Water Depth given Maximum Wave Height by Miche Criterion Calculator

✖Maximum Wave Height is most probable influenced by the difference between the elevations of a crest and a neighboring trough.ⓘ Maximum Wave Height [H_max]			+10% -10%
✖Wavelength of Coast is the distance between two successive crests or troughs of a wave.ⓘ Wavelength of Coast [λ]			+10% -10%
✖Wave Number for Waves in Coast is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance.ⓘ Wave Number for Waves in Coast [k]			+10% -10%

✖Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth given Maximum Wave Height by Miche Criterion [d]

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Water Depth given Maximum Wave Height by Miche Criterion

Formula

`"d" = ((atanh("H"_{"max"}/(0.14*"λ")))/"k")`

Example

`"0.943891m"=((atanh("0.7m"/(0.14*"26.8m")))/"0.2")`

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Water Depth given Maximum Wave Height by Miche Criterion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Water Depth = ((atanh(Maximum Wave Height/(0.14*Wavelength of Coast)))/Wave Number for Waves in Coast)
d = ((atanh(H_max/(0.14*λ)))/k)
This formula uses 2 Functions, 4 Variables

Functions Used

tanh - The hyperbolic tangent function (tanh) is a function that is defined as the ratio of the hyperbolic sine function (sinh) to the hyperbolic cosine function (cosh)., tanh(Number)
atanh - The inverse hyperbolic tangent function returns the value whose hyperbolic tangent is a number., atanh(Number)

Variables Used

Water Depth - (Measured in Meter) - Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.
Maximum Wave Height - (Measured in Meter) - Maximum Wave Height is most probable influenced by the difference between the elevations of a crest and a neighboring trough.
Wavelength of Coast - (Measured in Meter) - Wavelength of Coast is the distance between two successive crests or troughs of a wave.
Wave Number for Waves in Coast - Wave Number for Waves in Coast is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance.

STEP 1: Convert Input(s) to Base Unit

Maximum Wave Height: 0.7 Meter --> 0.7 Meter No Conversion Required
Wavelength of Coast: 26.8 Meter --> 26.8 Meter No Conversion Required
Wave Number for Waves in Coast: 0.2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = ((atanh(H_max/(0.14*λ)))/k) --> ((atanh(0.7/(0.14*26.8)))/0.2)

Evaluating ... ...

d = 0.943890799977719

STEP 3: Convert Result to Output's Unit

0.943890799977719 Meter --> No Conversion Required

FINAL ANSWER

0.943890799977719 ≈ 0.943891 Meter <-- Water Depth

(Calculation completed in 00.020 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< 13 Energy Flux Method Calculators

Maximum Wave Height given Energy Dissipation Rate

Go Maximum Wave Height = sqrt(Energy Dissipation Rate per unit Surface Area/(0.25*Water Density*[g]*Percentage of Waves Breaking*Mean Wave Frequency))

Energy Dissipation Rate per unit Surface Area due to Wave Breaking

Go Energy Dissipation Rate per unit Surface Area = (Decay Coefficient/Water Depth)*((Wave Energy*Wave Group Speed)-(Energy Flux associated with Stable Wave Height))

Water Depth given Energy Dissipation Rate per unit Surface Area due to Wave Breaking

Go Water Depth = Decay Coefficient*(Wave Energy*Wave Group Speed-(Energy Flux associated with Stable Wave Height))/Energy Dissipation Rate per unit Surface Area

Percentage of Waves Breaking given Energy Dissipation Rate

Go Percentage of Waves Breaking = Energy Dissipation Rate per unit Surface Area/(0.25*Water Density*[g]*Mean Wave Frequency*(Maximum Wave Height^2))

Mean Wave Frequency given Energy Dissipation Rate

Go Mean Wave Frequency = Energy Dissipation Rate per unit Surface Area/(0.25*Water Density*[g]*Percentage of Waves Breaking*Maximum Wave Height^2)

Energy Dissipation Rate by Battjes and Janssen

Go Energy Dissipation Rate per unit Surface Area = 0.25*Water Density*[g]*Percentage of Waves Breaking*Mean Wave Frequency*(Maximum Wave Height^2)

Water Depth given Maximum Wave Height by Miche Criterion

Go Water Depth = ((atanh(Maximum Wave Height/(0.14*Wavelength of Coast)))/Wave Number for Waves in Coast)

Wave Number given Maximum Wave Height by Miche Criterion

Go Wave Number for Waves in Coast = atanh(Maximum Wave Height/(0.14*Wavelength of Coast))/Water Depth

Wavelength given Maximum Wave Height by Miche Criterion

Go Wavelength of Coast = Maximum Wave Height/(0.14*tanh(Wave Number for Waves in Coast*Water Depth))

Maximum Wave Height using Miche Criterion

Go Maximum Wave Height = 0.14*Wavelength of Coast*tanh(Water Depth*Wave Number for Waves in Coast)

Energy Flux associated with Stable Wave Height

Go Energy Flux = Wave Energy*Wave Group Speed

Water Depth given Stable Wave Height

Go Water Depth = Stable Wave Height/0.4

Stable Wave Height

Go Stable Wave Height = 0.4*Water Depth

Water Depth given Maximum Wave Height by Miche Criterion Formula

Water Depth = ((atanh(Maximum Wave Height/(0.14*Wavelength of Coast)))/Wave Number for Waves in Coast)
d = ((atanh(H_max/(0.14*λ)))/k)

What is Wave Height and Wave Energy?

In fluid dynamics, the wave height of a surface wave is the difference between the elevations of a crest and a neighbouring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering.
Wave energy (or wave power) is the transport and capture of energy by ocean surface waves. The energy captured is then used for all different kinds of useful work, including electricity generation, water desalination, and pumping of water.

What is Breaking Wave and Group Velocity?

In fluid dynamics, a breaking wave or breaker is a wave whose amplitude reaches a critical level at which some process can suddenly start to occur causing large amounts of wave energy to be transformed into turbulent kinetic energy.
The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave propagates through space.

How to Calculate Water Depth given Maximum Wave Height by Miche Criterion?

Water Depth given Maximum Wave Height by Miche Criterion calculator uses Water Depth = ((atanh(Maximum Wave Height/(0.14*Wavelength of Coast)))/Wave Number for Waves in Coast) to calculate the Water Depth, The Water Depth given Maximum Wave Height by Miche Criterion formula is defined as a measure by soundings usually acquired by hydrographic surveys, measured from the water level to the bottom surface. Water Depth is denoted by d symbol.

How to calculate Water Depth given Maximum Wave Height by Miche Criterion using this online calculator? To use this online calculator for Water Depth given Maximum Wave Height by Miche Criterion, enter Maximum Wave Height (H_max), Wavelength of Coast (λ) & Wave Number for Waves in Coast (k) and hit the calculate button. Here is how the Water Depth given Maximum Wave Height by Miche Criterion calculation can be explained with given input values -> 0.943891 = ((atanh(0.7/(0.14*26.8)))/0.2).

FAQ

What is Water Depth given Maximum Wave Height by Miche Criterion?

The Water Depth given Maximum Wave Height by Miche Criterion formula is defined as a measure by soundings usually acquired by hydrographic surveys, measured from the water level to the bottom surface and is represented as d = ((atanh(H_max/(0.14*λ)))/k) or Water Depth = ((atanh(Maximum Wave Height/(0.14*Wavelength of Coast)))/Wave Number for Waves in Coast). Maximum Wave Height is most probable influenced by the difference between the elevations of a crest and a neighboring trough, Wavelength of Coast is the distance between two successive crests or troughs of a wave & Wave Number for Waves in Coast is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance.

How to calculate Water Depth given Maximum Wave Height by Miche Criterion?

The Water Depth given Maximum Wave Height by Miche Criterion formula is defined as a measure by soundings usually acquired by hydrographic surveys, measured from the water level to the bottom surface is calculated using Water Depth = ((atanh(Maximum Wave Height/(0.14*Wavelength of Coast)))/Wave Number for Waves in Coast). To calculate Water Depth given Maximum Wave Height by Miche Criterion, you need Maximum Wave Height (H_max), Wavelength of Coast (λ) & Wave Number for Waves in Coast (k). With our tool, you need to enter the respective value for Maximum Wave Height, Wavelength of Coast & Wave Number for Waves in Coast 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 Water Depth?

In this formula, Water Depth uses Maximum Wave Height, Wavelength of Coast & Wave Number for Waves in Coast. We can use 2 other way(s) to calculate the same, which is/are as follows -

Water Depth = Decay Coefficient*(Wave Energy*Wave Group Speed-(Energy Flux associated with Stable Wave Height))/Energy Dissipation Rate per unit Surface Area
Water Depth = Stable Wave Height/0.4

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