Radial Velocity For Lifting Flow Over Circular Cylinder Calculator

Radial Velocity Formula:

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

Cylinder Radius (R):

Radial Coordinate (r):

Freestream Velocity (V∞):

m/s

Polar Angle (θ):

rad

Radial Velocity (Vr):

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1. What is Radial Velocity For Lifting Flow Over Circular Cylinder?

The Radial Velocity for Lifting Flow Over Circular Cylinder represents the component of fluid velocity in the radial direction around a circular cylinder with circulation. It is derived from potential flow theory and describes how fluid particles move outward or inward from the cylinder's center.

2. How Does the Calculator Work?

The calculator uses the radial velocity formula:

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

Where:

\( V_r \) — Radial velocity (m/s)
\( R \) — Cylinder radius (m)
\( r \) — Radial coordinate (m)
\( V_{\infty} \) — Freestream velocity (m/s)
\( \theta \) — Polar angle (radians)

Explanation: The formula describes how the radial component of velocity varies with distance from the cylinder and angular position, accounting for the flow disturbance caused by the cylinder.

3. Importance of Radial Velocity Calculation

Details: Calculating radial velocity is essential for understanding fluid flow patterns around cylindrical objects, which has applications in aerodynamics, hydrodynamics, and various engineering fields involving flow around obstacles.

4. Using the Calculator

Tips: Enter cylinder radius and radial coordinate in meters, freestream velocity in m/s, and polar angle in radians. All values must be positive (radius > 0, radial coordinate > 0, velocity > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of radial velocity?
A: Radial velocity indicates how quickly fluid particles are moving toward or away from the cylinder's center, which helps understand flow patterns and pressure distributions.

Q2: How does radial velocity vary with distance from the cylinder?
A: Radial velocity decreases with increasing distance from the cylinder, approaching the freestream velocity component as r becomes large.

Q3: What is the range of valid polar angles?
A: Polar angle typically ranges from 0 to 2π radians (0° to 360°), representing the full circle around the cylinder.

Q4: Does this formula account for viscous effects?
A: No, this formula is derived from potential flow theory which assumes inviscid, irrotational flow. Real fluid effects require additional considerations.

Q5: What are typical applications of this calculation?
A: This calculation is used in aerodynamic studies of cylindrical structures, design of offshore platforms, analysis of flow around pipes, and educational demonstrations of potential flow theory.