1. What is Velocity Potential?

Velocity Potential is a scalar function in fluid dynamics whose gradient gives the velocity field. For uniform incompressible flow, it represents the potential function that describes the flow field where the velocity is constant in magnitude and direction.

2. How Does the Calculator Work?

The calculator uses the velocity potential formula for uniform flow:

Where:

• \( \phi \) — Velocity Potential (m²/s)
• \( V_{\infty} \) — Freestream Velocity (m/s)
• \( x \) — Distance on X-Axis (m)

Explanation: This formula calculates the velocity potential for uniform incompressible flow along the x-axis, where the flow velocity is constant throughout the field.

3. Importance of Velocity Potential Calculation

Details: Velocity potential is fundamental in potential flow theory, which is used to analyze inviscid, incompressible flows. It helps in solving complex flow problems around bodies and in understanding flow patterns in aerodynamics and hydrodynamics.

4. Using the Calculator

Tips: Enter freestream velocity in m/s and distance on x-axis in meters. Both values must be positive numbers greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is uniform incompressible flow?
A: Uniform incompressible flow is a type of flow where the velocity is constant throughout the flow field, and the fluid density remains constant.

Q2: When is this velocity potential formula applicable?
A: This formula applies specifically to uniform flow along the x-axis in potential flow theory for incompressible fluids.

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 velocity potential relate to stream function?
A: In two-dimensional potential flow, velocity potential and stream function are conjugate harmonic functions that together describe the flow field completely.

Q5: What are the limitations of potential flow theory?
A: Potential flow theory assumes inviscid (frictionless), incompressible flow and cannot accurately predict flows with separation, turbulence, or significant viscous effects.