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Freestream Velocity given Tangential Velocity Formula

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The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air. Check FAQs

V ∞ = \frac{V θ}{\sin (θ)} - \frac{μ}{4 \cdot π \cdot r^{3}}

V_∞ - Freestream Velocity?V_θ - Tangential Velocity?θ - Polar Angle?μ - Doublet Strength?r - Radial Coordinate?π - Archimedes' constant?

Freestream Velocity given Tangential Velocity Example

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Here is how the Freestream Velocity given Tangential Velocity equation looks like with Values.

Here is how the Freestream Velocity given Tangential Velocity equation looks like with Units.

Here is how the Freestream Velocity given Tangential Velocity equation looks like.

66.5547 = \frac{66}{\sin (0.7)} - \frac{9463}{4 \cdot 3.1416 \cdot {2.758}^{3}}

66.5547m/s = \frac{66m/s}{\sin (0.7rad)} - \frac{9463m³/s}{4 \cdot 3.1416 \cdot {2.758m}^{3}}

66.5547 = \frac{66}{\sin (0.7)} - \frac{9463}{4 \cdot 3.1416 \cdot {2.758}^{3}}

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Freestream Velocity given Tangential Velocity Solution

Follow our step by step solution on how to calculate Freestream Velocity given Tangential Velocity?

FIRST Step Consider the formula

V ∞ = \frac{V θ}{\sin (θ)} - \frac{μ}{4 \cdot π \cdot r^{3}}

Next Step Substitute values of Variables

∴

V ∞ = \frac{66m/s}{\sin (0.7rad)} - \frac{9463m³/s}{4 \cdot π \cdot {2.758m}^{3}}

Next Step Substitute values of Constants

∴

V ∞ = \frac{66m/s}{\sin (0.7rad)} - \frac{9463m³/s}{4 \cdot 3.1416 \cdot {2.758m}^{3}}

Next Step Prepare to Evaluate

∴

V ∞ = \frac{66}{\sin (0.7)} - \frac{9463}{4 \cdot 3.1416 \cdot {2.758}^{3}}

Next Step Evaluate

∴

V ∞ = 66.5546570282432m/s

LAST Step Rounding Answer

∴

V ∞ = 66.5547m/s

Freestream Velocity given Tangential Velocity Formula Elements

Variables

Constants

Functions

Freestream Velocity

The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air.

Symbol: V_∞

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Freestream Velocity

Tangential Velocity

Tangential Velocity is the component of velocity in the tangential direction.

Symbol: V_θ

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Tangential Velocity

Polar Angle

Polar Angle is the angular position of a point from a reference direction.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Polar Angle

Doublet Strength

Doublet Strength is defined as the product of the distance between a source-sink pair and source or sink strength.

Symbol: μ

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Doublet Strength

Radial Coordinate

Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radial Coordinate

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 Tangential Velocity category

Go Tangential Velocity for Flow over Sphere

V θ = (V ∞ + \frac{μ}{4 \cdot π \cdot r^{3}}) \cdot \sin (θ)

Go Polar Coordinate given Tangential Velocity

θ = a \sin (\frac{V θ}{V ∞ + \frac{μ}{4 \cdot π \cdot r^{3}}})

Go Radial Coordinate given Tangential Velocity

r = {(\frac{μ}{4 \cdot π \cdot (\frac{V θ}{\sin (θ)} - V ∞)})}^{\frac{1}{3}}

Go Doublet Strength given Tangential Velocity

μ = 4 \cdot π \cdot r^{3} \cdot (\frac{V θ}{\sin (θ)} - V ∞)

How to Evaluate Freestream Velocity given Tangential Velocity?

Freestream Velocity given Tangential Velocity evaluator uses Freestream Velocity = Tangential Velocity/sin(Polar Angle)-Doublet Strength/(4*pi*Radial Coordinate^3) to evaluate the Freestream Velocity, The Freestream Velocity given Tangential Velocity formula calculates the freestream velocity of the uniform velocity field around the flow that has been induced by the three-dimensional doublet. Freestream Velocity is denoted by V_∞ symbol.

How to evaluate Freestream Velocity given Tangential Velocity using this online evaluator? To use this online evaluator for Freestream Velocity given Tangential Velocity, enter Tangential Velocity (V_θ), Polar Angle (θ), Doublet Strength (μ) & Radial Coordinate (r) and hit the calculate button.

FAQs on Freestream Velocity given Tangential Velocity

What is the formula to find Freestream Velocity given Tangential Velocity?

The formula of Freestream Velocity given Tangential Velocity is expressed as Freestream Velocity = Tangential Velocity/sin(Polar Angle)-Doublet Strength/(4*pi*Radial Coordinate^3). Here is an example- 54.13649 = 66/sin(0.7)-9463/(4*pi*2.758^3).

How to calculate Freestream Velocity given Tangential Velocity?

With Tangential Velocity (V_θ), Polar Angle (θ), Doublet Strength (μ) & Radial Coordinate (r) we can find Freestream Velocity given Tangential Velocity using the formula - Freestream Velocity = Tangential Velocity/sin(Polar Angle)-Doublet Strength/(4*pi*Radial Coordinate^3). This formula also uses Archimedes' constant and Sine (sin) function(s).

Can the Freestream Velocity given Tangential Velocity be negative?

Yes, the Freestream Velocity given Tangential Velocity, measured in Speed can be negative.

Which unit is used to measure Freestream Velocity given Tangential Velocity?

Freestream Velocity given Tangential Velocity 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 Freestream Velocity given Tangential Velocity can be measured.

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Freestream Velocity given Tangential Velocity Formula

Freestream Velocity given Tangential Velocity Example

Freestream Velocity given Tangential Velocity Solution

Freestream Velocity given Tangential Velocity Formula Elements

Other formulas in Tangential Velocity category

How to Evaluate Freestream Velocity given Tangential Velocity?

FAQs on Freestream Velocity given Tangential Velocity

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