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

Formula Used:

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

Radial Velocity (Vr):

m/s

Radial Coordinate (r):

Cylinder Radius (R):

Freestream Velocity (V∞):

m/s

Polar Angle (θ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Angular Position Given Radial Velocity Formula?

The formula calculates the polar angle (θ) for non-lifting flow over a circular cylinder based on radial velocity, cylinder radius, radial coordinate, and freestream velocity. It's derived from potential flow theory for inviscid, incompressible flow around a cylinder.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the angular position where the radial velocity component matches the given input values in non-lifting flow around a circular cylinder.

3. Importance of Polar Angle Calculation

Details: Calculating polar angle from radial velocity is crucial in fluid dynamics for analyzing flow patterns, determining stagnation points, and understanding velocity distribution around cylindrical objects in non-lifting flow conditions.

4. Using the Calculator

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

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 is no circulation, resulting in symmetric flow patterns and zero lift force.

Q2: Why does the formula use arccos function?
A: The arccos function is used because the radial velocity component is related to the cosine of the polar angle in potential flow theory.

Q3: What are typical applications of this calculation?
A: This calculation is used in aerodynamics, hydrodynamics, and various engineering applications involving flow around cylindrical structures.

Q4: Are there limitations to this formula?
A: Yes, this formula assumes ideal potential flow, inviscid fluid, incompressible flow, and no circulation around the cylinder.

Q5: What if the calculated value is complex?
A: If the argument of arccos is outside [-1,1], the result is not physically meaningful, indicating invalid input parameters.