Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder Calculator

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Two-Dimensional Incompressible Flow

Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

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Flow and Lift Distribution

Elementary Flows

Flow over Airfoils and Wings

Lift Distribution

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Flow over Cylinder

Kutta-Joukowski Lift Theorem

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Lifting Flow over Cylinder

Nonlifting Flow over Cylinder

✖Stagnation Vortex Strength quantifies the intensity or magnitude of a vortex at stagnation point.ⓘ Stagnation Vortex Strength [Γ₀]			+10% -10%
✖The Stagnation Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles.ⓘ Stagnation Freestream Velocity [V_s,∞]			+10% -10%
✖The Cylinder Radius is the radius of its circular cross section.ⓘ Cylinder Radius [R]			+10% -10%

✖Polar Angle of Stagnation Point is the angular position of stagnation point from a reference direction.ⓘ Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder [θ₀]

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Formula

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Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder

Formula

`"θ"_{"0"} = arsin(-"Γ"_{"0"}/(4*pi*"V"_{"s,∞"}*"R"))`

Example

`"-1.055971rad"=arsin(-"7m²/s"/(4*pi*"8m/s"*"0.08m"))`

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Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Angle of Stagnation Point = arsin(-Stagnation Vortex Strength/(4*pi*Stagnation Freestream Velocity*Cylinder Radius))
θ₀ = arsin(-Γ₀/(4*pi*V_s,∞*R))
This formula uses 1 Constants, 2 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sin(Angle)
arsin - Arcsine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., arsin(Number)

Variables Used

Polar Angle of Stagnation Point - (Measured in Radian) - Polar Angle of Stagnation Point is the angular position of stagnation point from a reference direction.
Stagnation Vortex Strength - (Measured in Square Meter per Second) - Stagnation Vortex Strength quantifies the intensity or magnitude of a vortex at stagnation point.
Stagnation Freestream Velocity - (Measured in Meter per Second) - The Stagnation Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles.
Cylinder Radius - (Measured in Meter) - The Cylinder Radius is the radius of its circular cross section.

STEP 1: Convert Input(s) to Base Unit

Stagnation Vortex Strength: 7 Square Meter per Second --> 7 Square Meter per Second No Conversion Required
Stagnation Freestream Velocity: 8 Meter per Second --> 8 Meter per Second No Conversion Required
Cylinder Radius: 0.08 Meter --> 0.08 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ₀ = arsin(-Γ₀/(4*pi*V_s,∞*R)) --> arsin(-7/(4*pi*8*0.08))

Evaluating ... ...

θ₀ = -1.05597070220761

STEP 3: Convert Result to Output's Unit

-1.05597070220761 Radian --> No Conversion Required

FINAL ANSWER

-1.05597070220761 ≈ -1.055971 Radian <-- Polar Angle of Stagnation Point

(Calculation completed in 00.004 seconds)

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Created by Harsh Raj

Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal

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< 10+ Lifting Flow over Cylinder Calculators

Surface Pressure Coefficient for Lifting Flow over Circular Cylinder

Go Surface Pressure Coefficient = 1-((2*sin(Polar Angle))^2+(2*Vortex Strength*sin(Polar Angle))/(pi*Cylinder Radius*Freestream Velocity)+((Vortex Strength)/(2*pi*Cylinder Radius*Freestream Velocity))^2)

Stream Function for Lifting Flow over Circular Cylinder

Go Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2)+Vortex Strength/(2*pi)*ln(Radial Coordinate/Cylinder Radius)

Location of Stagnation Point Outside Cylinder for Lifting Flow

Go Radial Coordinate of Stagnation Point = Stagnation Vortex Strength/(4*pi*Freestream Velocity)+sqrt((Stagnation Vortex Strength/(4*pi*Freestream Velocity))^2-Cylinder Radius^2)

Tangential Velocity for Lifting Flow over Circular Cylinder

Go Tangential Velocity = -(1+((Cylinder Radius)/(Radial Coordinate))^2)*Freestream Velocity*sin(Polar Angle)-(Vortex Strength)/(2*pi*Radial Coordinate)

Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder

Go Polar Angle of Stagnation Point = arsin(-Stagnation Vortex Strength/(4*pi*Stagnation Freestream Velocity*Cylinder Radius))

Angular Position given Radial Velocity for Lifting Flow over Circular Cylinder

Go Polar Angle = arccos(Radial Velocity/((1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity))

Radial Velocity for Lifting Flow over Circular Cylinder

Go Radial Velocity = (1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity*cos(Polar Angle)

Freestream Velocity given 2-D Lift Coefficient for Lifting Flow

Go Freestream Velocity = Vortex Strength/(Cylinder Radius*Lift Coefficient)

Radius of Cylinder for Lifting Flow

Go Cylinder Radius = Vortex Strength/(Lift Coefficient*Freestream Velocity)

2-D Lift Coefficient for Cylinder

Go Lift Coefficient = Vortex Strength/(Cylinder Radius*Freestream Velocity)

Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder Formula

Polar Angle of Stagnation Point = arsin(-Stagnation Vortex Strength/(4*pi*Stagnation Freestream Velocity*Cylinder Radius))
θ₀ = arsin(-Γ₀/(4*pi*V_s,∞*R))

How to obtain velocity components for lifting flow over a cylinder?

The velocity components for lifting flow over a cylinder is obtained either by differentiating stream function or directly adding the velocity field of non-lifting flow over the cylinder and vortex flow.

How to Calculate Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder?

Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder calculator uses Polar Angle of Stagnation Point = arsin(-Stagnation Vortex Strength/(4*pi*Stagnation Freestream Velocity*Cylinder Radius)) to calculate the Polar Angle of Stagnation Point, The Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder formula is defined as specific angular orientation where the flow's stagnation point occurs concerning a circular cylinder in a lifting flow scenario. Polar Angle of Stagnation Point is denoted by θ₀ symbol.

How to calculate Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder using this online calculator? To use this online calculator for Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder, enter Stagnation Vortex Strength (Γ₀), Stagnation Freestream Velocity (V_s,∞) & Cylinder Radius (R) and hit the calculate button. Here is how the Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder calculation can be explained with given input values -> -1.055971 = arsin(-7/(4*pi*8*0.08)).

FAQ

What is Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder?

The Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder formula is defined as specific angular orientation where the flow's stagnation point occurs concerning a circular cylinder in a lifting flow scenario and is represented as θ₀ = arsin(-Γ₀/(4*pi*V_s,∞*R)) or Polar Angle of Stagnation Point = arsin(-Stagnation Vortex Strength/(4*pi*Stagnation Freestream Velocity*Cylinder Radius)). Stagnation Vortex Strength quantifies the intensity or magnitude of a vortex at stagnation point, The Stagnation Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles & The Cylinder Radius is the radius of its circular cross section.

How to calculate Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder?

The Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder formula is defined as specific angular orientation where the flow's stagnation point occurs concerning a circular cylinder in a lifting flow scenario is calculated using Polar Angle of Stagnation Point = arsin(-Stagnation Vortex Strength/(4*pi*Stagnation Freestream Velocity*Cylinder Radius)). To calculate Angular Position of Stagnation Point for Lifting Flow over Circular Cylinder, you need Stagnation Vortex Strength (Γ₀), Stagnation Freestream Velocity (V_s,∞) & Cylinder Radius (R). With our tool, you need to enter the respective value for Stagnation Vortex Strength, Stagnation Freestream Velocity & Cylinder Radius and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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