Phase Angle for Horizontal Fluid Particle Displacements Solution

STEP 0: Pre-Calculation Summary
Formula Used
Phase Angle = asin(((Fluid Particle Displacements/Wave Amplitude)*(sinh(2*pi*Water Depth/Wavelength)/cosh(2*pi*(Distance above the Bottom)/Wavelength)))^2)^2
θ = asin(((ε/a)*(sinh(2*pi*d/λ)/cosh(2*pi*(DZ+d)/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 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.
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. Water depth means the depth as measured from the water level to the bottom of the considered water body.
Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Distance above the Bottom - (Measured in Meter) - Distance above the Bottom expressing the local fluid velocity component.
STEP 1: Convert Input(s) to Base Unit
Fluid Particle Displacements: 0.4 Meter --> 0.4 Meter No Conversion Required
Wave Amplitude: 0.2 Meter --> 0.2 Meter No Conversion Required
Water Depth: 1.05 Meter --> 1.05 Meter No Conversion Required
Wavelength: 26.8 Meter --> 26.8 Meter No Conversion Required
Distance above the Bottom: 2 Meter --> 2 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*(DZ+d)/λ)))^2)^2 --> asin(((0.4/0.2)*(sinh(2*pi*1.05/26.8)/cosh(2*pi*(2)/26.8)))^2)^2
Evaluating ... ...
θ = 0.0405593001185275
STEP 3: Convert Result to Output's Unit
0.0405593001185275 Radian -->2.32387671679652 Degree (Check conversion here)
FINAL ANSWER
2.32387671679652 2.323877 Degree <-- Phase Angle
(Calculation completed in 00.020 seconds)

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13 Horizontal and Vertical Semi-axis of ellipse Calculators

Phase Angle for Horizontal Fluid Particle Displacements
Go Phase Angle = asin(((Fluid Particle Displacements/Wave Amplitude)*(sinh(2*pi*Water Depth/Wavelength)/cosh(2*pi*(Distance above the Bottom)/Wavelength)))^2)^2
Wave Height for Major Horizontal Semi-Axis Deep Water Condition
Go Height of The Wave = (2*Horizontal Semi-axis of water particle)/exp(2*pi*Seabed Elevation/Length of Water Wave)
Major Horizontal Semi Axis for Deep Water Condition
Go Horizontal Semi-axis of water particle = (Height of The Wave/2)*exp(2*pi*Seabed Elevation/Length of Water Wave)
Major Horizontal Semi Axis for Shallow Water Condition
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))
Water Depth for Major Horizontal Semi-Axis for Shallow Water Condition
Go Water Depth for Semi-Axis of Ellipse = (Height of The Wave*Length of Water Wave)/(4*pi*Horizontal Semi-axis of water particle)
Wave Height for Major Horizontal Semi-Axis for Shallow Water Condition
Go Height of The Wave = (4*Horizontal Semi-axis of water particle*pi*Water Depth for Semi-Axis of Ellipse)/Length of Water Wave
Wavelength for Major Horizontal Semi-Axis for Shallow Water Condition
Go Length of Water Wave = (4*pi*Water Depth for Semi-Axis of Ellipse*Horizontal Semi-axis of water particle)/Height of The Wave
Wave Height for Minor Vertical Semi-Axis Deep Water Condition
Go Height of The Wave = (2*Vertical Semi-axis)/exp(2*pi*Seabed Elevation/Length of Water Wave)
Minor Vertical Semi-Axis for Deep Water Condition
Go Vertical Semi-axis = (Height of The Wave/2)*exp(2*pi*Seabed Elevation/Length of Water Wave)
Wave Height Given Minor Vertical Semi-Axis for Shallow Water Condition
Go Height of The Wave = (2*Vertical Semi-axis)/(1+(Seabed Elevation/Water Depth for Semi-Axis of Ellipse))
Water Depth Given Minor Vertical Semi-Axis for Shallow Water Condition
Go Water Depth for Semi-Axis of Ellipse = Seabed Elevation/((Vertical Semi-axis/(Height of The Wave/2))-1)
Sea Bed Given Minor Vertical Semi-Axis for Shallow Water Condition
Go Seabed Elevation = Water Depth for Semi-Axis of Ellipse*((Vertical Semi-axis/(Height of The Wave/2))-1)
Minor Vertical Semi Axis for Shallow Water Condition
Go Vertical Semi-axis = (Height of The Wave/2)*(1+Seabed Elevation/Water Depth for Semi-Axis of Ellipse)

Phase Angle for Horizontal Fluid Particle Displacements Formula

Phase Angle = asin(((Fluid Particle Displacements/Wave Amplitude)*(sinh(2*pi*Water Depth/Wavelength)/cosh(2*pi*(Distance above the Bottom)/Wavelength)))^2)^2
θ = asin(((ε/a)*(sinh(2*pi*d/λ)/cosh(2*pi*(DZ+d)/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 Displacements?

Phase Angle for Horizontal Fluid Particle Displacements calculator uses Phase Angle = asin(((Fluid Particle Displacements/Wave Amplitude)*(sinh(2*pi*Water Depth/Wavelength)/cosh(2*pi*(Distance above the Bottom)/Wavelength)))^2)^2 to calculate the Phase Angle, The Phase Angle for Horizontal Fluid Particle Displacements is 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 Displacements using this online calculator? To use this online calculator for Phase Angle for Horizontal Fluid Particle Displacements, enter Fluid Particle Displacements (ε), Wave Amplitude (a), Water Depth (d), Wavelength (λ) & Distance above the Bottom (DZ+d) and hit the calculate button. Here is how the Phase Angle for Horizontal Fluid Particle Displacements calculation can be explained with given input values -> 108.8629 = asin(((0.4/0.2)*(sinh(2*pi*1.05/26.8)/cosh(2*pi*(2)/26.8)))^2)^2.

FAQ

What is Phase Angle for Horizontal Fluid Particle Displacements?
The Phase Angle for Horizontal Fluid Particle Displacements is 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*(DZ+d)/λ)))^2)^2 or Phase Angle = asin(((Fluid Particle Displacements/Wave Amplitude)*(sinh(2*pi*Water Depth/Wavelength)/cosh(2*pi*(Distance above the Bottom)/Wavelength)))^2)^2. Fluid Particle Displacements in horizontal and vertical directions, Wave Amplitude is a measurement of the vertical distance of the wave from the average, Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body, Wavelength can be defined as the distance between two successive crests or troughs of a wave & Distance above the Bottom expressing the local fluid velocity component.
How to calculate Phase Angle for Horizontal Fluid Particle Displacements?
The Phase Angle for Horizontal Fluid Particle Displacements is 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 Displacements/Wave Amplitude)*(sinh(2*pi*Water Depth/Wavelength)/cosh(2*pi*(Distance above the Bottom)/Wavelength)))^2)^2. To calculate Phase Angle for Horizontal Fluid Particle Displacements, you need Fluid Particle Displacements (ε), Wave Amplitude (a), Water Depth (d), Wavelength (λ) & Distance above the Bottom (DZ+d). With our tool, you need to enter the respective value for Fluid Particle Displacements, Wave Amplitude, Water Depth, Wavelength & Distance 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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