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Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman Formula

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Vertical Eddy Viscosity Coefficient is a coefficient relating the average shear stress within a turbulent flow of water or air to the vertical gradient of velocity. Check FAQs

ε v = \frac{{D Eddy}^{2} \cdot ρ water \cdot Ω E \cdot \sin (L)}{π^{2}}

ε_v - Vertical Eddy Viscosity Coefficient?D_Eddy - Depth of Frictional Influence by Eckman?ρ_water - Water Density?Ω_E - Angular Speed of the Earth?L - Latitude of a Position on Earth Surface?π - Archimedes' constant?

Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman Example

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Here is how the Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman equation looks like with Values.

Here is how the Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman equation looks like with Units.

Here is how the Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman equation looks like.

0.5693 = \frac{{15.01}^{2} \cdot 1000 \cdot 7.3E-5 \cdot \sin (20)}{{3.1416}^{2}}

0.5693 = \frac{{15.01m}^{2} \cdot 1000kg/m³ \cdot 7.3E-5rad/s \cdot \sin (20°)}{{3.1416}^{2}}

0.5693 = \frac{{15.01}^{2} \cdot 1000 \cdot 7.3E-5 \cdot \sin (20)}{{3.1416}^{2}}

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Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman Solution

Follow our step by step solution on how to calculate Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman?

FIRST Step Consider the formula

ε v = \frac{{D Eddy}^{2} \cdot ρ water \cdot Ω E \cdot \sin (L)}{π^{2}}

Next Step Substitute values of Variables

∴

ε v = \frac{{15.01m}^{2} \cdot 1000kg/m³ \cdot 7.3E-5rad/s \cdot \sin (20°)}{π^{2}}

Next Step Substitute values of Constants

∴

ε v = \frac{{15.01m}^{2} \cdot 1000kg/m³ \cdot 7.3E-5rad/s \cdot \sin (20°)}{{3.1416}^{2}}

Next Step Convert Units

∴

ε v = \frac{{15.01m}^{2} \cdot 1000kg/m³ \cdot 7.3E-5rad/s \cdot \sin (0.3491rad)}{{3.1416}^{2}}

Next Step Prepare to Evaluate

∴

ε v = \frac{{15.01}^{2} \cdot 1000 \cdot 7.3E-5 \cdot \sin (0.3491)}{{3.1416}^{2}}

Next Step Evaluate

∴

ε v = 0.569333693542187

LAST Step Rounding Answer

∴

ε v = 0.5693

Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman Formula Elements

Variables

Constants

Functions

Vertical Eddy Viscosity Coefficient

Vertical Eddy Viscosity Coefficient is a coefficient relating the average shear stress within a turbulent flow of water or air to the vertical gradient of velocity.

Symbol: ε_v

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Vertical Eddy Viscosity Coefficient

Depth of Frictional Influence by Eckman

Depth of Frictional Influence by Eckman is the layer where ocean currents slow due to surface friction.

Symbol: D_Eddy

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Depth of Frictional Influence by Eckman

Water Density

Water Density is mass per unit of water.

Symbol: ρ_water

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Water Density

Angular Speed of the Earth

Angular Speed of the Earth is the measure of how fast the central angle of a rotating body changes with respect to time.

Symbol: Ω_E

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Speed of the Earth

Latitude of a Position on Earth Surface

The Latitude of a Position on Earth Surface is the measurement of distance north or south of the Equator.

Symbol: L

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Latitude of a Position on Earth Surface

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

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.

Syntax: sin(Angle)

Other formulas in Eckman Wind Drift category

Go Velocity Component along Horizontal x Axis

u x = V s \cdot e^{π \cdot \frac{z}{D F}} \cdot \cos (45 + (π \cdot \frac{z}{D F}))

Go Velocity at Surface given Velocity Component along Horizontal x Axis

V s = \frac{u x}{e^{π \cdot \frac{z}{D F}} \cdot \cos (45 + (π \cdot \frac{z}{D F}))}

Go Depth of Frictional Influence by Eckman

D Eddy = π \cdot \sqrt{\frac{ε v}{ρ water \cdot Ω E \cdot \sin (L)}}

Go Latitude given Depth of Frictional Influence by Eckman

L = a \sin (\frac{ε v}{ρ water \cdot Ω E \cdot {(\frac{D Eddy}{π})}^{2}})

How to Evaluate Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman?

Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman evaluator uses Vertical Eddy Viscosity Coefficient = (Depth of Frictional Influence by Eckman^2*Water Density*Angular Speed of the Earth*sin(Latitude of a Position on Earth Surface))/pi^2 to evaluate the Vertical Eddy Viscosity Coefficient, The Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman is defined as the ocean surface remains horizontal; the only driving force comes from the wind shear stress. Vertical Eddy Viscosity Coefficient is denoted by ε_v symbol.

How to evaluate Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman using this online evaluator? To use this online evaluator for Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman, enter Depth of Frictional Influence by Eckman (D_Eddy), Water Density (ρ_water), Angular Speed of the Earth (Ω_E) & Latitude of a Position on Earth Surface (L) and hit the calculate button.

FAQs on Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman

What is the formula to find Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman?

The formula of Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman is expressed as Vertical Eddy Viscosity Coefficient = (Depth of Frictional Influence by Eckman^2*Water Density*Angular Speed of the Earth*sin(Latitude of a Position on Earth Surface))/pi^2. Here is an example- 0.568575 = (15.01^2*1000*7.2921159E-05*sin(0.3490658503988))/pi^2.

How to calculate Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman?

With Depth of Frictional Influence by Eckman (D_Eddy), Water Density (ρ_water), Angular Speed of the Earth (Ω_E) & Latitude of a Position on Earth Surface (L) we can find Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman using the formula - Vertical Eddy Viscosity Coefficient = (Depth of Frictional Influence by Eckman^2*Water Density*Angular Speed of the Earth*sin(Latitude of a Position on Earth Surface))/pi^2. This formula also uses Archimedes' constant and Sine (sin) function(s).

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Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman Formula

Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman Example

Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman Solution

Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman Formula Elements

Other formulas in Eckman Wind Drift category

How to Evaluate Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman?

FAQs on Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman

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