1. What is Velocity Potential?

Velocity Potential is a scalar function whose gradient gives velocity. In fluid dynamics, it represents the potential flow field where the flow is irrotational and incompressible.

2. How Does the Calculator Work?

The calculator uses the velocity potential formula for uniform incompressible flow in polar coordinates:

Where:

• \( \phi \) — Velocity Potential (m²/s)
• \( V_{\infty} \) — Freestream Velocity (m/s)
• \( r \) — Radial Coordinate (m)
• \( \theta \) — Polar Angle (rad)

Explanation: This formula calculates the velocity potential for uniform flow in polar coordinates, where the flow is steady, incompressible, and irrotational.

3. Importance of Velocity Potential Calculation

Details: Velocity potential is crucial in fluid dynamics for analyzing potential flow fields, calculating stream functions, and solving various aerodynamic and hydrodynamic problems involving irrotational flow.

4. Using the Calculator

Tips: Enter freestream velocity in m/s, radial coordinate in meters, and polar angle in radians. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of velocity potential?
A: Velocity potential represents a scalar field whose gradient gives the velocity vector field, simplifying the analysis of irrotational flows.

Q2: When is this formula applicable?
A: This formula applies to uniform, incompressible, irrotational flow in polar coordinates where the flow field is steady.

Q3: What are the units of velocity potential?
A: Velocity potential has units of square meters per second (m²/s) in the SI system.

Q4: How does polar angle affect the velocity potential?
A: The polar angle determines the directional component of the velocity potential through the cosine function, with maximum potential at θ = 0 and minimum at θ = π.

Q5: Can this calculator be used for compressible flow?
A: No, this specific formula is derived for incompressible flow conditions only.