Radial Velocity For Flow Over Sphere Calculator

Radial Velocity Formula:

\[ V_r = -\left(V_\infty - \frac{\mu}{2\pi r^3}\right) \cos(\theta) \]

Freestream Velocity (V∞):

m/s

Doublet Strength (μ):

m³/s

Radial Coordinate (r):

Polar Angle (θ):

rad

Radial Velocity (Vr):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Radial Velocity For Flow Over Sphere?

The radial velocity for flow over a sphere describes the velocity component in the radial direction when a fluid flows around a spherical object. This is derived from potential flow theory using the concept of a doublet to represent the sphere.

2. How Does the Calculator Work?

The calculator uses the radial velocity formula:

\[ V_r = -\left(V_\infty - \frac{\mu}{2\pi r^3}\right) \cos(\theta) \]

Where:

\( V_r \) — Radial velocity (m/s)
\( V_\infty \) — Freestream velocity (m/s)
\( \mu \) — Doublet strength (m³/s)
\( r \) — Radial coordinate (m)
\( \theta \) — Polar angle (rad)

Explanation: This formula calculates the radial component of velocity in spherical coordinates for potential flow over a sphere, where the doublet represents the effect of the sphere on the flow field.

3. Importance of Radial Velocity Calculation

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

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 (positive values, radial coordinate > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is doublet strength in fluid dynamics?
A: Doublet strength represents the product of source and sink strengths and their separation distance, used to model the flow around a sphere in potential flow theory.

Q2: What does negative radial velocity indicate?
A: Negative radial velocity indicates flow toward the center (sink-like behavior), while positive indicates flow away from the center (source-like behavior).

Q3: When is this potential flow model applicable?
A: This model works well for inviscid, incompressible flow at high Reynolds numbers where viscous effects are confined to thin boundary layers.

Q4: What are the limitations of this model?
A: The model doesn't account for viscosity, turbulence, separation, or compressibility effects that occur in real fluid flows.

Q5: How is doublet strength related to sphere size?
A: For flow over a sphere, the doublet strength is related to the sphere radius R by μ = 2πV∞R³, where the sphere surface corresponds to the zero-streamline.