Local Fluid Particle Acceleration of Horizontal Component Calculator

✖Height of the Wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Height of the Wave [H_w]			+10% -10%
✖Wavelength of Wave refers to the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings.ⓘ Wavelength of Wave [λ]			+10% -10%
✖Distance above the Bottom refers to the vertical measurement from the lowest point of a given surface (such as the bottom of waterbody) to a specified point above it.ⓘ Distance above the Bottom [D_Z+d]			+10% -10%
✖Water Depth for Fluid Velocity is the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth for Fluid Velocity [d]			+10% -10%
✖Phase Angle refers to the time lag between the maximum amplitude of a forcing function, such as waves or currents, and the response of the system, such as water level or sediment transport.ⓘ Phase Angle [θ]			+10% -10%

✖Local Fluid Particle Acceleration in X Direction is the change in velocity experienced by water particles along the horizontal axis in a coastal environment.ⓘ Local Fluid Particle Acceleration of Horizontal Component [a_x]

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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)
a_x = ([g]*pi*H_w/λ)*((cosh(2*pi*(D_Z+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 change in velocity experienced by water particles along the horizontal axis in a coastal environment.
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 refers to the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings.
Distance above the Bottom - (Measured in Meter) - Distance above the Bottom refers to the vertical measurement from the lowest point of a given surface (such as the bottom of waterbody) to a specified point above it.
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 refers to the time lag between the maximum amplitude of a forcing function, such as waves or currents, and the response of the system, such as water level or sediment transport.

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

a_x = ([g]*pi*H_w/λ)*((cosh(2*pi*(D_Z+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 ... ...

a_x = 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)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Local Fluid and Mass Transport Velocity » Local Fluid Velocity » Local Fluid Particle Acceleration of Horizontal Component

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< Local Fluid Velocity Calculators

Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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)

Local Fluid Particle Acceleration of Horizontal Component 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 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 formula 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 a_x 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 (H_w), Wavelength of Wave (λ), Distance above the Bottom (D_Z+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 formula 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 a_x = ([g]*pi*H_w/λ)*((cosh(2*pi*(D_Z+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 refers to the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings, Distance above the Bottom refers to the vertical measurement from the lowest point of a given surface (such as the bottom of waterbody) to a specified point above it, Water Depth for Fluid Velocity is the depth as measured from the water level to the bottom of the considered water body & Phase Angle refers to the time lag between the maximum amplitude of a forcing function, such as waves or currents, and the response of the system, such as water level or sediment transport.

How to calculate Local Fluid Particle Acceleration of Horizontal Component?

The Local Fluid Particle Acceleration of Horizontal Component formula 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 (H_w), Wavelength of Wave (λ), Distance above the Bottom (D_Z+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.

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