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Wave Height for Horizontal Fluid Particle Displacement Formula

GoWave Height given Wave Amplitude Formula

GoWave Height given Wave Steepness Formula

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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. Check FAQs

H = ε \cdot (4 \cdot π \cdot λ) \cdot \frac{\cosh (2 \cdot π \cdot \frac{D}{λ})}{[g] \cdot {T h}^{2}} \cdot ((\cosh (2 \cdot π \cdot \frac{D Z+d}{λ}))) \cdot \sin (θ)

H - Wave Height?ε - Fluid Particle Displacement?λ - Wavelength?D - Water Depth?T_h - Wave Period for Horizontal Fluid Particle?D_Z+d - Distance above Bottom?θ - Phase Angle?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Wave Height for Horizontal Fluid Particle Displacement Example

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Here is how the Wave Height for Horizontal Fluid Particle Displacement equation looks like with Values.

Here is how the Wave Height for Horizontal Fluid Particle Displacement equation looks like with Units.

Here is how the Wave Height for Horizontal Fluid Particle Displacement equation looks like.

3.0556 = 1.55 \cdot (4 \cdot 3.1416 \cdot 26.8) \cdot \frac{\cosh (2 \cdot 3.1416 \cdot \frac{12}{26.8})}{9.8066 \cdot 9^{2}} \cdot ((\cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8}))) \cdot \sin (30)

3.0556m = 1.55m \cdot (4 \cdot 3.1416 \cdot 26.8m) \cdot \frac{\cosh (2 \cdot 3.1416 \cdot \frac{12m}{26.8m})}{9.8066m/s² \cdot {9s}^{2}} \cdot ((\cosh (2 \cdot 3.1416 \cdot \frac{2m}{26.8m}))) \cdot \sin (30°)

3.0556 = 1.55 \cdot (4 \cdot 3.1416 \cdot 26.8) \cdot \frac{\cosh (2 \cdot 3.1416 \cdot \frac{12}{26.8})}{9.8066 \cdot 9^{2}} \cdot ((\cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8}))) \cdot \sin (30)

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Wave Height for Horizontal Fluid Particle Displacement Solution

Follow our step by step solution on how to calculate Wave Height for Horizontal Fluid Particle Displacement?

FIRST Step Consider the formula

H = ε \cdot (4 \cdot π \cdot λ) \cdot \frac{\cosh (2 \cdot π \cdot \frac{D}{λ})}{[g] \cdot {T h}^{2}} \cdot ((\cosh (2 \cdot π \cdot \frac{D Z+d}{λ}))) \cdot \sin (θ)

Next Step Substitute values of Variables

∴

H = 1.55m \cdot (4 \cdot π \cdot 26.8m) \cdot \frac{\cosh (2 \cdot π \cdot \frac{12m}{26.8m})}{[g] \cdot {9s}^{2}} \cdot ((\cosh (2 \cdot π \cdot \frac{2m}{26.8m}))) \cdot \sin (30°)

Next Step Substitute values of Constants

∴

H = 1.55m \cdot (4 \cdot 3.1416 \cdot 26.8m) \cdot \frac{\cosh (2 \cdot 3.1416 \cdot \frac{12m}{26.8m})}{9.8066m/s² \cdot {9s}^{2}} \cdot ((\cosh (2 \cdot 3.1416 \cdot \frac{2m}{26.8m}))) \cdot \sin (30°)

Next Step Convert Units

∴

H = 1.55m \cdot (4 \cdot 3.1416 \cdot 26.8m) \cdot \frac{\cosh (2 \cdot 3.1416 \cdot \frac{12m}{26.8m})}{9.8066m/s² \cdot {9s}^{2}} \cdot ((\cosh (2 \cdot 3.1416 \cdot \frac{2m}{26.8m}))) \cdot \sin (0.5236rad)

Next Step Prepare to Evaluate

∴

H = 1.55 \cdot (4 \cdot 3.1416 \cdot 26.8) \cdot \frac{\cosh (2 \cdot 3.1416 \cdot \frac{12}{26.8})}{9.8066 \cdot 9^{2}} \cdot ((\cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8}))) \cdot \sin (0.5236)

Next Step Evaluate

∴

H = 3.05555549436218m

LAST Step Rounding Answer

∴

H = 3.0556m

Wave Height for Horizontal Fluid Particle Displacement Formula Elements

Variables

Constants

Functions

Wave Height

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.

Symbol: H

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wave Height

Fluid Particle Displacement

Fluid Particle Displacement is the movement of individual particles of fluid within a flow field over time. Understanding particle displacement helps in predicting how waves travel through water.

Symbol: ε

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Fluid Particle Displacement

Wavelength

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.

Symbol: λ

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wavelength

Water Depth

Water Depth is the vertical distance between the water surface and the seabed or ocean floor at a particular location. It determines the accessibility of waterways and ports for ships.

Symbol: D

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth

Wave Period for Horizontal Fluid Particle

Wave Period for Horizontal Fluid Particle is the time interval between successive crests (or troughs) of waves passing a fixed point of horizontal fluid particle.

Symbol: T_h

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Wave Period for Horizontal Fluid Particle

Distance above Bottom

Distance above Bottom is the vertical distance measured from the seabed or the ocean floor to a specific point in the water column.

Symbol: D_Z+d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance above Bottom

Phase Angle

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.

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 to find Wave Height

Go Wave Height given Wave Amplitude

H = 2 \cdot a

Go Wave Height given Wave Steepness

H = ε s \cdot λ

Other formulas in Wave Height category

Go Wave Height for Vertical Fluid Particle Displacement

H' = ε \cdot (4 \cdot π \cdot λ) \cdot \frac{\cosh (2 \cdot π \cdot \frac{D}{λ})}{[g] \cdot {T p}^{2} \cdot \sinh (2 \cdot π \cdot \frac{D Z+d}{λ}) \cdot \cos (θ)}

Go Significant Wave Height given Wave Period for North Sea

H s = {(\frac{T NS}{3.94})}^{\frac{1}{0.376}}

How to Evaluate Wave Height for Horizontal Fluid Particle Displacement?

Wave Height for Horizontal Fluid Particle Displacement evaluator uses 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) to evaluate the Wave Height, The Wave Height for Horizontal Fluid Particle Displacement formula is defined as 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 evaluate Wave Height for Horizontal Fluid Particle Displacement using this online evaluator? To use this online evaluator for Wave Height for Horizontal Fluid Particle Displacement, enter Fluid Particle Displacement (ε), Wavelength (λ), Water Depth (D), Wave Period for Horizontal Fluid Particle (T_h), Distance above Bottom (D_Z+d) & Phase Angle (θ) and hit the calculate button.

FAQs on Wave Height for Horizontal Fluid Particle Displacement

What is the formula to find Wave Height for Horizontal Fluid Particle Displacement?

The formula of Wave Height for Horizontal Fluid Particle Displacement is expressed as 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). Here is an example- 0.78853 = 1.55*(4*pi*26.8)*(cosh(2*pi*12/26.8))/([g]*9^2)*((cosh(2*pi*(2)/26.8)))*sin(0.5235987755982).

How to calculate Wave Height for Horizontal Fluid Particle Displacement?

With Fluid Particle Displacement (ε), Wavelength (λ), Water Depth (D), Wave Period for Horizontal Fluid Particle (T_h), Distance above Bottom (D_Z+d) & Phase Angle (θ) we can find Wave Height for Horizontal Fluid Particle Displacement using the formula - 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). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and , Sine (sin), Hyperbolic Cosine (cosh) function(s).

What are the other ways to Calculate Wave Height?

Here are the different ways to Calculate Wave Height-

Wave Height=2*Wave Amplitude
Wave Height=Wave Steepness*Wavelength
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))

Can the Wave Height for Horizontal Fluid Particle Displacement be negative?

Yes, the Wave Height for Horizontal Fluid Particle Displacement, measured in Length can be negative.

Which unit is used to measure Wave Height for Horizontal Fluid Particle Displacement?

Wave Height for Horizontal Fluid Particle Displacement is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Wave Height for Horizontal Fluid Particle Displacement can be measured.

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Wave Height for Horizontal Fluid Particle Displacement Formula

​GoWave Height given Wave Amplitude Formula

​GoWave Height given Wave Steepness Formula

Wave Height for Horizontal Fluid Particle Displacement Example

Wave Height for Horizontal Fluid Particle Displacement Solution

Wave Height for Horizontal Fluid Particle Displacement Formula Elements

Other Formulas to find Wave Height

Other formulas in Wave Height category

How to Evaluate Wave Height for Horizontal Fluid Particle Displacement?

FAQs on Wave Height for Horizontal Fluid Particle Displacement

Variable Name

GoWave Height given Wave Amplitude Formula

GoWave Height given Wave Steepness Formula