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Water Depth given Wave Celerity and Wavelength Formula

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Water Depth of the considered catchment is measured from the water level to the bottom of the considered water body. Check FAQs

d = \frac{λ \cdot a \tanh (\frac{2 \cdot π \cdot C}{[g] \cdot T})}{2 \cdot π}

d - Water Depth?λ - Wavelength?C - Wave Celerity?T - Wave Period?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Water Depth given Wave Celerity and Wavelength Example

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Here is how the Water Depth given Wave Celerity and Wavelength equation looks like with Values.

Here is how the Water Depth given Wave Celerity and Wavelength equation looks like with Units.

Here is how the Water Depth given Wave Celerity and Wavelength equation looks like.

1.5564 = \frac{10.11 \cdot a \tanh (\frac{2 \cdot 3.1416 \cdot 3.5}{9.8066 \cdot 3})}{2 \cdot 3.1416}

1.5564m = \frac{10.11m \cdot a \tanh (\frac{2 \cdot 3.1416 \cdot 3.5m/s}{9.8066m/s² \cdot 3s})}{2 \cdot 3.1416}

1.5564 = \frac{10.11 \cdot a \tanh (\frac{2 \cdot 3.1416 \cdot 3.5}{9.8066 \cdot 3})}{2 \cdot 3.1416}

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Water Depth given Wave Celerity and Wavelength Solution

Follow our step by step solution on how to calculate Water Depth given Wave Celerity and Wavelength?

FIRST Step Consider the formula

d = \frac{λ \cdot a \tanh (\frac{2 \cdot π \cdot C}{[g] \cdot T})}{2 \cdot π}

Next Step Substitute values of Variables

∴

d = \frac{10.11m \cdot a \tanh (\frac{2 \cdot π \cdot 3.5m/s}{[g] \cdot 3s})}{2 \cdot π}

Next Step Substitute values of Constants

∴

d = \frac{10.11m \cdot a \tanh (\frac{2 \cdot 3.1416 \cdot 3.5m/s}{9.8066m/s² \cdot 3s})}{2 \cdot 3.1416}

Next Step Prepare to Evaluate

∴

d = \frac{10.11 \cdot a \tanh (\frac{2 \cdot 3.1416 \cdot 3.5}{9.8066 \cdot 3})}{2 \cdot 3.1416}

Next Step Evaluate

∴

d = 1.55635146349087m

LAST Step Rounding Answer

∴

d = 1.5564m

Water Depth given Wave Celerity and Wavelength Formula Elements

Variables

Constants

Functions

Water Depth

Water Depth of the considered catchment is measured from the water level to the bottom of the considered water body.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth

Wavelength

Wavelength can be defined as the distance between two successive crests or troughs of a wave.

Symbol: λ

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Wavelength

Wave Celerity

Wave Celerity is the speed at which an individual wave advances or propagates.

Symbol: C

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Wave Celerity

Wave Period

Wave Period is the time between successive peaks or troughs.

Symbol: T

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Wave Period

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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).

Syntax: tanh(Number)

atanh

The inverse hyperbolic tangent function returns the value whose hyperbolic tangent is a number.

Syntax: atanh(Number)

Other formulas in Wavelength category

Go Wavelength given Wave Celerity

λ = C \cdot T

Go Wavelength given Wave Celerity and Wave Speed

λ = \frac{2 \cdot π \cdot d}{a \tanh (\frac{2 \cdot C \cdot π}{[g] \cdot T})}

Go Wavelength as Function of Depth and Wave Period

λ = (\frac{[g] \cdot T^{2}}{2 \cdot π}) \cdot \tanh (k \cdot d)

Go Deepwater Wavelength given Wave Celerity

λ o = C o \cdot T

How to Evaluate Water Depth given Wave Celerity and Wavelength?

Water Depth given Wave Celerity and Wavelength evaluator uses Water Depth = (Wavelength*atanh((2*pi*Wave Celerity)/([g]*Wave Period)))/(2*pi) to evaluate 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 evaluate Water Depth given Wave Celerity and Wavelength using this online evaluator? To use this online evaluator for Water Depth given Wave Celerity and Wavelength, enter Wavelength (λ), Wave Celerity (C) & Wave Period (T) and hit the calculate button.

FAQs on Water Depth given Wave Celerity and Wavelength

What is the formula to find Water Depth given Wave Celerity and Wavelength?

The formula of Water Depth given Wave Celerity and Wavelength is expressed as Water Depth = (Wavelength*atanh((2*pi*Wave Celerity)/([g]*Wave Period)))/(2*pi). Here is an example- 1.556351 = (10.11*atanh((2*pi*3.5)/([g]*3)))/(2*pi).

How to calculate Water Depth given Wave Celerity and Wavelength?

With Wavelength (λ), Wave Celerity (C) & Wave Period (T) we can find Water Depth given Wave Celerity and Wavelength using the formula - Water Depth = (Wavelength*atanh((2*pi*Wave Celerity)/([g]*Wave Period)))/(2*pi). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and , Hyperbolic Tangent (tanh), Inverse Hyperbolic Tangent (atanh) function(s).

Can the Water Depth given Wave Celerity and Wavelength be negative?

No, the Water Depth given Wave Celerity and Wavelength, measured in Length cannot be negative.

Which unit is used to measure Water Depth given Wave Celerity and Wavelength?

Water Depth given Wave Celerity and Wavelength is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Water Depth given Wave Celerity and Wavelength can be measured.

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Water Depth given Wave Celerity and Wavelength Formula

Water Depth given Wave Celerity and Wavelength Example

Water Depth given Wave Celerity and Wavelength Solution

Water Depth given Wave Celerity and Wavelength Formula Elements

Other formulas in Wavelength category

How to Evaluate Water Depth given Wave Celerity and Wavelength?

FAQs on Water Depth given Wave Celerity and Wavelength

Variable Name