Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity 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 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.ⓘ Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity [a_y]

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Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
a_y = -([g]*pi*H_w/λ)*((sinh(2*pi*(D_Z+d)/λ))/(cosh(2*pi*d/λ)))*cos(θ)
This formula uses 2 Constants, 3 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

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., 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., cosh(Number)

Variables Used

Local Fluid Particle Acceleration in Y Direction - (Measured in Meter per Square Second) - 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.
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_y = -([g]*pi*H_w/λ)*((sinh(2*pi*(D_Z+d)/λ))/(cosh(2*pi*d/λ)))*cos(θ) --> -([g]*pi*14/32)*((sinh(2*pi*(2)/32))/(cosh(2*pi*17/32)))*cos(0.5235987755982)

Evaluating ... ...

a_y = -0.333562650142865

STEP 3: Convert Result to Output's Unit

-0.333562650142865 Meter per Square Second --> No Conversion Required

FINAL ANSWER

-0.333562650142865 ≈ -0.333563 Meter per Square Second <-- Local Fluid Particle Acceleration in Y Direction

(Calculation completed in 00.020 seconds)

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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 Vertical Component of Fluid Velocity 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 Vertical Component of Fluid Velocity?

Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity calculator 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 calculate 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 calculate Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity using this online calculator? To use this online calculator 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. Here is how the Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity calculation can be explained with given input values -> -0.333563 = -([g]*pi*14/32)*((sinh(2*pi*(2)/32))/(cosh(2*pi*17/32)))*cos(0.5235987755982).

FAQ

What is Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity?

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 and is represented as a_y = -([g]*pi*H_w/λ)*((sinh(2*pi*(D_Z+d)/λ))/(cosh(2*pi*d/λ)))*cos(θ) or 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). 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 Vertical Component of Fluid Velocity?

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 is calculated using 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 calculate Local Fluid Particle Acceleration of Vertical Component of Fluid Velocity, 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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