Tangential Velocity For Flow Over Sphere Calculator

Tangential Velocity Formula:

\[ V_{\theta} = \left( V_{\infty} + \frac{\mu}{4\pi r^3} \right) \sin(\theta) \]

Freestream Velocity (V∞):

m/s

Doublet Strength (μ):

m³/s

Radial Coordinate (r):

Polar Angle (θ):

rad

Tangential Velocity (Vθ):

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1. What is Tangential Velocity for Flow Over Sphere?

The tangential velocity component describes the velocity of fluid flow in the tangential direction around a sphere. It is derived from potential flow theory and represents the rotational component of the velocity field around the spherical object.

2. How Does the Calculator Work?

The calculator uses the tangential velocity formula:

\[ V_{\theta} = \left( V_{\infty} + \frac{\mu}{4\pi r^3} \right) \sin(\theta) \]

Where:

\( V_{\theta} \) — Tangential velocity (m/s)
\( V_{\infty} \) — Freestream velocity (m/s)
\( \mu \) — Doublet strength (m³/s)
\( r \) — Radial coordinate (m)
\( \theta \) — Polar angle (rad)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula combines the freestream velocity component with the doublet-induced velocity component, scaled by the sine of the polar angle to determine the tangential velocity component.

3. Importance of Tangential Velocity Calculation

Details: Calculating tangential velocity is crucial for analyzing fluid flow patterns around spherical objects, understanding boundary layer behavior, and predicting flow separation points in aerodynamic and hydrodynamic applications.

4. Using the Calculator

Tips: Enter freestream velocity in m/s, doublet strength in m³/s, radial coordinate in meters, and polar angle in radians. All values must be valid (radial coordinate > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is doublet strength in fluid dynamics?
A: Doublet strength represents the product of distance between a source-sink pair and their strength, creating a dipole-like flow field around the sphere.

Q2: How does polar angle affect tangential velocity?
A: The tangential velocity varies sinusoidally with polar angle, reaching maximum at θ = π/2 (90°) and zero at θ = 0 and θ = π (0° and 180°).

Q3: What are typical applications of this calculation?
A: This calculation is used in aerodynamics for flow around spherical objects, hydrodynamics for underwater spheres, and various engineering applications involving spherical flow patterns.

Q4: Are there limitations to this equation?
A: This equation assumes potential flow and may not accurately represent viscous effects, boundary layer development, or flow separation in real fluid applications.

Q5: How does radial distance affect tangential velocity?
A: The doublet-induced component decreases rapidly with increasing radial distance (as 1/r³), making the tangential velocity approach the freestream velocity component at large distances from the sphere.