Water Depth given Wavelength, Wave Period and Water Number Calculator

✖Wavelength is the distance between successive crests, troughs, or any corresponding points on a wave.ⓘ Wavelength [L]			+10% -10%
✖Wave Angular Frequency is the rate of change of the phase of the wave over time, given by the symbol ω (omega).ⓘ Wave Angular Frequency [ω]			+10% -10%
✖Wave period is the time it takes for successive wave crests or troughs to pass a fixed point.ⓘ Wave Period [T]			+10% -10%
✖The wave number for water waves quantifies the number of waves per unit length along the surface of the water.ⓘ Wave Number for Water Wave [k]			+10% -10%

✖Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth given Wavelength, Wave Period and Water Number [d]

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Water Depth given Wavelength, Wave Period and Water Number

Formula

`"d" = (atanh(("L"*"ω")/("[g]"*"T")))/"k"`

Example

`"2.157505m"=(atanh(("0.4m"*"6.2rad/s")/("[g]"*"0.622s")))/"0.2"`

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Water Depth given Wavelength, Wave Period and Water Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Water Depth = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Wave Number for Water Wave
d = (atanh((L*ω)/([g]*T)))/k
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

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. Water depth means the depth as measured from the water level to the bottom of the considered water body.
Wavelength - (Measured in Meter) - Wavelength is the distance between successive crests, troughs, or any corresponding points on a wave.
Wave Angular Frequency - (Measured in Radian per Second) - Wave Angular Frequency is the rate of change of the phase of the wave over time, given by the symbol ω (omega).
Wave Period - (Measured in Second) - Wave period is the time it takes for successive wave crests or troughs to pass a fixed point.
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.

STEP 1: Convert Input(s) to Base Unit

Wavelength: 0.4 Meter --> 0.4 Meter No Conversion Required
Wave Angular Frequency: 6.2 Radian per Second --> 6.2 Radian per Second No Conversion Required
Wave Period: 0.622 Second --> 0.622 Second No Conversion Required
Wave Number for Water Wave: 0.2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = (atanh((L*ω)/([g]*T)))/k --> (atanh((0.4*6.2)/([g]*0.622)))/0.2

Evaluating ... ...

d = 2.15750500220341

STEP 3: Convert Result to Output's Unit

2.15750500220341 Meter --> No Conversion Required

FINAL ANSWER

2.15750500220341 ≈ 2.157505 Meter <-- Water Depth

(Calculation completed in 00.004 seconds)

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< 4 Predicting Waves in Deep Water Calculators

Significant Wave Height from Bretschneider Empirical Relationships

Go Wave Height for Deep Water = (Wind Speed^2*0.283*tanh(0.0125*(([g]*Fetch Length)/Wind Speed^2)^0.42))/[g]

Water Depth given Wavelength, Wave Period and Water Number

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

Wave Number given Wavelength, Wave Period and Water Depth

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

Significant Wave Period from Bretschneider Empirical Relationships

Go Wave Period = (Wind Speed*7.54*tanh(0.077*(([g]*Fetch Length)/Wind Speed^2)^0.25))/[g]

Water Depth given Wavelength, Wave Period and Water Number Formula

Water Depth = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Wave Number for Water Wave
d = (atanh((L*ω)/([g]*T)))/k

What is Wave Number?

Wave Number is the distance between corresponding points of two consecutive waves. “Corresponding points” refers to two points or particles in the same phase—i.e., points that have completed identical fractions of their periodic motion.

How to Calculate Water Depth given Wavelength, Wave Period and Water Number?

Water Depth given Wavelength, Wave Period and Water Number calculator uses Water Depth = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Wave Number for Water Wave to calculate the Water Depth, The Water Depth given Wavelength, Wave Period and Water Number 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 Wavelength, Wave Period and Water Number using this online calculator? To use this online calculator for Water Depth given Wavelength, Wave Period and Water Number, enter Wavelength (L), Wave Angular Frequency (ω), Wave Period (T) & Wave Number for Water Wave (k) and hit the calculate button. Here is how the Water Depth given Wavelength, Wave Period and Water Number calculation can be explained with given input values -> 2.157505 = (atanh((0.4*6.2)/([g]*0.622)))/0.2.

FAQ

What is Water Depth given Wavelength, Wave Period and Water Number?

The Water Depth given Wavelength, Wave Period and Water Number is defined as the depth as measured from the water level to the referenced bottom considered and is represented as d = (atanh((L*ω)/([g]*T)))/k or Water Depth = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Wave Number for Water Wave. Wavelength is the distance between successive crests, troughs, or any corresponding points on a wave, Wave Angular Frequency is the rate of change of the phase of the wave over time, given by the symbol ω (omega), Wave period is the time it takes for successive wave crests or troughs to pass a fixed point & The wave number for water waves quantifies the number of waves per unit length along the surface of the water.

How to calculate Water Depth given Wavelength, Wave Period and Water Number?

The Water Depth given Wavelength, Wave Period and Water Number is defined as the depth as measured from the water level to the referenced bottom considered is calculated using Water Depth = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Wave Number for Water Wave. To calculate Water Depth given Wavelength, Wave Period and Water Number, you need Wavelength (L), Wave Angular Frequency (ω), Wave Period (T) & Wave Number for Water Wave (k). With our tool, you need to enter the respective value for Wavelength, Wave Angular Frequency, Wave Period & Wave Number for Water Wave 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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