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

✖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%
✖Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.ⓘ Distance from the Bottom to the Wave Trough [y_t]			+10% -10%
✖Wavelength of Wave can be defined as the distance between two successive crests or troughs of a wave.ⓘ Wavelength of Wave [λ]			+10% -10%
✖Complete Elliptic Integral of the First Kind is a mathematical tool that finds applications in coastal and ocean engineering, particularly in wave theory and harmonic analysis of wave data.ⓘ Complete Elliptic Integral of the First Kind [K_k]			+10% -10%
✖Complete Elliptic Integral of the Second Kind influencing the wavelength and the distance from bottom to wave trough.ⓘ Complete Elliptic Integral of the Second Kind [E_k]			+10% -10%

✖Height of The Wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Wave Height given Distance from Bottom to Wave Trough and Water Depth [H_w]

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Formula

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

Formula

`"H"_{"w"} = -"d"_{"c"}*(("y"_{"t"}/"d"_{"c"})-1-((16*"d"_{"c"}^2/(3*"λ"^2))*"K"_{"k"}*("K"_{"k"}-"E"_{"k"})))`

Example

`"14.11467m"=-"16m"*(("21m"/"16m")-1-((16*("16m")^2/(3*("32m")^2))*"28"*("28"-"27.968")))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
H_w = -d_c*((y_t/d_c)-1-((16*d_c^2/(3*λ^2))*K_k*(K_k-E_k)))
This formula uses 6 Variables

Variables Used

Height of The Wave - (Measured in Meter) - Height of The Wave is the difference between the elevations of a crest and a neighboring trough.
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.
Distance from the Bottom to the Wave Trough - (Measured in Meter) - Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.
Wavelength of Wave - (Measured in Meter) - Wavelength of Wave can be defined as the distance between two successive crests or troughs of a wave.
Complete Elliptic Integral of the First Kind - Complete Elliptic Integral of the First Kind is a mathematical tool that finds applications in coastal and ocean engineering, particularly in wave theory and harmonic analysis of wave data.
Complete Elliptic Integral of the Second Kind - Complete Elliptic Integral of the Second Kind influencing the wavelength and the distance from bottom to wave trough.

STEP 1: Convert Input(s) to Base Unit

Water Depth for Cnoidal Wave: 16 Meter --> 16 Meter No Conversion Required
Distance from the Bottom to the Wave Trough: 21 Meter --> 21 Meter No Conversion Required
Wavelength of Wave: 32 Meter --> 32 Meter No Conversion Required
Complete Elliptic Integral of the First Kind: 28 --> No Conversion Required
Complete Elliptic Integral of the Second Kind: 27.968 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H_w = -d_c*((y_t/d_c)-1-((16*d_c^2/(3*λ^2))*K_k*(K_k-E_k))) --> -16*((21/16)-1-((16*16^2/(3*32^2))*28*(28-27.968)))

Evaluating ... ...

H_w = 14.1146666666667

STEP 3: Convert Result to Output's Unit

14.1146666666667 Meter --> No Conversion Required

FINAL ANSWER

14.1146666666667 ≈ 14.11467 Meter <-- Height of The Wave

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Cnoidal Wave Theory » Wave Height given Distance from Bottom to Wave Trough and Water Depth

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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)

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

What are the Characteristics of Progressive Waves?

A progressive wave is formed due to continuous vibration of the particles of the medium.
The wave travels with a certain velocity.
There is a flow of energy in the direction of the wave.
No particles in the medium are at rest.
The amplitude of all the particles is the same.

How to Calculate Wave Height given Distance from Bottom to Wave Trough and Water Depth?

Wave Height given Distance from Bottom to Wave Trough and Water Depth calculator uses 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))) to calculate the Height of The Wave, The Wave Height given Distance from Bottom to Wave Trough and Water Depth formula is defined as the difference between elevations of the crest and neighboring trough. Wave height is a term used by mariners, as well as in coastal, ocean, and naval engineering. Height of The Wave is denoted by H_w symbol.

How to calculate Wave Height given Distance from Bottom to Wave Trough and Water Depth using this online calculator? To use this online calculator for Wave Height given Distance from Bottom to Wave Trough and Water Depth, enter Water Depth for Cnoidal Wave (d_c), Distance from the Bottom to the Wave Trough (y_t), Wavelength of Wave (λ), Complete Elliptic Integral of the First Kind (K_k) & Complete Elliptic Integral of the Second Kind (E_k) and hit the calculate button. Here is how the Wave Height given Distance from Bottom to Wave Trough and Water Depth calculation can be explained with given input values -> 14.11467 = -16*((21/16)-1-((16*16^2/(3*32^2))*28*(28-27.968))).

FAQ

What is Wave Height given Distance from Bottom to Wave Trough and Water Depth?

The Wave Height given Distance from Bottom to Wave Trough and Water Depth formula is defined as the difference between elevations of the crest and neighboring trough. Wave height is a term used by mariners, as well as in coastal, ocean, and naval engineering and is represented as H_w = -d_c*((y_t/d_c)-1-((16*d_c^2/(3*λ^2))*K_k*(K_k-E_k))) or 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))). Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating, Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave, Wavelength of Wave can be defined as the distance between two successive crests or troughs of a wave, Complete Elliptic Integral of the First Kind is a mathematical tool that finds applications in coastal and ocean engineering, particularly in wave theory and harmonic analysis of wave data & Complete Elliptic Integral of the Second Kind influencing the wavelength and the distance from bottom to wave trough.

How to calculate Wave Height given Distance from Bottom to Wave Trough and Water Depth?

The Wave Height given Distance from Bottom to Wave Trough and Water Depth formula is defined as the difference between elevations of the crest and neighboring trough. Wave height is a term used by mariners, as well as in coastal, ocean, and naval engineering is calculated using 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))). To calculate Wave Height given Distance from Bottom to Wave Trough and Water Depth, you need Water Depth for Cnoidal Wave (d_c), Distance from the Bottom to the Wave Trough (y_t), Wavelength of Wave (λ), Complete Elliptic Integral of the First Kind (K_k) & Complete Elliptic Integral of the Second Kind (E_k). With our tool, you need to enter the respective value for Water Depth for Cnoidal Wave, Distance from the Bottom to the Wave Trough, Wavelength of Wave, Complete Elliptic Integral of the First Kind & Complete Elliptic Integral of the Second Kind and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Height of The Wave?

In this formula, Height of The Wave uses Water Depth for Cnoidal Wave, Distance from the Bottom to the Wave Trough, Wavelength of Wave, Complete Elliptic Integral of the First Kind & Complete Elliptic Integral of the Second Kind. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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