Guo Formula of Linear Dispersion Relation Calculator

✖Wave Angular Frequency is a fundamental parameter used to describe the periodic motion of waves.ⓘ Wave Angular Frequency [ω]			+10% -10%
✖Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.ⓘ Coastal Mean Depth [d]			+10% -10%

✖Linear Dispersion Relation is the most important expression in coastal and ocean engineering, showing us how the dimensionless wave speed depends on the relative wavelength.ⓘ Guo Formula of Linear Dispersion Relation [kd]

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Guo Formula of Linear Dispersion Relation

Formula

`"kd" = ("ω"^2*"d"/"[g]")*(1-exp(-("ω"*sqrt("d"/"[g]")^(5/2))^(-2/5)))`

Example

`"14.87764"=(("6.2rad/s")^2*"10m"/"[g]")*(1-exp(-("6.2rad/s"*sqrt("10m"/"[g]")^(5/2))^(-2/5)))`

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Guo Formula of Linear Dispersion Relation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Linear Dispersion Relation = (Wave Angular Frequency^2*Coastal Mean Depth/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5)))
kd = (ω^2*d/[g])*(1-exp(-(ω*sqrt(d/[g])^(5/2))^(-2/5)))
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

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

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)
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

Linear Dispersion Relation - Linear Dispersion Relation is the most important expression in coastal and ocean engineering, showing us how the dimensionless wave speed depends on the relative wavelength.
Wave Angular Frequency - (Measured in Radian per Second) - Wave Angular Frequency is a fundamental parameter used to describe the periodic motion of waves.
Coastal Mean Depth - (Measured in Meter) - Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.

STEP 1: Convert Input(s) to Base Unit

Wave Angular Frequency: 6.2 Radian per Second --> 6.2 Radian per Second No Conversion Required
Coastal Mean Depth: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

kd = (ω^2*d/[g])*(1-exp(-(ω*sqrt(d/[g])^(5/2))^(-2/5))) --> (6.2^2*10/[g])*(1-exp(-(6.2*sqrt(10/[g])^(5/2))^(-2/5)))

Evaluating ... ...

kd = 14.8776369750258

STEP 3: Convert Result to Output's Unit

14.8776369750258 --> No Conversion Required

FINAL ANSWER

14.8776369750258 ≈ 14.87764 <-- Linear Dispersion Relation

(Calculation completed in 00.004 seconds)

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< 12 Linear Dispersion Relation of Linear Wave Calculators

Velocity of Propagation in Linear Dispersion Relation given Wavelength

Go Velocity of Propagation = sqrt(([g]*Coastal Mean Depth*tanh(2*pi*Coastal Mean Depth/Deep Water Wavelength of Coast))/(2*pi*Coastal Mean Depth/Deep Water Wavelength of Coast))

Guo Formula of Linear Dispersion Relation for Wave Number

Go Wave Number for Water Wave = ((Angular Frequency of Wave^2*Coastal Mean Depth)/[g])*(1-exp(-(Angular Frequency of Wave*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5)))/Coastal Mean Depth

Guo Formula of Linear Dispersion Relation

Go Linear Dispersion Relation = (Wave Angular Frequency^2*Coastal Mean Depth/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5)))

Velocity of Propagation in Linear Dispersion Relation

Go Velocity of Propagation = sqrt(([g]*Coastal Mean Depth*tanh(Wave Number for Water Wave*Coastal Mean Depth))/(Wave Number for Water Wave*Coastal Mean Depth))

Wave Number of Convenient Empirical Explicit Approximation

Go Wave Number for Water Wave = (Angular Frequency of Wave^2/[g])*(coth((Angular Frequency of Wave*sqrt(Coastal Mean Depth/[g])^(3/2))^(2/3)))

Radian Frequency of Wave

Go Angular Frequency of Wave = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Coastal Mean Depth))

Dimensionless Wave Speed

Go Wave Speed = Propagation Velocity/sqrt([g]*Coastal Mean Depth)

Wave Number for Steady Two-dimensional Waves

Go Wave Number for Water Wave = (2*pi)/Deep Water Wavelength of Coast

Wavelength given Wave Number

Go Deep Water Wavelength of Coast = (2*pi)/Wave Number for Water Wave

Relative Wavelength

Go Relative Wavelength = Deep-Water Wavelength/Coastal Mean Depth

Wave period given Radian Frequency of Waves

Go Wave Period = 2*pi/Wave Angular Frequency

Radian Frequency of Waves

Go Wave Angular Frequency = 2*pi/Wave Period

Guo Formula of Linear Dispersion Relation Formula

What is Wave Number?

The Wavenumber is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance.

How to Calculate Guo Formula of Linear Dispersion Relation?

Guo Formula of Linear Dispersion Relation calculator uses Linear Dispersion Relation = (Wave Angular Frequency^2*Coastal Mean Depth/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5))) to calculate the Linear Dispersion Relation, The Guo Formula of Linear Dispersion Relation is defined as the linear dispersion relation of water waves. It's particularly useful for determining wave properties like phase speed and wavelength, which are crucial in designing coastal structures and predicting wave behavior. Linear Dispersion Relation is denoted by kd symbol.

How to calculate Guo Formula of Linear Dispersion Relation using this online calculator? To use this online calculator for Guo Formula of Linear Dispersion Relation, enter Wave Angular Frequency (ω) & Coastal Mean Depth (d) and hit the calculate button. Here is how the Guo Formula of Linear Dispersion Relation calculation can be explained with given input values -> 14.87764 = (6.2^2*10/[g])*(1-exp(-(6.2*sqrt(10/[g])^(5/2))^(-2/5))).

FAQ

What is Guo Formula of Linear Dispersion Relation?

The Guo Formula of Linear Dispersion Relation is defined as the linear dispersion relation of water waves. It's particularly useful for determining wave properties like phase speed and wavelength, which are crucial in designing coastal structures and predicting wave behavior and is represented as kd = (ω^2*d/[g])*(1-exp(-(ω*sqrt(d/[g])^(5/2))^(-2/5))) or Linear Dispersion Relation = (Wave Angular Frequency^2*Coastal Mean Depth/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5))). Wave Angular Frequency is a fundamental parameter used to describe the periodic motion of waves & Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.

How to calculate Guo Formula of Linear Dispersion Relation?

The Guo Formula of Linear Dispersion Relation is defined as the linear dispersion relation of water waves. It's particularly useful for determining wave properties like phase speed and wavelength, which are crucial in designing coastal structures and predicting wave behavior is calculated using Linear Dispersion Relation = (Wave Angular Frequency^2*Coastal Mean Depth/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5))). To calculate Guo Formula of Linear Dispersion Relation, you need Wave Angular Frequency (ω) & Coastal Mean Depth (d). With our tool, you need to enter the respective value for Wave Angular Frequency & Coastal Mean Depth 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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