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Shear Stress at Water Surface given Velocity at Surface Formula

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Shear Stress at the Water Surface referred to as the “tractive force” is a measure of the internal resistance of a fluid to deformation when subjected to a force acting parallel to its surface. Check FAQs

τ = V s \cdot \frac{\sqrt{2 \cdot D F \cdot ρ water \cdot Ω E \cdot \sin (L)}}{π}

τ - Shear Stress at the Water Surface?V_s - Velocity at the Surface?D_F - Depth of Frictional Influence?ρ_water - Water Density?Ω_E - Angular Speed of the Earth?L - Latitude of the Line?π - Archimedes' constant?

Shear Stress at Water Surface given Velocity at Surface Example

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Here is how the Shear Stress at Water Surface given Velocity at Surface equation looks like with Values.

Here is how the Shear Stress at Water Surface given Velocity at Surface equation looks like with Units.

Here is how the Shear Stress at Water Surface given Velocity at Surface equation looks like.

0.5983 = 0.5 \cdot \frac{\sqrt{2 \cdot 120 \cdot 1000 \cdot 7.3E-5 \cdot \sin (0.94)}}{3.1416}

0.5983N/m² = 0.5m/s \cdot \frac{\sqrt{2 \cdot 120m \cdot 1000kg/m³ \cdot 7.3E-5rad/s \cdot \sin (0.94m)}}{3.1416}

0.5983 = 0.5 \cdot \frac{\sqrt{2 \cdot 120 \cdot 1000 \cdot 7.3E-5 \cdot \sin (0.94)}}{3.1416}

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Shear Stress at Water Surface given Velocity at Surface Solution

Follow our step by step solution on how to calculate Shear Stress at Water Surface given Velocity at Surface?

FIRST Step Consider the formula

τ = V s \cdot \frac{\sqrt{2 \cdot D F \cdot ρ water \cdot Ω E \cdot \sin (L)}}{π}

Next Step Substitute values of Variables

∴

τ = 0.5m/s \cdot \frac{\sqrt{2 \cdot 120m \cdot 1000kg/m³ \cdot 7.3E-5rad/s \cdot \sin (0.94m)}}{π}

Next Step Substitute values of Constants

∴

τ = 0.5m/s \cdot \frac{\sqrt{2 \cdot 120m \cdot 1000kg/m³ \cdot 7.3E-5rad/s \cdot \sin (0.94m)}}{3.1416}

Next Step Prepare to Evaluate

∴

τ = 0.5 \cdot \frac{\sqrt{2 \cdot 120 \cdot 1000 \cdot 7.3E-5 \cdot \sin (0.94)}}{3.1416}

Next Step Evaluate

∴

τ = 0.598328131836061Pa

Next Step Convert to Output's Unit

∴

τ = 0.598328131836061N/m²

LAST Step Rounding Answer

∴

τ = 0.5983N/m²

Shear Stress at Water Surface given Velocity at Surface Formula Elements

Variables

Constants

Functions

Shear Stress at the Water Surface

Shear Stress at the Water Surface referred to as the “tractive force” is a measure of the internal resistance of a fluid to deformation when subjected to a force acting parallel to its surface.

Symbol: τ

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Shear Stress at the Water Surface

Velocity at the Surface

Velocity at the Surface is the speed and direction of water flow at the very top layer of the ocean or coastal water body. This velocity is influenced by various factors, including wind, waves etc.

Symbol: V_s

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity at the Surface

Depth of Frictional Influence

Depth of Frictional Influence is the vertical extent in a water column where frictional forces from the seabed affect the flow of water.

Symbol: D_F

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Frictional Influence

Water Density

Water Density is mass per unit volume 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 rate at which the Earth rotates around its own axis. It is the angle through which the Earth rotates in a unit of 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 the Line

Latitude of the Line is the point at which a specific line or structure is located, this term often pertains to the position of coastal features relative to the Earth's equatorial plane.

Symbol: L

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Latitude of the Line

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)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Mooring Forces category

Go Drag Force due to Wind

F D = 0.5 \cdot ρ air \cdot C D' \cdot A \cdot {V 10}^{2}

Go Mass Density of Air given Drag Force due to Wind

ρ air = \frac{F D}{0.5 \cdot C D' \cdot A \cdot {V 10}^{2}}

Go Coefficient of Drag for Winds Measured at 10 m given Drag Force due to Wind

C D' = \frac{F D}{0.5 \cdot ρ air \cdot A \cdot {V 10}^{2}}

Go Projected Area of Vessel above Waterline given Drag Force due to Wind

A = \frac{F D}{0.5 \cdot ρ air \cdot C D' \cdot {V 10}^{2}}

How to Evaluate Shear Stress at Water Surface given Velocity at Surface?

Shear Stress at Water Surface given Velocity at Surface evaluator uses Shear Stress at the Water Surface = Velocity at the Surface*sqrt(2*Depth of Frictional Influence*Water Density*Angular Speed of the Earth*sin(Latitude of the Line))/pi to evaluate the Shear Stress at the Water Surface, The Shear Stress at Water Surface given Velocity at Surface formula is defined as the wind shear stress or surface shear stress, is a measure of the force exerted by the wind on the surface of the water. It is a critical parameter in understanding how wind energy is transferred to the water, which drives various physical processes in coastal and ocean engineering. Shear Stress at the Water Surface is denoted by τ symbol.

How to evaluate Shear Stress at Water Surface given Velocity at Surface using this online evaluator? To use this online evaluator for Shear Stress at Water Surface given Velocity at Surface, enter Velocity at the Surface (V_s), Depth of Frictional Influence (D_F), Water Density (ρ_water), Angular Speed of the Earth (Ω_E) & Latitude of the Line (L) and hit the calculate button.

FAQs on Shear Stress at Water Surface given Velocity at Surface

What is the formula to find Shear Stress at Water Surface given Velocity at Surface?

The formula of Shear Stress at Water Surface given Velocity at Surface is expressed as Shear Stress at the Water Surface = Velocity at the Surface*sqrt(2*Depth of Frictional Influence*Water Density*Angular Speed of the Earth*sin(Latitude of the Line))/pi. Here is an example- 0.598328 = 0.5*sqrt(2*120*1000*7.2921159E-05*sin(0.94))/pi.

How to calculate Shear Stress at Water Surface given Velocity at Surface?

With Velocity at the Surface (V_s), Depth of Frictional Influence (D_F), Water Density (ρ_water), Angular Speed of the Earth (Ω_E) & Latitude of the Line (L) we can find Shear Stress at Water Surface given Velocity at Surface using the formula - Shear Stress at the Water Surface = Velocity at the Surface*sqrt(2*Depth of Frictional Influence*Water Density*Angular Speed of the Earth*sin(Latitude of the Line))/pi. This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt) function(s).

Can the Shear Stress at Water Surface given Velocity at Surface be negative?

No, the Shear Stress at Water Surface given Velocity at Surface, measured in Pressure cannot be negative.

Which unit is used to measure Shear Stress at Water Surface given Velocity at Surface?

Shear Stress at Water Surface given Velocity at Surface is usually measured using the Newton per Square Meter[N/m²] for Pressure. Pascal[N/m²], Kilopascal[N/m²], Bar[N/m²] are the few other units in which Shear Stress at Water Surface given Velocity at Surface can be measured.

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Shear Stress at Water Surface given Velocity at Surface Formula

Shear Stress at Water Surface given Velocity at Surface Example

Shear Stress at Water Surface given Velocity at Surface Solution

Shear Stress at Water Surface given Velocity at Surface Formula Elements

Other formulas in Mooring Forces category

How to Evaluate Shear Stress at Water Surface given Velocity at Surface?

FAQs on Shear Stress at Water Surface given Velocity at Surface

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