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Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity Formula

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Local Fluid Particle Acceleration in Y Direction is the rate of change of velocity of fluid particles along the vertical axis within a specific region of a body of water, such as the ocean. Check FAQs

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)

a_y - Local Fluid Particle Acceleration in Y 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 Vertical Component of Fluid Velocity Example

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

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

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

-0.3336 = - (9.8066 \cdot 3.1416 \cdot \frac{14}{32}) \cdot (\frac{\sinh (2 \cdot 3.1416 \cdot \frac{2}{32})}{\cosh (2 \cdot 3.1416 \cdot \frac{17}{32})}) \cdot \cos (30)

-0.3336m/s² = - (9.8066m/s² \cdot 3.1416 \cdot \frac{14m}{32m}) \cdot (\frac{\sinh (2 \cdot 3.1416 \cdot \frac{2m}{32m})}{\cosh (2 \cdot 3.1416 \cdot \frac{17m}{32m})}) \cdot \cos (30°)

-0.3336 = - (9.8066 \cdot 3.1416 \cdot \frac{14}{32}) \cdot (\frac{\sinh (2 \cdot 3.1416 \cdot \frac{2}{32})}{\cosh (2 \cdot 3.1416 \cdot \frac{17}{32})}) \cdot \cos (30)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity

Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity Solution

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

FIRST Step Consider the formula

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)

Next Step Substitute values of Variables

∴

a y = - ([g] \cdot π \cdot \frac{14m}{32m}) \cdot (\frac{\sinh (2 \cdot π \cdot \frac{2m}{32m})}{\cosh (2 \cdot π \cdot \frac{17m}{32m})}) \cdot \cos (30°)

Next Step Substitute values of Constants

∴

a y = - (9.8066m/s² \cdot 3.1416 \cdot \frac{14m}{32m}) \cdot (\frac{\sinh (2 \cdot 3.1416 \cdot \frac{2m}{32m})}{\cosh (2 \cdot 3.1416 \cdot \frac{17m}{32m})}) \cdot \cos (30°)

Next Step Convert Units

∴

a y = - (9.8066m/s² \cdot 3.1416 \cdot \frac{14m}{32m}) \cdot (\frac{\sinh (2 \cdot 3.1416 \cdot \frac{2m}{32m})}{\cosh (2 \cdot 3.1416 \cdot \frac{17m}{32m})}) \cdot \cos (0.5236rad)

Next Step Prepare to Evaluate

∴

a y = - (9.8066 \cdot 3.1416 \cdot \frac{14}{32}) \cdot (\frac{\sinh (2 \cdot 3.1416 \cdot \frac{2}{32})}{\cosh (2 \cdot 3.1416 \cdot \frac{17}{32})}) \cdot \cos (0.5236)

Next Step Evaluate

∴

a y = -0.333562650142865m/s²

LAST Step Rounding Answer

∴

a y = -0.3336m/s²

Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity Formula Elements

Variables

Constants

Functions

Local Fluid Particle Acceleration in Y Direction

Local Fluid Particle Acceleration in Y Direction is the rate of change of velocity of fluid particles along the vertical axis within a specific region of a body of water, such as the ocean.

Symbol: a_y

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

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.

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.

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.

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.

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.

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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

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.

Syntax: 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.

Syntax: cosh(Number)

Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Formula and 2000+ more formulas!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Formula and 1700+ more formulas!

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 Horizontal Component

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)

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 Vertical Component of Fluid Velocity?

Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity evaluator uses 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) to evaluate the Local Fluid Particle Acceleration in Y Direction, The Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity formula is defined as the rate of change of the vertical speed of a fluid particle concerning time at a specific location. Local Fluid Particle Acceleration in Y Direction is denoted by a_y symbol.

How to evaluate Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity using this online evaluator? To use this online evaluator for Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity, 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 Vertical Component of Fluid Velocity

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

The formula of Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity is expressed as 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). Here is an example- -0.333563 = -([g]*pi*14/32)*((sinh(2*pi*(2)/32))/(cosh(2*pi*17/32)))*cos(0.5235987755982).

How to calculate Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity?

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 Vertical Component of Fluid Velocity using the formula - 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). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and , Cosine (cos), Hyperbolic Sine (sinh), Hyperbolic Cosine (cosh) function(s).

Can the Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity be negative?

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

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

Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity 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 Vertical Component of Fluid Velocity can be measured.

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Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity Formula

Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity Example

Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity Solution

Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity Formula Elements

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Other formulas in Local Fluid Velocity category

How to Evaluate Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity?

FAQs on Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity

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