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Local Fluid Particle Acceleration of Horizontal Component Formula

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Local Fluid Particle Acceleration in X Direction is the change in velocity experienced by water particles along the horizontal axis in a coastal environment. Check FAQs

a x = ([g] \cdot π \cdot \frac{H w}{λ}) \cdot (\frac{\cosh (2 \cdot π \cdot \frac{D Z+d}{λ})}{\cosh (2 \cdot π \cdot \frac{d}{λ})}) \cdot \sin (θ)

a_x - Local Fluid Particle Acceleration in X Direction?H_w - Height of the Wave?λ - Wavelength of Wave?D_Z+d - Distance above the Bottom?d - Water Depth for Fluid Velocity?θ - Phase Angle?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Local Fluid Particle Acceleration of Horizontal Component Example

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Here is how the Local Fluid Particle Acceleration of Horizontal Component equation looks like with Values.

Here is how the Local Fluid Particle Acceleration of Horizontal Component equation looks like with Units.

Here is how the Local Fluid Particle Acceleration of Horizontal Component equation looks like.

0.5154 = (9.8066 \cdot 3.1416 \cdot \frac{14}{32}) \cdot (\frac{\cosh (2 \cdot 3.1416 \cdot \frac{2}{32})}{\cosh (2 \cdot 3.1416 \cdot \frac{17}{32})}) \cdot \sin (30)

0.5154m/s² = (9.8066m/s² \cdot 3.1416 \cdot \frac{14m}{32m}) \cdot (\frac{\cosh (2 \cdot 3.1416 \cdot \frac{2m}{32m})}{\cosh (2 \cdot 3.1416 \cdot \frac{17m}{32m})}) \cdot \sin (30°)

0.5154 = (9.8066 \cdot 3.1416 \cdot \frac{14}{32}) \cdot (\frac{\cosh (2 \cdot 3.1416 \cdot \frac{2}{32})}{\cosh (2 \cdot 3.1416 \cdot \frac{17}{32})}) \cdot \sin (30)

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Local Fluid Particle Acceleration of Horizontal Component Solution

Follow our step by step solution on how to calculate Local Fluid Particle Acceleration of Horizontal Component?

FIRST Step Consider the formula

a x = ([g] \cdot π \cdot \frac{H w}{λ}) \cdot (\frac{\cosh (2 \cdot π \cdot \frac{D Z+d}{λ})}{\cosh (2 \cdot π \cdot \frac{d}{λ})}) \cdot \sin (θ)

Next Step Substitute values of Variables

∴

a x = ([g] \cdot π \cdot \frac{14m}{32m}) \cdot (\frac{\cosh (2 \cdot π \cdot \frac{2m}{32m})}{\cosh (2 \cdot π \cdot \frac{17m}{32m})}) \cdot \sin (30°)

Next Step Substitute values of Constants

∴

a x = (9.8066m/s² \cdot 3.1416 \cdot \frac{14m}{32m}) \cdot (\frac{\cosh (2 \cdot 3.1416 \cdot \frac{2m}{32m})}{\cosh (2 \cdot 3.1416 \cdot \frac{17m}{32m})}) \cdot \sin (30°)

Next Step Convert Units

∴

a x = (9.8066m/s² \cdot 3.1416 \cdot \frac{14m}{32m}) \cdot (\frac{\cosh (2 \cdot 3.1416 \cdot \frac{2m}{32m})}{\cosh (2 \cdot 3.1416 \cdot \frac{17m}{32m})}) \cdot \sin (0.5236rad)

Next Step Prepare to Evaluate

∴

a x = (9.8066 \cdot 3.1416 \cdot \frac{14}{32}) \cdot (\frac{\cosh (2 \cdot 3.1416 \cdot \frac{2}{32})}{\cosh (2 \cdot 3.1416 \cdot \frac{17}{32})}) \cdot \sin (0.5236)

Next Step Evaluate

∴

a x = 0.515360840744022m/s²

LAST Step Rounding Answer

∴

a x = 0.5154m/s²

Local Fluid Particle Acceleration of Horizontal Component Formula Elements

Variables

Constants

Functions

Local Fluid Particle Acceleration in X Direction

Local Fluid Particle Acceleration in X Direction is the change in velocity experienced by water particles along the horizontal axis in a coastal environment.

Symbol: a_x

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Local Fluid Particle Acceleration in X Direction

Height of the Wave

Height of the Wave is the difference between the elevations of a crest and a neighboring trough.

Symbol: H_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Height of the Wave

Wavelength of Wave

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.

Symbol: λ

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wavelength of Wave

Distance above the Bottom

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.

Symbol: D_Z+d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance above the Bottom

Water Depth for Fluid Velocity

Water Depth for Fluid Velocity is the depth as measured from the water level to the bottom of the considered water body.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth for Fluid Velocity

Phase Angle

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.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Phase Angle

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: 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.

Syntax: cosh(Number)

Other formulas in Local Fluid Velocity category

Go Horizontal Component of Local Fluid Velocity

H v = (H w \cdot [g] \cdot \frac{T p}{2 \cdot λ}) \cdot (\frac{\cosh (\frac{2 \cdot π \cdot D Z+d}{λ})}{\cosh (\frac{2 \cdot π \cdot d}{λ})}) \cdot \cos (θ)

Go Vertical Component of Local Fluid Velocity

V v = (H w \cdot [g] \cdot \frac{T p}{2 \cdot λ}) \cdot (\frac{\sinh (2 \cdot π \cdot \frac{D Z+d}{λ})}{\cosh (2 \cdot π \cdot \frac{d}{λ})}) \cdot \sin (θ)

Go Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity

a y = - ([g] \cdot π \cdot \frac{H w}{λ}) \cdot (\frac{\sinh (2 \cdot π \cdot \frac{D Z+d}{λ})}{\cosh (2 \cdot π \cdot \frac{d}{λ})}) \cdot \cos (θ)

Go Wave Period for Horizontal Component of Local Fluid Velocity

T p = H v \cdot 2 \cdot λ \cdot \frac{\cosh (2 \cdot π \cdot \frac{d}{λ})}{H w \cdot [g] \cdot \cosh (2 \cdot π \cdot \frac{D Z+d}{λ}) \cdot \cos (θ)}

How to Evaluate Local Fluid Particle Acceleration of Horizontal Component?

Local Fluid Particle Acceleration of Horizontal Component evaluator 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 evaluate 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 evaluate Local Fluid Particle Acceleration of Horizontal Component using this online evaluator? To use this online evaluator 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.

FAQs on Local Fluid Particle Acceleration of Horizontal Component

What is the formula to find Local Fluid Particle Acceleration of Horizontal Component?

The formula of Local Fluid Particle Acceleration of Horizontal Component is expressed as 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). Here is an example- 0.515361 = ([g]*pi*14/32)*((cosh(2*pi*(2)/32))/(cosh(2*pi*17/32)))*sin(0.5235987755982).

How to calculate Local Fluid Particle Acceleration of Horizontal Component?

With 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) we can find Local Fluid Particle Acceleration of Horizontal Component using the 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). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and , Sine (sin), Hyperbolic Cosine (cosh) function(s).

Can the Local Fluid Particle Acceleration of Horizontal Component be negative?

Yes, the Local Fluid Particle Acceleration of Horizontal Component, measured in Acceleration can be negative.

Which unit is used to measure Local Fluid Particle Acceleration of Horizontal Component?

Local Fluid Particle Acceleration of Horizontal Component is usually measured using the Meter per Square Second[m/s²] for Acceleration. Kilometer per Square Second[m/s²], Micrometer per Square Second[m/s²], Mile per Square Second[m/s²] are the few other units in which Local Fluid Particle Acceleration of Horizontal Component can be measured.

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Local Fluid Particle Acceleration of Horizontal Component Formula

Local Fluid Particle Acceleration of Horizontal Component Example

Local Fluid Particle Acceleration of Horizontal Component Solution

Local Fluid Particle Acceleration of Horizontal Component Formula Elements

Other formulas in Local Fluid Velocity category

How to Evaluate Local Fluid Particle Acceleration of Horizontal Component?

FAQs on Local Fluid Particle Acceleration of Horizontal Component

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