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Wave Height for Simplified Vertical 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 2 \cdot \frac{\sinh (2 \cdot π \cdot \frac{D}{λ vp})}{\sinh (2 \cdot π \cdot \frac{D Z+d}{λ vp})} \cdot \cos (θ)

H - Wave Height?ε' - Particle Displacement?D - Water Depth?λ_vp - Wavelength of Vertical Fluid Particle?D_Z+d - Distance above Bottom?θ - Phase Angle?π - Archimedes' constant?

Wave Height for Simplified Vertical Fluid Particle Displacement Example

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

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

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

3.0199 = 0.22 \cdot 2 \cdot \frac{\sinh (2 \cdot 3.1416 \cdot \frac{12}{55.9})}{\sinh (2 \cdot 3.1416 \cdot \frac{2}{55.9})} \cdot \cos (30)

3.0199m = 0.22m \cdot 2 \cdot \frac{\sinh (2 \cdot 3.1416 \cdot \frac{12m}{55.9m})}{\sinh (2 \cdot 3.1416 \cdot \frac{2m}{55.9m})} \cdot \cos (30°)

3.0199 = 0.22 \cdot 2 \cdot \frac{\sinh (2 \cdot 3.1416 \cdot \frac{12}{55.9})}{\sinh (2 \cdot 3.1416 \cdot \frac{2}{55.9})} \cdot \cos (30)

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Wave Height for Simplified Vertical Fluid Particle Displacement Solution

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

FIRST Step Consider the formula

H = ε' \cdot 2 \cdot \frac{\sinh (2 \cdot π \cdot \frac{D}{λ vp})}{\sinh (2 \cdot π \cdot \frac{D Z+d}{λ vp})} \cdot \cos (θ)

Next Step Substitute values of Variables

∴

H = 0.22m \cdot 2 \cdot \frac{\sinh (2 \cdot π \cdot \frac{12m}{55.9m})}{\sinh (2 \cdot π \cdot \frac{2m}{55.9m})} \cdot \cos (30°)

Next Step Substitute values of Constants

∴

H = 0.22m \cdot 2 \cdot \frac{\sinh (2 \cdot 3.1416 \cdot \frac{12m}{55.9m})}{\sinh (2 \cdot 3.1416 \cdot \frac{2m}{55.9m})} \cdot \cos (30°)

Next Step Convert Units

∴

H = 0.22m \cdot 2 \cdot \frac{\sinh (2 \cdot 3.1416 \cdot \frac{12m}{55.9m})}{\sinh (2 \cdot 3.1416 \cdot \frac{2m}{55.9m})} \cdot \cos (0.5236rad)

Next Step Prepare to Evaluate

∴

H = 0.22 \cdot 2 \cdot \frac{\sinh (2 \cdot 3.1416 \cdot \frac{12}{55.9})}{\sinh (2 \cdot 3.1416 \cdot \frac{2}{55.9})} \cdot \cos (0.5236)

Next Step Evaluate

∴

H = 3.01990580342196m

LAST Step Rounding Answer

∴

H = 3.0199m

Wave Height for Simplified Vertical 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

Particle Displacement

Particle Displacement is the movement of fluid particles due to various forces and processes in aquatic environments.

Symbol: ε'

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Particle Displacement

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

Wavelength of Vertical Fluid Particle

Wavelength of Vertical Fluid Particle is the horizontal distance between successive crests of wave vertical fluid particle. It provides information about the shape of waves in water bodies.

Symbol: λ_vp

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wavelength of Vertical 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

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)

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

Go Wave Height for Horizontal Fluid Particle Displacement

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)

Go Wave Height for Horizontal Component of Local Fluid Velocity

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)}

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}}

Go Wave Height Represented by Rayleigh Distribution

H iw = (\frac{2 \cdot H}{{H rms}^{2}}) \cdot \exp (- (\frac{H^{2}}{{H rms}^{2}}))

Go Wave Height Represented by Rayleigh Distribution under Narrow Band Condition

H iw = - (1 - \exp (\frac{H^{2}}{{H rms}^{2}}))

How to Evaluate Wave Height for Simplified Vertical Fluid Particle Displacement?

Wave Height for Simplified Vertical Fluid Particle Displacement evaluator uses Wave Height = Particle Displacement*2*sinh(2*pi*Water Depth/Wavelength of Vertical Fluid Particle)/sinh(2*pi*(Distance above Bottom)/Wavelength of Vertical Fluid Particle)*cos(Phase Angle) to evaluate the Wave Height, The Wave Height for Simplified Vertical 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 Simplified Vertical Fluid Particle Displacement using this online evaluator? To use this online evaluator for Wave Height for Simplified Vertical Fluid Particle Displacement, enter Particle Displacement (ε'), Water Depth (D), Wavelength of Vertical Fluid Particle (λ_vp), Distance above Bottom (D_Z+d) & Phase Angle (θ) and hit the calculate button.

FAQs on Wave Height for Simplified Vertical Fluid Particle Displacement

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

The formula of Wave Height for Simplified Vertical Fluid Particle Displacement is expressed as Wave Height = Particle Displacement*2*sinh(2*pi*Water Depth/Wavelength of Vertical Fluid Particle)/sinh(2*pi*(Distance above Bottom)/Wavelength of Vertical Fluid Particle)*cos(Phase Angle). Here is an example- 3.019906 = 0.22*2*sinh(2*pi*12/55.9)/sinh(2*pi*(2)/55.9)*cos(0.5235987755982).

How to calculate Wave Height for Simplified Vertical Fluid Particle Displacement?

With Particle Displacement (ε'), Water Depth (D), Wavelength of Vertical Fluid Particle (λ_vp), Distance above Bottom (D_Z+d) & Phase Angle (θ) we can find Wave Height for Simplified Vertical Fluid Particle Displacement using the formula - Wave Height = Particle Displacement*2*sinh(2*pi*Water Depth/Wavelength of Vertical Fluid Particle)/sinh(2*pi*(Distance above Bottom)/Wavelength of Vertical Fluid Particle)*cos(Phase Angle). This formula also uses Archimedes' constant and , Cosine (cos), Hyperbolic Sine (sinh) 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=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)

Can the Wave Height for Simplified Vertical Fluid Particle Displacement be negative?

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

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

Wave Height for Simplified Vertical 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 Simplified Vertical Fluid Particle Displacement can be measured.

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Wave Height for Simplified Vertical Fluid Particle Displacement Formula

​GoWave Height given Wave Amplitude Formula

​GoWave Height given Wave Steepness Formula

Wave Height for Simplified Vertical Fluid Particle Displacement Example

Wave Height for Simplified Vertical Fluid Particle Displacement Solution

Wave Height for Simplified Vertical Fluid Particle Displacement Formula Elements

Other Formulas to find Wave Height

Other formulas in Wave Height category

How to Evaluate Wave Height for Simplified Vertical Fluid Particle Displacement?

FAQs on Wave Height for Simplified Vertical Fluid Particle Displacement

Variable Name

GoWave Height given Wave Amplitude Formula

GoWave Height given Wave Steepness Formula