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Complete Elliptic Integral of Second Kind Formula

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

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)

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

Complete Elliptic Integral of Second Kind Example

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Here is how the Complete Elliptic Integral of Second Kind equation looks like with Values.

Here is how the Complete Elliptic Integral of Second Kind equation looks like with Units.

Here is how the Complete Elliptic Integral of Second Kind equation looks like.

27.9682 = - ((((\frac{21}{16}) + (\frac{14}{16}) - 1) \cdot \frac{3 \cdot 32^{2}}{(16 \cdot 16^{2}) \cdot 28}) - 28)

27.9682 = - ((((\frac{21m}{16m}) + (\frac{14m}{16m}) - 1) \cdot \frac{3 \cdot {32m}^{2}}{(16 \cdot {16m}^{2}) \cdot 28}) - 28)

27.9682 = - ((((\frac{21}{16}) + (\frac{14}{16}) - 1) \cdot \frac{3 \cdot 32^{2}}{(16 \cdot 16^{2}) \cdot 28}) - 28)

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Complete Elliptic Integral of Second Kind Solution

Follow our step by step solution on how to calculate Complete Elliptic Integral of Second Kind?

FIRST Step Consider the formula

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)

Next Step Substitute values of Variables

∴

E k = - ((((\frac{21m}{16m}) + (\frac{14m}{16m}) - 1) \cdot \frac{3 \cdot {32m}^{2}}{(16 \cdot {16m}^{2}) \cdot 28}) - 28)

Next Step Prepare to Evaluate

∴

E k = - ((((\frac{21}{16}) + (\frac{14}{16}) - 1) \cdot \frac{3 \cdot 32^{2}}{(16 \cdot 16^{2}) \cdot 28}) - 28)

Next Step Evaluate

∴

E k = 27.9681919642857

LAST Step Rounding Answer

∴

E k = 27.9682

Complete Elliptic Integral of Second Kind Formula Elements

Variables

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

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

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

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

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

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 Trough to Crest Wave Height

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

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 Complete Elliptic Integral of Second Kind?

Complete Elliptic Integral of Second Kind evaluator uses Complete Elliptic Integral of the Second Kind = -((((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of the Wave/Water Depth for Cnoidal Wave)-1)*(3*Wavelength of Wave^2)/((16*Water Depth for Cnoidal Wave^2)*Complete Elliptic Integral of the First Kind))-Complete Elliptic Integral of the First Kind) to evaluate the Complete Elliptic Integral of the Second Kind, The Complete Elliptic Integral of Second Kind formula is defined as the parameter influencing the wave periodic function with maximum amplitude equal to unity, distance from the bottom to the crest etc. Complete Elliptic Integral of the Second Kind is denoted by E_k symbol.

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

FAQs on Complete Elliptic Integral of Second Kind

What is the formula to find Complete Elliptic Integral of Second Kind?

The formula of Complete Elliptic Integral of Second Kind is expressed as Complete Elliptic Integral of the Second Kind = -((((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of the Wave/Water Depth for Cnoidal Wave)-1)*(3*Wavelength of Wave^2)/((16*Water Depth for Cnoidal Wave^2)*Complete Elliptic Integral of the First Kind))-Complete Elliptic Integral of the First Kind). Here is an example- 27.96819 = -((((21/16)+(14/16)-1)*(3*32^2)/((16*16^2)*28))-28).

How to calculate Complete Elliptic Integral of Second Kind?

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

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Complete Elliptic Integral of Second Kind Formula

Complete Elliptic Integral of Second Kind Example

Complete Elliptic Integral of Second Kind Solution

Complete Elliptic Integral of Second Kind Formula Elements

Other formulas in Cnoidal Wave Theory category

How to Evaluate Complete Elliptic Integral of Second Kind?

FAQs on Complete Elliptic Integral of Second Kind

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