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Freestream Velocity given Radial 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{μ}{2 \cdot π \cdot r^{3}} - \frac{V r}{\cos (θ)}

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

Freestream Velocity given Radial Velocity Example

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

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

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

67.9987 = \frac{9463}{2 \cdot 3.1416 \cdot {2.758}^{3}} - \frac{2.9}{\cos (0.7)}

67.9987m/s = \frac{9463m³/s}{2 \cdot 3.1416 \cdot {2.758m}^{3}} - \frac{2.9m/s}{\cos (0.7rad)}

67.9987 = \frac{9463}{2 \cdot 3.1416 \cdot {2.758}^{3}} - \frac{2.9}{\cos (0.7)}

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Freestream Velocity given Radial Velocity Solution

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

FIRST Step Consider the formula

V ∞ = \frac{μ}{2 \cdot π \cdot r^{3}} - \frac{V r}{\cos (θ)}

Next Step Substitute values of Variables

∴

V ∞ = \frac{9463m³/s}{2 \cdot π \cdot {2.758m}^{3}} - \frac{2.9m/s}{\cos (0.7rad)}

Next Step Substitute values of Constants

∴

V ∞ = \frac{9463m³/s}{2 \cdot 3.1416 \cdot {2.758m}^{3}} - \frac{2.9m/s}{\cos (0.7rad)}

Next Step Prepare to Evaluate

∴

V ∞ = \frac{9463}{2 \cdot 3.1416 \cdot {2.758}^{3}} - \frac{2.9}{\cos (0.7)}

Next Step Evaluate

∴

V ∞ = 67.9987372486239m/s

LAST Step Rounding Answer

∴

V ∞ = 67.9987m/s

Freestream Velocity given Radial 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

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

Radial Velocity

The Radial Velocity of an object with respect to a given point is the rate of change of the distance between the object and the point.

Symbol: V_r

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Radial 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

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 in Radial Velocity category

Go Radial Velocity for Flow over Sphere

V r = - (V ∞ - \frac{μ}{2 \cdot π \cdot r^{3}}) \cdot \cos (θ)

Go Polar Coordinate given Radial Velocity

θ = a \cos (\frac{V r}{\frac{μ}{2 \cdot π \cdot r^{3}} - V ∞})

Go Radial Coordinate given Radial Velocity

r = {(\frac{μ}{2 \cdot π \cdot (V ∞ + \frac{V r}{\cos (θ)})})}^{\frac{1}{3}}

Go Doublet Strength given Radial Velocity

μ = 2 \cdot π \cdot r^{3} \cdot (V ∞ + \frac{V r}{\cos (θ)})

How to Evaluate Freestream Velocity given Radial Velocity?

Freestream Velocity given Radial Velocity evaluator uses Freestream Velocity = Doublet Strength/(2*pi*Radial Coordinate^3)-Radial Velocity/cos(Polar Angle) to evaluate the Freestream Velocity, The Freestream Velocity given Radial 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 Radial Velocity using this online evaluator? To use this online evaluator for Freestream Velocity given Radial Velocity, enter Doublet Strength (μ), Radial Coordinate (r), Radial Velocity (V_r) & Polar Angle (θ) and hit the calculate button.

FAQs on Freestream Velocity given Radial Velocity

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

The formula of Freestream Velocity given Radial Velocity is expressed as Freestream Velocity = Doublet Strength/(2*pi*Radial Coordinate^3)-Radial Velocity/cos(Polar Angle). Here is an example- 67.99874 = 9463/(2*pi*2.758^3)-2.9/cos(0.7).

How to calculate Freestream Velocity given Radial Velocity?

With Doublet Strength (μ), Radial Coordinate (r), Radial Velocity (V_r) & Polar Angle (θ) we can find Freestream Velocity given Radial Velocity using the formula - Freestream Velocity = Doublet Strength/(2*pi*Radial Coordinate^3)-Radial Velocity/cos(Polar Angle). This formula also uses Archimedes' constant and Cosine function(s).

Can the Freestream Velocity given Radial Velocity be negative?

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

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

Freestream Velocity given Radial 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 Radial Velocity can be measured.

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Freestream Velocity given Radial Velocity Formula

Freestream Velocity given Radial Velocity Example

Freestream Velocity given Radial Velocity Solution

Freestream Velocity given Radial Velocity Formula Elements

Other formulas in Radial Velocity category

How to Evaluate Freestream Velocity given Radial Velocity?

FAQs on Freestream Velocity given Radial Velocity

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