Velocity Component along Horizontal x Axis Calculator

✖Velocity at the Surface is the speed of an object or fluid at the immediate boundary with another medium.ⓘ Velocity at the Surface [V_s]			+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]			+10% -10%

✖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 Horizontal x Axis [u_x]

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Formula

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Velocity Component along Horizontal x Axis

Formula

`"u"_{"x"} = "V"_{"s"}*e^(pi*"z"/"D")*cos(45+(pi*"z"/"D"))`

Example

`"15.6365m/s"="0.5m/s"*e^(pi*"160"/"120m")*cos(45+(pi*"160"/"120m"))`

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Velocity Component along Horizontal x Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
u_x = V_s*e^(pi*z/D)*cos(45+(pi*z/D))
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 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.
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.
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 at the Surface: 0.5 Meter per Second --> 0.5 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

u_x = V_s*e^(pi*z/D)*cos(45+(pi*z/D)) --> 0.5*e^(pi*160/120)*cos(45+(pi*160/120))

Evaluating ... ...

u_x = 15.6364972628207

STEP 3: Convert Result to Output's Unit

15.6364972628207 Meter per Second --> No Conversion Required

FINAL ANSWER

15.6364972628207 ≈ 15.6365 Meter per Second <-- Velocity Component along a Horizontal x Axis

(Calculation completed in 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< 15 Eckman Wind Drift Calculators

Velocity at Surface given Velocity Component along Horizontal x Axis

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

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

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)))

Latitude given Depth of Frictional Influence by Eckman

Go Latitude of a Position on Earth Surface = asin(Vertical Eddy Viscosity Coefficient/(Water Density*Angular Speed of the Earth*(Depth of Frictional Influence by Eckman/pi)^2))

Vertical Eddy Viscosity Coefficient given Depth of Frictional Influence by Eckman

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 in Current Profile in Three Dimensions by introducing Polar Coordinates

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

Volume Flow Rates per unit of Ocean Width

Go Volume Flow Rates per unit of Ocean Width = (Velocity at the Surface*Depth of Frictional Influence)/(pi*sqrt(2))

Depth given Volume Flow rate per unit of Ocean Width

Go Depth of Frictional Influence = (Volume Flow Rates per unit of Ocean Width*pi*sqrt(2))/Velocity at the Surface

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

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

Vertical Coordinate from Ocean Surface given Angle between Wind and Current Direction

Go Vertical Coordinate = Depth of Frictional Influence*(Angle between the Wind and Current Direction-45)/pi

Depth given Angle between Wind and Current Direction

Go Depth of Frictional Influence = pi*Vertical Coordinate/(Angle between the Wind and Current Direction-45)

Angle between Wind and Current Direction

Go Angle between the Wind and Current Direction = 45+(pi*Vertical Coordinate/Depth of Frictional Influence)

Density given Atmospheric Pressure whose value of Thousand is reduced from Density Value

Go Density of Salt Water = Difference of Density Values+1000

Atmospheric Pressure as function of Salinity and Temperature

Go Difference of Density Values = 0.75*Salinity of Water

Salinity given Atmospheric Pressure

Go Salinity of Water = Difference of Density Values/0.75

Velocity Component along Horizontal x Axis Formula

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 Component along Horizontal x Axis?

Velocity Component along Horizontal x Axis calculator uses 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)) to calculate the Velocity Component along a Horizontal x Axis, The Velocity Component along Horizontal x Axis is defined as influenced when ocean surface remains horizontal, only driving force comes from wind shear stress. Velocity Component along a Horizontal x Axis is denoted by u_x symbol.

How to calculate Velocity Component along Horizontal x Axis using this online calculator? To use this online calculator for Velocity Component along Horizontal x Axis, enter Velocity at the Surface (V_s), Vertical Coordinate (z) & Depth of Frictional Influence (D) and hit the calculate button. Here is how the Velocity Component along Horizontal x Axis calculation can be explained with given input values -> 15.6365 = 0.5*e^(pi*160/120)*cos(45+(pi*160/120)).

FAQ

What is Velocity Component along Horizontal x Axis?

The Velocity Component along Horizontal x Axis is defined as influenced when ocean surface remains horizontal, only driving force comes from wind shear stress and is represented as u_x = V_s*e^(pi*z/D)*cos(45+(pi*z/D)) or 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)). Velocity at the Surface is the speed of an object or fluid at the immediate boundary with another medium, 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 Component along Horizontal x Axis?

The Velocity Component along Horizontal x Axis is defined as influenced when ocean surface remains horizontal, only driving force comes from wind shear stress is calculated using 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)). To calculate Velocity Component along Horizontal x Axis, you need Velocity at the Surface (V_s), Vertical Coordinate (z) & Depth of Frictional Influence (D). With our tool, you need to enter the respective value for Velocity at the Surface, 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.

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