Local Fluid Particle Acceleration of Horizontal Component Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
ax = ([g]*pi*Hw/λ)*((cosh(2*pi*(DZ+d)/λ))/(cosh(2*pi*d/λ)))*sin(θ)
This formula uses 2 Constants, 2 Functions, 6 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)
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
Local Fluid Particle Acceleration in X Direction - (Measured in Meter per Square Second) - Local Fluid Particle Acceleration in X Direction is the acceleration of the local fluid in x direction (horizontal direction).
Height of The Wave - (Measured in Meter) - Height of The Wave is the difference between the elevations of a crest and a neighboring trough.
Wavelength of Wave - (Measured in Meter) - Wavelength of Wave 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.
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.
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
Height of The Wave: 14 Meter --> 14 Meter No Conversion Required
Wavelength of Wave: 32 Meter --> 32 Meter No Conversion Required
Distance above the Bottom: 2 Meter --> 2 Meter No Conversion Required
Water Depth for Fluid Velocity: 17 Meter --> 17 Meter No Conversion Required
Phase Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ax = ([g]*pi*Hw/λ)*((cosh(2*pi*(DZ+d)/λ))/(cosh(2*pi*d/λ)))*sin(θ) --> ([g]*pi*14/32)*((cosh(2*pi*(2)/32))/(cosh(2*pi*17/32)))*sin(0.5235987755982)
Evaluating ... ...
ax = 0.515360840744022
STEP 3: Convert Result to Output's Unit
0.515360840744022 Meter per Square Second --> No Conversion Required
FINAL ANSWER
0.515360840744022 0.515361 Meter per Square Second <-- Local Fluid Particle Acceleration in X Direction
(Calculation completed in 00.020 seconds)

Credits

Created by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
Mithila Muthamma PA has created this Calculator and 2000+ more calculators!
Verified by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
Chandana P Dev has verified this Calculator and 1700+ more calculators!

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))

Local Fluid Particle Acceleration of Horizontal Component Formula

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)
ax = ([g]*pi*Hw/λ)*((cosh(2*pi*(DZ+d)/λ))/(cosh(2*pi*d/λ)))*sin(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 Local Fluid Particle Acceleration of Horizontal Component?

Local Fluid Particle Acceleration of Horizontal Component calculator uses 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) to calculate the Local Fluid Particle Acceleration in X Direction, The Local fluid particle acceleration of horizontal component is defined as the acceleration and velocity that are periodic in both x and t direction during the passage of a wave in a specific direction. Local Fluid Particle Acceleration in X Direction is denoted by ax symbol.

How to calculate Local Fluid Particle Acceleration of Horizontal Component using this online calculator? To use this online calculator for Local Fluid Particle Acceleration of Horizontal Component, enter Height of The Wave (Hw), Wavelength of Wave (λ), Distance above the Bottom (DZ+d), Water Depth for Fluid Velocity (d) & Phase Angle (θ) and hit the calculate button. Here is how the Local Fluid Particle Acceleration of Horizontal Component calculation can be explained with given input values -> 0.515361 = ([g]*pi*14/32)*((cosh(2*pi*(2)/32))/(cosh(2*pi*17/32)))*sin(0.5235987755982).

FAQ

What is Local Fluid Particle Acceleration of Horizontal Component?
The Local fluid particle acceleration of horizontal component is defined as the acceleration and velocity that are periodic in both x and t direction during the passage of a wave in a specific direction and is represented as ax = ([g]*pi*Hw/λ)*((cosh(2*pi*(DZ+d)/λ))/(cosh(2*pi*d/λ)))*sin(θ) or 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). Height of The Wave is the difference between the elevations of a crest and a neighboring trough, Wavelength of Wave 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, Water Depth for Fluid Velocity is the depth as measured from the water level to the bottom of the considered water body & 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 Local Fluid Particle Acceleration of Horizontal Component?
The Local fluid particle acceleration of horizontal component is defined as the acceleration and velocity that are periodic in both x and t direction during the passage of a wave in a specific direction is calculated using 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). To calculate Local Fluid Particle Acceleration of Horizontal Component, you need Height of The Wave (Hw), Wavelength of Wave (λ), Distance above the Bottom (DZ+d), Water Depth for Fluid Velocity (d) & Phase Angle (θ). With our tool, you need to enter the respective value for Height of The Wave, Wavelength of Wave, Distance above the Bottom, Water Depth for Fluid Velocity & Phase Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!