Velocity at Surface given Velocity Component along Horizontal x Axis Calculator

✖Velocity Component along a Horizontal x Axis is the speed in the direction parallel to the x-axis in a two-dimensional system.ⓘ Velocity Component along a Horizontal x Axis [u_x]			+10% -10%
✖Vertical Coordinate measure aligned with the Earth's gravitational force, indicating height or depth in a perpendicular direction.ⓘ Vertical Coordinate [z]			+10% -10%
✖Depth of Frictional Influence is the depth over which the turbulent eddy viscosity is important.ⓘ Depth of Frictional Influence [D_F]			+10% -10%

✖Velocity at the Surface is the speed of an object or fluid at the immediate boundary with another medium.ⓘ Velocity at Surface given Velocity Component along Horizontal x Axis [V_s]

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Velocity at Surface given Velocity Component along Horizontal x Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
V_s = u_x/(e^(pi*z/D_F)*cos(45+(pi*z/D_F)))
This formula uses 2 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Velocity at the Surface - (Measured in Meter per Second) - Velocity at the Surface is the speed of an object or fluid at the immediate boundary with another medium.
Velocity Component along a Horizontal x Axis - (Measured in Meter per Second) - Velocity Component along a Horizontal x Axis is the speed in the direction parallel to the x-axis in a two-dimensional system.
Vertical Coordinate - Vertical Coordinate measure aligned with the Earth's gravitational force, indicating height or depth in a perpendicular direction.
Depth of Frictional Influence - (Measured in Meter) - Depth of Frictional Influence is the depth over which the turbulent eddy viscosity is important.

STEP 1: Convert Input(s) to Base Unit

Velocity Component along a Horizontal x Axis: 15 Meter per Second --> 15 Meter per Second No Conversion Required
Vertical Coordinate: 160 --> No Conversion Required
Depth of Frictional Influence: 120 Meter --> 120 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_s = u_x/(e^(pi*z/D_F)*cos(45+(pi*z/D_F))) --> 15/(e^(pi*160/120)*cos(45+(pi*160/120)))

Evaluating ... ...

V_s = 0.479647063785374

STEP 3: Convert Result to Output's Unit

0.479647063785374 Meter per Second --> No Conversion Required

FINAL ANSWER

0.479647063785374 ≈ 0.479647 Meter per Second <-- Velocity at the Surface

(Calculation completed in 00.004 seconds)

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Velocity at Surface given Velocity Component along Horizontal x Axis

LaTeX Go 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)))

Velocity Component along Horizontal x Axis

LaTeX Go Velocity Component along a Horizontal x Axis = Velocity at the Surface*e^(pi*Vertical Coordinate/Depth of Frictional Influence)*cos(45+(pi*Vertical Coordinate/Depth of Frictional Influence))

Depth of Frictional Influence by Eckman

LaTeX Go Depth of Frictional Influence by Eckman = pi*sqrt(Vertical Eddy Viscosity Coefficient/(Water Density*Angular Speed of the Earth*sin(Latitude of a Position on Earth Surface)))

Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman

LaTeX Go 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

Velocity at Surface given Velocity Component along Horizontal x Axis Formula

LaTeX Go

What is Ocean dynamics?

Ocean dynamics define and describe the motion of water within the oceans. Ocean temperature and motion fields can be separated into three distinct layers: mixed (surface) layer, upper ocean (above the thermocline), and deep ocean. Ocean dynamics has traditionally been investigated by sampling from instruments in situ.

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

Velocity at Surface given Velocity Component along Horizontal x Axis calculator 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 calculate 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 calculate Velocity at Surface given Velocity Component along Horizontal x Axis using this online calculator? To use this online calculator 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. Here is how the Velocity at Surface given Velocity Component along Horizontal x Axis calculation can be explained with given input values -> 0.479647 = 15/(e^(pi*160/120)*cos(45+(pi*160/120))).

FAQ

What is Velocity at Surface given Velocity Component along Horizontal x Axis?

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 and is represented as V_s = u_x/(e^(pi*z/D_F)*cos(45+(pi*z/D_F))) or 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))). Velocity Component along a Horizontal x Axis is the speed in the direction parallel to the x-axis in a two-dimensional system, Vertical Coordinate measure aligned with the Earth's gravitational force, indicating height or depth in a perpendicular direction & Depth of Frictional Influence is the depth over which the turbulent eddy viscosity is important.

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

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 is calculated using 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 calculate Velocity at Surface given Velocity Component along Horizontal x Axis, you need Velocity Component along a Horizontal x Axis (u_x), Vertical Coordinate (z) & Depth of Frictional Influence (D_F). With our tool, you need to enter the respective value for Velocity Component along a Horizontal x Axis, Vertical Coordinate & Depth of Frictional Influence 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 Velocity at the Surface?

In this formula, Velocity at the Surface uses Velocity Component along a Horizontal x Axis, Vertical Coordinate & Depth of Frictional Influence. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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