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Stream Function for Lifting Flow over Circular Cylinder Formula

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Stream Function is a mathematical function used in fluid dynamics to describe the flow patterns within a fluid. Check FAQs

ψ = V ∞ \cdot r \cdot \sin (θ) \cdot (1 - {(\frac{R}{r})}^{2}) + \frac{Γ}{2 \cdot π} \cdot \ln (\frac{r}{R})

ψ - Stream Function?V_∞ - Freestream Velocity?r - Radial Coordinate?θ - Polar Angle?R - Cylinder Radius?Γ - Vortex Strength?π - Archimedes' constant?

Stream Function for Lifting Flow over Circular Cylinder Example

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Here is how the Stream Function for Lifting Flow over Circular Cylinder equation looks like with Values.

Here is how the Stream Function for Lifting Flow over Circular Cylinder equation looks like with Units.

Here is how the Stream Function for Lifting Flow over Circular Cylinder equation looks like.

1.4667 = 6.9 \cdot 0.27 \cdot \sin (0.9) \cdot (1 - {(\frac{0.08}{0.27})}^{2}) + \frac{0.7}{2 \cdot 3.1416} \cdot \ln (\frac{0.27}{0.08})

1.4667m²/s = 6.9m/s \cdot 0.27m \cdot \sin (0.9rad) \cdot (1 - {(\frac{0.08m}{0.27m})}^{2}) + \frac{0.7m²/s}{2 \cdot 3.1416} \cdot \ln (\frac{0.27m}{0.08m})

1.4667 = 6.9 \cdot 0.27 \cdot \sin (0.9) \cdot (1 - {(\frac{0.08}{0.27})}^{2}) + \frac{0.7}{2 \cdot 3.1416} \cdot \ln (\frac{0.27}{0.08})

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Stream Function for Lifting Flow over Circular Cylinder Solution

Follow our step by step solution on how to calculate Stream Function for Lifting Flow over Circular Cylinder?

FIRST Step Consider the formula

ψ = V ∞ \cdot r \cdot \sin (θ) \cdot (1 - {(\frac{R}{r})}^{2}) + \frac{Γ}{2 \cdot π} \cdot \ln (\frac{r}{R})

Next Step Substitute values of Variables

∴

ψ = 6.9m/s \cdot 0.27m \cdot \sin (0.9rad) \cdot (1 - {(\frac{0.08m}{0.27m})}^{2}) + \frac{0.7m²/s}{2 \cdot π} \cdot \ln (\frac{0.27m}{0.08m})

Next Step Substitute values of Constants

∴

ψ = 6.9m/s \cdot 0.27m \cdot \sin (0.9rad) \cdot (1 - {(\frac{0.08m}{0.27m})}^{2}) + \frac{0.7m²/s}{2 \cdot 3.1416} \cdot \ln (\frac{0.27m}{0.08m})

Next Step Prepare to Evaluate

∴

ψ = 6.9 \cdot 0.27 \cdot \sin (0.9) \cdot (1 - {(\frac{0.08}{0.27})}^{2}) + \frac{0.7}{2 \cdot 3.1416} \cdot \ln (\frac{0.27}{0.08})

Next Step Evaluate

∴

ψ = 1.46673729478434m²/s

LAST Step Rounding Answer

∴

ψ = 1.4667m²/s

Stream Function for Lifting Flow over Circular Cylinder Formula Elements

Variables

Constants

Functions

Stream Function

Stream Function is a mathematical function used in fluid dynamics to describe the flow patterns within a fluid.

Symbol: ψ

Measurement: Velocity PotentialUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Stream Function

Freestream Velocity

The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles.

Symbol: V_∞

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Freestream Velocity

Radial Coordinate

Radial Coordinate represents the distance measured from a central point or axis.

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

Cylinder Radius

The Cylinder Radius is the radius of its circular cross section.

Symbol: R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Cylinder Radius

Vortex Strength

Vortex Strength quantifies the intensity or magnitude of a vortex in fluid dynamics.

Symbol: Γ

Measurement: Velocity PotentialUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Vortex Strength

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)

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Lifting Flow over Cylinder category

Go Radial Velocity for Lifting Flow over Circular Cylinder

V r = (1 - {(\frac{R}{r})}^{2}) \cdot V ∞ \cdot \cos (θ)

Go Tangential Velocity for Lifting Flow over Circular Cylinder

V θ = - (1 + {(\frac{R}{r})}^{2}) \cdot V ∞ \cdot \sin (θ) - \frac{Γ}{2 \cdot π \cdot r}

Go Surface Pressure Coefficient for Lifting Flow over Circular Cylinder

C p = 1 - ({(2 \cdot \sin (θ))}^{2} + \frac{2 \cdot Γ \cdot \sin (θ)}{π \cdot R \cdot V ∞} + {(\frac{Γ}{2 \cdot π \cdot R \cdot V ∞})}^{2})

Go Location of Stagnation Point Outside Cylinder for Lifting Flow

r 0 = \frac{Γ 0}{4 \cdot π \cdot V ∞} + \sqrt{{(\frac{Γ 0}{4 \cdot π \cdot V ∞})}^{2} - R^{2}}

How to Evaluate Stream Function for Lifting Flow over Circular Cylinder?

Stream Function for Lifting Flow over Circular Cylinder evaluator uses Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2)+Vortex Strength/(2*pi)*ln(Radial Coordinate/Cylinder Radius) to evaluate the Stream Function, The Stream function for lifting flow over circular cylinder formula is the function of vortex strength, radial distance, the radius of the cylinder, polar angle and freestream velocity. Stream Function is denoted by ψ symbol.

How to evaluate Stream Function for Lifting Flow over Circular Cylinder using this online evaluator? To use this online evaluator for Stream Function for Lifting Flow over Circular Cylinder, enter Freestream Velocity (V_∞), Radial Coordinate (r), Polar Angle (θ), Cylinder Radius (R) & Vortex Strength (Γ) and hit the calculate button.

FAQs on Stream Function for Lifting Flow over Circular Cylinder

What is the formula to find Stream Function for Lifting Flow over Circular Cylinder?

The formula of Stream Function for Lifting Flow over Circular Cylinder is expressed as Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2)+Vortex Strength/(2*pi)*ln(Radial Coordinate/Cylinder Radius). Here is an example- 3.84796 = 6.9*0.27*sin(0.9)*(1-(0.08/0.27)^2)+0.7/(2*pi)*ln(0.27/0.08).

How to calculate Stream Function for Lifting Flow over Circular Cylinder?

With Freestream Velocity (V_∞), Radial Coordinate (r), Polar Angle (θ), Cylinder Radius (R) & Vortex Strength (Γ) we can find Stream Function for Lifting Flow over Circular Cylinder using the formula - Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2)+Vortex Strength/(2*pi)*ln(Radial Coordinate/Cylinder Radius). This formula also uses Archimedes' constant and , Sine (sin), Natural Logarithm (ln) function(s).

Can the Stream Function for Lifting Flow over Circular Cylinder be negative?

Yes, the Stream Function for Lifting Flow over Circular Cylinder, measured in Velocity Potential can be negative.

Which unit is used to measure Stream Function for Lifting Flow over Circular Cylinder?

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

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Stream Function for Lifting Flow over Circular Cylinder Formula

Stream Function for Lifting Flow over Circular Cylinder Example

Stream Function for Lifting Flow over Circular Cylinder Solution

Stream Function for Lifting Flow over Circular Cylinder Formula Elements

Other formulas in Lifting Flow over Cylinder category

How to Evaluate Stream Function for Lifting Flow over Circular Cylinder?

FAQs on Stream Function for Lifting Flow over Circular Cylinder

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