Wave Period for Horizontal Component of Local Fluid Velocity Solution

STEP 0: Pre-Calculation Summary
Formula Used
Wave Period = Horizontal Component of Velocity*2*Wavelength of Wave*cosh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)/(Height of The Wave*[g]*cosh(2*pi*(Distance above the Bottom)/Wavelength of Wave)*cos(Phase Angle))
Tp = Hv*2*λ*cosh(2*pi*d/λ)/(Hw*[g]*cosh(2*pi*(DZ+d)/λ)*cos(θ))
This formula uses 2 Constants, 2 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
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
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 - (Measured in Second) - Wave Period is defined as the time it takes for two successive crests to pass a given point.
Horizontal Component of Velocity - (Measured in Meter per Second) - Horizontal Component of Velocity is the velocity of the particle which is resolved along the horizontal direction.
Wavelength of Wave - (Measured in Meter) - Wavelength of Wave can be defined as the distance between two successive crests or troughs of a wave.
Water Depth for Fluid Velocity - (Measured in Meter) - Water Depth for Fluid Velocity is the depth as measured from the water level to the bottom of the considered water body.
Height of The Wave - (Measured in Meter) - Height of The 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.
STEP 1: Convert Input(s) to Base Unit
Horizontal Component of Velocity: 13.5 Meter per Second --> 13.5 Meter per Second No Conversion Required
Wavelength of Wave: 32 Meter --> 32 Meter No Conversion Required
Water Depth for Fluid Velocity: 17 Meter --> 17 Meter No Conversion Required
Height of The Wave: 14 Meter --> 14 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)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tp = Hv*2*λ*cosh(2*pi*d/λ)/(Hw*[g]*cosh(2*pi*(DZ+d)/λ)*cos(θ)) --> 13.5*2*32*cosh(2*pi*17/32)/(14*[g]*cosh(2*pi*(2)/32)*cos(0.5235987755982))
Evaluating ... ...
Tp = 95.025812911246
STEP 3: Convert Result to Output's Unit
95.025812911246 Second --> No Conversion Required
FINAL ANSWER
95.025812911246 95.02581 Second <-- Wave Period
(Calculation completed in 00.020 seconds)

Credits

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Coorg Institute of Technology (CIT), Coorg
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6 Local Fluid Velocity Calculators

Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity
Go Local Fluid Particle Acceleration in Y Direction = -([g]*pi*Height of The Wave/Wavelength of Wave)*((sinh(2*pi*(Distance above the Bottom)/Wavelength of Wave))/(cosh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)))*cos(Phase Angle)
Local Fluid Particle Acceleration of Horizontal Component
Go Local Fluid Particle Acceleration in X Direction = ([g]*pi*Height of The Wave/Wavelength of Wave)*((cosh(2*pi*(Distance above the Bottom)/Wavelength of Wave))/(cosh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)))*sin(Phase Angle)
Horizontal Component of Local Fluid Velocity
Go Horizontal Component of Velocity = (Height of The Wave*[g]*Wave Period/(2*Wavelength of Wave))*((cosh((2*pi*Distance above the Bottom)/Wavelength of Wave))/(cosh((2*pi*Water Depth for Fluid Velocity)/Wavelength of Wave)))*cos(Phase Angle)
Vertical Component of Local Fluid Velocity
Go Vertical Component of Velocity = (Height of The Wave*[g]*Wave Period/(2*Wavelength of Wave))*((sinh(2*pi*(Distance above the Bottom)/Wavelength of Wave))/(cosh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)))*sin(Phase Angle)
Wave Period for Horizontal Component of Local Fluid Velocity
Go Wave Period = Horizontal Component of Velocity*2*Wavelength of Wave*cosh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)/(Height of The Wave*[g]*cosh(2*pi*(Distance above the Bottom)/Wavelength of Wave)*cos(Phase Angle))
Wave Period for Vertical Component of Local Fluid Velocity
Go Wave Period = Vertical Component of Velocity*2*Wavelength of Wave*cosh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)/(Height of The Wave*[g]*sinh(2*pi*(Distance above the Bottom)/Wavelength of Wave)*sin(Phase Angle))

Wave Period for Horizontal Component of Local Fluid Velocity Formula

Wave Period = Horizontal Component of Velocity*2*Wavelength of Wave*cosh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)/(Height of The Wave*[g]*cosh(2*pi*(Distance above the Bottom)/Wavelength of Wave)*cos(Phase Angle))
Tp = Hv*2*λ*cosh(2*pi*d/λ)/(Hw*[g]*cosh(2*pi*(DZ+d)/λ)*cos(θ))

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 Component of Local Fluid Velocity?

Wave Period for Horizontal Component of Local Fluid Velocity calculator uses Wave Period = Horizontal Component of Velocity*2*Wavelength of Wave*cosh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)/(Height of The Wave*[g]*cosh(2*pi*(Distance above the Bottom)/Wavelength of Wave)*cos(Phase Angle)) to calculate the Wave Period, The Wave Period for Horizontal Component of Local Fluid Velocity is Known is defined as the time for a particle on a medium to make one complete vibrational cycle. Wave Period is denoted by Tp symbol.

How to calculate Wave Period for Horizontal Component of Local Fluid Velocity using this online calculator? To use this online calculator for Wave Period for Horizontal Component of Local Fluid Velocity, enter Horizontal Component of Velocity (Hv), Wavelength of Wave (λ), Water Depth for Fluid Velocity (d), Height of The Wave (Hw), Distance above the Bottom (DZ+d) & Phase Angle (θ) and hit the calculate button. Here is how the Wave Period for Horizontal Component of Local Fluid Velocity calculation can be explained with given input values -> 95.02581 = 13.5*2*32*cosh(2*pi*17/32)/(14*[g]*cosh(2*pi*(2)/32)*cos(0.5235987755982)).

FAQ

What is Wave Period for Horizontal Component of Local Fluid Velocity?
The Wave Period for Horizontal Component of Local Fluid Velocity is Known is defined as the time for a particle on a medium to make one complete vibrational cycle and is represented as Tp = Hv*2*λ*cosh(2*pi*d/λ)/(Hw*[g]*cosh(2*pi*(DZ+d)/λ)*cos(θ)) or Wave Period = Horizontal Component of Velocity*2*Wavelength of Wave*cosh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)/(Height of The Wave*[g]*cosh(2*pi*(Distance above the Bottom)/Wavelength of Wave)*cos(Phase Angle)). Horizontal Component of Velocity is the velocity of the particle which is resolved along the horizontal direction, Wavelength of Wave can be defined as the distance between two successive crests or troughs of a wave, Water Depth for Fluid Velocity is the depth as measured from the water level to the bottom of the considered water body, Height of The 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.
How to calculate Wave Period for Horizontal Component of Local Fluid Velocity?
The Wave Period for Horizontal Component of Local Fluid Velocity is Known is defined as the time for a particle on a medium to make one complete vibrational cycle is calculated using Wave Period = Horizontal Component of Velocity*2*Wavelength of Wave*cosh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)/(Height of The Wave*[g]*cosh(2*pi*(Distance above the Bottom)/Wavelength of Wave)*cos(Phase Angle)). To calculate Wave Period for Horizontal Component of Local Fluid Velocity, you need Horizontal Component of Velocity (Hv), Wavelength of Wave (λ), Water Depth for Fluid Velocity (d), Height of The Wave (Hw), Distance above the Bottom (DZ+d) & Phase Angle (θ). With our tool, you need to enter the respective value for Horizontal Component of Velocity, Wavelength of Wave, Water Depth for Fluid Velocity, Height of The Wave, Distance above the Bottom & Phase Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Wave Period?
In this formula, Wave Period uses Horizontal Component of Velocity, Wavelength of Wave, Water Depth for Fluid Velocity, Height of The Wave, Distance above the Bottom & Phase Angle. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Wave Period = Vertical Component of Velocity*2*Wavelength of Wave*cosh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)/(Height of The Wave*[g]*sinh(2*pi*(Distance above the Bottom)/Wavelength of Wave)*sin(Phase Angle))
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