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 of a fluid flow is a measure of the average depth of the fluid in a channel, pipe, or other conduit through which the fluid is flowing.ⓘ 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 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 of a fluid flow is a measure of the average depth of the fluid in a channel, pipe, or other conduit through which the fluid is flowing.

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 00.020 seconds)

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< Linear Dispersion Relation of Linear Wave Calculators

Velocity of Propagation in Linear Dispersion Relation given Wavelength

LaTeX 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))

Velocity of Propagation in Linear Dispersion Relation

LaTeX 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))

Wavelength given Wave Number

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

Relative Wavelength

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

Guo Formula of Linear Dispersion Relation Formula

LaTeX Go

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 refers to 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 refers to 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 of a fluid flow is a measure of the average depth of the fluid in a channel, pipe, or other conduit through which the fluid is flowing.

How to calculate Guo Formula of Linear Dispersion Relation?

The Guo Formula of Linear Dispersion Relation refers to 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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