1. What is Velocity Potential for 2-D Source Flow?

Velocity Potential is a scalar function in fluid dynamics whose gradient gives the velocity field. For a 2-D source flow, it represents the potential function for fluid emanating from a point source in a two-dimensional plane.

2. How Does the Calculator Work?

The calculator uses the velocity potential formula:

Where:

• \( \phi \) — Velocity Potential (m²/s)
• \( \Lambda \) — Source Strength (m²/s)
• \( r \) — Radial Coordinate (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \ln \) — Natural logarithm function

Explanation: The formula calculates the velocity potential at a radial distance r from a 2-D source with strength Λ.

3. Importance of Velocity Potential Calculation

Details: Velocity potential is fundamental in potential flow theory, which is used to model inviscid, incompressible fluid flows. It helps in analyzing flow patterns around objects and understanding fluid behavior in various engineering applications.

4. Using the Calculator

Tips: Enter source strength in m²/s and radial coordinate in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a source in fluid dynamics?
A: A source is a theoretical point from which fluid flows outward radially in all directions at a constant rate.

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: Can this formula be used for sink flow?
A: Yes, for sink flow (fluid flowing inward), the source strength Λ would be negative.

Q4: What are the limitations of this model?
A: This model assumes ideal, inviscid, incompressible flow and is valid for 2-D flows only. Real fluids with viscosity may behave differently.

Q5: How is velocity derived from velocity potential?
A: Velocity components are obtained by taking the gradient of the velocity potential: \( \vec{v} = \nabla\phi \).