Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth Calculator

✖Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Wave Height [H]			+10% -10%
✖Distance above the Bottom expressing the local fluid velocity component.ⓘ Distance above the Bottom [D_Z+d]			+10% -10%
✖Wavelength can be defined as the distance between two successive crests or troughs of a wave.ⓘ Wavelength [λ]			+10% -10%
✖Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [d]			+10% -10%

✖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.ⓘ Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth [A]

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Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth

Formula

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

Example

`"7.758974"=("3m"/2)*(cosh(2*pi*("2m")/"26.8m"))/sinh(2*pi*"0.91m"/"26.8m")`

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Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Wave Height - (Measured in Meter) - Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.
Distance above the Bottom - (Measured in Meter) - Distance above the Bottom expressing the local fluid velocity component.
Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.

STEP 1: Convert Input(s) to Base Unit

Wave Height: 3 Meter --> 3 Meter No Conversion Required
Distance above the Bottom: 2 Meter --> 2 Meter No Conversion Required
Wavelength: 26.8 Meter --> 26.8 Meter No Conversion Required
Water Depth: 0.91 Meter --> 0.91 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (H/2)*(cosh(2*pi*(D_Z+d)/λ))/sinh(2*pi*d/λ) --> (3/2)*(cosh(2*pi*(2)/26.8))/sinh(2*pi*0.91/26.8)

Evaluating ... ...

A = 7.75897399145263

STEP 3: Convert Result to Output's Unit

7.75897399145263 --> No Conversion Required

FINAL ANSWER

7.75897399145263 ≈ 7.758974 <-- Horizontal Semi-axis of Water Particle

(Calculation completed in 00.020 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< 18 Wave Parameters Calculators

Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth

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

Minor Vertical Semi-Axis given Wavelength, Wave Height and Water Depth

Go Vertical Semi-Axis = (Wave Height/2)*(sinh(2*pi*(Distance above the Bottom)/Wavelength))/sinh(2*pi*Water Depth/Wavelength)

Eckart's Equation for Wavelength

Go Wavelength = (([g]*Wave Period^2/2*pi)*sqrt(tanh(4*pi^2*Water Depth)/Wave Period^2*[g]))

Water Depth for Maximum Wave Steepness of Waves Travelling

Go Water Depth = Wavelength*atanh(Wave Steepness/0.142)/(2*pi)

Wavelength for Maximum Wave Steepness

Go Wavelength = 2*pi*Water Depth/atanh(Wave Steepness/0.142)

Maximum Wave Steepness for Waves Travelling

Go Wave Steepness = 0.142*tanh(2*pi*Water Depth/Wavelength)

Wave Amplitude given Elevation of Water Surface Relative to SWL

Go Wave Amplitude = Elevation of Water Surface/cos(Theta)

Elevation of Water Surface Relative to SWL

Go Elevation of Water Surface = Wave Amplitude*cos(Theta)

Phase Velocity or Wave Celerity given Radian Frequency and Wavenumber

Go Celerity of The Wave = Wave Angular Frequency/Wave Number

Radian Frequency given Wave Celerity

Go Wave Angular Frequency = Celerity of The Wave*Wave Number

Wave Number given Wave Celerity

Go Wave Number = Wave Angular Frequency/Celerity of The Wave

Phase Velocity or Wave Celerity

Go Celerity of The Wave = Wavelength/Wave Period

Angular of Radian Frequency of Wave

Go Wave Angular Frequency = 2*pi/Wave Period

Wave Steepness

Go Wave Steepness = Wave Height/Wavelength

Wave number given wavelength

Go Wave Number = 2*pi/Wavelength

Wave Height given Maximum Wave Steepness Limit by Michell

Go Wave Height = Wavelength*0.142

Wavelength given Maximum Wave Steepness Limit by Michell

Go Wavelength = Wave Height/0.142

Wave Amplitude

Go Wave Amplitude = Wave Height/2

Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth Formula

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

What is wavelength?

The wavelength of a wave is measured as the distance between any two corresponding points on adjacent waves, which would mean from a crest to the next adjacent crest.

How to Calculate Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth?

Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth calculator uses Horizontal Semi-axis of Water Particle = (Wave Height/2)*(cosh(2*pi*(Distance above the Bottom)/Wavelength))/sinh(2*pi*Water Depth/Wavelength) to calculate the Horizontal Semi-axis of Water Particle, The Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth formula is defined as the parameters of ellipse influencing fluid particle displacement in horizontal and vertical direction. Horizontal Semi-axis of Water Particle is denoted by A symbol.

How to calculate Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth using this online calculator? To use this online calculator for Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth, enter Wave Height (H), Distance above the Bottom (D_Z+d), Wavelength (λ) & Water Depth (d) and hit the calculate button. Here is how the Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth calculation can be explained with given input values -> 7.758974 = (3/2)*(cosh(2*pi*(2)/26.8))/sinh(2*pi*0.91/26.8).

FAQ

What is Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth?

The Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth formula is defined as the parameters of ellipse influencing fluid particle displacement in horizontal and vertical direction and is represented as A = (H/2)*(cosh(2*pi*(D_Z+d)/λ))/sinh(2*pi*d/λ) or Horizontal Semi-axis of Water Particle = (Wave Height/2)*(cosh(2*pi*(Distance above the Bottom)/Wavelength))/sinh(2*pi*Water Depth/Wavelength). Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough, Distance above the Bottom expressing the local fluid velocity component, Wavelength can be defined as the distance between two successive crests or troughs of a wave & Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.

How to calculate Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth?

The Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth formula is defined as the parameters of ellipse influencing fluid particle displacement in horizontal and vertical direction is calculated using Horizontal Semi-axis of Water Particle = (Wave Height/2)*(cosh(2*pi*(Distance above the Bottom)/Wavelength))/sinh(2*pi*Water Depth/Wavelength). To calculate Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth, you need Wave Height (H), Distance above the Bottom (D_Z+d), Wavelength (λ) & Water Depth (d). With our tool, you need to enter the respective value for Wave Height, Distance above the Bottom, Wavelength & Water Depth and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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