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Particle Velocities given Free Surface Elevation of Solitary Waves Formula

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Particle Velocity refers to the velocity at which water particles move as a result of the passage of waves or currents. Check FAQs

u = η \cdot \sqrt{[g] \cdot d c} \cdot \frac{\frac{H w}{d c}}{H w}

u - Particle Velocity?η - Free Surface Elevation?d_c - Water Depth for Cnoidal Wave?H_w - Height of the Wave?[g] - Gravitational acceleration on Earth?

Particle Velocities given Free Surface Elevation of Solitary Waves Example

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Here is how the Particle Velocities given Free Surface Elevation of Solitary Waves equation looks like with Values.

Here is how the Particle Velocities given Free Surface Elevation of Solitary Waves equation looks like with Units.

Here is how the Particle Velocities given Free Surface Elevation of Solitary Waves equation looks like.

19.995 = 25.54 \cdot \sqrt{9.8066 \cdot 16} \cdot \frac{\frac{14}{16}}{14}

19.995m/s = 25.54m \cdot \sqrt{9.8066m/s² \cdot 16m} \cdot \frac{\frac{14m}{16m}}{14m}

19.995 = 25.54 \cdot \sqrt{9.8066 \cdot 16} \cdot \frac{\frac{14}{16}}{14}

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Particle Velocities given Free Surface Elevation of Solitary Waves Solution

Follow our step by step solution on how to calculate Particle Velocities given Free Surface Elevation of Solitary Waves?

FIRST Step Consider the formula

u = η \cdot \sqrt{[g] \cdot d c} \cdot \frac{\frac{H w}{d c}}{H w}

Next Step Substitute values of Variables

∴

u = 25.54m \cdot \sqrt{[g] \cdot 16m} \cdot \frac{\frac{14m}{16m}}{14m}

Next Step Substitute values of Constants

∴

u = 25.54m \cdot \sqrt{9.8066m/s² \cdot 16m} \cdot \frac{\frac{14m}{16m}}{14m}

Next Step Prepare to Evaluate

∴

u = 25.54 \cdot \sqrt{9.8066 \cdot 16} \cdot \frac{\frac{14}{16}}{14}

Next Step Evaluate

∴

u = 19.9949922154586m/s

LAST Step Rounding Answer

∴

u = 19.995m/s

Particle Velocities given Free Surface Elevation of Solitary Waves Formula Elements

Variables

Constants

Functions

Particle Velocity

Particle Velocity refers to the velocity at which water particles move as a result of the passage of waves or currents.

Symbol: u

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Particle Velocity

Free Surface Elevation

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.

Symbol: η

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Free Surface Elevation

Water Depth for Cnoidal Wave

Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.

Symbol: d_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth for Cnoidal Wave

Height of the Wave

Height of the Wave is the difference between the elevations of a crest and a neighboring trough.

Symbol: H_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Height of the Wave

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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.

Syntax: sqrt(Number)

Other formulas in Cnoidal Wave Theory category

Go Distance from Bottom to Wave Trough

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

Go Distance from Bottom to Crest

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

Go Trough to Crest Wave Height

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

Go Complete Elliptic Integral of Second Kind

E k = - ((((\frac{y t}{d c}) + (\frac{H w}{d c}) - 1) \cdot \frac{3 \cdot λ^{2}}{(16 \cdot {d c}^{2}) \cdot K k}) - K k)

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

Particle Velocities given Free Surface Elevation of Solitary Waves evaluator 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 evaluate 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 evaluate Particle Velocities given Free Surface Elevation of Solitary Waves using this online evaluator? To use this online evaluator 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.

FAQs on Particle Velocities given Free Surface Elevation of Solitary Waves

What is the formula to find Particle Velocities given Free Surface Elevation of Solitary Waves?

The formula of Particle Velocities given Free Surface Elevation of Solitary Waves is expressed as 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. Here is an example- 19.99499 = 25.54*sqrt([g]*16)*(14/16)/14.

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

With Free Surface Elevation (η), Water Depth for Cnoidal Wave (d_c) & Height of the Wave (H_w) we can find Particle Velocities given Free Surface Elevation of Solitary Waves using the 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. This formula also uses Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

Can the Particle Velocities given Free Surface Elevation of Solitary Waves be negative?

Yes, the Particle Velocities given Free Surface Elevation of Solitary Waves, measured in Speed can be negative.

Which unit is used to measure Particle Velocities given Free Surface Elevation of Solitary Waves?

Particle Velocities given Free Surface Elevation of Solitary Waves is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Particle Velocities given Free Surface Elevation of Solitary Waves can be measured.

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Particle Velocities given Free Surface Elevation of Solitary Waves Formula

Particle Velocities given Free Surface Elevation of Solitary Waves Example

Particle Velocities given Free Surface Elevation of Solitary Waves Solution

Particle Velocities given Free Surface Elevation of Solitary Waves Formula Elements

Other formulas in Cnoidal Wave Theory category

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

FAQs on Particle Velocities given Free Surface Elevation of Solitary Waves

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