Velocity Potential For 3D Incompressible Doublet Flow Calculator

Velocity Potential Formula:

\[ \phi = -\frac{\mu \cdot \cos(\theta)}{4\pi r^2} \]

Velocity Potential (φ):

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1. What Is Velocity Potential For 3D Incompressible Doublet Flow?

The velocity potential for a 3D incompressible doublet flow represents a scalar function whose gradient gives the velocity field of the flow. It characterizes the flow pattern generated by a doublet in three-dimensional space.

2. How Does The Calculator Work?

The calculator uses the velocity potential formula:

\[ \phi = -\frac{\mu \cdot \cos(\theta)}{4\pi r^2} \]

Where:

\( \phi \) — Velocity potential (m²/s)
\( \mu \) — Doublet strength (m³/s)
\( \theta \) — Polar angle (radians)
\( r \) — Radial coordinate (meters)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula describes the velocity potential field generated by a doublet in three-dimensional incompressible flow, where the potential decreases with the square of the radial distance and varies with the cosine of the polar angle.

3. Importance Of Velocity Potential Calculation

Details: Calculating velocity potential is essential for analyzing potential flow fields, solving fluid dynamics problems, and understanding the behavior of incompressible flows around obstacles and in various engineering applications.

4. Using The Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a doublet in fluid dynamics?
A: A doublet is a combination of a source and sink of equal strength placed infinitesimally close together, creating a specific flow pattern.

Q2: What are the units of velocity potential?
A: Velocity potential has units of square meters per second (m²/s) in the SI system.

Q3: How is velocity related to velocity potential?
A: The velocity vector is the gradient of the velocity potential (v = ∇φ), meaning velocity components can be obtained by differentiating the potential function.

Q4: What are the assumptions behind this formula?
A: This formula assumes incompressible, irrotational flow and that the flow is generated by an ideal doublet in an unbounded fluid.

Q5: When is this velocity potential model applicable?
A: This model is applicable for potential flow analysis around streamlined bodies and for educational purposes in fluid dynamics, but has limitations for real viscous flows.