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 = (Hw/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 measured is the elevation of a geographic location is its height above or below a fixed reference point.
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 - The wave number for water waves quantifies the number of waves per unit length along the surface of the water.
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 angular displacement of the wave per unit time. Its units are therefore degrees (or radians) per second.
Time - (Measured in Second) - Time can be defined as the ongoing and continuous sequence of events that occur in succession, from the past through the present to the future.
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 = (Hw/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)

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
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Wave Speed given Group Velocity
Go Wave Speed = Group Velocity of Waves/(0.5*(1+((Wave Number for Water Wave*Mean Depth)/(sinh(Wave Number for Water Wave*Mean Depth)*cosh(Wave Number for Water Wave*Mean Depth)))))
Group Velocity of Waves
Go Group Velocity of Waves = 0.5*Wave Speed*(1+((Wave Number for Water Wave*Mean Depth)/(sinh(Wave Number for Water Wave*Mean Depth)*cosh(Wave Number for Water Wave*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 of 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 of Area
Wave Power per unit Crest Width
Go Wave Power per unit Crest Width = Total Energy per unit of Area*Group Velocity of Waves
Wavenumber given Wave Speed
Go Wave Number for Water Wave = Wave Angular Frequency/Wave Speed
Wave Speed
Go Wave Speed = Wave Angular Frequency/Wave Number for Water Wave

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 = (Hw/2)*cos((k*x)-(ω*t))

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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 (Hw), 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 -> 0.493707 = (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 = (Hw/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, The wave number for water waves quantifies the number of waves per unit length along the surface of the water, The Propagation of Wave in One Direction is the transmission or spread of a wave occurring predominantly in a single direction, Wave Angular Frequency angular displacement of the wave per unit time. Its units are therefore degrees (or radians) per second & Time can be defined as the ongoing and continuous sequence of events that occur in succession, from the past through the present to the future.
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 (Hw), 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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