Particle Velocities given Free Surface Elevation of Solitary Waves Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
u = η*sqrt([g]*dc)*(Hw/dc)/Hw
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Particle Velocity - (Measured in Meter per Second) - Particle Velocity of Solitary Wave Profile.
Free Surface Elevation - (Measured in Meter) - Free Surface Elevation of Solitary Waves.
Water Depth for Cnoidal Wave - (Measured in Meter) - Water Depth for Cnoidal Wave is the y depth from bed under cnoidal 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
Free Surface Elevation: 25.54 Meter --> 25.54 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
STEP 2: Evaluate Formula
Substituting Input Values in Formula
u = η*sqrt([g]*dc)*(Hw/dc)/Hw --> 25.54*sqrt([g]*16)*(14/16)/14
Evaluating ... ...
u = 19.9949922154586
STEP 3: Convert Result to Output's Unit
19.9949922154586 Meter per Second --> No Conversion Required
FINAL ANSWER
19.9949922154586 19.99499 Meter per Second <-- Particle Velocity
(Calculation completed in 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg
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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)

Particle Velocities given Free Surface Elevation of Solitary Waves Formula

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
u = η*sqrt([g]*dc)*(Hw/dc)/Hw

What is Cnoidal wave?

In fluid dynamics, a cnoidal wave is a nonlinear and exact periodic wave solution of the Korteweg–de Vries equation. These solutions are in terms of the Jacobi elliptic function cn, which is why they are coined cnoidal waves.

How to Calculate Particle Velocities given Free Surface Elevation of Solitary Waves?

Particle Velocities given Free Surface Elevation of Solitary Waves calculator uses 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 to calculate the Particle Velocity, Particle Velocities given Free Surface Elevation of Solitary Waves formula is velocity of particle (real or imagined) in medium as it transmits wave. SI unit of particle velocity is meter per second (m/s). Particle Velocity is denoted by u symbol.

How to calculate Particle Velocities given Free Surface Elevation of Solitary Waves using this online calculator? To use this online calculator for Particle Velocities given Free Surface Elevation of Solitary Waves, enter Free Surface Elevation (η), Water Depth for Cnoidal Wave (dc) & Height of The Wave (Hw) and hit the calculate button. Here is how the Particle Velocities given Free Surface Elevation of Solitary Waves calculation can be explained with given input values -> 19.99499 = 25.54*sqrt([g]*16)*(14/16)/14.

FAQ

What is Particle Velocities given Free Surface Elevation of Solitary Waves?
Particle Velocities given Free Surface Elevation of Solitary Waves formula is velocity of particle (real or imagined) in medium as it transmits wave. SI unit of particle velocity is meter per second (m/s) and is represented as u = η*sqrt([g]*dc)*(Hw/dc)/Hw or 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. Free Surface Elevation of Solitary Waves, Water Depth for Cnoidal Wave is the y depth from bed under cnoidal wave & Height of The Wave is the difference between the elevations of a crest and a neighboring trough.
How to calculate Particle Velocities given Free Surface Elevation of Solitary Waves?
Particle Velocities given Free Surface Elevation of Solitary Waves formula is velocity of particle (real or imagined) in medium as it transmits wave. SI unit of particle velocity is meter per second (m/s) is calculated using 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. To calculate Particle Velocities given Free Surface Elevation of Solitary Waves, you need Free Surface Elevation (η), Water Depth for Cnoidal Wave (dc) & Height of The Wave (Hw). With our tool, you need to enter the respective value for Free Surface Elevation, Water Depth for Cnoidal Wave & 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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