Phase Angle for Horizontal Fluid Particle Displacement Calculator

✖Fluid Particle Displacement refers to the movement of individual particles within a fluid medium, such as water or air.ⓘ Fluid Particle Displacement [ε]			+10% -10%
✖Wave Amplitude is a measurement of the vertical distance of the wave from the average.ⓘ Wave Amplitude [a]			+10% -10%
✖Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [d]			+10% -10%
✖Wavelength of Coast refers to the distance between two successive crests or troughs of a wave as it travels through the water near the shore.ⓘ Wavelength of Coast [λ]			+10% -10%
✖Elevation above the Bottom refers to the height or depth of an object or feature above the seabed or ocean floor.ⓘ Elevation above the Bottom [y]			+10% -10%

✖Phase Angle refers to the difference in phase between two wave components, usually waves propagating from different directions or generated by different mechanisms.ⓘ Phase Angle for Horizontal Fluid Particle Displacement [θ]

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Phase Angle for Horizontal Fluid Particle Displacement Solution

STEP 0: Pre-Calculation Summary

Formula Used

Phase Angle = asin(((Fluid Particle Displacement/Wave Amplitude)*(sinh(2*pi*Water Depth/Wavelength of Coast)/cosh(2*pi*(Elevation above the Bottom)/Wavelength of Coast)))^2)^2
θ = asin(((ε/a)*(sinh(2*pi*d/λ)/cosh(2*pi*(y)/λ)))^2)^2
This formula uses 1 Constants, 4 Functions, 6 Variables

Constants Used

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)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)
sinh - The hyperbolic sine function, also known as the sinh function, is a mathematical function that is defined as the hyperbolic analogue of the sine function., sinh(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

Phase Angle - (Measured in Radian) - Phase Angle refers to the difference in phase between two wave components, usually waves propagating from different directions or generated by different mechanisms.
Fluid Particle Displacement - (Measured in Meter) - Fluid Particle Displacement refers to the movement of individual particles within a fluid medium, such as water or air.
Wave Amplitude - (Measured in Meter) - Wave Amplitude is a measurement of the vertical distance of the wave from the average.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.
Wavelength of Coast - (Measured in Meter) - Wavelength of Coast refers to the distance between two successive crests or troughs of a wave as it travels through the water near the shore.
Elevation above the Bottom - (Measured in Meter) - Elevation above the Bottom refers to the height or depth of an object or feature above the seabed or ocean floor.

STEP 1: Convert Input(s) to Base Unit

Fluid Particle Displacement: 0.4 Meter --> 0.4 Meter No Conversion Required
Wave Amplitude: 1.56 Meter --> 1.56 Meter No Conversion Required
Water Depth: 1.05 Meter --> 1.05 Meter No Conversion Required
Wavelength of Coast: 26.8 Meter --> 26.8 Meter No Conversion Required
Elevation above the Bottom: 4.92 Meter --> 4.92 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = asin(((ε/a)*(sinh(2*pi*d/λ)/cosh(2*pi*(y)/λ)))^2)^2 --> asin(((0.4/1.56)*(sinh(2*pi*1.05/26.8)/cosh(2*pi*(4.92)/26.8)))^2)^2

Evaluating ... ...

θ = 1.7931958817265E-06

STEP 3: Convert Result to Output's Unit

1.7931958817265E-06 Radian -->0.000102742555863188 Degree (Check conversion here)

FINAL ANSWER

0.000102742555863188 ≈ 0.000103 Degree <-- Phase Angle

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Horizontal and Vertical Semi Axis of Ellipse » Phase Angle for Horizontal Fluid Particle Displacement

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< Horizontal and Vertical Semi Axis of Ellipse Calculators

Major Horizontal Semi Axis for Deep Water Condition

LaTeX Go Horizontal Semi-axis of Water Particle = (Height of the Wave/2)*exp(2*pi*Sea Bed Elevation/Length of Water Wave)

Major Horizontal Semi Axis for Shallow Water Condition

LaTeX Go Horizontal Semi-axis of Water Particle = (Height of the Wave/2)*(Length of Water Wave/(2*pi*Water Depth for Semi-Axis of Ellipse))

Minor Vertical Semi-Axis for Deep Water Condition

LaTeX Go Vertical Semi-Axis = (Height of the Wave/2)*exp(2*pi*Sea Bed Elevation/Length of Water Wave)

Minor Vertical Semi Axis for Shallow Water Condition

LaTeX Go Vertical Semi-Axis = (Height of the Wave/2)*(1+Sea Bed Elevation/Water Depth for Semi-Axis of Ellipse)

Phase Angle for Horizontal Fluid Particle Displacement Formula

LaTeX Go

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 Phase Angle for Horizontal Fluid Particle Displacement?

Phase Angle for Horizontal Fluid Particle Displacement calculator uses Phase Angle = asin(((Fluid Particle Displacement/Wave Amplitude)*(sinh(2*pi*Water Depth/Wavelength of Coast)/cosh(2*pi*(Elevation above the Bottom)/Wavelength of Coast)))^2)^2 to calculate the Phase Angle, The Phase Angle for Horizontal Fluid Particle Displacement formula is defined as the characteristic of a periodic wave. Phase angle in degrees or radians is that the waveform has shifted either left or right from the reference point. Phase Angle is denoted by θ symbol.

How to calculate Phase Angle for Horizontal Fluid Particle Displacement using this online calculator? To use this online calculator for Phase Angle for Horizontal Fluid Particle Displacement, enter Fluid Particle Displacement (ε), Wave Amplitude (a), Water Depth (d), Wavelength of Coast (λ) & Elevation above the Bottom (y) and hit the calculate button. Here is how the Phase Angle for Horizontal Fluid Particle Displacement calculation can be explained with given input values -> 21.83808 = asin(((0.4/1.56)*(sinh(2*pi*1.05/26.8)/cosh(2*pi*(4.92)/26.8)))^2)^2.

FAQ

What is Phase Angle for Horizontal Fluid Particle Displacement?

The Phase Angle for Horizontal Fluid Particle Displacement formula is defined as the characteristic of a periodic wave. Phase angle in degrees or radians is that the waveform has shifted either left or right from the reference point and is represented as θ = asin(((ε/a)*(sinh(2*pi*d/λ)/cosh(2*pi*(y)/λ)))^2)^2 or Phase Angle = asin(((Fluid Particle Displacement/Wave Amplitude)*(sinh(2*pi*Water Depth/Wavelength of Coast)/cosh(2*pi*(Elevation above the Bottom)/Wavelength of Coast)))^2)^2. Fluid Particle Displacement refers to the movement of individual particles within a fluid medium, such as water or air, Wave Amplitude is a measurement of the vertical distance of the wave from the average, Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body, Wavelength of Coast refers to the distance between two successive crests or troughs of a wave as it travels through the water near the shore & Elevation above the Bottom refers to the height or depth of an object or feature above the seabed or ocean floor.

How to calculate Phase Angle for Horizontal Fluid Particle Displacement?

The Phase Angle for Horizontal Fluid Particle Displacement formula is defined as the characteristic of a periodic wave. Phase angle in degrees or radians is that the waveform has shifted either left or right from the reference point is calculated using Phase Angle = asin(((Fluid Particle Displacement/Wave Amplitude)*(sinh(2*pi*Water Depth/Wavelength of Coast)/cosh(2*pi*(Elevation above the Bottom)/Wavelength of Coast)))^2)^2. To calculate Phase Angle for Horizontal Fluid Particle Displacement, you need Fluid Particle Displacement (ε), Wave Amplitude (a), Water Depth (d), Wavelength of Coast (λ) & Elevation above the Bottom (y). With our tool, you need to enter the respective value for Fluid Particle Displacement, Wave Amplitude, Water Depth, Wavelength of Coast & Elevation above the Bottom 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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