Free Surface Elevation of Solitary Waves Calculator

✖Height of The Wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Height of The Wave [H_w]			+10% -10%
✖Particle Velocity refers to the velocity at which water particles move as a result of the passage of waves or currents.ⓘ Particle Velocity [u]			+10% -10%
✖Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.ⓘ Water Depth for Cnoidal Wave [d_c]			+10% -10%

✖Free Surface Elevation refers to the instantaneous vertical displacement of the water surface caused by various factors such as waves, tides, currents, and atmospheric conditions.ⓘ Free Surface Elevation of Solitary Waves [η]

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Formula

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Free Surface Elevation of Solitary Waves

Formula

`"η" = "H"_{"w"}*("u"/(sqrt("[g]"*"d"_{"c"})*("H"_{"w"}/"d"_{"c"})))`

Example

`"25.5464m"="14m"*("20m/s"/(sqrt("[g]"*"16m")*("14m"/"16m")))`

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Free Surface Elevation of Solitary Waves Solution

STEP 0: Pre-Calculation Summary

Formula Used

Free Surface Elevation = Height of The Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave)))
η = H_w*(u/(sqrt([g]*d_c)*(H_w/d_c)))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Free Surface Elevation - (Measured in Meter) - Free Surface Elevation refers to the instantaneous vertical displacement of the water surface caused by various factors such as waves, tides, currents, and atmospheric conditions.
Height of The Wave - (Measured in Meter) - Height of The Wave is the difference between the elevations of a crest and a neighboring trough.
Particle Velocity - (Measured in Meter per Second) - Particle Velocity refers to the velocity at which water particles move as a result of the passage of waves or currents.
Water Depth for Cnoidal Wave - (Measured in Meter) - Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.

STEP 1: Convert Input(s) to Base Unit

Height of The Wave: 14 Meter --> 14 Meter No Conversion Required
Particle Velocity: 20 Meter per Second --> 20 Meter per Second No Conversion Required
Water Depth for Cnoidal Wave: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η = H_w*(u/(sqrt([g]*d_c)*(H_w/d_c))) --> 14*(20/(sqrt([g]*16)*(14/16)))

Evaluating ... ...

η = 25.5463965424847

STEP 3: Convert Result to Output's Unit

25.5463965424847 Meter --> No Conversion Required

FINAL ANSWER

25.5463965424847 ≈ 25.5464 Meter <-- Free Surface Elevation

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Cnoidal Wave Theory » Free Surface Elevation of Solitary Waves

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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National Institute of Technology (NIT), Warangal

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< 14 Cnoidal Wave Theory Calculators

Wavelength for Distance from Bottom to Wave Trough

Go Wavelength of Wave = sqrt((16*Water Depth for Cnoidal Wave^2*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind))/(3*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of The Wave/Water Depth for Cnoidal Wave)-1)))

Complete Elliptic Integral of Second Kind

Go Complete Elliptic Integral of the Second Kind = -((((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of The Wave/Water Depth for Cnoidal Wave)-1)*(3*Wavelength of Wave^2)/((16*Water Depth for Cnoidal Wave^2)*Complete Elliptic Integral of the First Kind))-Complete Elliptic Integral of the First Kind)

Wave Height given Distance from Bottom to Wave Trough and Water Depth

Go Height of The Wave = -Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)-1-((16*Water Depth for Cnoidal Wave^2/(3*Wavelength of Wave^2))*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind)))

Wave Height Required to Produce Difference in Pressure on Seabed

Go Cnoidal Wave Height = Change in Pressure of Coast/((Density of Salt Water*[g])*(0.5+(0.5*sqrt(1-((3*Change in Pressure of Coast)/(Density of Salt Water*[g]*Water Depth for Cnoidal Wave))))))

Free Surface Elevation of Solitary Waves

Go Free Surface Elevation = Height of The Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave)))

Particle Velocities given Free Surface Elevation of Solitary Waves

Go Particle Velocity = Free Surface Elevation*sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave)/Height of The Wave

Distance from Bottom to Wave Trough

Go Distance from the Bottom to the Wave Trough = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Height of The Wave/Water Depth for Cnoidal Wave))

Distance from Bottom to Crest

Go Distance from the Bottom to the Crest = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of The Wave/Water Depth for Cnoidal Wave))

Trough to Crest Wave Height

Go Height of The Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave))

Wave Height when Free Surface Elevation of Solitary Waves

Go Cnoidal Wave Height = Free Surface Elevation*sqrt([g]*Water Depth for Cnoidal Wave)/(Particle Velocity*Water Depth for Cnoidal Wave)

Wavelength for Complete Elliptic Integral of First Kind

Go Wavelength of Wave = sqrt(16*Water Depth for Cnoidal Wave^3/(3*Height of The Wave))*Modulus of the Elliptic Integrals*Complete Elliptic Integral of the First Kind

Elevation above Bottom given Pressure under Cnoidal Wave in Hydrostatic Form

Go Elevation above the Bottom = -((Pressure Under Wave/(Density of Salt Water*[g]))-Ordinate of the Water Surface)

Ordinate of Water Surface given Pressure under Cnoidal Wave in Hydrostatic Form

Go Ordinate of the Water Surface = (Pressure Under Wave/(Density of Salt Water*[g]))+Elevation above the Bottom

Pressure under Cnoidal Wave in Hydrostatic Form

Go Pressure Under Wave = Density of Salt Water*[g]*(Ordinate of the Water Surface-Elevation above the Bottom)

Free Surface Elevation of Solitary Waves Formula

Free Surface Elevation = Height of The Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave)))
η = H_w*(u/(sqrt([g]*d_c)*(H_w/d_c)))

What Causes Waves?

Waves are most commonly caused by wind. Wind-driven waves, or surface waves, are created by the friction between wind and surface water. As wind blows across the surface of the ocean or a lake, the continual disturbance creates a wave crest. The gravitational pull of the sun and moon on the earth also causes waves.

How to Calculate Free Surface Elevation of Solitary Waves?

Free Surface Elevation of Solitary Waves calculator uses Free Surface Elevation = Height of The Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave))) to calculate the Free Surface Elevation, The Free Surface Elevation of Solitary Waves is defined as the surface elevation of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. Free Surface Elevation is denoted by η symbol.

How to calculate Free Surface Elevation of Solitary Waves using this online calculator? To use this online calculator for Free Surface Elevation of Solitary Waves, enter Height of The Wave (H_w), Particle Velocity (u) & Water Depth for Cnoidal Wave (d_c) and hit the calculate button. Here is how the Free Surface Elevation of Solitary Waves calculation can be explained with given input values -> 25.5464 = 14*(20/(sqrt([g]*16)*(14/16))).

FAQ

What is Free Surface Elevation of Solitary Waves?

The Free Surface Elevation of Solitary Waves is defined as the surface elevation of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids and is represented as η = H_w*(u/(sqrt([g]*d_c)*(H_w/d_c))) or Free Surface Elevation = Height of The Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave))). Height of The Wave is the difference between the elevations of a crest and a neighboring trough, Particle Velocity refers to the velocity at which water particles move as a result of the passage of waves or currents & Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.

How to calculate Free Surface Elevation of Solitary Waves?

The Free Surface Elevation of Solitary Waves is defined as the surface elevation of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids is calculated using Free Surface Elevation = Height of The Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave))). To calculate Free Surface Elevation of Solitary Waves, you need Height of The Wave (H_w), Particle Velocity (u) & Water Depth for Cnoidal Wave (d_c). With our tool, you need to enter the respective value for Height of The Wave, Particle Velocity & Water Depth for Cnoidal Wave and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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