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Velocity at Surface given Velocity Component along Horizontal x Axis Formula

GoVelocity at Surface given Velocity detail of Current Profile in Three Dimensions Formula

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Velocity at the Surface is the speed of an object or fluid at the immediate boundary with another medium. Check FAQs

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

V_s - Velocity at the Surface?u_x - Velocity Component along a Horizontal x Axis?z - Vertical Coordinate?D_F - Depth of Frictional Influence?π - Archimedes' constant?

Velocity at Surface given Velocity Component along Horizontal x Axis Example

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Here is how the Velocity at Surface given Velocity Component along Horizontal x Axis equation looks like with Values.

Here is how the Velocity at Surface given Velocity Component along Horizontal x Axis equation looks like with Units.

Here is how the Velocity at Surface given Velocity Component along Horizontal x Axis equation looks like.

0.4796 = \frac{15}{e^{3.1416 \cdot \frac{160}{120}} \cdot \cos (45 + (3.1416 \cdot \frac{160}{120}))}

0.4796m/s = \frac{15m/s}{e^{3.1416 \cdot \frac{160}{120m}} \cdot \cos (45 + (3.1416 \cdot \frac{160}{120m}))}

0.4796 = \frac{15}{e^{3.1416 \cdot \frac{160}{120}} \cdot \cos (45 + (3.1416 \cdot \frac{160}{120}))}

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Velocity at Surface given Velocity Component along Horizontal x Axis Solution

Follow our step by step solution on how to calculate Velocity at Surface given Velocity Component along Horizontal x Axis?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V s = \frac{15m/s}{e^{π \cdot \frac{160}{120m}} \cdot \cos (45 + (π \cdot \frac{160}{120m}))}

Next Step Substitute values of Constants

∴

V s = \frac{15m/s}{e^{3.1416 \cdot \frac{160}{120m}} \cdot \cos (45 + (3.1416 \cdot \frac{160}{120m}))}

Next Step Prepare to Evaluate

∴

V s = \frac{15}{e^{3.1416 \cdot \frac{160}{120}} \cdot \cos (45 + (3.1416 \cdot \frac{160}{120}))}

Next Step Evaluate

∴

V s = 0.479647063785374m/s

LAST Step Rounding Answer

∴

V s = 0.4796m/s

Velocity at Surface given Velocity Component along Horizontal x Axis Formula Elements

Variables

Constants

Functions

Velocity at the Surface

Velocity at the Surface is the speed of an object or fluid at the immediate boundary with another medium.

Symbol: V_s

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity at the Surface

Velocity Component along a Horizontal x Axis

Velocity Component along a Horizontal x Axis is the speed in the direction parallel to the x-axis in a two-dimensional system.

Symbol: u_x

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity Component along a Horizontal x Axis

Vertical Coordinate

Vertical Coordinate measure aligned with the Earth's gravitational force, indicating height or depth in a perpendicular direction.

Symbol: z

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Vertical Coordinate

Depth of Frictional Influence

Depth of Frictional Influence is the depth over which the turbulent eddy viscosity is important.

Symbol: D_F

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Frictional Influence

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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Velocity at the Surface

Go Velocity at Surface given Velocity detail of Current Profile in Three Dimensions

V s = \frac{v}{e^{π \cdot \frac{z}{D F}}}

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 Depth of Frictional Influence by Eckman

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

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

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

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 Velocity at Surface given Velocity Component along Horizontal x Axis?

Velocity at Surface given Velocity Component along Horizontal x Axis evaluator uses Velocity at the Surface = Velocity Component along a Horizontal x Axis/(e^(pi*Vertical Coordinate/Depth of Frictional Influence)*cos(45+(pi*Vertical Coordinate/Depth of Frictional Influence))) to evaluate the Velocity at the Surface, The Velocity at Surface given Velocity Component along Horizontal x Axis is defined as rate of change of its position with respect to frame of reference, and is function of time in x direction. Velocity at the Surface is denoted by V_s symbol.

How to evaluate Velocity at Surface given Velocity Component along Horizontal x Axis using this online evaluator? To use this online evaluator for Velocity at Surface given Velocity Component along Horizontal x Axis, enter Velocity Component along a Horizontal x Axis (u_x), Vertical Coordinate (z) & Depth of Frictional Influence (D_F) and hit the calculate button.

FAQs on Velocity at Surface given Velocity Component along Horizontal x Axis

What is the formula to find Velocity at Surface given Velocity Component along Horizontal x Axis?

The formula of Velocity at Surface given Velocity Component along Horizontal x Axis is expressed as Velocity at the Surface = Velocity Component along a Horizontal x Axis/(e^(pi*Vertical Coordinate/Depth of Frictional Influence)*cos(45+(pi*Vertical Coordinate/Depth of Frictional Influence))). Here is an example- 0.479647 = 15/(e^(pi*160/120)*cos(45+(pi*160/120))).

How to calculate Velocity at Surface given Velocity Component along Horizontal x Axis?

With Velocity Component along a Horizontal x Axis (u_x), Vertical Coordinate (z) & Depth of Frictional Influence (D_F) we can find Velocity at Surface given Velocity Component along Horizontal x Axis using the formula - Velocity at the Surface = Velocity Component along a Horizontal x Axis/(e^(pi*Vertical Coordinate/Depth of Frictional Influence)*cos(45+(pi*Vertical Coordinate/Depth of Frictional Influence))). This formula also uses Archimedes' constant and Cosine (cos) function(s).

What are the other ways to Calculate Velocity at the Surface?

Here are the different ways to Calculate Velocity at the Surface-

Velocity at the Surface=Current Profile Velocity/(e^(pi*Vertical Coordinate/Depth of Frictional Influence))

Can the Velocity at Surface given Velocity Component along Horizontal x Axis be negative?

Yes, the Velocity at Surface given Velocity Component along Horizontal x Axis, measured in Speed can be negative.

Which unit is used to measure Velocity at Surface given Velocity Component along Horizontal x Axis?

Velocity at Surface given Velocity Component along Horizontal x Axis is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Velocity at Surface given Velocity Component along Horizontal x Axis can be measured.

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