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Surface Elevation Formula

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Surface Elevation refers to the fluctuation of water level at the interface between the ocean or sea and the adjacent landmass. Check FAQs

η = (\frac{H w}{2}) \cdot \cos ((k \cdot x) - (ω \cdot t))

η - Surface Elevation?H_w - Wave Height for Surface Gravity Waves?k - Wave Number for Water Wave?x - Propagation of Wave in One Direction?ω - Wave Angular Frequency?t - Time?

Surface Elevation Example

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Here is how the Surface Elevation equation looks like with Values.

Here is how the Surface Elevation equation looks like with Units.

Here is how the Surface Elevation equation looks like.

0.4761 = (\frac{3}{2}) \cdot \cos ((0.2 \cdot 31) - (6.2 \cdot 16))

0.4761m = (\frac{3m}{2}) \cdot \cos ((0.2 \cdot 31) - (6.2rad/s \cdot 16s))

0.4761 = (\frac{3}{2}) \cdot \cos ((0.2 \cdot 31) - (6.2 \cdot 16))

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Surface Elevation Solution

Follow our step by step solution on how to calculate Surface Elevation?

FIRST Step Consider the formula

η = (\frac{H w}{2}) \cdot \cos ((k \cdot x) - (ω \cdot t))

Next Step Substitute values of Variables

∴

η = (\frac{3m}{2}) \cdot \cos ((0.2 \cdot 31) - (6.2rad/s \cdot 16s))

Next Step Prepare to Evaluate

∴

η = (\frac{3}{2}) \cdot \cos ((0.2 \cdot 31) - (6.2 \cdot 16))

Next Step Evaluate

∴

η = 0.476143052279552m

LAST Step Rounding Answer

∴

η = 0.4761m

Surface Elevation Formula Elements

Variables

Functions

Surface Elevation

Surface Elevation refers to the fluctuation of water level at the interface between the ocean or sea and the adjacent landmass.

Symbol: η

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Surface Elevation

Wave Height for Surface Gravity Waves

The Wave Height for Surface Gravity Waves refers to the vertical distance between the trough (bottom) and crest (top) of a wave, measured from sea level.

Symbol: H_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Wave Height for Surface Gravity Waves

Wave Number for Water Wave

Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wave Number for Water Wave

Propagation of Wave in One Direction

The Propagation of Wave in One Direction is the transmission or spread of a wave occurring predominantly in a single direction.

Symbol: x

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Propagation of Wave in One Direction

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

Time

Time is a crucial aspect in coastal and ocean engineering, as it influences various processes and phenomena in marine environments.

Symbol: t

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Group Velocity, Beats, Energy Transport category

Go Wave Power per unit Crest Width

P = E \cdot V g

Go Total Energy per unit Area given Wave Power per unit Crest Width

E = \frac{P}{V g}

Go Group Velocity given Wave Power per unit Crest Width

V g = \frac{P}{E}

Go Wave Speed

v = \frac{ω}{k''}

How to Evaluate Surface Elevation?

Surface Elevation evaluator uses Surface Elevation = (Wave Height for Surface Gravity Waves/2)*cos((Wave Number for Water Wave*Propagation of Wave in One Direction)-(Wave Angular Frequency*Time)) to evaluate the Surface Elevation, The Surface Elevation formula is defined as the elevation of a geographic location is its height above or below a fixed reference point. Surface Elevation is denoted by η symbol.

How to evaluate Surface Elevation using this online evaluator? To use this online evaluator for Surface Elevation, enter Wave Height for Surface Gravity Waves (H_w), Wave Number for Water Wave (k), Propagation of Wave in One Direction (x), Wave Angular Frequency (ω) & Time (t) and hit the calculate button.

FAQs on Surface Elevation

What is the formula to find Surface Elevation?

The formula of Surface Elevation is expressed as Surface Elevation = (Wave Height for Surface Gravity Waves/2)*cos((Wave Number for Water Wave*Propagation of Wave in One Direction)-(Wave Angular Frequency*Time)). Here is an example- 0.476143 = (3/2)*cos((0.2*31)-(6.2*16)).

How to calculate Surface Elevation?

With Wave Height for Surface Gravity Waves (H_w), Wave Number for Water Wave (k), Propagation of Wave in One Direction (x), Wave Angular Frequency (ω) & Time (t) we can find Surface Elevation using the formula - Surface Elevation = (Wave Height for Surface Gravity Waves/2)*cos((Wave Number for Water Wave*Propagation of Wave in One Direction)-(Wave Angular Frequency*Time)). This formula also uses Cosine (cos) function(s).

Can the Surface Elevation be negative?

Yes, the Surface Elevation, measured in Length can be negative.

Which unit is used to measure Surface Elevation?

Surface Elevation is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Surface Elevation can be measured.

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Surface Elevation Formula

Surface Elevation Example

Surface Elevation Solution

Surface Elevation Formula Elements

Other formulas in Group Velocity, Beats, Energy Transport category

How to Evaluate Surface Elevation?

FAQs on Surface Elevation

Variable Name