Velocity Potential For 2-D Vortex Flow Calculator

Velocity Potential Formula:

\[ \phi = -\left(\frac{\Gamma}{2\pi}\right) \times \theta \]

Velocity Potential (φ):

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The Velocity Potential for 2-D Vortex Flow is a scalar function used in fluid dynamics to describe the velocity field of an irrotational vortex flow. It represents the potential whose gradient gives the velocity components in the flow field.

2. How Does the Calculator Work?

The calculator uses the Velocity Potential formula:

\[ \phi = -\left(\frac{\Gamma}{2\pi}\right) \times \theta \]

Where:

\( \phi \) — Velocity Potential (m²/s)
\( \Gamma \) — Vortex Strength (m²/s)
\( \theta \) — Polar Angle (radians)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the velocity potential for a 2-D vortex flow, where the velocity potential decreases linearly with the polar angle and is proportional to the vortex strength.

3. Importance of Velocity Potential Calculation

Details: Velocity potential is crucial in fluid dynamics for analyzing irrotational flows, solving potential flow problems, and understanding vortex behavior in various engineering applications.

4. Using the Calculator

Tips: Enter vortex strength in m²/s and polar angle in radians. Both values are required for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is vortex strength?
A: Vortex strength (Γ) is a measure of the intensity or magnitude of a vortex, representing the circulation around the vortex core.

Q2: Why is the velocity potential negative in the formula?
A: The negative sign indicates that the velocity potential decreases in the direction of increasing polar angle, consistent with the clockwise rotation typically associated with vortex flows.

Q3: What are typical units for velocity potential?
A: Velocity potential is measured in square meters per second (m²/s), which represents the potential function whose gradient gives velocity (m/s).

Q4: Can this formula be used for 3-D vortex flows?
A: No, this specific formula is for 2-D vortex flows. Three-dimensional vortex flows require more complex formulations.

Q5: What is the relationship between velocity potential and stream function?
A: In 2-D potential flows, velocity potential and stream function are conjugate harmonic functions that together completely describe the flow field.