Radial Coordinate of Stagnation Point for Flow over Sphere Calculator

Formula Used:

\[ r = \left( \frac{\mu}{2\pi V_{\infty}} \right)^{1/3} \]

Radial Coordinate (r):

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1. What is the Radial Coordinate of Stagnation Point?

The radial coordinate of the stagnation point for flow over a sphere represents the distance from the center of the sphere to the point where the flow velocity becomes zero. This is a critical parameter in fluid dynamics for understanding flow patterns around spherical objects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \left( \frac{\mu}{2\pi V_{\infty}} \right)^{1/3} \]

Where:

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

Explanation: This formula calculates the radial distance from the center of the sphere to the stagnation point in a potential flow field, where the doublet strength represents the combined effect of source and sink in the flow field.

3. Importance of Stagnation Point Calculation

Details: Determining the stagnation point is crucial for analyzing pressure distribution, flow separation, and aerodynamic forces on spherical bodies. It helps in designing efficient aerodynamic shapes and understanding fluid behavior around obstacles.

4. Using the Calculator

Tips: Enter doublet strength in m³/s and freestream velocity in m/s. Both values must be positive numbers. The calculator will compute the radial coordinate in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is doublet strength in fluid dynamics?
A: Doublet strength is a measure of the combined effect of a source and sink pair in potential flow theory, representing the strength of the flow field disturbance caused by the spherical object.

Q2: How does freestream velocity affect the stagnation point?
A: Higher freestream velocities result in stagnation points closer to the sphere's surface, while lower velocities move the stagnation point further away from the sphere.

Q3: Is this calculation valid for all flow conditions?
A: This formula is derived for potential flow (inviscid, incompressible flow) and provides accurate results for ideal flow conditions around spheres.

Q4: What are typical values for doublet strength?
A: Doublet strength values depend on the specific flow configuration and sphere size, typically ranging from 0.001 to 100 m³/s for various engineering applications.

Q5: Can this calculator be used for other shapes?
A: This specific formula is derived for spherical objects. Other shapes require different mathematical formulations to calculate stagnation points.