Stream Function 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

✖The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles.ⓘ Freestream Velocity [V_∞]			+10% -10%
✖Radial Coordinate represents the distance measured from a central point or axis.ⓘ Radial Coordinate [r]			+10% -10%
✖Polar Angle is the angular position of a point from a reference direction.ⓘ Polar Angle [θ]			+10% -10%
✖The Cylinder Radius is the radius of its circular cross section.ⓘ Cylinder Radius [R]			+10% -10%
✖Vortex Strength quantifies the intensity or magnitude of a vortex in fluid dynamics.ⓘ Vortex Strength [Γ]			+10% -10%

✖Stream Function is a mathematical function used in fluid dynamics to describe the flow patterns within a fluid.ⓘ Stream Function for Lifting Flow over Circular Cylinder [ψ]

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Formula

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Stream Function for Lifting Flow over Circular Cylinder

Formula

`"ψ" = "V"_{"∞"}*"r"*sin("θ")*(1-("R"/"r")^2)+"Γ"/(2*pi)*ln("r"/"R")`

Example

`"1.466737m²/s"="6.9m/s"*"0.27m"*sin("0.9rad")*(1-("0.08m"/"0.27m")^2)+"0.7m²/s"/(2*pi)*ln("0.27m"/"0.08m")`

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Stream Function for Lifting Flow over Circular Cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2)+Vortex Strength/(2*pi)*ln(Radial Coordinate/Cylinder Radius)
ψ = V_∞*r*sin(θ)*(1-(R/r)^2)+Γ/(2*pi)*ln(r/R)
This formula uses 1 Constants, 2 Functions, 6 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)
ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Stream Function - (Measured in Square Meter per Second) - Stream Function is a mathematical function used in fluid dynamics to describe the flow patterns within a fluid.
Freestream Velocity - (Measured in Meter per Second) - The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles.
Radial Coordinate - (Measured in Meter) - Radial Coordinate represents the distance measured from a central point or axis.
Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
Cylinder Radius - (Measured in Meter) - The Cylinder Radius is the radius of its circular cross section.
Vortex Strength - (Measured in Square Meter per Second) - Vortex Strength quantifies the intensity or magnitude of a vortex in fluid dynamics.

STEP 1: Convert Input(s) to Base Unit

Freestream Velocity: 6.9 Meter per Second --> 6.9 Meter per Second No Conversion Required
Radial Coordinate: 0.27 Meter --> 0.27 Meter No Conversion Required
Polar Angle: 0.9 Radian --> 0.9 Radian No Conversion Required
Cylinder Radius: 0.08 Meter --> 0.08 Meter No Conversion Required
Vortex Strength: 0.7 Square Meter per Second --> 0.7 Square Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ = V_∞*r*sin(θ)*(1-(R/r)^2)+Γ/(2*pi)*ln(r/R) --> 6.9*0.27*sin(0.9)*(1-(0.08/0.27)^2)+0.7/(2*pi)*ln(0.27/0.08)

Evaluating ... ...

ψ = 1.46673729478434

STEP 3: Convert Result to Output's Unit

1.46673729478434 Square Meter per Second --> No Conversion Required

FINAL ANSWER

1.46673729478434 ≈ 1.466737 Square Meter per Second <-- Stream Function

(Calculation completed in 00.014 seconds)

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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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)

Stream Function for Lifting Flow over Circular Cylinder Formula

How to obtain lifting flow over cylinder?

The lifting flow over a cylinder is obtained by superimposing non-lifting flow over a cylinder with vortex flow. The non-lifting flow over a circular cylinder is obtained by the superimposition of uniform flow and doublet flow.

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

Stream Function for Lifting Flow over Circular Cylinder calculator 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 calculate 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 calculate Stream Function for Lifting Flow over Circular Cylinder using this online calculator? To use this online calculator 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. Here is how the Stream Function for Lifting Flow over Circular Cylinder calculation can be explained with given input values -> 3.84796 = 6.9*0.27*sin(0.9)*(1-(0.08/0.27)^2)+0.7/(2*pi)*ln(0.27/0.08).

FAQ

What is Stream Function for Lifting Flow over Circular Cylinder?

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 and is represented as ψ = V_∞*r*sin(θ)*(1-(R/r)^2)+Γ/(2*pi)*ln(r/R) or Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2)+Vortex Strength/(2*pi)*ln(Radial Coordinate/Cylinder Radius). The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles, Radial Coordinate represents the distance measured from a central point or axis, Polar Angle is the angular position of a point from a reference direction, The Cylinder Radius is the radius of its circular cross section & Vortex Strength quantifies the intensity or magnitude of a vortex in fluid dynamics.

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

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 is calculated using 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 calculate Stream Function for Lifting Flow over Circular Cylinder, you need Freestream Velocity (V_∞), Radial Coordinate (r), Polar Angle (θ), Cylinder Radius (R) & Vortex Strength (Γ). With our tool, you need to enter the respective value for Freestream Velocity, Radial Coordinate, Polar Angle, Cylinder Radius & Vortex Strength 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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