✖Horizontal Semi-axis of Water Particle is a plane curve surrounding two focal points, such that for all points on the curve, sum of two distances to focal points is constant.ⓘ Horizontal Semi-axis of Water Particle [A]			+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%
✖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%
✖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%

✖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 Major Horizontal Semi-Axis given Wavelength [H]

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Wave Height for Major Horizontal Semi-Axis given Wavelength

Formula

`"H" = "A"*2*sinh(2*pi*"d"/"λ")/cosh(2*pi*("D"_{"Z+d"})/"λ")`

Example

`"2.564334m"="6.707"*2*sinh(2*pi*"0.9m"/"26.8m")/cosh(2*pi*("2m")/"26.8m")`

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Wave Height for Major Horizontal Semi-Axis given Wavelength Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wave Height = Horizontal Semi-axis of Water Particle*2*sinh(2*pi*Depth of Water Wave/Wavelength)/cosh(2*pi*(Distance above Bottom)/Wavelength)
H = A*2*sinh(2*pi*d/λ)/cosh(2*pi*(D_Z+d)/λ)
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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 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.
Horizontal Semi-axis of Water Particle - Horizontal Semi-axis of Water Particle is a plane curve surrounding two focal points, such that for all points on the curve, sum of two distances to focal points is constant.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Horizontal Semi-axis of Water Particle: 6.707 --> No Conversion Required
Depth of Water Wave: 0.9 Meter --> 0.9 Meter No Conversion Required
Wavelength: 26.8 Meter --> 26.8 Meter No Conversion Required
Distance above Bottom: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H = A*2*sinh(2*pi*d/λ)/cosh(2*pi*(D_Z+d)/λ) --> 6.707*2*sinh(2*pi*0.9/26.8)/cosh(2*pi*(2)/26.8)

Evaluating ... ...

H = 2.56433397155362

STEP 3: Convert Result to Output's Unit

2.56433397155362 Meter --> No Conversion Required

FINAL ANSWER

2.56433397155362 ≈ 2.564334 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 Major Horizontal Semi-Axis given Wavelength

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< 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 Major Horizontal Semi-Axis given Wavelength Formula

Wave Height = Horizontal Semi-axis of Water Particle*2*sinh(2*pi*Depth of Water Wave/Wavelength)/cosh(2*pi*(Distance above Bottom)/Wavelength)
H = A*2*sinh(2*pi*d/λ)/cosh(2*pi*(D_Z+d)/λ)

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.

Define wave height

The wave height 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.

How to Calculate Wave Height for Major Horizontal Semi-Axis given Wavelength?

Wave Height for Major Horizontal Semi-Axis given Wavelength calculator uses Wave Height = Horizontal Semi-axis of Water Particle*2*sinh(2*pi*Depth of Water Wave/Wavelength)/cosh(2*pi*(Distance above Bottom)/Wavelength) to calculate the Wave Height, The Wave Height for Major Horizontal Semi-Axis given Wavelength 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 Major Horizontal Semi-Axis given Wavelength using this online calculator? To use this online calculator for Wave Height for Major Horizontal Semi-Axis given Wavelength, enter Horizontal Semi-axis of Water Particle (A), Depth of Water Wave (d), Wavelength (λ) & Distance above Bottom (D_Z+d) and hit the calculate button. Here is how the Wave Height for Major Horizontal Semi-Axis given Wavelength calculation can be explained with given input values -> 2.564334 = 6.707*2*sinh(2*pi*0.9/26.8)/cosh(2*pi*(2)/26.8).

FAQ

What is Wave Height for Major Horizontal Semi-Axis given Wavelength?

The Wave Height for Major Horizontal Semi-Axis given Wavelength 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 = A*2*sinh(2*pi*d/λ)/cosh(2*pi*(D_Z+d)/λ) or Wave Height = Horizontal Semi-axis of Water Particle*2*sinh(2*pi*Depth of Water Wave/Wavelength)/cosh(2*pi*(Distance above Bottom)/Wavelength). Horizontal Semi-axis of Water Particle is a plane curve surrounding two focal points, such that for all points on the curve, sum of two distances to focal points is constant, 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, 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 & Distance above Bottom is the vertical distance measured from the seabed or the ocean floor to a specific point in the water column.

How to calculate Wave Height for Major Horizontal Semi-Axis given Wavelength?

The Wave Height for Major Horizontal Semi-Axis given Wavelength 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 = Horizontal Semi-axis of Water Particle*2*sinh(2*pi*Depth of Water Wave/Wavelength)/cosh(2*pi*(Distance above Bottom)/Wavelength). To calculate Wave Height for Major Horizontal Semi-Axis given Wavelength, you need Horizontal Semi-axis of Water Particle (A), Depth of Water Wave (d), Wavelength (λ) & Distance above Bottom (D_Z+d). With our tool, you need to enter the respective value for Horizontal Semi-axis of Water Particle, Depth of Water Wave, Wavelength & Distance above Bottom 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 Horizontal Semi-axis of Water Particle, Depth of Water Wave, Wavelength & Distance above Bottom. 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 = 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 = 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 = ((Wave Period for Mediterranean Sea-4)/2)^(1/0.7)
Wave Height = Wave Period for North Sea/2.5

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