Water depth given wave celerity and wavelength Calculator

✖Wavelength can be defined as the distance between two successive crests or troughs of a wave.ⓘ Wavelength [λ]			+10% -10%
✖Wave Celerity is the speed at which an individual wave advances or propagates.ⓘ Wave Celerity [C]			+10% -10%
✖Wave Period is the time between successive peaks or troughs.ⓘ Wave Period [T]			+10% -10%

✖Water Depth of the considered catchment is measured from the water level to the bottom of the considered water body.ⓘ Water depth given wave celerity and wavelength [d]

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Formula

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Water depth given wave celerity and wavelength

Formula

`"d" = ("λ"*atanh((2*pi*"C")/("[g]"*"T")))/(2*pi)`

Example

`"1.556351m"=("10.11m"*atanh((2*pi*"3.5m/s")/("[g]"*"3s")))/(2*pi)`

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Water depth given wave celerity and wavelength Solution

STEP 0: Pre-Calculation Summary

Formula Used

Water Depth = (Wavelength*atanh((2*pi*Wave Celerity)/([g]*Wave Period)))/(2*pi)
d = (λ*atanh((2*pi*C)/([g]*T)))/(2*pi)
This formula uses 2 Constants, 2 Functions, 4 Variables

Constants Used

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

Functions Used

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)
atanh - The inverse hyperbolic tangent function returns the value whose hyperbolic tangent is a number., atanh(Number)

Variables Used

Water Depth - (Measured in Meter) - Water Depth of the considered catchment is measured from the water level to the bottom of the considered water body.
Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Wave Celerity - (Measured in Meter per Second) - Wave Celerity is the speed at which an individual wave advances or propagates.
Wave Period - (Measured in Second) - Wave Period is the time between successive peaks or troughs.

STEP 1: Convert Input(s) to Base Unit

Wavelength: 10.11 Meter --> 10.11 Meter No Conversion Required
Wave Celerity: 3.5 Meter per Second --> 3.5 Meter per Second No Conversion Required
Wave Period: 3 Second --> 3 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = (λ*atanh((2*pi*C)/([g]*T)))/(2*pi) --> (10.11*atanh((2*pi*3.5)/([g]*3)))/(2*pi)

Evaluating ... ...

d = 1.55635146349087

STEP 3: Convert Result to Output's Unit

1.55635146349087 Meter --> No Conversion Required

FINAL ANSWER

1.55635146349087 ≈ 1.556351 Meter <-- Water Depth

(Calculation completed in 00.004 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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< 14 Wavelength Calculators

Water depth given wave celerity and wavelength

Go Water Depth = (Wavelength*atanh((2*pi*Wave Celerity)/([g]*Wave Period)))/(2*pi)

Wavelength given Wave Celerity and Wave Speed

Go Wavelength = (2*pi*Water Depth)/(atanh((2*Wave Celerity*pi)/([g]*Wave Period)))

Wavelength as Function of Water Depth and Wave Period

Go Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth)

Eckert's Equation for Wavelength

Go Wavelength = DeepWater Wavelength*sqrt(tanh((2*pi*Water Depth)/DeepWater Wavelength))

Wavelength as Function of Depth and Wave Period

Go Wavelength = (([g]*Wave Period^2)/(2*pi))*tanh(Wave Number*Water Depth)

Wavelength given Deepwater Wavelength

Go Wavelength = DeepWater Wavelength*tanh(Wave Number*Water Depth)

Long Wave Simplification for Wavelength

Go Wavelength = Wave Period*sqrt([g]*Water Depth)

Wavelength given Deepwater Celerity and Deepwater Wavelength

Go Wavelength = (DeepWater Wavelength*Wave Celerity)/Deepwater Wave Celerity

Deepwater Wavelength given Deepwater Celerity

Go DeepWater Wavelength = (Wavelength*Deepwater Wave Celerity)/Wave Celerity

Deepwater Wavelength given Celerity of Deepwater Wave

Go DeepWater Wavelength = (Deepwater Wave Celerity^2*2*pi)/[g]

Deepwater Wavelength given Wave Celerity

Go DeepWater Wavelength = Deepwater Wave Celerity*Wave Period

Wavelength given Wave Celerity

Go Wavelength = Wave Celerity*Wave Period

Deepwater Wavelength given Units of Feet

Go DeepWater Wavelength in Feet = 5.12*Wave Period^2

Deepwater Wavelength when SI systems Units of meters is Considered

Go DeepWater Wavelength = 1.56*Wave Period^2

Water depth given wave celerity and wavelength Formula

Water Depth = (Wavelength*atanh((2*pi*Wave Celerity)/([g]*Wave Period)))/(2*pi)
d = (λ*atanh((2*pi*C)/([g]*T)))/(2*pi)

What are Water Waves & Wave Energy?

A wave, a ridge or swell on the surface of a body of water, normally having a forward motion distinct from the oscillatory motion of the particles that successively compose it. Water waves are considered oscillatory or nearly oscillatory if the motion described by the water particles is circular orbits that are closed or nearly closed for each wave period.
Wave energy (or wave power) is the transport and capture of energy by ocean surface waves. The energy captured is then used for all different kinds of useful work, including electricity generation, water desalination, and pumping of water.

How does Depth affect Wavelength?

The change from deep to shallow water waves occurs when the depth of the water, d, becomes less than one-half of the wavelength of the wave. The speed of deep-water waves depends on the wavelength of the waves. We say that deep-water waves show dispersion. A wave with a longer wavelength travel at a higher speed.

How to Calculate Water depth given wave celerity and wavelength?

Water depth given wave celerity and wavelength calculator uses Water Depth = (Wavelength*atanh((2*pi*Wave Celerity)/([g]*Wave Period)))/(2*pi) to calculate the Water Depth, Water depth given wave celerity and wavelength is defined as the the depth as measured from the water level to the referenced bottom considered. Water Depth is denoted by d symbol.

How to calculate Water depth given wave celerity and wavelength using this online calculator? To use this online calculator for Water depth given wave celerity and wavelength, enter Wavelength (λ), Wave Celerity (C) & Wave Period (T) and hit the calculate button. Here is how the Water depth given wave celerity and wavelength calculation can be explained with given input values -> 1.556351 = (10.11*atanh((2*pi*3.5)/([g]*3)))/(2*pi).

FAQ

What is Water depth given wave celerity and wavelength?

Water depth given wave celerity and wavelength is defined as the the depth as measured from the water level to the referenced bottom considered and is represented as d = (λ*atanh((2*pi*C)/([g]*T)))/(2*pi) or Water Depth = (Wavelength*atanh((2*pi*Wave Celerity)/([g]*Wave Period)))/(2*pi). Wavelength can be defined as the distance between two successive crests or troughs of a wave, Wave Celerity is the speed at which an individual wave advances or propagates & Wave Period is the time between successive peaks or troughs.

How to calculate Water depth given wave celerity and wavelength?

Water depth given wave celerity and wavelength is defined as the the depth as measured from the water level to the referenced bottom considered is calculated using Water Depth = (Wavelength*atanh((2*pi*Wave Celerity)/([g]*Wave Period)))/(2*pi). To calculate Water depth given wave celerity and wavelength, you need Wavelength (λ), Wave Celerity (C) & Wave Period (T). With our tool, you need to enter the respective value for Wavelength, Wave Celerity & Wave Period 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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