Complete Elliptic Integral of Second Kind Calculator

✖Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.ⓘ Distance from the Bottom to the Wave Trough [y_t]			+10% -10%
✖Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.ⓘ Water Depth for Cnoidal Wave [d_c]			+10% -10%
✖Height of the Wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Height of the Wave [H_w]			+10% -10%
✖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.ⓘ Wavelength of Wave [λ]			+10% -10%
✖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.ⓘ Complete Elliptic Integral of the First Kind [K_k]			+10% -10%

✖Complete Elliptic Integral of the Second Kind influencing the wavelength and the distance from bottom to wave trough.ⓘ Complete Elliptic Integral of Second Kind [E_k]

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Complete Elliptic Integral of Second Kind Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
E_k = -((((y_t/d_c)+(H_w/d_c)-1)*(3*λ^2)/((16*d_c^2)*K_k))-K_k)
This formula uses 6 Variables

Variables Used

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.
Distance from the Bottom to the Wave Trough - (Measured in Meter) - Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.
Water Depth for Cnoidal Wave - (Measured in Meter) - Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.
Height of the Wave - (Measured in Meter) - Height of the Wave is the difference between the elevations of a crest and a neighboring trough.
Wavelength of Wave - (Measured in Meter) - 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.
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.

STEP 1: Convert Input(s) to Base Unit

Distance from the Bottom to the Wave Trough: 21 Meter --> 21 Meter No Conversion Required
Water Depth for Cnoidal Wave: 16 Meter --> 16 Meter No Conversion Required
Height of the Wave: 14 Meter --> 14 Meter No Conversion Required
Wavelength of Wave: 32 Meter --> 32 Meter No Conversion Required
Complete Elliptic Integral of the First Kind: 28 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_k = -((((y_t/d_c)+(H_w/d_c)-1)*(3*λ^2)/((16*d_c^2)*K_k))-K_k) --> -((((21/16)+(14/16)-1)*(3*32^2)/((16*16^2)*28))-28)

Evaluating ... ...

E_k = 27.9681919642857

STEP 3: Convert Result to Output's Unit

27.9681919642857 --> No Conversion Required

FINAL ANSWER

27.9681919642857 ≈ 27.96819 <-- Complete Elliptic Integral of the Second Kind

(Calculation completed in 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< Cnoidal Wave Theory Calculators

Complete Elliptic Integral of Second Kind

LaTeX Go 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)

Distance from Bottom to Wave Trough

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

Distance from Bottom to Crest

LaTeX Go 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)+(Height of the Wave/Water Depth for Cnoidal Wave))

Trough to Crest Wave Height

LaTeX Go 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))

Complete Elliptic Integral of Second Kind Formula

LaTeX Go

What Causes Waves?

Waves are most commonly caused by wind. Wind-driven waves, or surface waves, are created by the friction between wind and surface water. As wind blows across the surface of the ocean or a lake, the continual disturbance creates a wave crest. The gravitational pull of the sun and moon on the earth also causes waves.

How to Calculate Complete Elliptic Integral of Second Kind?

Complete Elliptic Integral of Second Kind calculator 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 calculate 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 calculate Complete Elliptic Integral of Second Kind using this online calculator? To use this online calculator 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. Here is how the Complete Elliptic Integral of Second Kind calculation can be explained with given input values -> 27.96819 = -((((21/16)+(14/16)-1)*(3*32^2)/((16*16^2)*28))-28).

FAQ

What is Complete Elliptic Integral of 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 and is represented as E_k = -((((y_t/d_c)+(H_w/d_c)-1)*(3*λ^2)/((16*d_c^2)*K_k))-K_k) or 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). Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave, Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating, Height of the Wave is the difference between the elevations of a crest and a neighboring trough, 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 & 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.

How to calculate Complete Elliptic Integral of 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 is calculated using 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 calculate Complete Elliptic Integral of Second Kind, you need 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). With our tool, you need to enter the respective value for Distance from the Bottom to the Wave Trough, Water Depth for Cnoidal Wave, Height of the Wave, Wavelength of Wave & Complete Elliptic Integral of the First Kind 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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