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 refers to the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings.ⓘ 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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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 refers to the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings.
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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Coorg Institute of Technology (CIT), Coorg

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< Cnoidal Wave Theory Calculators

Complete Elliptic Integral of Second Kind

LaTeX 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)

Distance from Bottom to Wave Trough

LaTeX 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

LaTeX 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

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

LaTeX Go

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 refers to the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings, 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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