/(n1)^2 `
`(Q2)/(Q1) = (n2)/(n1) `

where :

ΔP1 and ΔP2 = the delta pressure for pump 1 and 2
Q1 and Q2 = the flowrate for pump 1 and 2
n1 and n2 = the rotation speed for pump 1 and 2
ρ1 and ρ2 = the fluid density for pump 1 and 2

The pump curve is calculated using a three term quadratic curve:

`ΔP = ΔPo (1 - A Q - B Q^2 ) `

where :

ΔPo = the shut in delta pressure
A and B are constants

The design pump speed can be calculated by solving the quadratic equation for the design delta pressure and flowrate. For fluids with a kinematic viscosity ν > 20 cSt, the viscous calculation is recommended.

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

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CALCULATOR MODULE : Velocity Of Sound In A Solid   ±

Calculate the velocity of sound in a solid.

The speed of sound in a solid is calculated from the solid density and bulk modulus.

`a = √(K / ρ) `

where :

a = speed of sound
K = bulk modulus
ρ = density

The bulk modulus can be calculated from the elastic modulus and Poisson's ratio, or from the speed of sound in the solid.

`K = a^2 ρ `
`K = E / (3 (1 - 2 γ )) `

where :

E = elastic modulus
γ = Poisson ratio

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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 : Morison's Equation Wave And Current Load   ±

          Calculate wave and current loads on submerged structures using Morison's equation (Airy Stokes and Cnoidal waves).

          For vertical structures the load forces are due to the horizontal velocity and acceleration only. For horizontal structures the load forces also include vertical velocity and acceleration. Lateral (lift) forces are due to non symmetric flow around the structure, either because of proximity to the seabed or another structure, or by non symmetric cross section. The Keulegan Carpenter number is a measure of the ratio of wave inertial forces and drag forces.

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          CALCULATOR MODULE : Ocean Wave And Current Velocity And Acceleration   ±

          Calculate ocean wave and current velocity and acceleration for Airy, Stokes, cnoidal and JONSWAP waves.

          Wave velocity and acceleration can be calculated for Airy, Stokes, and Cnoidal waves. The recommended wave type is displayed below the calc bar. Use the Result Plot option to compare the Airy, Stokes, and cnoidal wave profiles. The seabed significant wave velocity and zero upcrossing period can be calculated from the JONSWAP surface spectrum.

          Current velocity can be calculated near the seabed using either the logarithmic profile, or the 1/7th power law profile. The logarithmic and power law profiles are not valid For large elevations above the seabed.

          Note : The Stokes and cnoidal waves use trucated infinite series. Under certain conditions the truncated series do not converge properly. The Stokes wave is not suitable for shallow water waves. The cnoidal wave is not suitable for deep water waves. The recommended wave type is displayed below the calc bar. The JONSWAP wave uses an Airy wave transfer function to calculate seabed velocity. The JONSWAP wave is not suitable for very shallow waves (near breaking).

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          CALCULATOR MODULE : Ocean Wave Velocity And Acceleration   ±

          Calculate ocean wave velocity and acceleration for Airy, Stokes, cnoidal and JONSWAP waves.

          Wave velocity and acceleration can be calculated for Airy, Stokes, and Cnoidal waves. The recommended wave type is displayed below the calc bar. Use the Result Plot option to compare the Airy, Stokes, and cnoidal wave profiles. The seabed significant wave velocity and zero upcrossing period can be calculated from the JONSWAP surface spectrum.

          Note : The Stokes and cnoidal waves use trucated infinite series. Under certain conditions the truncated series do not converge properly. The Stokes wave is not suitable for shallow water waves. The cnoidal wave is not suitable for deep water waves. The recommended wave type is displayed below the calc bar. The JONSWAP wave uses an Airy wave transfer function to calculate seabed velocity. The JONSWAP wave is not suitable for very shallow waves (near breaking).

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          CALCULATOR MODULE : Ocean Wave Directionality And Spreading   ±

          Calculate ocean wave velocity reduction factor from relative heading and spreading factor.

          The spreading factor accounts for wave "choppiness" or superimposed multi directional waves. Locally generated waves are generally short crested and more "choppy", and are characterised by small spreading factors. Long range swells are generally long crested uni directional waves, and are characterised by large spreading factors.

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          CALCULATOR MODULE : Ocean Wave Probability And Return Period   ±

          Calculate ocean wave height and period from return period data using the Weibull, Gumbel or Frechet probability distributions.

          The three parameter distribution and Z offset is used to account for a minimum value, the smallest event which can occur in any sample period. The best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for return period versus amplitude (the X and Z values are swapped). The regression data points and regression parameters are displayed in the output view at the bottom of the page.

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          CALCULATOR MODULE : Ocean Current Probability And Return Period   ±

          Calculate ocean current velocity from return period data using the Weibull, Gumbel or Frechet probability distributions.

          The three parameter distribution and Z offset is used to account for a minimum value, the smallest event which can occur in any sample period. The best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for return period versus amplitude (the X and Z values are swapped). Use the Data Plot option on the plot bar to display the data points and the calculated best fit. The regression data points and regression parameters are displayed in the output view at the bottom of the page.

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          CALCULATOR MODULE : Ocean Wave And Current Probability And Return Period   ±

          Calculate ocean wave height, wave period and current velocity from return period data using the Weibull, Gumbel or Frechet probability distributions.

          The three parameter distribution and Z offset is used to account for a minimum value, the smallest event which can occur in any sample period. The best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for return period versus amplitude (the X and Z values are swapped). Use the Data Plot option on the plot bar to display the data points and the calculated best fit. The regression data points and regression parameters are displayed in the output view at the bottom of the page.

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          CALCULATOR MODULE : JONSWAP Wave Velocity And Period   ±

          Calculate JONSWAP wave seabed velocity and zero upcrossing period from spectral moments.

          The seabed velocity and upcrossing period is calculated using a first order Airy wave transformation. The Airy wave transformation may not be valid in shallow water. The calculation has been optimised for elevations on or near the seabed, and is not recommended for elevations greater than half the water depth. Return period data can be analysed using either the Weibull, Gumbel or Frechet distribution.

          Reference : Hasselmann K et al : Measurements of Wind-Wave Growth And Swell Decay During The Joint North Sea Wave Project (JONSWAP)

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          CALCULATOR MODULE : JONSWAP Wave Directionality And Spreading   ±

          Calculate JONSWAP wave spreading and velocity reduction factor from relative heading and spreading factor.

          Wave spreading accounts for the effect of short crested "choppy" waves with non uniform velocity and heading. By comparison, long ocean swells tend to have uniform velocity and direction, expecially in mid ocean. Use small spreading factors for "choppy" waves, and large spreading factors for ocena swells.

          Reference : Hasselmann K et al : Measurements of Wind-Wave Growth And Swell Decay During The Joint North Sea Wave Project (JONSWAP)

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          CALCULATOR MODULE : JONSWAP Combined Wave And Current Velocity   ±

          Calculate JONSWAP seabed wave and current amplitude from return period data.

          Return period data can be analysed using either the Weibull, Gumbel or Frechet distribution. Current velocity can be calculated using either the logarithmic profile, or the 1/7th power law profile. The logarithmic and power law profiles are only valid in the boundary layer on or near the seabed. The seabed velocity and upcrossing period is calculated from the JONSWAP surface spectrum using a first order Airy wave transformation. The calculation may not be valid in shallow water, and is not recommended for elevations greater than half the water depth.

          Reference : Hasselmann K et al : Measurements of Wind-Wave Growth And Swell Decay During The Joint North Sea Wave Project (JONSWAP)

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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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          CALCULATOR MODULE : DNVGL RP F109 Wave Seabed Velocity   ±

          Calculate DNVGL RP-F109 wave seabed velocity from the JONSWAP surface spectrum.

          An Airy wave transform is used to calculate the significant seabed velocity, and zero upcrossing wave period. The calculation is not valid in shallow water, or at elevations greater than half the water depth.

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

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