Surface Velocity For Incompressible Flow Over Sphere Calculator

Formula Used:

\[ V_{\theta} = \frac{3}{2} \times V_{\infty} \times \sin(\theta) \]

Tangential Velocity (Vθ):

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1. What is Surface Velocity for Incompressible Flow Over Sphere?

The surface velocity calculation for incompressible flow over a sphere determines the tangential velocity component at any point on the sphere's surface. This is derived from potential flow theory and provides insights into the flow behavior around spherical objects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_{\theta} = \frac{3}{2} \times V_{\infty} \times \sin(\theta) \]

Where:

\( V_{\theta} \) — Tangential velocity (m/s)
\( V_{\infty} \) — Freestream velocity (m/s)
\( \theta \) — Polar angle measured from the stagnation point (radians)

Explanation: This formula represents the tangential velocity component on the surface of a sphere in potential flow, where the flow is assumed to be inviscid and incompressible.

3. Importance of Tangential Velocity Calculation

Details: Calculating surface velocity is crucial for understanding flow patterns, pressure distribution, and potential separation points around spherical objects in fluid dynamics applications.

4. Using the Calculator

Tips: Enter freestream velocity in m/s and polar angle in radians. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for this formula?
A: This formula is valid for potential flow (inviscid, incompressible flow) over a sphere and provides accurate results for Reynolds numbers where viscous effects are negligible.

Q2: How does polar angle affect the tangential velocity?
A: The tangential velocity reaches its maximum at θ = π/2 (90°) and is zero at both θ = 0 and θ = π (stagnation points).

Q3: Can this formula be used for compressible flow?
A: No, this formula is specifically derived for incompressible flow conditions. Compressible flow requires different equations that account for density variations.

Q4: What are the limitations of this approach?
A: The formula neglects viscous effects, turbulence, and flow separation, which become significant at higher Reynolds numbers in real-world applications.

Q5: How is this result used in practical applications?
A: This calculation is used in aerodynamic studies, hydrodynamics, and various engineering applications involving flow around spherical objects.