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Guo Formula of Linear Dispersion Relation Formula

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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. Check FAQs

kd = (ω^{2} \cdot \frac{d}{[g]}) \cdot (1 - \exp (- {(ω \cdot {\sqrt{\frac{d}{[g]}}}^{\frac{5}{2}})}^{- \frac{2}{5}}))

kd - Linear Dispersion Relation?ω - Wave Angular Frequency?d - Coastal Mean Depth?[g] - Gravitational acceleration on Earth?[g] - Gravitational acceleration on Earth?

Guo Formula of Linear Dispersion Relation Example

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Here is how the Guo Formula of Linear Dispersion Relation equation looks like with Values.

Here is how the Guo Formula of Linear Dispersion Relation equation looks like with Units.

Here is how the Guo Formula of Linear Dispersion Relation equation looks like.

14.8776 = ({6.2}^{2} \cdot \frac{10}{9.8066}) \cdot (1 - \exp (- {(6.2 \cdot {\sqrt{\frac{10}{9.8066}}}^{\frac{5}{2}})}^{- \frac{2}{5}}))

14.8776 = ({6.2rad/s}^{2} \cdot \frac{10m}{9.8066m/s²}) \cdot (1 - \exp (- {(6.2rad/s \cdot {\sqrt{\frac{10m}{9.8066m/s²}}}^{\frac{5}{2}})}^{- \frac{2}{5}}))

14.8776 = ({6.2}^{2} \cdot \frac{10}{9.8066}) \cdot (1 - \exp (- {(6.2 \cdot {\sqrt{\frac{10}{9.8066}}}^{\frac{5}{2}})}^{- \frac{2}{5}}))

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Guo Formula of Linear Dispersion Relation Solution

Follow our step by step solution on how to calculate Guo Formula of Linear Dispersion Relation?

FIRST Step Consider the formula

kd = (ω^{2} \cdot \frac{d}{[g]}) \cdot (1 - \exp (- {(ω \cdot {\sqrt{\frac{d}{[g]}}}^{\frac{5}{2}})}^{- \frac{2}{5}}))

Next Step Substitute values of Variables

∴

kd = ({6.2rad/s}^{2} \cdot \frac{10m}{[g]}) \cdot (1 - \exp (- {(6.2rad/s \cdot {\sqrt{\frac{10m}{[g]}}}^{\frac{5}{2}})}^{- \frac{2}{5}}))

Next Step Substitute values of Constants

∴

kd = ({6.2rad/s}^{2} \cdot \frac{10m}{9.8066m/s²}) \cdot (1 - \exp (- {(6.2rad/s \cdot {\sqrt{\frac{10m}{9.8066m/s²}}}^{\frac{5}{2}})}^{- \frac{2}{5}}))

Next Step Prepare to Evaluate

∴

kd = ({6.2}^{2} \cdot \frac{10}{9.8066}) \cdot (1 - \exp (- {(6.2 \cdot {\sqrt{\frac{10}{9.8066}}}^{\frac{5}{2}})}^{- \frac{2}{5}}))

Next Step Evaluate

∴

kd = 14.8776369750258

LAST Step Rounding Answer

∴

kd = 14.8776

Guo Formula of Linear Dispersion Relation Formula Elements

Variables

Constants

Functions

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.

Symbol: kd

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Linear Dispersion Relation

Wave Angular Frequency

Wave Angular Frequency is a fundamental parameter used to describe the periodic motion of waves.

Symbol: ω

Measurement: Angular FrequencyUnit: rad/s

Note: Value can be positive or negative.

Formulas to find Wave Angular Frequency

Coastal Mean Depth

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.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Coastal Mean Depth

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

exp

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

Syntax: 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.

Syntax: sqrt(Number)

Other formulas in Linear Dispersion Relation of Linear Wave category

Go Velocity of Propagation in Linear Dispersion Relation

C v = \sqrt{\frac{[g] \cdot d \cdot \tanh (k \cdot d)}{k \cdot d}}

Go Wavelength given Wave Number

λ'' = \frac{2 \cdot π}{k}

Go Relative Wavelength

λ r = \frac{λ o}{d}

Go Velocity of Propagation in Linear Dispersion Relation given Wavelength

C v = \sqrt{\frac{[g] \cdot d \cdot \tanh (2 \cdot π \cdot \frac{d}{λ''})}{2 \cdot π \cdot \frac{d}{λ''}}}

How to Evaluate Guo Formula of Linear Dispersion Relation?

Guo Formula of Linear Dispersion Relation evaluator 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 evaluate 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 evaluate Guo Formula of Linear Dispersion Relation using this online evaluator? To use this online evaluator for Guo Formula of Linear Dispersion Relation, enter Wave Angular Frequency (ω) & Coastal Mean Depth (d) and hit the calculate button.

FAQs on Guo Formula of Linear Dispersion Relation

What is the formula to find Guo Formula of Linear Dispersion Relation?

The formula of Guo Formula of Linear Dispersion Relation is expressed as 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))). Here is an example- 14.87764 = (6.2^2*10/[g])*(1-exp(-(6.2*sqrt(10/[g])^(5/2))^(-2/5))).

How to calculate Guo Formula of Linear Dispersion Relation?

With Wave Angular Frequency (ω) & Coastal Mean Depth (d) we can find Guo Formula of Linear Dispersion Relation using the formula - 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))). This formula also uses Gravitational acceleration on Earth, Gravitational acceleration on Earth constant(s) and , Exponential Growth (exp), Square Root (sqrt) function(s).

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Guo Formula of Linear Dispersion Relation Formula

Guo Formula of Linear Dispersion Relation Example

Guo Formula of Linear Dispersion Relation Solution

Guo Formula of Linear Dispersion Relation Formula Elements

Other formulas in Linear Dispersion Relation of Linear Wave category

How to Evaluate Guo Formula of Linear Dispersion Relation?

FAQs on Guo Formula of Linear Dispersion Relation

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