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

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

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

STEP 0: Pre-Calculation Summary

Formula Used

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

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 - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
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.

STEP 1: Convert Input(s) to Base Unit

Tangential Velocity: -6.29 Meter per Second --> -6.29 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 = -arsin(V_θ/((1+R^2/r^2)*V_∞)) --> -arsin((-6.29)/((1+0.08^2/0.27^2)*6.9))

Evaluating ... ...

θ = 0.993649623833101

STEP 3: Convert Result to Output's Unit

0.993649623833101 Radian --> No Conversion Required

FINAL ANSWER

0.993649623833101 ≈ 0.99365 Radian <-- Polar Angle

(Calculation completed in 00.004 seconds)

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

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< Nonlifting Flow over Cylinder Calculators

Stream Function for Non-Lifting Flow over Circular Cylinder

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

Tangential Velocity for Non-Lifting Flow over Circular Cylinder

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

Radial Velocity for Non-Lifting Flow over Circular Cylinder

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

Radius of Cylinder for Non-Lifting Flow

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

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

LaTeX Go

Polar Angle = -arsin(Tangential Velocity/((1+Cylinder Radius^2/Radial Coordinate^2)*Freestream Velocity))
θ = -arsin(V_θ/((1+R^2/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 Tangential Velocity for Non-Lifting Flow over Circular Cylinder?

Angular Position given Tangential Velocity for Non-Lifting Flow over Circular Cylinder calculator uses Polar Angle = -arsin(Tangential Velocity/((1+Cylinder Radius^2/Radial Coordinate^2)*Freestream Velocity)) to calculate the Polar Angle, Angular Position given Tangential Velocity for Non-Lifting Flow over Circular Cylinder formula is defined as a method to determine the angular position of flow around a circular cylinder based on the tangential velocity and the characteristics of the flow field. Polar Angle is denoted by θ symbol.

How to calculate Angular Position given Tangential Velocity for Non-Lifting Flow over Circular Cylinder using this online calculator? To use this online calculator for Angular Position given Tangential Velocity for Non-Lifting Flow over Circular Cylinder, enter Tangential Velocity (V_θ), Cylinder Radius (R), Radial Coordinate (r) & Freestream Velocity (V_∞) and hit the calculate button. Here is how the Angular Position given Tangential Velocity for Non-Lifting Flow over Circular Cylinder calculation can be explained with given input values -> 0.452258 = -arsin((-6.29)/((1+0.08^2/0.27^2)*6.9)).

FAQ

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

Angular Position given Tangential Velocity for Non-Lifting Flow over Circular Cylinder formula is defined as a method to determine the angular position of flow around a circular cylinder based on the tangential velocity and the characteristics of the flow field and is represented as θ = -arsin(V_θ/((1+R^2/r^2)*V_∞)) or Polar Angle = -arsin(Tangential Velocity/((1+Cylinder Radius^2/Radial Coordinate^2)*Freestream Velocity)). Tangential Velocity refers to the speed at which an object moves along a tangent to the curve's 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 Tangential Velocity for Non-Lifting Flow over Circular Cylinder?

Angular Position given Tangential Velocity for Non-Lifting Flow over Circular Cylinder formula is defined as a method to determine the angular position of flow around a circular cylinder based on the tangential velocity and the characteristics of the flow field is calculated using Polar Angle = -arsin(Tangential Velocity/((1+Cylinder Radius^2/Radial Coordinate^2)*Freestream Velocity)). To calculate Angular Position given Tangential Velocity for Non-Lifting Flow over Circular Cylinder, you need Tangential Velocity (V_θ), Cylinder Radius (R), Radial Coordinate (r) & Freestream Velocity (V_∞). With our tool, you need to enter the respective value for Tangential 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 Tangential 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 = arccos(Radial Velocity/((1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity))

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