Particle Velocities given Free Surface Elevation of Solitary Waves Calculator

✖Free Surface Elevation refers to the instantaneous vertical displacement of the water surface caused by various factors such as waves, tides, currents, and atmospheric conditions.ⓘ Free Surface Elevation [η]			+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%

✖Particle Velocity refers to the velocity at which water particles move as a result of the passage of waves or currents.ⓘ Particle Velocities given Free Surface Elevation of Solitary Waves [u]

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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]*d_c)*(H_w/d_c)/H_w
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 refers to the velocity at which water particles move as a result of the passage of waves or currents.
Free Surface Elevation - (Measured in Meter) - Free Surface Elevation refers to the instantaneous vertical displacement of the water surface caused by various factors such as waves, tides, currents, and atmospheric conditions.
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.

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]*d_c)*(H_w/d_c)/H_w --> 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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< 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))

Particle Velocities given Free Surface Elevation of Solitary Waves Formula

LaTeX 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
u = η*sqrt([g]*d_c)*(H_w/d_c)/H_w

What is Cnoidal Waves?

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, The Particle Velocities given Free Surface Elevation of Solitary Waves formula is defined as the 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 (d_c) & Height of the Wave (H_w) 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?

The Particle Velocities given Free Surface Elevation of Solitary Waves formula is defined as the 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]*d_c)*(H_w/d_c)/H_w 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 refers to the instantaneous vertical displacement of the water surface caused by various factors such as waves, tides, currents, and atmospheric conditions, 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.

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

The Particle Velocities given Free Surface Elevation of Solitary Waves formula is defined as the 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 (d_c) & Height of the Wave (H_w). 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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