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Freestream Velocity given Circulation at Origin Formula

GoFreestream Velocity given Induced Angle of Attack 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 ∞ = π \cdot b \cdot \frac{Γ o}{2 \cdot S 0 \cdot C L,ELD}

V_∞ - Freestream Velocity?b - Wingspan?Γ_o - Circulation at Origin?S₀ - Reference Area Origin?C_L,ELD - Lift Coefficient ELD?π - Archimedes' constant?

Freestream Velocity given Circulation at Origin Example

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Here is how the Freestream Velocity given Circulation at Origin equation looks like with Values.

Here is how the Freestream Velocity given Circulation at Origin equation looks like with Units.

Here is how the Freestream Velocity given Circulation at Origin equation looks like.

15.6273 = 3.1416 \cdot 2340 \cdot \frac{14}{2 \cdot 2.21 \cdot 1.49}

15.6273m/s = 3.1416 \cdot 2340mm \cdot \frac{14m²/s}{2 \cdot 2.21m² \cdot 1.49}

15.6273 = 3.1416 \cdot 2340 \cdot \frac{14}{2 \cdot 2.21 \cdot 1.49}

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Freestream Velocity given Circulation at Origin Solution

Follow our step by step solution on how to calculate Freestream Velocity given Circulation at Origin?

FIRST Step Consider the formula

V ∞ = π \cdot b \cdot \frac{Γ o}{2 \cdot S 0 \cdot C L,ELD}

Next Step Substitute values of Variables

∴

V ∞ = π \cdot 2340mm \cdot \frac{14m²/s}{2 \cdot 2.21m² \cdot 1.49}

Next Step Substitute values of Constants

∴

V ∞ = 3.1416 \cdot 2340mm \cdot \frac{14m²/s}{2 \cdot 2.21m² \cdot 1.49}

Next Step Convert Units

∴

V ∞ = 3.1416 \cdot 2.34m \cdot \frac{14m²/s}{2 \cdot 2.21m² \cdot 1.49}

Next Step Prepare to Evaluate

∴

V ∞ = 3.1416 \cdot 2.34 \cdot \frac{14}{2 \cdot 2.21 \cdot 1.49}

Next Step Evaluate

∴

V ∞ = 15.6273460068028m/s

LAST Step Rounding Answer

∴

V ∞ = 15.6273m/s

Freestream Velocity given Circulation at Origin Formula Elements

Variables

Constants

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

Wingspan

The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Wingspan

Circulation at Origin

Circulation at Origin is the circulation when the origin is taken at the center of the bound vortex.

Symbol: Γ_o

Measurement: Momentum DiffusivityUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Circulation at Origin

Reference Area Origin

Reference Area Origin is arbitrarily an area that is characteristic of the object being considered. For an aircraft wing, the wing's planform area is called the reference wing area.

Symbol: S₀

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Reference Area Origin

Lift Coefficient ELD

The Lift Coefficient ELD is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area.

Symbol: C_L,ELD

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Lift Coefficient ELD

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

Other Formulas to find Freestream Velocity

Go Freestream Velocity given Induced Angle of Attack

V ∞ = \frac{Γ o}{2 \cdot b \cdot α i}

Other formulas in Elliptical Lift Distribution category

Go Circulation at given Distance along Wingspan

Γ = Γ o \cdot \sqrt{1 - {(2 \cdot \frac{a}{b})}^{2}}

Go Lift at given Distance along Wingspan

L = ρ ∞ \cdot V ∞ \cdot Γ o \cdot \sqrt{1 - {(2 \cdot \frac{a}{b})}^{2}}

Go Downwash in Elliptical Lift Distribution

w = - \frac{Γ o}{2 \cdot b}

Go Induced Angle of Attack given Aspect Ratio

α i = \frac{C l}{π \cdot AR ELD}

How to Evaluate Freestream Velocity given Circulation at Origin?

Freestream Velocity given Circulation at Origin evaluator uses Freestream Velocity = pi*Wingspan*Circulation at Origin/(2*Reference Area Origin*Lift Coefficient ELD) to evaluate the Freestream Velocity, The freestream velocity given circulation at origin formula calculates the velocity of the fluid flowing around the wing when the circulation at the origin is given which is constant for the elliptical lift distribution. Freestream Velocity is denoted by V_∞ symbol.

How to evaluate Freestream Velocity given Circulation at Origin using this online evaluator? To use this online evaluator for Freestream Velocity given Circulation at Origin, enter Wingspan (b), Circulation at Origin (Γ_o), Reference Area Origin (S₀) & Lift Coefficient ELD (C_L,ELD) and hit the calculate button.

FAQs on Freestream Velocity given Circulation at Origin

What is the formula to find Freestream Velocity given Circulation at Origin?

The formula of Freestream Velocity given Circulation at Origin is expressed as Freestream Velocity = pi*Wingspan*Circulation at Origin/(2*Reference Area Origin*Lift Coefficient ELD). Here is an example- 15.62735 = pi*2.34*14/(2*2.21*1.49).

How to calculate Freestream Velocity given Circulation at Origin?

With Wingspan (b), Circulation at Origin (Γ_o), Reference Area Origin (S₀) & Lift Coefficient ELD (C_L,ELD) we can find Freestream Velocity given Circulation at Origin using the formula - Freestream Velocity = pi*Wingspan*Circulation at Origin/(2*Reference Area Origin*Lift Coefficient ELD). This formula also uses Archimedes' constant .

What are the other ways to Calculate Freestream Velocity?

Here are the different ways to Calculate Freestream Velocity-

Freestream Velocity=Circulation at Origin/(2*Wingspan*Induced Angle of Attack)

Can the Freestream Velocity given Circulation at Origin be negative?

Yes, the Freestream Velocity given Circulation at Origin, measured in Speed can be negative.

Which unit is used to measure Freestream Velocity given Circulation at Origin?

Freestream Velocity given Circulation at Origin 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 Circulation at Origin can be measured.

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Freestream Velocity given Circulation at Origin Formula

​GoFreestream Velocity given Induced Angle of Attack Formula

Freestream Velocity given Circulation at Origin Example

Freestream Velocity given Circulation at Origin Solution

Freestream Velocity given Circulation at Origin Formula Elements

Other Formulas to find Freestream Velocity

Other formulas in Elliptical Lift Distribution category

How to Evaluate Freestream Velocity given Circulation at Origin?

FAQs on Freestream Velocity given Circulation at Origin

Variable Name

GoFreestream Velocity given Induced Angle of Attack Formula