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)

Credits

Creator Image
Created by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
Mithila Muthamma PA has created this Calculator and 2000+ more calculators!
Verifier Image
Verified by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
Chandana P Dev has verified this Calculator and 1700+ more calculators!

Wavelength Calculators

Wavelength given Wave Celerity and Wave Speed
​ LaTeX ​ Go Wavelength = (2*pi*Water Depth)/(atanh((2*Wave Celerity*pi)/([g]*Wave Period)))
Wavelength as Function of Depth and Wave Period
​ LaTeX ​ Go Wavelength = (([g]*Wave Period^2)/(2*pi))*tanh(Wave Number*Water Depth)
Deepwater Wavelength given Wave Celerity
​ LaTeX ​ Go DeepWater Wavelength = Deepwater Wave Celerity*Wave Period
Wavelength given Wave Celerity
​ LaTeX ​ Go Wavelength = Wave Celerity*Wave Period

Water Depth given Wave Celerity and Wavelength Formula

​LaTeX ​Go
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 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 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 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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!