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))
yt = dc*((yc/dc)-(Hw/dc))
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 is the y depth from bed under cnoidal wave.
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
yt = dc*((yc/dc)-(Hw/dc)) --> 16*((35/16)-(14/16))
Evaluating ... ...
yt = 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)

Credits

Created by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
Mithila Muthamma PA has created this Calculator and 2000+ more calculators!
Verified by M Naveen
National Institute of Technology (NIT), Warangal
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14 Cnoidal Wave Theory Calculators

Wavelength for Distance from Bottom to Wave Trough
Go Wavelength of Wave = sqrt((16*Water Depth for Cnoidal Wave^2*Complete Elliptic Integral of the first kind*(Complete Elliptic Integral of the first kind-Complete Elliptic Integral of the Second Kind))/(3*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of The Wave/Water Depth for Cnoidal Wave)-1)))
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)
Wave Height given Distance from Bottom to Wave Trough and Water Depth
Go 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)))
Wave Height Required to Produce Difference in Pressure on Seabed
Go Height of The Wave = Change in Pressure/((Density of Salt Water*[g])*(0.5+(0.5*sqrt(1-((3*Change in Pressure)/(Density of Salt Water*[g]*Water Depth for Cnoidal Wave))))))
Free Surface Elevation of Solitary Waves
Go Free Surface Elevation = Height of The Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave)))
Particle Velocities given Free Surface Elevation of Solitary Waves
Go Particle Velocity = Free Surface Elevation*sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave)/Height of The Wave
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))
Wave Height when Free Surface Elevation of Solitary Waves
Go Height of The Wave = Free Surface Elevation*sqrt([g]*Water Depth for Cnoidal Wave)/(Particle Velocity*Water Depth for Cnoidal Wave)
Wavelength for Complete Elliptic Integral of First Kind
Go Wavelength of Wave = sqrt(16*Water Depth for Cnoidal Wave^3/(3*Height of The Wave))*Modulus of the Elliptic Integrals*Complete Elliptic Integral of the first kind
Elevation above Bottom given Pressure under Cnoidal Wave in Hydrostatic Form
Go Any Elevation above the Bottom = -((Pressure under A Wave/(Density of Salt Water*[g]))-Ordinate of the Water Surface)
Ordinate of Water Surface given Pressure under Cnoidal Wave in Hydrostatic Form
Go Ordinate of the Water Surface = (Pressure under A Wave/(Density of Salt Water*[g]))+Any Elevation above the Bottom
Pressure under Cnoidal Wave in Hydrostatic Form
Go Pressure under A Wave = Density of Salt Water*[g]*(Ordinate of the Water Surface-Any Elevation above the Bottom)

Distance from Bottom to Wave Trough Formula

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))
yt = dc*((yc/dc)-(Hw/dc))

What causes wave?

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 is defined as total stretch from bottom to trough of wave. Distance from the Bottom to the Wave Trough is denoted by yt 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 (dc), Distance from the Bottom to the Crest (yc) & Height of The Wave (Hw) 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 is defined as total stretch from bottom to trough of wave and is represented as yt = dc*((yc/dc)-(Hw/dc)) 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 is the y depth from bed under cnoidal wave, 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 is defined as 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 (dc), Distance from the Bottom to the Crest (yc) & Height of The Wave (Hw). 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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