Wave period for horizontal fluid particle displacements Calculator

✖Wavelength is the distance between two successive crests or troughs of a wave.ⓘ Wavelength [λ]			+10% -10%
✖Water Depth means the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [D]			+10% -10%
✖Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Wave Height [H]			+10% -10%
✖Distance above the Bottom expressing the local fluid velocity component.ⓘ Distance above the Bottom [D_Z+d]			+10% -10%
✖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.ⓘ Phase Angle [θ]			+10% -10%
✖Fluid Particle Displacements in horizontal and vertical directions.ⓘ Fluid Particle Displacements [ε]			+10% -10%

✖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.ⓘ Wave period for horizontal fluid particle displacements [P_h]

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Wave period for horizontal fluid particle displacements

Formula

`"P"_{"h"} = sqrt(4*pi*"λ"*cosh(2*pi*"D"/("λ")/"H"*"[g]"*cosh(2*pi*("D"_{"Z+d"})/"λ")*sin("θ"))-("ε"))`

Example

`"20.1876"=sqrt(4*pi*"26.8m"*cosh(2*pi*"1.5m"/("26.8m")/"3m"*"[g]"*cosh(2*pi*("2m")/"26.8m")*sin("30°"))-("0.4m"))`

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Wave period for horizontal fluid particle displacements Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
P_h = sqrt(4*pi*λ*cosh(2*pi*D/(λ)/H*[g]*cosh(2*pi*(D_Z+d)/λ)*sin(θ))-(ε))
This formula uses 2 Constants, 3 Functions, 7 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., 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., 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., cosh(Number)

Variables Used

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.
Wavelength - (Measured in Meter) - Wavelength is the distance between two successive crests or troughs of a wave.
Water Depth - (Measured in Meter) - Water Depth means the depth as measured from the water level to the bottom of the considered water body.
Wave Height - (Measured in Meter) - Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.
Distance above the Bottom - (Measured in Meter) - Distance above the Bottom expressing the local fluid velocity component.
Phase Angle - (Measured in Radian) - 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.
Fluid Particle Displacements - (Measured in Meter) - Fluid Particle Displacements in horizontal and vertical directions.

STEP 1: Convert Input(s) to Base Unit

Wavelength: 26.8 Meter --> 26.8 Meter No Conversion Required
Water Depth: 1.5 Meter --> 1.5 Meter No Conversion Required
Wave Height: 3 Meter --> 3 Meter No Conversion Required
Distance above the Bottom: 2 Meter --> 2 Meter No Conversion Required
Phase Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Fluid Particle Displacements: 0.4 Meter --> 0.4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_h = sqrt(4*pi*λ*cosh(2*pi*D/(λ)/H*[g]*cosh(2*pi*(D_Z+d)/λ)*sin(θ))-(ε)) --> 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))

Evaluating ... ...

P_h = 20.1875989516397

STEP 3: Convert Result to Output's Unit

20.1875989516397 --> No Conversion Required

FINAL ANSWER

20.1875989516397 ≈ 20.1876 <-- Wave Period for Horizontal Fluid Particle

(Calculation completed in 00.020 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< 16 Wave Period Calculators

Wave period for horizontal fluid particle displacements

Go 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))

Wave Period given Wavelength and Water Depth

Go Wave Period = 2*pi/((2*pi*[g]/Wavelength)*tanh(2*pi*Water Depth/Wavelength))^0.5

Wave Period given Wave Celerity and Wavelength

Go Coastal Wave Period = (Celerity of the Wave*2*pi)/([g]*tanh(2*pi*Water Depth/Wavelength))

Wave period given wave depth and wavelength

Go Wave Period = (Wavelength*Wave Angular Frequency)/[g]*tanh(Wave Number*Water Depth)

Wave Period for Known Deepwater Celerity

Go Coastal Wave Period = (Celerity of the Wave*2*pi)/[g]

Wave Period given Deepwater Wavelength of SI Systems Units of Meters and Seconds

Go Period of Wave = sqrt(Deep-Water Wavelength/1.56)

Wave Period given Deepwater Wavelength of Units of Meters and Seconds

Go Period of Wave = sqrt(Deep-Water Wavelength/5.12)

Wave Period given Radian Frequency of Wave

Go Period of Wave = (2*pi)/Wave Angular Frequency

Wave Period given Wave Celerity

Go Period of Wave = Wavelength/Celerity of the Wave

Wave Period for North Sea

Go Wave Period in North Sea = 3.94*Significant Wave Height^0.376

Wave Period given Deepwater Celerity of SI systems Units of Meters and Seconds

Go Coastal Wave Period = Celerity of the Wave/1.56

Wave Period for Mediterranean Sea

Go Coastal Wave Period = 4+2*(Wave Height)^0.7

Wave Period given Deepwater Celerity of Units of Meters and Seconds

Go Period of Wave = Celerity of the Wave/5.12

Average Period for Wave Period of Same Energy as Irregular Train

Go Average Time = Coastal Wave Period/1.23

Wave Period of same Energy

Go Coastal Wave Period = 1.23*Average Time

Wave Period for North Atlantic Ocean

Go Coastal Wave Period = 2.5*Wave Height

Wave period for horizontal fluid particle displacements Formula

How does depth affect wavelength?

The change from deep to shallow water waves occurs when the depth of the water, d, becomes less than one half of the wavelength of the wave, λ. The speed of deep-water waves depends on the wavelength of the waves. We say that deep-water waves show dispersion. A wave with a longer wavelength travels at higher speed.

How to Calculate Wave period for horizontal fluid particle displacements?

Wave period for horizontal fluid particle displacements calculator 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 calculate 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 calculate Wave period for horizontal fluid particle displacements using this online calculator? To use this online calculator 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. Here is how the Wave period for horizontal fluid particle displacements calculation can be explained with given input values -> 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)).

FAQ

What is Wave period for horizontal fluid particle displacements?

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 and is represented as P_h = sqrt(4*pi*λ*cosh(2*pi*D/(λ)/H*[g]*cosh(2*pi*(D_Z+d)/λ)*sin(θ))-(ε)) or 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)). Wavelength is the distance between two successive crests or troughs of a wave, Water Depth means the depth as measured from the water level to the bottom of the considered water body, Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough, Distance above the Bottom expressing the local fluid velocity component, 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 & Fluid Particle Displacements in horizontal and vertical directions.

How to calculate Wave period for horizontal fluid particle displacements?

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 is calculated using 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 calculate Wave period for horizontal fluid particle displacements, you need Wavelength (λ), Water Depth (D), Wave Height (H), Distance above the Bottom (D_Z+d), Phase Angle (θ) & Fluid Particle Displacements (ε). With our tool, you need to enter the respective value for Wavelength, Water Depth, Wave Height, Distance above the Bottom, Phase Angle & Fluid Particle Displacements 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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