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Wave Height given Distance from Bottom to Wave Trough and Water Depth Formula

GoTrough to Crest Wave Height Formula

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Height of the Wave is the difference between the elevations of a crest and a neighboring trough. Check FAQs

H w = - d c \cdot ((\frac{y t}{d c}) - 1 - ((16 \cdot \frac{{d c}^{2}}{3 \cdot λ^{2}}) \cdot K k \cdot (K k - E k)))

H_w - Height of the Wave?d_c - Water Depth for Cnoidal Wave?y_t - Distance from the Bottom to the Wave Trough?λ - Wavelength of Wave?K_k - Complete Elliptic Integral of the First Kind?E_k - Complete Elliptic Integral of the Second Kind?

Wave Height given Distance from Bottom to Wave Trough and Water Depth Example

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Here is how the Wave Height given Distance from Bottom to Wave Trough and Water Depth equation looks like with Values.

Here is how the Wave Height given Distance from Bottom to Wave Trough and Water Depth equation looks like with Units.

Here is how the Wave Height given Distance from Bottom to Wave Trough and Water Depth equation looks like.

14.1147 = - 16 \cdot ((\frac{21}{16}) - 1 - ((16 \cdot \frac{16^{2}}{3 \cdot 32^{2}}) \cdot 28 \cdot (28 - 27.968)))

14.1147m = - 16m \cdot ((\frac{21m}{16m}) - 1 - ((16 \cdot \frac{{16m}^{2}}{3 \cdot {32m}^{2}}) \cdot 28 \cdot (28 - 27.968)))

14.1147 = - 16 \cdot ((\frac{21}{16}) - 1 - ((16 \cdot \frac{16^{2}}{3 \cdot 32^{2}}) \cdot 28 \cdot (28 - 27.968)))

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Wave Height given Distance from Bottom to Wave Trough and Water Depth Solution

Follow our step by step solution on how to calculate Wave Height given Distance from Bottom to Wave Trough and Water Depth?

FIRST Step Consider the formula

H w = - d c \cdot ((\frac{y t}{d c}) - 1 - ((16 \cdot \frac{{d c}^{2}}{3 \cdot λ^{2}}) \cdot K k \cdot (K k - E k)))

Next Step Substitute values of Variables

∴

H w = - 16m \cdot ((\frac{21m}{16m}) - 1 - ((16 \cdot \frac{{16m}^{2}}{3 \cdot {32m}^{2}}) \cdot 28 \cdot (28 - 27.968)))

Next Step Prepare to Evaluate

∴

H w = - 16 \cdot ((\frac{21}{16}) - 1 - ((16 \cdot \frac{16^{2}}{3 \cdot 32^{2}}) \cdot 28 \cdot (28 - 27.968)))

Next Step Evaluate

∴

H w = 14.1146666666667m

LAST Step Rounding Answer

∴

H w = 14.1147m

Wave Height given Distance from Bottom to Wave Trough and Water Depth Formula Elements

Variables

Height of the Wave

Height of the Wave is the difference between the elevations of a crest and a neighboring trough.

Symbol: H_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Height of the Wave

Water Depth for Cnoidal Wave

Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.

Symbol: d_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth for Cnoidal Wave

Distance from the Bottom to the Wave Trough

Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.

Symbol: y_t

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance from the Bottom to the Wave Trough

Wavelength of Wave

Wavelength of Wave refers to the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings.

Symbol: λ

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wavelength of Wave

Complete Elliptic Integral of the First Kind

Complete Elliptic Integral of the First Kind is a mathematical tool that finds applications in coastal and ocean engineering, particularly in wave theory and harmonic analysis of wave data.

Symbol: K_k

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Complete Elliptic Integral of the First Kind

Complete Elliptic Integral of the Second Kind

Complete Elliptic Integral of the Second Kind influencing the wavelength and the distance from bottom to wave trough.

Symbol: E_k

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Complete Elliptic Integral of the Second Kind

Other Formulas to find Height of the Wave

Go Trough to Crest Wave Height

H w = d c \cdot ((\frac{y c}{d c}) - (\frac{y t}{d c}))

Other formulas in Cnoidal Wave Theory category

Go Distance from Bottom to Wave Trough

y t = d c \cdot ((\frac{y c}{d c}) - (\frac{H w}{d c}))

Go Distance from Bottom to Crest

y c = d c \cdot ((\frac{y t}{d c}) + (\frac{H w}{d c}))

Go Complete Elliptic Integral of Second Kind

E k = - ((((\frac{y t}{d c}) + (\frac{H w}{d c}) - 1) \cdot \frac{3 \cdot λ^{2}}{(16 \cdot {d c}^{2}) \cdot K k}) - K k)

Go Wavelength for Distance from Bottom to Wave Trough

λ = \sqrt{\frac{16 \cdot {d c}^{2} \cdot K k \cdot (K k - E k)}{3 \cdot ((\frac{y t}{d c}) + (\frac{H w}{d c}) - 1)}}

How to Evaluate Wave Height given Distance from Bottom to Wave Trough and Water Depth?

Wave Height given Distance from Bottom to Wave Trough and Water Depth evaluator uses Height of the Wave = -Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)-1-((16*Water Depth for Cnoidal Wave^2/(3*Wavelength of Wave^2))*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind))) to evaluate the Height of the Wave, The Wave Height given Distance from Bottom to Wave Trough and Water Depth formula is defined as the difference between elevations of the crest and neighboring trough. Wave height is a term used by mariners, as well as in coastal, ocean, and naval engineering. Height of the Wave is denoted by H_w symbol.

How to evaluate Wave Height given Distance from Bottom to Wave Trough and Water Depth using this online evaluator? To use this online evaluator for Wave Height given Distance from Bottom to Wave Trough and Water Depth, enter Water Depth for Cnoidal Wave (d_c), Distance from the Bottom to the Wave Trough (y_t), Wavelength of Wave (λ), Complete Elliptic Integral of the First Kind (K_k) & Complete Elliptic Integral of the Second Kind (E_k) and hit the calculate button.

FAQs on Wave Height given Distance from Bottom to Wave Trough and Water Depth

What is the formula to find Wave Height given Distance from Bottom to Wave Trough and Water Depth?

The formula of Wave Height given Distance from Bottom to Wave Trough and Water Depth is expressed as Height of the Wave = -Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)-1-((16*Water Depth for Cnoidal Wave^2/(3*Wavelength of Wave^2))*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind))). Here is an example- 14.11467 = -16*((21/16)-1-((16*16^2/(3*32^2))*28*(28-27.968))).

How to calculate Wave Height given Distance from Bottom to Wave Trough and Water Depth?

With Water Depth for Cnoidal Wave (d_c), Distance from the Bottom to the Wave Trough (y_t), Wavelength of Wave (λ), Complete Elliptic Integral of the First Kind (K_k) & Complete Elliptic Integral of the Second Kind (E_k) we can find Wave Height given Distance from Bottom to Wave Trough and Water Depth using the formula - Height of the Wave = -Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)-1-((16*Water Depth for Cnoidal Wave^2/(3*Wavelength of Wave^2))*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind))).

What are the other ways to Calculate Height of the Wave?

Here are the different ways to Calculate Height of the Wave-

Height of the Wave=Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave))

Can the Wave Height given Distance from Bottom to Wave Trough and Water Depth be negative?

Yes, the Wave Height given Distance from Bottom to Wave Trough and Water Depth, measured in Length can be negative.

Which unit is used to measure Wave Height given Distance from Bottom to Wave Trough and Water Depth?

Wave Height given Distance from Bottom to Wave Trough and Water Depth is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Wave Height given Distance from Bottom to Wave Trough and Water Depth can be measured.

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Wave Height given Distance from Bottom to Wave Trough and Water Depth Formula

​GoTrough to Crest Wave Height Formula

Wave Height given Distance from Bottom to Wave Trough and Water Depth Example

Wave Height given Distance from Bottom to Wave Trough and Water Depth Solution

Wave Height given Distance from Bottom to Wave Trough and Water Depth Formula Elements

Other Formulas to find Height of the Wave

Other formulas in Cnoidal Wave Theory category

How to Evaluate Wave Height given Distance from Bottom to Wave Trough and Water Depth?

FAQs on Wave Height given Distance from Bottom to Wave Trough and Water Depth

Variable Name

GoTrough to Crest Wave Height Formula