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Wave period for horizontal fluid particle displacements Formula

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Wave Period for Horizontal Fluid Particle is the time it takes for the particle to complete one full oscillation cycle in response to the wave passing through it. Check FAQs

P h = \sqrt{4 \cdot π \cdot λ \cdot \cosh (2 \cdot π \cdot \frac{D}{λ} / H \cdot [g] \cdot \cosh (2 \cdot π \cdot \frac{D Z+d}{λ}) \cdot \sin (θ)) - (ε)}

P_h - Wave Period for Horizontal Fluid Particle?λ - Wavelength?D - Water Depth?H - Wave Height?D_Z+d - Distance above the Bottom?θ - Phase Angle?ε - Fluid Particle Displacements?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Wave period for horizontal fluid particle displacements Example

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Here is how the Wave period for horizontal fluid particle displacements equation looks like with Values.

Here is how the Wave period for horizontal fluid particle displacements equation looks like with Units.

Here is how the Wave period for horizontal fluid particle displacements equation looks like.

20.1876 = \sqrt{4 \cdot 3.1416 \cdot 26.8 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{1.5}{26.8} / 3 \cdot 9.8066 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8}) \cdot \sin (30)) - (0.4)}

20.1876 = \sqrt{4 \cdot 3.1416 \cdot 26.8m \cdot \cosh (2 \cdot 3.1416 \cdot \frac{1.5m}{26.8m} / 3m \cdot 9.8066m/s² \cdot \cosh (2 \cdot 3.1416 \cdot \frac{2m}{26.8m}) \cdot \sin (30°)) - (0.4m)}

20.1876 = \sqrt{4 \cdot 3.1416 \cdot 26.8 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{1.5}{26.8} / 3 \cdot 9.8066 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8}) \cdot \sin (30)) - (0.4)}

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Wave period for horizontal fluid particle displacements Solution

Follow our step by step solution on how to calculate Wave period for horizontal fluid particle displacements?

FIRST Step Consider the formula

P h = \sqrt{4 \cdot π \cdot λ \cdot \cosh (2 \cdot π \cdot \frac{D}{λ} / H \cdot [g] \cdot \cosh (2 \cdot π \cdot \frac{D Z+d}{λ}) \cdot \sin (θ)) - (ε)}

Next Step Substitute values of Variables

∴

P h = \sqrt{4 \cdot π \cdot 26.8m \cdot \cosh (2 \cdot π \cdot \frac{1.5m}{26.8m} / 3m \cdot [g] \cdot \cosh (2 \cdot π \cdot \frac{2m}{26.8m}) \cdot \sin (30°)) - (0.4m)}

Next Step Substitute values of Constants

∴

P h = \sqrt{4 \cdot 3.1416 \cdot 26.8m \cdot \cosh (2 \cdot 3.1416 \cdot \frac{1.5m}{26.8m} / 3m \cdot 9.8066m/s² \cdot \cosh (2 \cdot 3.1416 \cdot \frac{2m}{26.8m}) \cdot \sin (30°)) - (0.4m)}

Next Step Convert Units

∴

P h = \sqrt{4 \cdot 3.1416 \cdot 26.8m \cdot \cosh (2 \cdot 3.1416 \cdot \frac{1.5m}{26.8m} / 3m \cdot 9.8066m/s² \cdot \cosh (2 \cdot 3.1416 \cdot \frac{2m}{26.8m}) \cdot \sin (0.5236rad)) - (0.4m)}

Next Step Prepare to Evaluate

∴

P h = \sqrt{4 \cdot 3.1416 \cdot 26.8 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{1.5}{26.8} / 3 \cdot 9.8066 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8}) \cdot \sin (0.5236)) - (0.4)}

Next Step Evaluate

∴

P h = 20.1875989516397

LAST Step Rounding Answer

∴

P h = 20.1876

Wave period for horizontal fluid particle displacements Formula Elements

Variables

Constants

Functions

Wave Period for Horizontal Fluid Particle

Wave Period for Horizontal Fluid Particle is the time it takes for the particle to complete one full oscillation cycle in response to the wave passing through it.

Symbol: P_h

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wave Period for Horizontal Fluid Particle

Wavelength

Wavelength is the distance between two successive crests or troughs of a wave.

Symbol: λ

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wavelength

Water Depth

Water Depth means the depth as measured from the water level to the bottom of the considered water body.

Symbol: D

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth

Wave Height

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

Symbol: H

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wave Height

Distance above the Bottom

Distance above the Bottom refers to the vertical measurement from the lowest point of a given surface (such as the bottom of waterbody) to a specified point above it.

Symbol: D_Z+d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance above the Bottom

Phase Angle

Phase Angle characteristic of a periodic wave. The angular component periodic wave is known as the phase angle. It is a complex quantity measured by angular units like radians or degrees.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Phase Angle

Fluid Particle Displacements

Fluid Particle Displacements in horizontal and vertical directions.

Symbol: ε

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Fluid Particle Displacements

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

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

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)

cosh

The hyperbolic cosine function is a mathematical function that is defined as the ratio of the sum of the exponential functions of x and negative x to 2.

Syntax: cosh(Number)

Other formulas in Wave Period category

Go Wave Period given Radian Frequency of Wave

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Go Wave Period given Wave Celerity

T = \frac{λ}{C}

How to Evaluate Wave period for horizontal fluid particle displacements?

Wave period for horizontal fluid particle displacements evaluator uses Wave Period for Horizontal Fluid Particle = sqrt(4*pi*Wavelength*cosh(2*pi*Water Depth/(Wavelength)/Wave Height*[g]*cosh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle))-(Fluid Particle Displacements)) to evaluate the Wave Period for Horizontal Fluid Particle, The Wave period for horizontal fluid particle displacements formula is defined as is the time for a particle on a medium to make one complete vibrational cycle. Wave Period for Horizontal Fluid Particle is denoted by P_h symbol.

How to evaluate Wave period for horizontal fluid particle displacements using this online evaluator? To use this online evaluator for Wave period for horizontal fluid particle displacements, enter Wavelength (λ), Water Depth (D), Wave Height (H), Distance above the Bottom (D_Z+d), Phase Angle (θ) & Fluid Particle Displacements (ε) and hit the calculate button.

FAQs on Wave period for horizontal fluid particle displacements

What is the formula to find Wave period for horizontal fluid particle displacements?

The formula of Wave period for horizontal fluid particle displacements is expressed as Wave Period for Horizontal Fluid Particle = sqrt(4*pi*Wavelength*cosh(2*pi*Water Depth/(Wavelength)/Wave Height*[g]*cosh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle))-(Fluid Particle Displacements)). Here is an example- 20.1876 = sqrt(4*pi*26.8*cosh(2*pi*1.5/(26.8)/3*[g]*cosh(2*pi*(2)/26.8)*sin(0.5235987755982))-(0.4)).

How to calculate Wave period for horizontal fluid particle displacements?

With Wavelength (λ), Water Depth (D), Wave Height (H), Distance above the Bottom (D_Z+d), Phase Angle (θ) & Fluid Particle Displacements (ε) we can find Wave period for horizontal fluid particle displacements using the formula - Wave Period for Horizontal Fluid Particle = sqrt(4*pi*Wavelength*cosh(2*pi*Water Depth/(Wavelength)/Wave Height*[g]*cosh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle))-(Fluid Particle Displacements)). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and , Sine (sin), Square Root (sqrt), Hyperbolic Cosine (cosh) function(s).

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Wave period for horizontal fluid particle displacements Formula

Wave period for horizontal fluid particle displacements Example

Wave period for horizontal fluid particle displacements Solution

Wave period for horizontal fluid particle displacements Formula Elements

Other formulas in Wave Period category

How to Evaluate Wave period for horizontal fluid particle displacements?

FAQs on Wave period for horizontal fluid particle displacements

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