✖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.ⓘ Fluid Particle Displacement [ε]			+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%
✖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.ⓘ Water Depth [D]			+10% -10%
✖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.ⓘ Wave Period for Horizontal Fluid Particle [T_h]			+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 Fluid Particle Displacement [H]

⎘ Copy

👎

Formula

✖

Wave Height for Horizontal Fluid Particle Displacement

Formula

`"H" = "ε"*(4*pi*"λ")*(cosh(2*pi*"D"/"λ"))/("[g]"*"T"_{"h"}^2)*((cosh(2*pi*("D"_{"Z+d"})/"λ")))*sin("θ")`

Example

`"3.055555m"="1.55m"*(4*pi*"26.8m")*(cosh(2*pi*"12m"/"26.8m"))/("[g]"*("9s")^2)*((cosh(2*pi*("2m")/"26.8m")))*sin("30°")`

Calculator

LaTeX

Reset

👍

Download Wave Height Formulas PDF PDF Image

Wave Height for Horizontal Fluid Particle Displacement Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
H = ε*(4*pi*λ)*(cosh(2*pi*D/λ))/([g]*T_h^2)*((cosh(2*pi*(D_Z+d)/λ)))*sin(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

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)
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.
Fluid Particle Displacement - (Measured in Meter) - 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.
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.
Water Depth - (Measured in Meter) - 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.
Wave Period for Horizontal Fluid Particle - (Measured in Second) - 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.
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

Fluid Particle Displacement: 1.55 Meter --> 1.55 Meter No Conversion Required
Wavelength: 26.8 Meter --> 26.8 Meter No Conversion Required
Water Depth: 12 Meter --> 12 Meter No Conversion Required
Wave Period for Horizontal Fluid Particle: 9 Second --> 9 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 = ε*(4*pi*λ)*(cosh(2*pi*D/λ))/([g]*T_h^2)*((cosh(2*pi*(D_Z+d)/λ)))*sin(θ) --> 1.55*(4*pi*26.8)*(cosh(2*pi*12/26.8))/([g]*9^2)*((cosh(2*pi*(2)/26.8)))*sin(0.5235987755982)

Evaluating ... ...

H = 3.05555549436218

STEP 3: Convert Result to Output's Unit

3.05555549436218 Meter --> No Conversion Required

FINAL ANSWER

3.05555549436218 ≈ 3.055555 Meter <-- Wave Height

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Wave Height » Wave Height for Horizontal Fluid Particle Displacement

Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Calculator and 1700+ more calculators!

< 20 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 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 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 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 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 Bottom)/Wavelength)*sin(Phase Angle))

Wave Height for Simplified Horizontal Fluid Particle Displacement

Go Wave Height = Fluid Particle Displacement*2*sinh(2*pi*Water Depth/Wavelength of Horizontal Fluid Particle)/cosh(2*pi*(Distance above Bottom)/Wavelength of Horizontal Fluid Particle)*sin(Phase Angle)

Wave Height for Simplified Vertical Fluid Particle Displacement

Go 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)

Wave Height for Major Horizontal Semi-Axis given Wavelength

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

Wave Height for Minor Vertical Semi-Axis given Wavelength

Go Wave Height = Vertical Semi-Axis*2*sinh(2*pi*Depth of Water Wave/Wavelength)/sinh(2*pi*(Distance above 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 for North Sea/3.94)^(1/0.376)

Wave Height given Wave Period for Mediterranean Sea

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

Maximum Wave Height

Go Maximum Wave Height = 1.86*Significant Wave Height

Wave Height given Wave Period for North Atlantic Ocean

Go Wave Height = Wave Period for North Sea/2.5

Wave Height given Wave Amplitude

Go Wave Height = 2*Wave Amplitude

Wave Height for Horizontal Fluid Particle Displacement 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 Fluid Particle Displacement?

Wave Height for Horizontal Fluid Particle Displacement calculator 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 calculate 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 calculate Wave Height for Horizontal Fluid Particle Displacement using this online calculator? To use this online calculator 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. Here is how the Wave Height for Horizontal Fluid Particle Displacement calculation can be explained with given input values -> 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).

FAQ

What is Wave Height for Horizontal Fluid Particle Displacement?

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 and is represented as H = ε*(4*pi*λ)*(cosh(2*pi*D/λ))/([g]*T_h^2)*((cosh(2*pi*(D_Z+d)/λ)))*sin(θ) or 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). 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, 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, 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, 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, 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 Fluid Particle Displacement?

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 is calculated using 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 calculate Wave Height for Horizontal Fluid Particle Displacement, you need 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). With our tool, you need to enter the respective value for Fluid Particle Displacement, Wavelength, Water Depth, Wave Period for Horizontal Fluid Particle, 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 Fluid Particle Displacement, Wavelength, Water Depth, Wave Period for Horizontal Fluid Particle, Distance above Bottom & Phase Angle. We can use 12 other way(s) to calculate the same, which is/are as follows -

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

Home

FREE PDFs

🔍 Search