Tangential Velocity For Non-Lifting Flow Over Circular Cylinder Calculator

Tangential Velocity Formula:

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

Cylinder Radius (R):

Radial Coordinate (r):

Freestream Velocity (V∞):

m/s

Polar Angle (θ):

rad

Tangential Velocity (Vθ):

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1. What is Tangential Velocity For Non-Lifting Flow Over Circular Cylinder?

The tangential velocity in non-lifting flow over a circular cylinder describes the velocity component tangent to the cylinder's surface. It represents how fluid particles move along circular paths around the cylinder in potential flow theory.

2. How Does the Calculator Work?

The calculator uses the tangential velocity formula:

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

Where:

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

Explanation: This formula calculates the tangential velocity component in potential flow around a circular cylinder, where the flow is non-lifting and symmetric.

3. Importance of Tangential Velocity Calculation

Details: Calculating tangential velocity is essential for understanding fluid flow patterns around cylindrical objects, analyzing pressure distributions, and studying aerodynamic or hydrodynamic behavior in potential flow theory.

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, freestream velocity > 0, polar angle ≥ 0).

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 and therefore no lift force generated.

Q2: Why is the tangential velocity negative in the formula?
A: The negative sign indicates that the tangential velocity is in the opposite direction to the conventional polar coordinate system orientation.

Q3: What are typical applications of this calculation?
A: This calculation is used in aerodynamics, hydrodynamics, and fluid mechanics studies involving flow around cylindrical structures like pipes, towers, or aircraft components.

Q4: What are the limitations of this formula?
A: This formula assumes ideal potential flow, inviscid fluid, and no separation effects. It may not accurately represent real viscous flows with boundary layer separation.

Q5: How does radial coordinate affect tangential velocity?
A: As radial coordinate increases (moving away from the cylinder), the tangential velocity decreases due to the (R/r)² term in the formula.