Wave Celerity given Wavelength and Water Depth Calculator

✖Deep-Water Wavelength, deep water waves are defined as those occurring in ocean depths greater than twice the wavelength of the wave.ⓘ Deep-Water Wavelength [λ_o]			+10% -10%
✖Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [d]			+10% -10%

✖Deepwater Wave Celerity is the speed at which an individual wave advances or propagates occurring or existing in water of great depth.ⓘ Wave Celerity given Wavelength and Water Depth [C_o]

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Wave Celerity given Wavelength and Water Depth

Formula

`"C"_{"o"} = sqrt((("λ"_{"o"}*"[g]")/(2*pi))*tanh((2*pi*"d")/"λ"_{"o"}))`

Example

`"4.461154m/s"=sqrt((("13m"*"[g]")/(2*pi))*tanh((2*pi*"4.8m")/"13m"))`

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Wave Celerity given Wavelength and Water Depth Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deepwater Wave Celerity = sqrt(((Deep-Water Wavelength*[g])/(2*pi))*tanh((2*pi*Water Depth)/Deep-Water Wavelength))
C_o = sqrt(((λ_o*[g])/(2*pi))*tanh((2*pi*d)/λ_o))
This formula uses 2 Constants, 2 Functions, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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)
tanh - The hyperbolic tangent function (tanh) is a function that is defined as the ratio of the hyperbolic sine function (sinh) to the hyperbolic cosine function (cosh)., tanh(Number)

Variables Used

Deepwater Wave Celerity - (Measured in Meter per Second) - Deepwater Wave Celerity is the speed at which an individual wave advances or propagates occurring or existing in water of great depth.
Deep-Water Wavelength - (Measured in Meter) - Deep-Water Wavelength, deep water waves are defined as those occurring in ocean depths greater than twice the wavelength of the wave.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.

STEP 1: Convert Input(s) to Base Unit

Deep-Water Wavelength: 13 Meter --> 13 Meter No Conversion Required
Water Depth: 4.8 Meter --> 4.8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_o = sqrt(((λ_o*[g])/(2*pi))*tanh((2*pi*d)/λ_o)) --> sqrt(((13*[g])/(2*pi))*tanh((2*pi*4.8)/13))

Evaluating ... ...

C_o = 4.46115390318095

STEP 3: Convert Result to Output's Unit

4.46115390318095 Meter per Second --> No Conversion Required

FINAL ANSWER

4.46115390318095 ≈ 4.461154 Meter per Second <-- Deepwater Wave Celerity

(Calculation completed in 00.020 seconds)

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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 Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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< 12 Wave Celerity Calculators

Wave Celerity given Wavelength and Water Depth

Go Deepwater Wave Celerity = sqrt(((Deep-Water Wavelength*[g])/(2*pi))*tanh((2*pi*Water Depth)/Deep-Water Wavelength))

Wave Celerity given Wave Period and Wavelength

Go Deepwater Wave Celerity = (([g]*Wave Period)/(2*pi))*tanh((2*pi*Water Depth)/Deep-Water Wavelength)

Celerity of Wave given Deepwater Celerity and Wavelength

Go Celerity for Shallow Depth = (Deepwater Wave Celerity*Wavelength for Shallow Depth)/Deep-Water Wavelength

Deepwater Celerity for Deepwater wavelength

Go Deepwater Wave Celerity = (Celerity for Shallow Depth*Deep-Water Wavelength)/Wavelength for Shallow Depth

Celerity of Deepwater Wave

Go Deepwater Wave Celerity = sqrt(([g]*Deep-Water Wavelength)/(2*pi))

Wave Celerity when Relative Water Depth becomes Shallow

Go Celerity for Shallow Depth = sqrt([g]*Shallow Depth)

Deepwater Celerity given Wave Period

Go Deepwater Wave Celerity = ([g]*Wave Period)/(2*pi)

Wave Celerity given Wavelength and Wave Period

Go Deepwater Wave Celerity = Deep-Water Wavelength/Wave Period

Wave Period given Deepwater Celerity

Go Wave Period = Deep-Water Wavelength/Deepwater Wave Celerity

Deepwater Wave Celerity

Go Deepwater Wave Celerity = Deep-Water Wavelength/Wave Period

Deepwater Celerity when SI systems Units of meters and seconds is considered

Go Deepwater Wave Celerity = 1.56*Wave Period

Deepwater Celerity given Units of Feet and Seconds

Go Celerity in FPS Unit = 5.12*Wave Period

Wave Celerity given Wavelength and Water Depth Formula

Deepwater Wave Celerity = sqrt(((Deep-Water Wavelength*[g])/(2*pi))*tanh((2*pi*Water Depth)/Deep-Water Wavelength))
C_o = sqrt(((λ_o*[g])/(2*pi))*tanh((2*pi*d)/λ_o))

What are Water Waves ?

Water waves are oscillations on the surface of bodies of water caused by the transfer of energy from wind or other sources.

How to Calculate Wave Celerity given Wavelength and Water Depth?

Wave Celerity given Wavelength and Water Depth calculator uses Deepwater Wave Celerity = sqrt(((Deep-Water Wavelength*[g])/(2*pi))*tanh((2*pi*Water Depth)/Deep-Water Wavelength)) to calculate the Deepwater Wave Celerity, Wave Celerity given Wavelength and Water Depth is the speed at which the wave travels through water depths greater than half its wavelength and can be calculated based on the wavelength and water depth of the wave. Deepwater Wave Celerity is denoted by C_o symbol.

How to calculate Wave Celerity given Wavelength and Water Depth using this online calculator? To use this online calculator for Wave Celerity given Wavelength and Water Depth, enter Deep-Water Wavelength (λ_o) & Water Depth (d) and hit the calculate button. Here is how the Wave Celerity given Wavelength and Water Depth calculation can be explained with given input values -> 3.081473 = sqrt(((13*[g])/(2*pi))*tanh((2*pi*4.8)/13)).

FAQ

What is Wave Celerity given Wavelength and Water Depth?

Wave Celerity given Wavelength and Water Depth is the speed at which the wave travels through water depths greater than half its wavelength and can be calculated based on the wavelength and water depth of the wave and is represented as C_o = sqrt(((λ_o*[g])/(2*pi))*tanh((2*pi*d)/λ_o)) or Deepwater Wave Celerity = sqrt(((Deep-Water Wavelength*[g])/(2*pi))*tanh((2*pi*Water Depth)/Deep-Water Wavelength)). Deep-Water Wavelength, deep water waves are defined as those occurring in ocean depths greater than twice the wavelength of the wave & Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.

How to calculate Wave Celerity given Wavelength and Water Depth?

Wave Celerity given Wavelength and Water Depth is the speed at which the wave travels through water depths greater than half its wavelength and can be calculated based on the wavelength and water depth of the wave is calculated using Deepwater Wave Celerity = sqrt(((Deep-Water Wavelength*[g])/(2*pi))*tanh((2*pi*Water Depth)/Deep-Water Wavelength)). To calculate Wave Celerity given Wavelength and Water Depth, you need Deep-Water Wavelength (λ_o) & Water Depth (d). With our tool, you need to enter the respective value for Deep-Water Wavelength & Water Depth and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Deepwater Wave Celerity?

In this formula, Deepwater Wave Celerity uses Deep-Water Wavelength & Water Depth. We can use 7 other way(s) to calculate the same, which is/are as follows -

Deepwater Wave Celerity = Deep-Water Wavelength/Wave Period
Deepwater Wave Celerity = (([g]*Wave Period)/(2*pi))*tanh((2*pi*Water Depth)/Deep-Water Wavelength)
Deepwater Wave Celerity = Deep-Water Wavelength/Wave Period
Deepwater Wave Celerity = sqrt(([g]*Deep-Water Wavelength)/(2*pi))
Deepwater Wave Celerity = ([g]*Wave Period)/(2*pi)
Deepwater Wave Celerity = 1.56*Wave Period
Deepwater Wave Celerity = (Celerity for Shallow Depth*Deep-Water Wavelength)/Wavelength for Shallow Depth

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