Surface Elevation Calculator

✖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.ⓘ Wave Height for Surface Gravity Waves [H_w]			+10% -10%
✖Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance.ⓘ Wave Number for Water Wave [k]			+10% -10%
✖The Propagation of Wave in One Direction is the transmission or spread of a wave occurring predominantly in a single direction.ⓘ Propagation of Wave in One Direction [x]			+10% -10%
✖Wave Angular Frequency is a fundamental parameter used to describe the periodic motion of waves.ⓘ Wave Angular Frequency [ω]			+10% -10%
✖Time is a crucial aspect in coastal and ocean engineering, as it influences various processes and phenomena in marine environments.ⓘ Time [t]			+10% -10%

✖Surface Elevation refers to the fluctuation of water level at the interface between the ocean or sea and the adjacent landmass.ⓘ Surface Elevation [η]

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Formula

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Surface Elevation

Formula

`"η" = ("H"_{"w"}/2)*cos(("k"*"x")-("ω"*"t"))`

Example

`"0.476143m"=("3m"/2)*cos(("0.2"*"31")-("6.2rad/s"*"16s"))`

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Surface Elevation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
η = (H_w/2)*cos((k*x)-(ω*t))
This formula uses 1 Functions, 6 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Surface Elevation - (Measured in Meter) - Surface Elevation refers to the fluctuation of water level at the interface between the ocean or sea and the adjacent landmass.
Wave Height for Surface Gravity Waves - (Measured in Meter) - 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.
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.
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.
Wave Angular Frequency - (Measured in Radian per Second) - Wave Angular Frequency is a fundamental parameter used to describe the periodic motion of waves.
Time - (Measured in Second) - Time is a crucial aspect in coastal and ocean engineering, as it influences various processes and phenomena in marine environments.

STEP 1: Convert Input(s) to Base Unit

Wave Height for Surface Gravity Waves: 3 Meter --> 3 Meter No Conversion Required
Wave Number for Water Wave: 0.2 --> No Conversion Required
Propagation of Wave in One Direction: 31 --> No Conversion Required
Wave Angular Frequency: 6.2 Radian per Second --> 6.2 Radian per Second No Conversion Required
Time: 16 Second --> 16 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η = (H_w/2)*cos((k*x)-(ω*t)) --> (3/2)*cos((0.2*31)-(6.2*16))

Evaluating ... ...

η = 0.476143052279552

STEP 3: Convert Result to Output's Unit

0.476143052279552 Meter --> No Conversion Required

FINAL ANSWER

0.476143052279552 ≈ 0.476143 Meter <-- Surface Elevation

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surface Gravity Waves » Group Velocity, Beats, Energy Transport » Surface Elevation

Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

M Naveen has verified this Calculator and 900+ more calculators!

< 9 Group Velocity, Beats, Energy Transport Calculators

Wave Speed given Group Velocity

Go Wave Speed = Group Velocity of Waves/(0.5*(1+((Wave Number for Water Wave*Coastal Mean Depth)/(sinh(Wave Number for Water Wave*Coastal Mean Depth)*cosh(Wave Number for Water Wave*Coastal Mean Depth)))))

Group Velocity of Waves

Go Group Velocity of Waves = 0.5*Wave Speed*(1+((Wave Number for Water Wave*Coastal Mean Depth)/(sinh(Wave Number for Water Wave*Coastal Mean Depth)*cosh(Wave Number for Water Wave*Coastal Mean Depth))))

Surface Elevation

Go 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))

Radian Frequency given Wave Propagation

Go Wave Angular Frequency = Wave Number for Water Wave*Propagation of Wave in One Direction

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

Go Total Energy Per Unit Area = Wave Power Per Unit Crest Width/Group Velocity of Waves

Group Velocity given Wave Power per unit Crest Width

Go Group Velocity of Waves = Wave Power Per Unit Crest Width/Total Energy Per Unit Area

Wave Power per unit Crest Width

Go Wave Power Per Unit Crest Width = Total Energy Per Unit Area*Group Velocity of Waves

Wavenumber given Wave Speed

Go Wave Number = Wave Angular Frequency/Wave Speed

Wave Speed

Go Wave Speed = Wave Angular Frequency/Wave Number

Surface Elevation 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))
η = (H_w/2)*cos((k*x)-(ω*t))

What is Wave Power and How does it Work?

Wave power is produced by the up and down motion of floating devices placed on the surface of the ocean. In other words, wind produces waves, and then waves produce energy. As the waves travel across the ocean, high-tech devices capture the natural movements of ocean currents and the flow of swells to generate power.

How to Calculate Surface Elevation?

Surface Elevation calculator 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 calculate the Surface Elevation, The Surface Elevation 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 calculate Surface Elevation using this online calculator? To use this online calculator 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. Here is how the Surface Elevation calculation can be explained with given input values -> 0.476143 = (3/2)*cos((0.2*31)-(6.2*16)).

FAQ

What is Surface Elevation?

The Surface Elevation is defined as the elevation of a geographic location is its height above or below a fixed reference point and is represented as η = (H_w/2)*cos((k*x)-(ω*t)) or 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)). 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, Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance, The Propagation of Wave in One Direction is the transmission or spread of a wave occurring predominantly in a single direction, Wave Angular Frequency is a fundamental parameter used to describe the periodic motion of waves & Time is a crucial aspect in coastal and ocean engineering, as it influences various processes and phenomena in marine environments.

How to calculate Surface Elevation?

The Surface Elevation is defined as the elevation of a geographic location is its height above or below a fixed reference point is calculated using 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 calculate Surface Elevation, you need 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). With our tool, you need to enter the respective value for Wave Height for Surface Gravity Waves, Wave Number for Water Wave, Propagation of Wave in One Direction, Wave Angular Frequency & Time 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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