Wave Height for Vertical Component of Local Fluid Velocity Calculator

✖Vertical Component of Velocity is the velocity of the particle which is resolved along the vertical direction.ⓘ Vertical Component of Velocity [V_v]			+10% -10%
✖Wavelength can be defined as the distance between two successive crests or troughs of a wave.ⓘ Wavelength [λ]			+10% -10%
✖Water depth means the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [D]			+10% -10%
✖Wave Period is defined as the time it takes for two successive crests to pass a given point.ⓘ Wave Period [T_p]			+10% -10%
✖Distance above the Bottom expressing the local fluid velocity component.ⓘ Distance above the Bottom [D_Z+d]			+10% -10%
✖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.ⓘ Phase Angle [θ]			+10% -10%

✖Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Wave Height for Vertical Component of Local Fluid Velocity [H]

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Formula

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Wave Height for Vertical Component of Local Fluid Velocity

Formula

`"H" = ("V"_{"v"}*2*"λ")*cosh(2*pi*"D"/"λ")/("[g]"*"T"_{"p"}*sinh(2*pi*("D"_{"Z+d"})/"λ")*sin("θ"))`

Example

`"5.760748m"=("2.911m/s"*2*"26.8m")*cosh(2*pi*"12m"/"26.8m")/("[g]"*"95s"*sinh(2*pi*("2m")/"26.8m")*sin("30°"))`

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Wave Height for Vertical Component of Local Fluid Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wave Height = (Vertical Component of Velocity*2*Wavelength)*cosh(2*pi*Water Depth/Wavelength)/([g]*Wave Period*sinh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle))
H = (V_v*2*λ)*cosh(2*pi*D/λ)/([g]*T_p*sinh(2*pi*(D_Z+d)/λ)*sin(θ))
This formula uses 2 Constants, 3 Functions, 7 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)
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

Wave Height - (Measured in Meter) - Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.
Vertical Component of Velocity - (Measured in Meter per Second) - Vertical Component of Velocity is the velocity of the particle which is resolved along the vertical direction.
Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Water Depth - (Measured in Meter) - Water depth means the depth as measured from the water level to the bottom of the considered water body.
Wave Period - (Measured in Second) - Wave Period is defined as the time it takes for two successive crests to pass a given point.
Distance above the Bottom - (Measured in Meter) - Distance above the Bottom expressing the local fluid velocity component.
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

Vertical Component of Velocity: 2.911 Meter per Second --> 2.911 Meter per Second No Conversion Required
Wavelength: 26.8 Meter --> 26.8 Meter No Conversion Required
Water Depth: 12 Meter --> 12 Meter No Conversion Required
Wave Period: 95 Second --> 95 Second No Conversion Required
Distance above the Bottom: 2 Meter --> 2 Meter No Conversion Required
Phase Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H = (V_v*2*λ)*cosh(2*pi*D/λ)/([g]*T_p*sinh(2*pi*(D_Z+d)/λ)*sin(θ)) --> (2.911*2*26.8)*cosh(2*pi*12/26.8)/([g]*95*sinh(2*pi*(2)/26.8)*sin(0.5235987755982))

Evaluating ... ...

H = 5.76074820138167

STEP 3: Convert Result to Output's Unit

5.76074820138167 Meter --> No Conversion Required

FINAL ANSWER

5.76074820138167 ≈ 5.760748 Meter <-- Wave Height

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Wave Height » Wave Height for Vertical Component of Local Fluid Velocity

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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< 20 Wave Height Calculators

Wave Height for Horizontal Fluid Particle Displacements

Go Wave Height = -Fluid Particle Displacements*(4*pi*Wavelength)*(cosh(2*pi*Water Depth/Wavelength))/([g]*Wave Period^2)*((cosh(2*pi*(Distance above the Bottom)/Wavelength)))*sin(Phase Angle)

Wave Height for Vertical Fluid Particle Displacements

Go Wave Height = Fluid Particle Displacements*(4*pi*Wavelength)*cosh(2*pi*Water Depth/Wavelength)/([g]*Wave Period^2*sinh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle))

Wave Height for Vertical Component of Local Fluid Velocity

Go Wave Height = (Vertical Component of Velocity*2*Wavelength)*cosh(2*pi*Water Depth/Wavelength)/([g]*Wave Period*sinh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle))

Wave Height for Horizontal Component of Local Fluid Velocity

Go Wave Height = Water Particle Velocity*2*Wavelength*cosh(2*pi*Depth of Water Wave/Wavelength)/([g]*Wave Period*cosh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle))

Wave height for local fluid particle acceleration of vertical component

Go Wave Height = -(Local Fluid Particle Acceleration*Wavelength*cosh(2*pi*Water Depth/Wavelength)/([g]*pi*sinh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle)))

Wave height for local fluid particle acceleration of horizontal component

Go Wave Height = Local Fluid Particle Acceleration*Wavelength*cosh(2*pi*Water Depth/Wavelength)/([g]*pi*cosh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle))

Wave Height for simplified horizontal fluid particle displacements

Go Wave Height = -Fluid Particle Displacements*2*sinh(2*pi*Water Depth/Wavelength)/cosh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle)

Wave Height for simplified vertical fluid particle displacements

Go Wave Height = Fluid Particle Displacements*2*sinh(2*pi*Water Depth/Wavelength)/sinh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle)

Wave height for major horizontal semi-axis given wavelength and wave height

Go Wave Height = Horizontal Semi-axis of Water Particle*2*sinh(2*pi*Depth of Water Wave/Wavelength)/cosh(2*pi*(Distance above the Bottom)/Wavelength)

Wave height for minor vertical semi-axis given wavelength, wave height and water depth

Go Wave Height = Vertical Semi-Axis*2*sinh(2*pi*Depth of Water Wave/Wavelength)/sinh(2*pi*(Distance above the Bottom)/Wavelength)

Wave Height represented by Rayleigh Distribution

Go Individual Wave Height = (2*Wave Height/Root Mean Square Wave Height^2)*exp(-(Wave Height^2/Root Mean Square Wave Height^2))

Wave Height represented by Rayleigh Distribution under Narrow Band Condition

Go Individual Wave Height = 1-exp(-Wave Height^2/Root Mean Square Wave Height^2)

Mean Wave Period given Maximum Wave Period

Go Mean Wave Period = Maximum Wave Period/Coefficient Eckman

Wave Height given wave steepness

Go Wave Height = Wave Steepness*Wavelength

Wavelength given wave steepness

Go Wavelength = Wave Height/Wave Steepness

Significant Wave Height given Wave Period for North Sea

Go Significant Wave Height = (Wave Period/3.94)^1/0.376

Maximum Wave Height

Go Maximum Wave Height = 1.86*Significant Wave Height

Wave Height given Wave Period for Mediterranean Sea

Go Wave Height = ((Wave Period-4)/2)^(1/0.7)

Wave Height given Wave Amplitude

Go Wave Height = 2*Wave Amplitude

Wave Height given Wave Period for North Atlantic Ocean

Go Wave Height = Wave Period/2.5

Wave Height for Vertical Component of Local Fluid Velocity Formula

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 Wave Height for Vertical Component of Local Fluid Velocity?

Wave Height for Vertical Component of Local Fluid Velocity calculator uses Wave Height = (Vertical Component of Velocity*2*Wavelength)*cosh(2*pi*Water Depth/Wavelength)/([g]*Wave Period*sinh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle)) to calculate the Wave Height, The Wave Height for Vertical Component of Local Fluid Velocity is Known of a surface wave is the difference between the elevations of a crest and a neighboring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering. Wave Height is denoted by H symbol.

How to calculate Wave Height for Vertical Component of Local Fluid Velocity using this online calculator? To use this online calculator for Wave Height for Vertical Component of Local Fluid Velocity, enter Vertical Component of Velocity (V_v), Wavelength (λ), Water Depth (D), Wave Period (T_p), Distance above the Bottom (D_Z+d) & Phase Angle (θ) and hit the calculate button. Here is how the Wave Height for Vertical Component of Local Fluid Velocity calculation can be explained with given input values -> 5.760748 = (2.911*2*26.8)*cosh(2*pi*12/26.8)/([g]*95*sinh(2*pi*(2)/26.8)*sin(0.5235987755982)).

FAQ

What is Wave Height for Vertical Component of Local Fluid Velocity?

The Wave Height for Vertical Component of Local Fluid Velocity is Known of a surface wave is the difference between the elevations of a crest and a neighboring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering and is represented as H = (V_v*2*λ)*cosh(2*pi*D/λ)/([g]*T_p*sinh(2*pi*(D_Z+d)/λ)*sin(θ)) or Wave Height = (Vertical Component of Velocity*2*Wavelength)*cosh(2*pi*Water Depth/Wavelength)/([g]*Wave Period*sinh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle)). Vertical Component of Velocity is the velocity of the particle which is resolved along the vertical direction, Wavelength can be defined as the distance between two successive crests or troughs of a wave, Water depth means the depth as measured from the water level to the bottom of the considered water body, Wave Period is defined as the time it takes for two successive crests to pass a given point, Distance above the Bottom expressing the local fluid velocity component & 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 Wave Height for Vertical Component of Local Fluid Velocity?

The Wave Height for Vertical Component of Local Fluid Velocity is Known of a surface wave is the difference between the elevations of a crest and a neighboring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering is calculated using Wave Height = (Vertical Component of Velocity*2*Wavelength)*cosh(2*pi*Water Depth/Wavelength)/([g]*Wave Period*sinh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle)). To calculate Wave Height for Vertical Component of Local Fluid Velocity, you need Vertical Component of Velocity (V_v), Wavelength (λ), Water Depth (D), Wave Period (T_p), Distance above the Bottom (D_Z+d) & Phase Angle (θ). With our tool, you need to enter the respective value for Vertical Component of Velocity, Wavelength, Water Depth, Wave Period, Distance above the Bottom & Phase Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Wave Height?

In this formula, Wave Height uses Vertical Component of Velocity, Wavelength, Water Depth, Wave Period, Distance above the Bottom & Phase Angle. We can use 13 other way(s) to calculate the same, which is/are as follows -

Wave Height = 2*Wave Amplitude
Wave Height = Wave Steepness*Wavelength
Wave Height = -Fluid Particle Displacements*(4*pi*Wavelength)*(cosh(2*pi*Water Depth/Wavelength))/([g]*Wave Period^2)*((cosh(2*pi*(Distance above the Bottom)/Wavelength)))*sin(Phase Angle)
Wave Height = Fluid Particle Displacements*(4*pi*Wavelength)*cosh(2*pi*Water Depth/Wavelength)/([g]*Wave Period^2*sinh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle))
Wave Height = Water Particle Velocity*2*Wavelength*cosh(2*pi*Depth of Water Wave/Wavelength)/([g]*Wave Period*cosh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle))
Wave Height = Local Fluid Particle Acceleration*Wavelength*cosh(2*pi*Water Depth/Wavelength)/([g]*pi*cosh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle))
Wave Height = -(Local Fluid Particle Acceleration*Wavelength*cosh(2*pi*Water Depth/Wavelength)/([g]*pi*sinh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle)))
Wave Height = Fluid Particle Displacements*2*sinh(2*pi*Water Depth/Wavelength)/sinh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle)
Wave Height = -Fluid Particle Displacements*2*sinh(2*pi*Water Depth/Wavelength)/cosh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle)
Wave Height = Vertical Semi-Axis*2*sinh(2*pi*Depth of Water Wave/Wavelength)/sinh(2*pi*(Distance above the Bottom)/Wavelength)
Wave Height = Horizontal Semi-axis of Water Particle*2*sinh(2*pi*Depth of Water Wave/Wavelength)/cosh(2*pi*(Distance above the Bottom)/Wavelength)
Wave Height = ((Wave Period-4)/2)^(1/0.7)
Wave Height = Wave Period/2.5

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