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

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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. Check FAQs

A = (\frac{H}{2}) \cdot \frac{\cosh (2 \cdot π \cdot \frac{D Z+d}{λ})}{\sinh (2 \cdot π \cdot \frac{d}{λ})}

A - Horizontal Semi-axis of Water Particle?H - Wave Height?D_Z+d - Distance above the Bottom?λ - Wavelength?d - Water Depth?π - Archimedes' constant?

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

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Here is how the Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth equation looks like with Values.

Here is how the Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth equation looks like with Units.

Here is how the Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth equation looks like.

7.759 = (\frac{3}{2}) \cdot \frac{\cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8})}{\sinh (2 \cdot 3.1416 \cdot \frac{0.91}{26.8})}

7.759 = (\frac{3m}{2}) \cdot \frac{\cosh (2 \cdot 3.1416 \cdot \frac{2m}{26.8m})}{\sinh (2 \cdot 3.1416 \cdot \frac{0.91m}{26.8m})}

7.759 = (\frac{3}{2}) \cdot \frac{\cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8})}{\sinh (2 \cdot 3.1416 \cdot \frac{0.91}{26.8})}

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

Follow our step by step solution on how to calculate Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth?

FIRST Step Consider the formula

A = (\frac{H}{2}) \cdot \frac{\cosh (2 \cdot π \cdot \frac{D Z+d}{λ})}{\sinh (2 \cdot π \cdot \frac{d}{λ})}

Next Step Substitute values of Variables

∴

A = (\frac{3m}{2}) \cdot \frac{\cosh (2 \cdot π \cdot \frac{2m}{26.8m})}{\sinh (2 \cdot π \cdot \frac{0.91m}{26.8m})}

Next Step Substitute values of Constants

∴

A = (\frac{3m}{2}) \cdot \frac{\cosh (2 \cdot 3.1416 \cdot \frac{2m}{26.8m})}{\sinh (2 \cdot 3.1416 \cdot \frac{0.91m}{26.8m})}

Next Step Prepare to Evaluate

∴

A = (\frac{3}{2}) \cdot \frac{\cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8})}{\sinh (2 \cdot 3.1416 \cdot \frac{0.91}{26.8})}

Next Step Evaluate

∴

A = 7.75897399145263

LAST Step Rounding Answer

∴

A = 7.759

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

Variables

Constants

Functions

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.

Symbol: A

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Horizontal Semi-axis of Water Particle

Wave Height

Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.

Symbol: H

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wave Height

Distance above the Bottom

Distance above the Bottom refers to the vertical measurement from the lowest point of a given surface (such as the bottom of waterbody) to a specified point above it.

Symbol: D_Z+d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance above the Bottom

Wavelength

Wavelength can be defined as the distance between two successive crests or troughs of a wave.

Symbol: λ

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wavelength

Water Depth

Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Water Depth

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

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)

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 in Wave Parameters category

Go Wave Amplitude

a = \frac{H}{2}

Go Angular of Radian Frequency of Wave

ω = 2 \cdot \frac{π}{P}

Go Wave number given wavelength

k = 2 \cdot \frac{π}{λ}

Go Phase Velocity or Wave Celerity

C = \frac{λ}{P}

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

Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth evaluator 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 evaluate 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 evaluate Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth using this online evaluator? To use this online evaluator 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.

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

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

The formula of Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth is expressed as Horizontal Semi-axis of Water Particle = (Wave Height/2)*(cosh(2*pi*(Distance above the Bottom)/Wavelength))/sinh(2*pi*Water Depth/Wavelength). Here is an example- 7.758974 = (3/2)*(cosh(2*pi*(2)/26.8))/sinh(2*pi*0.91/26.8).

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

With Wave Height (H), Distance above the Bottom (D_Z+d), Wavelength (λ) & Water Depth (d) we can find Major Horizontal Semi-Axis given wavelength, Wave Height and Water Depth using the formula - Horizontal Semi-axis of Water Particle = (Wave Height/2)*(cosh(2*pi*(Distance above the Bottom)/Wavelength))/sinh(2*pi*Water Depth/Wavelength). This formula also uses Archimedes' constant and , Hyperbolic Sine (sinh), Hyperbolic Cosine (cosh) function(s).

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

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

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

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

Other formulas in Wave Parameters category

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

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

Variable Name