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Stream Function for Flow over Rankine Oval Formula

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Rankine Oval Stream Function is a mathematical function used to describe the flow pattern around an oval-shaped object in potential flow theory. Check FAQs

ψ r = V ∞ \cdot r \cdot \sin (θ) + (\frac{Λ}{2 \cdot π}) \cdot (θ 1 - θ 2)

ψ_r - Rankine Oval Stream Function?V_∞ - Freestream Velocity?r - Radial Coordinate?θ - Polar Angle?Λ - Source Strength?θ₁ - Polar Angle from Source?θ₂ - Polar Angle from Sink?π - Archimedes' constant?

Stream Function for Flow over Rankine Oval Example

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Here is how the Stream Function for Flow over Rankine Oval equation looks like with Values.

Here is how the Stream Function for Flow over Rankine Oval equation looks like with Units.

Here is how the Stream Function for Flow over Rankine Oval equation looks like.

-48.2001 = 6.4 \cdot 9 \cdot \sin (0.7) + (\frac{134}{2 \cdot 3.1416}) \cdot (10 - 14)

-48.2001m²/s = 6.4m/s \cdot 9m \cdot \sin (0.7rad) + (\frac{134m²/s}{2 \cdot 3.1416}) \cdot (10rad - 14rad)

-48.2001 = 6.4 \cdot 9 \cdot \sin (0.7) + (\frac{134}{2 \cdot 3.1416}) \cdot (10 - 14)

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Stream Function for Flow over Rankine Oval Solution

Follow our step by step solution on how to calculate Stream Function for Flow over Rankine Oval?

FIRST Step Consider the formula

ψ r = V ∞ \cdot r \cdot \sin (θ) + (\frac{Λ}{2 \cdot π}) \cdot (θ 1 - θ 2)

Next Step Substitute values of Variables

∴

ψ r = 6.4m/s \cdot 9m \cdot \sin (0.7rad) + (\frac{134m²/s}{2 \cdot π}) \cdot (10rad - 14rad)

Next Step Substitute values of Constants

∴

ψ r = 6.4m/s \cdot 9m \cdot \sin (0.7rad) + (\frac{134m²/s}{2 \cdot 3.1416}) \cdot (10rad - 14rad)

Next Step Prepare to Evaluate

∴

ψ r = 6.4 \cdot 9 \cdot \sin (0.7) + (\frac{134}{2 \cdot 3.1416}) \cdot (10 - 14)

Next Step Evaluate

∴

ψ r = -48.2001107123649m²/s

LAST Step Rounding Answer

∴

ψ r = -48.2001m²/s

Stream Function for Flow over Rankine Oval Formula Elements

Variables

Constants

Functions

Rankine Oval Stream Function

Rankine Oval Stream Function is a mathematical function used to describe the flow pattern around an oval-shaped object in potential flow theory.

Symbol: ψ_r

Measurement: Velocity PotentialUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Rankine Oval Stream Function

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

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

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

Source Strength

Source Strength measures the magnitude or intensity of a source, which is a theoretical construct used to represent fluid flow emanating from a point.

Symbol: Λ

Measurement: Velocity PotentialUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Source Strength

Polar Angle from Source

Polar Angle from Source is the angular position of a point in polar coordinates where origin is at the source.

Symbol: θ₁

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Polar Angle from Source

Polar Angle from Sink

Polar Angle from Sink is the angular position of a point in polar coordinates where origin is at the sink.

Symbol: θ₂

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Polar Angle from Sink

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 Source Flow category

Go Velocity Potential for 2-D Source Flow

ϕ = \frac{Λ}{2 \cdot π} \cdot \ln (r)

Go Radial Velocity for 2-D Incompressible Source Flow

V r = \frac{Λ}{2 \cdot π \cdot r}

How to Evaluate Stream Function for Flow over Rankine Oval?

Stream Function for Flow over Rankine Oval evaluator uses Rankine Oval Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+(Source Strength/(2*pi))*(Polar Angle from Source-Polar Angle from Sink) to evaluate the Rankine Oval Stream Function, The Stream Function for Flow over Rankine Oval formula is obtained as the summation of stream functions for uniform flow and source-sink pair, this expression describes the flow pattern around a Rankine oval in potential flow theory, it accounts for the free stream flow, the presence of the oval, and any circulation around the oval. Rankine Oval Stream Function is denoted by ψ_r symbol.

How to evaluate Stream Function for Flow over Rankine Oval using this online evaluator? To use this online evaluator for Stream Function for Flow over Rankine Oval, enter Freestream Velocity (V_∞), Radial Coordinate (r), Polar Angle (θ), Source Strength (Λ), Polar Angle from Source (θ₁) & Polar Angle from Sink (θ₂) and hit the calculate button.

FAQs on Stream Function for Flow over Rankine Oval

What is the formula to find Stream Function for Flow over Rankine Oval?

The formula of Stream Function for Flow over Rankine Oval is expressed as Rankine Oval Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+(Source Strength/(2*pi))*(Polar Angle from Source-Polar Angle from Sink). Here is an example- -48.200111 = 6.4*9*sin(0.7)+(134/(2*pi))*(10-14).

How to calculate Stream Function for Flow over Rankine Oval?

With Freestream Velocity (V_∞), Radial Coordinate (r), Polar Angle (θ), Source Strength (Λ), Polar Angle from Source (θ₁) & Polar Angle from Sink (θ₂) we can find Stream Function for Flow over Rankine Oval using the formula - Rankine Oval Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+(Source Strength/(2*pi))*(Polar Angle from Source-Polar Angle from Sink). This formula also uses Archimedes' constant and Sine (sin) function(s).

Can the Stream Function for Flow over Rankine Oval be negative?

Yes, the Stream Function for Flow over Rankine Oval, measured in Velocity Potential can be negative.

Which unit is used to measure Stream Function for Flow over Rankine Oval?

Stream Function for Flow over Rankine Oval is usually measured using the Square Meter per Second[m²/s] for Velocity Potential. are the few other units in which Stream Function for Flow over Rankine Oval can be measured.

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Stream Function for Flow over Rankine Oval Formula

Stream Function for Flow over Rankine Oval Example

Stream Function for Flow over Rankine Oval Solution

Stream Function for Flow over Rankine Oval Formula Elements

Other formulas in Source Flow category

How to Evaluate Stream Function for Flow over Rankine Oval?

FAQs on Stream Function for Flow over Rankine Oval

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