Distance from Bottom to Wave Trough Calculator

✖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%
✖Distance from the Bottom to the Crest is defined as the total stretch from the bottom to the crest of the wave.ⓘ Distance from the Bottom to the Crest [y_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%

✖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 Bottom to Wave Trough [y_t]

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Formula

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Distance from Bottom to Wave Trough

Formula

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

Example

21 m = 16 m \cdot ((\frac{35 m}{16 m}) - (\frac{14 m}{16 m}))

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Distance from Bottom to Wave Trough Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
y_t = d_c*((y_c/d_c)-(H_w/d_c))
This formula uses 4 Variables

Variables Used

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.
Distance from the Bottom to the Crest - (Measured in Meter) - Distance from the Bottom to the Crest is defined as the total stretch from the bottom to the crest of the wave.
Height of the Wave - (Measured in Meter) - Height of the Wave is the difference between the elevations of a crest and a neighboring trough.

STEP 1: Convert Input(s) to Base Unit

Water Depth for Cnoidal Wave: 16 Meter --> 16 Meter No Conversion Required
Distance from the Bottom to the Crest: 35 Meter --> 35 Meter No Conversion Required
Height of the Wave: 14 Meter --> 14 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y_t = d_c*((y_c/d_c)-(H_w/d_c)) --> 16*((35/16)-(14/16))

Evaluating ... ...

y_t = 21

STEP 3: Convert Result to Output's Unit

21 Meter --> No Conversion Required

FINAL ANSWER

21 Meter <-- Distance from the Bottom to the Wave Trough

(Calculation completed in 00.004 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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National Institute of Technology (NIT), Warangal

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< Cnoidal Wave Theory Calculators

Complete Elliptic Integral of Second Kind

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

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

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

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))

Distance from Bottom to Wave Trough Formula

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 Distance from Bottom to Wave Trough?

Distance from Bottom to Wave Trough calculator uses 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)) to calculate the Distance from the Bottom to the Wave Trough, The Distance from Bottom to Wave Trough formula is defined as the total stretch from bottom to trough of wave. Distance from the Bottom to the Wave Trough is denoted by y_t symbol.

How to calculate Distance from Bottom to Wave Trough using this online calculator? To use this online calculator for Distance from Bottom to Wave Trough, enter Water Depth for Cnoidal Wave (d_c), Distance from the Bottom to the Crest (y_c) & Height of the Wave (H_w) and hit the calculate button. Here is how the Distance from Bottom to Wave Trough calculation can be explained with given input values -> 21 = 16*((35/16)-(14/16)).

FAQ

What is Distance from Bottom to Wave Trough?

The Distance from Bottom to Wave Trough formula is defined as the total stretch from bottom to trough of wave and is represented as y_t = d_c*((y_c/d_c)-(H_w/d_c)) or 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)). Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating, Distance from the Bottom to the Crest is defined as the total stretch from the bottom to the crest of the wave & Height of the Wave is the difference between the elevations of a crest and a neighboring trough.

How to calculate Distance from Bottom to Wave Trough?

The Distance from Bottom to Wave Trough formula is defined as the total stretch from bottom to trough of wave is calculated using 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)). To calculate Distance from Bottom to Wave Trough, you need Water Depth for Cnoidal Wave (d_c), Distance from the Bottom to the Crest (y_c) & Height of the Wave (H_w). With our tool, you need to enter the respective value for Water Depth for Cnoidal Wave, Distance from the Bottom to the Crest & Height of the 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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