Angular Position given Radial Velocity for Non-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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Nonlifting Flow over Cylinder

Lifting Flow over Cylinder

✖Radial Velocity represents the speed of an object's motion along the radial direction.ⓘ Radial Velocity [V_r]			+10% -10%
✖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.ⓘ Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder [θ]

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Formula

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Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder

Formula

`"θ" = arccos("V"_{"r"}/((1-("R"/"r")^2)*"V"_{"∞"}))`

Example

`"0.902545rad"=arccos("3.9m/s"/((1-("0.08m"/"0.27m")^2)*"6.9m/s"))`

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Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Angle = arccos(Radial Velocity/((1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity))
θ = arccos(V_r/((1-(R/r)^2)*V_∞))
This formula uses 2 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
arccos - Arccosine function, is the inverse function of the cosine function.It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., arccos(Number)

Variables Used

Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
Radial Velocity - (Measured in Meter per Second) - Radial Velocity represents the speed of an object's motion along the radial 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.

STEP 1: Convert Input(s) to Base Unit

Radial Velocity: 3.9 Meter per Second --> 3.9 Meter per Second No Conversion Required
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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = arccos(V_r/((1-(R/r)^2)*V_∞)) --> arccos(3.9/((1-(0.08/0.27)^2)*6.9))

Evaluating ... ...

θ = 0.902545174954991

STEP 3: Convert Result to Output's Unit

0.902545174954991 Radian --> No Conversion Required

FINAL ANSWER

0.902545174954991 ≈ 0.902545 Radian <-- Polar Angle

(Calculation completed in 00.007 seconds)

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Home » Physics » Aerodynamics » Two-Dimensional Incompressible Flow » Flow and Lift Distribution » Flow over Cylinder » Nonlifting Flow over Cylinder » Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder

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Created by Harsh Raj

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

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< 10+ Nonlifting Flow over Cylinder Calculators

Stream Function for Non-Lifting Flow over Circular Cylinder

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

Angular Position given Tangential Velocity for Non-Lifting Flow over Circular Cylinder

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

Tangential Velocity for Non-Lifting Flow over Circular Cylinder

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

Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder

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

Radial Velocity for Non-Lifting Flow over Circular Cylinder

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

Radius of Cylinder for Non-Lifting Flow

Go Cylinder Radius = sqrt(Doublet Strength/(2*pi*Freestream Velocity))

Freestream Velocity given Doublet Strength for Non-Lifting Flow over Circular Cylinder

Go Freestream Velocity = Doublet Strength/(Cylinder Radius^2*2*pi)

Doublet Strength given Radius of Cylinder for Non-Lifting Flow

Go Doublet Strength = Cylinder Radius^2*2*pi*Freestream Velocity

Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder

Go Polar Angle = arsin(sqrt(1-(Surface Pressure Coefficient))/2)

Surface Pressure Coefficient for Non-Lifting Flow over Circular Cylinder

Go Surface Pressure Coefficient = 1-4*(sin(Polar Angle))^2

Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder Formula

Polar Angle = arccos(Radial Velocity/((1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity))
θ = arccos(V_r/((1-(R/r)^2)*V_∞))

How to obtain non-lifting flow over circular cylinder?

The non-lifting flow over a circular cylinder is obtained by the superimposition of uniform flow and doublet flow. The pressure distribution is symmetrical about the horizontal and vertical axis for non-lifting flow.

How to Calculate Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder?

Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder calculator uses Polar Angle = arccos(Radial Velocity/((1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity)) to calculate the Polar Angle, The Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder formula is defined as the specific angle at any given moment, influenced by the radial velocity's interaction with the flow dynamics around the cylinder. Polar Angle is denoted by θ symbol.

How to calculate Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder using this online calculator? To use this online calculator for Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder, enter Radial Velocity (V_r), Cylinder Radius (R), Radial Coordinate (r) & Freestream Velocity (V_∞) and hit the calculate button. Here is how the Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder calculation can be explained with given input values -> 0.902545 = arccos(3.9/((1-(0.08/0.27)^2)*6.9)).

FAQ

What is Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder?

The Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder formula is defined as the specific angle at any given moment, influenced by the radial velocity's interaction with the flow dynamics around the cylinder and is represented as θ = arccos(V_r/((1-(R/r)^2)*V_∞)) or Polar Angle = arccos(Radial Velocity/((1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity)). Radial Velocity represents the speed of an object's motion along the radial direction, 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.

How to calculate Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder?

The Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder formula is defined as the specific angle at any given moment, influenced by the radial velocity's interaction with the flow dynamics around the cylinder is calculated using Polar Angle = arccos(Radial Velocity/((1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity)). To calculate Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder, you need Radial Velocity (V_r), Cylinder Radius (R), Radial Coordinate (r) & Freestream Velocity (V_∞). With our tool, you need to enter the respective value for Radial Velocity, Cylinder Radius, Radial Coordinate & Freestream Velocity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Polar Angle?

In this formula, Polar Angle uses Radial Velocity, Cylinder Radius, Radial Coordinate & Freestream Velocity. We can use 2 other way(s) to calculate the same, which is/are as follows -

Polar Angle = arsin(sqrt(1-(Surface Pressure Coefficient))/2)
Polar Angle = -arsin(Tangential Velocity/((1+Cylinder Radius^2/Radial Coordinate^2)*Freestream Velocity))

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