1. What is Velocity Potential For 2-D Doublet Flow?

The velocity potential for 2-D doublet flow represents a scalar function whose gradient gives the velocity field. It describes the flow pattern created by a doublet, which is a combination of a source and sink of equal strength placed infinitesimally close together.

2. How Does the Calculator Work?

The calculator uses the velocity potential formula:

Where:

• \( \phi \) — Velocity potential (m²/s)
• \( \kappa \) — Doublet strength (m³/s)
• \( r \) — Radial coordinate (m)
• \( \theta \) — Polar angle (rad)
• \( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula calculates the velocity potential at a given point in a 2-D doublet flow field based on the doublet strength and the polar coordinates of the point.

3. Importance of Velocity Potential Calculation

Details: Velocity potential is crucial in potential flow theory for analyzing irrotational flow fields. It helps in determining velocity components and understanding flow patterns around objects in fluid dynamics.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a doublet in fluid mechanics?
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 components can be obtained by taking the gradient of the velocity potential function.

Q4: What are the applications of doublet flow?
A: Doublet flow is used to model flow around circular cylinders and other bluff bodies in potential flow theory.

Q5: Can this calculator handle 3-D flows?
A: No, this calculator is specifically designed for 2-D doublet flow calculations.