Wave Height for Horizontal Component of Local Fluid Velocity Calculator

✖Water Particle Velocity is the speed at which water particles move due to wave motion or currents. This movement typically decreases with depth below the surface.ⓘ Water Particle Velocity [u]			+10% -10%
✖Wavelength is the horizontal distance between successive crests (or troughs) of a wave. It provides crucial information about the size and shape of waves propagating in water bodies.ⓘ Wavelength [λ]			+10% -10%
✖Depth of Water Wave is the vertical distance from the still water level to the seabed, specifically related to the depth at which the water particle motion due to the wave becomes negligible.ⓘ Depth of Water Wave [d]			+10% -10%
✖Wave Period is the time interval between successive crests (or troughs) of waves passing a fixed point. The period of a wave is directly related to its energy content.ⓘ Wave Period [T_p]			+10% -10%
✖Distance above Bottom is the vertical distance measured from the seabed or the ocean floor to a specific point in the water column.ⓘ Distance above Bottom [D_Z+d]			+10% -10%
✖Phase Angle is a measure of the displacement between the peaks, troughs, or any specific point of a wave cycle compared to a reference point.ⓘ Phase Angle [θ]			+10% -10%

✖Wave Height is the vertical distance between the trough (lowest point) and the crest (highest point) of a wave. The average height of the highest third of the waves in a given wave dataset.ⓘ Wave Height for Horizontal Component of Local Fluid Velocity [H]

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Wave Height for Horizontal Component of Local Fluid Velocity

Formula

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

Example

3.05399 m = 50 m/s \cdot 2 \cdot 26.8 m \cdot \frac{\cosh (2 \cdot π \cdot \frac{0.9 m}{26.8 m})}{[g] \cdot 95 s \cdot \cosh (2 \cdot π \cdot \frac{2 m}{26.8 m}) \cdot \cos (30 °)}

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Wave Height for Horizontal Component of Local Fluid Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wave Height = Water Particle Velocity*2*Wavelength*cosh(2*pi*Depth of Water Wave/Wavelength)/([g]*Wave Period*cosh(2*pi*(Distance above Bottom)/Wavelength)*cos(Phase Angle))
H = u*2*λ*cosh(2*pi*d/λ)/([g]*T_p*cosh(2*pi*(D_Z+d)/λ)*cos(θ))
This formula uses 2 Constants, 2 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

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

Wave Height - (Measured in Meter) - Wave Height is the vertical distance between the trough (lowest point) and the crest (highest point) of a wave. The average height of the highest third of the waves in a given wave dataset.
Water Particle Velocity - (Measured in Meter per Second) - Water Particle Velocity is the speed at which water particles move due to wave motion or currents. This movement typically decreases with depth below the surface.
Wavelength - (Measured in Meter) - Wavelength is the horizontal distance between successive crests (or troughs) of a wave. It provides crucial information about the size and shape of waves propagating in water bodies.
Depth of Water Wave - (Measured in Meter) - Depth of Water Wave is the vertical distance from the still water level to the seabed, specifically related to the depth at which the water particle motion due to the wave becomes negligible.
Wave Period - (Measured in Second) - Wave Period is the time interval between successive crests (or troughs) of waves passing a fixed point. The period of a wave is directly related to its energy content.
Distance above Bottom - (Measured in Meter) - Distance above Bottom is the vertical distance measured from the seabed or the ocean floor to a specific point in the water column.
Phase Angle - (Measured in Radian) - Phase Angle is a measure of the displacement between the peaks, troughs, or any specific point of a wave cycle compared to a reference point.

STEP 1: Convert Input(s) to Base Unit

Water Particle Velocity: 50 Meter per Second --> 50 Meter per Second No Conversion Required
Wavelength: 26.8 Meter --> 26.8 Meter No Conversion Required
Depth of Water Wave: 0.9 Meter --> 0.9 Meter No Conversion Required
Wave Period: 95 Second --> 95 Second No Conversion Required
Distance above 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 = u*2*λ*cosh(2*pi*d/λ)/([g]*T_p*cosh(2*pi*(D_Z+d)/λ)*cos(θ)) --> 50*2*26.8*cosh(2*pi*0.9/26.8)/([g]*95*cosh(2*pi*(2)/26.8)*cos(0.5235987755982))

Evaluating ... ...

H = 3.05399048326168

STEP 3: Convert Result to Output's Unit

3.05399048326168 Meter --> No Conversion Required

FINAL ANSWER

3.05399048326168 ≈ 3.05399 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 Horizontal Component of Local Fluid Velocity

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< Wave Height Calculators

Wave Height for Horizontal Fluid Particle Displacement

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

Wave Height for Vertical Fluid Particle Displacement

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

Wave Height given Wave Steepness

Go Wave Height = Wave Steepness*Wavelength

Wave Height given Wave Amplitude

Go Wave Height = 2*Wave Amplitude

Wave Height for Horizontal 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 Horizontal Component of Local Fluid Velocity?

Wave Height for Horizontal Component of Local Fluid Velocity calculator uses Wave Height = Water Particle Velocity*2*Wavelength*cosh(2*pi*Depth of Water Wave/Wavelength)/([g]*Wave Period*cosh(2*pi*(Distance above Bottom)/Wavelength)*cos(Phase Angle)) to calculate the Wave Height, The Wave Height for Horizontal Component of Local Fluid Velocity formula is defined as the vertical distance between the trough (lowest point) and the crest (highest point) of a wave. The average height of the highest third of the waves in a given wave dataset. Wave Height is denoted by H symbol.

How to calculate Wave Height for Horizontal Component of Local Fluid Velocity using this online calculator? To use this online calculator for Wave Height for Horizontal Component of Local Fluid Velocity, enter Water Particle Velocity (u), Wavelength (λ), Depth of Water Wave (d), Wave Period (T_p), Distance above Bottom (D_Z+d) & Phase Angle (θ) and hit the calculate button. Here is how the Wave Height for Horizontal Component of Local Fluid Velocity calculation can be explained with given input values -> -2.664696 = 50*2*26.8*cosh(2*pi*0.9/26.8)/([g]*95*cosh(2*pi*(2)/26.8)*cos(0.5235987755982)).

FAQ

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

The Wave Height for Horizontal Component of Local Fluid Velocity formula is defined as the vertical distance between the trough (lowest point) and the crest (highest point) of a wave. The average height of the highest third of the waves in a given wave dataset and is represented as H = u*2*λ*cosh(2*pi*d/λ)/([g]*T_p*cosh(2*pi*(D_Z+d)/λ)*cos(θ)) or Wave Height = Water Particle Velocity*2*Wavelength*cosh(2*pi*Depth of Water Wave/Wavelength)/([g]*Wave Period*cosh(2*pi*(Distance above Bottom)/Wavelength)*cos(Phase Angle)). Water Particle Velocity is the speed at which water particles move due to wave motion or currents. This movement typically decreases with depth below the surface, Wavelength is the horizontal distance between successive crests (or troughs) of a wave. It provides crucial information about the size and shape of waves propagating in water bodies, Depth of Water Wave is the vertical distance from the still water level to the seabed, specifically related to the depth at which the water particle motion due to the wave becomes negligible, Wave Period is the time interval between successive crests (or troughs) of waves passing a fixed point. The period of a wave is directly related to its energy content, Distance above Bottom is the vertical distance measured from the seabed or the ocean floor to a specific point in the water column & Phase Angle is a measure of the displacement between the peaks, troughs, or any specific point of a wave cycle compared to a reference point.

How to calculate Wave Height for Horizontal Component of Local Fluid Velocity?

The Wave Height for Horizontal Component of Local Fluid Velocity formula is defined as the vertical distance between the trough (lowest point) and the crest (highest point) of a wave. The average height of the highest third of the waves in a given wave dataset is calculated using Wave Height = Water Particle Velocity*2*Wavelength*cosh(2*pi*Depth of Water Wave/Wavelength)/([g]*Wave Period*cosh(2*pi*(Distance above Bottom)/Wavelength)*cos(Phase Angle)). To calculate Wave Height for Horizontal Component of Local Fluid Velocity, you need Water Particle Velocity (u), Wavelength (λ), Depth of Water Wave (d), Wave Period (T_p), Distance above Bottom (D_Z+d) & Phase Angle (θ). With our tool, you need to enter the respective value for Water Particle Velocity, Wavelength, Depth of Water Wave, Wave Period, Distance above 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 Water Particle Velocity, Wavelength, Depth of Water Wave, Wave Period, Distance above Bottom & Phase Angle. We can use 3 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 Displacement*(4*pi*Wavelength)*(cosh(2*pi*Water Depth/Wavelength))/([g]*Wave Period for Horizontal Fluid Particle^2)*((cosh(2*pi*(Distance above Bottom)/Wavelength)))*sin(Phase Angle)

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