Angular Position Given Tangential Velocity For Non Lifting Flow Over Circular Cylinder Calculator

Formula Used:

\[ \theta = -\arcsin\left(\frac{V_\theta}{\left(1 + \frac{R^2}{r^2}\right) \cdot V_\infty}\right) \]

Tangential Velocity (Vθ):

m/s

Cylinder Radius (R):

Radial Coordinate (r):

Freestream Velocity (V∞):

m/s

Polar Angle (θ):

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1. What is Angular Position Given Tangential Velocity For Non Lifting Flow Over Circular Cylinder?

This calculation determines the polar angle (θ) for non-lifting flow over a circular cylinder based on tangential velocity, cylinder radius, radial coordinate, and freestream velocity. It's derived from potential flow theory for ideal fluid flow around cylindrical objects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta = -\arcsin\left(\frac{V_\theta}{\left(1 + \frac{R^2}{r^2}\right) \cdot V_\infty}\right) \]

Where:

\( \theta \) — Polar Angle (radians)
\( V_\theta \) — Tangential Velocity (m/s)
\( R \) — Cylinder Radius (m)
\( r \) — Radial Coordinate (m)
\( V_\infty \) — Freestream Velocity (m/s)

Explanation: This formula calculates the angular position where the tangential velocity component matches the given value in non-lifting potential flow around a circular cylinder.

3. Importance of Polar Angle Calculation

Details: Determining angular positions with specific velocity components is crucial for analyzing flow patterns, pressure distributions, and potential flow characteristics around cylindrical structures in fluid dynamics.

4. Using the Calculator

Tips: Enter all velocity values in m/s, radius and coordinate values in meters. Ensure radial coordinate is greater than cylinder radius for valid results. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is non-lifting flow over a circular cylinder?
A: Non-lifting flow refers to potential flow around a cylinder where there's no circulation and consequently no lift force generated.

Q2: What are the assumptions behind this formula?
A: This formula assumes ideal, inviscid, incompressible flow with no separation and follows potential flow theory principles.

Q3: What is the range of valid polar angles?
A: Polar angles typically range from -π to π radians (-180° to 180°) in this coordinate system.

Q4: How does cylinder radius affect the flow pattern?
A: Larger cylinder radii create greater flow disturbance and affect the velocity distribution around the cylinder.

Q5: When is this calculation most applicable?
A: This calculation is most accurate for high Reynolds number flows where viscous effects are negligible and potential flow theory applies.