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 00.004 seconds)

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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
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

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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