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

✖Tangential Velocity refers to the speed at which an object moves along a tangent to the curve's direction.ⓘ Tangential Velocity for Lifting Flow over Circular Cylinder [V_θ]

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Formula

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Tangential Velocity for Lifting Flow over Circular Cylinder

Formula

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

Example

`"-6.292089m/s"=-(1+(("0.08m")/("0.27m"))^2)*"6.9m/s"*sin("0.9rad")-("0.7m²/s")/(2*pi*"0.27m")`

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Tangential Velocity for Lifting Flow over Circular Cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Tangential Velocity = -(1+((Cylinder Radius)/(Radial Coordinate))^2)*Freestream Velocity*sin(Polar Angle)-(Vortex Strength)/(2*pi*Radial Coordinate)
V_θ = -(1+((R)/(r))^2)*V_∞*sin(θ)-(Γ)/(2*pi*r)
This formula uses 1 Constants, 1 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)

Variables Used

Tangential Velocity - (Measured in Meter per Second) - Tangential Velocity refers to the speed at which an object moves along a tangent to the curve's direction.
Cylinder Radius - (Measured in Meter) - The Cylinder Radius is the radius of its circular cross section.
Radial Coordinate - (Measured in Meter) - Radial Coordinate represents the distance measured from a central point or axis.
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.
Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
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

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

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

Evaluating ... ...

V_θ = -6.29208874328173

STEP 3: Convert Result to Output's Unit

-6.29208874328173 Meter per Second --> No Conversion Required

FINAL ANSWER

-6.29208874328173 ≈ -6.292089 Meter per Second <-- Tangential Velocity

(Calculation completed in 00.004 seconds)

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Home » Physics » Aerodynamics » Two-Dimensional Incompressible Flow » Flow and Lift Distribution » Flow over Cylinder » Lifting Flow over Cylinder » Tangential Velocity for Lifting Flow over Circular Cylinder

Credits

Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has created this Calculator and 100+ more calculators!

Verified by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has verified this Calculator and 200+ more calculators!

< 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)

Tangential Velocity for Lifting Flow over Circular Cylinder Formula

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 Tangential Velocity for Lifting Flow over Circular Cylinder?

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

How to calculate Tangential Velocity for Lifting Flow over Circular Cylinder using this online calculator? To use this online calculator for Tangential Velocity for Lifting Flow over Circular Cylinder, enter Cylinder Radius (R), Radial Coordinate (r), Freestream Velocity (V_∞), Polar Angle (θ) & Vortex Strength (Γ) and hit the calculate button. Here is how the Tangential Velocity for Lifting Flow over Circular Cylinder calculation can be explained with given input values -> -13.542481 = -(1+((0.08)/(0.27))^2)*6.9*sin(0.9)-(0.7)/(2*pi*0.27).

FAQ

What is Tangential Velocity for Lifting Flow over Circular Cylinder?

The Tangential velocity for lifting flow over circular cylinder formula is a function of radial coordinate, freestream velocity, the radius of the cylinder, vortex strength and polar angle and is represented as V_θ = -(1+((R)/(r))^2)*V_∞*sin(θ)-(Γ)/(2*pi*r) or Tangential Velocity = -(1+((Cylinder Radius)/(Radial Coordinate))^2)*Freestream Velocity*sin(Polar Angle)-(Vortex Strength)/(2*pi*Radial Coordinate). The Cylinder Radius is the radius of its circular cross section, Radial Coordinate represents the distance measured from a central point or axis, The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles, Polar Angle is the angular position of a point from a reference direction & Vortex Strength quantifies the intensity or magnitude of a vortex in fluid dynamics.

How to calculate Tangential Velocity for Lifting Flow over Circular Cylinder?

The Tangential velocity for lifting flow over circular cylinder formula is a function of radial coordinate, freestream velocity, the radius of the cylinder, vortex strength and polar angle is calculated using Tangential Velocity = -(1+((Cylinder Radius)/(Radial Coordinate))^2)*Freestream Velocity*sin(Polar Angle)-(Vortex Strength)/(2*pi*Radial Coordinate). To calculate Tangential Velocity for Lifting Flow over Circular Cylinder, you need Cylinder Radius (R), Radial Coordinate (r), Freestream Velocity (V_∞), Polar Angle (θ) & Vortex Strength (Γ). With our tool, you need to enter the respective value for Cylinder Radius, Radial Coordinate, Freestream Velocity, Polar Angle & 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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