Radial Velocity for Non-Lifting Flow over Circular Cylinder Calculator

Radial Velocity Formula:

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

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 Non-Lifting Flow over Circular Cylinder?

The radial velocity represents the component of fluid velocity in the radial direction for non-lifting flow over a circular cylinder. It describes how fluid particles move toward or away from the cylinder's center at different positions around the cylinder.

2. How Does the Calculator Work?

The calculator uses the radial velocity formula:

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

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 calculates the radial component of velocity in potential flow around a circular cylinder, derived from the superposition of uniform flow and a doublet.

3. Importance of Radial Velocity Calculation

Details: Understanding radial velocity distribution is crucial for analyzing 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, freestream velocity > 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 without circulation, resulting in symmetric flow patterns and zero lift force on the cylinder.

Q2: What does radial velocity tell us about the flow?
A: Radial velocity indicates how fluid moves toward or away from the cylinder center, helping understand the flow divergence/convergence patterns around the cylinder.

Q3: How does radial velocity vary with polar angle?
A: Radial velocity follows a cosine distribution, being maximum at θ = 0 and π (along the flow direction) and zero at θ = π/2 and 3π/2 (perpendicular to flow).

Q4: What are the limitations of this formula?
A: This formula assumes ideal potential flow, inviscid fluid, and steady-state conditions. It doesn't account for viscosity, turbulence, or real fluid effects.

Q5: Where is this calculation typically applied?
A: This calculation is used in theoretical fluid dynamics, aerodynamics studies, and as a foundation for more complex flow analyses involving cylindrical objects.