1. What is Tangential Velocity For 2-D Vortex Flow?

Tangential Velocity in 2-D Vortex Flow refers to the velocity component perpendicular to the radial direction in a vortex flow field. It describes how fluid particles move in circular paths around the vortex center, with velocity decreasing as distance from the center increases.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V_\theta \) — Tangential velocity (m/s)
• \( \gamma \) — Vortex strength (m²/s)
• \( r \) — Radial coordinate from vortex center (m)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The negative sign indicates that the tangential velocity is in the opposite direction to the positive angular direction convention. The velocity magnitude decreases inversely with radial distance from the vortex center.

3. Importance of Tangential Velocity Calculation

Details: Calculating tangential velocity is essential for understanding vortex dynamics in fluid mechanics, analyzing rotational flows, designing turbomachinery, and studying atmospheric phenomena like tornadoes and hurricanes.

4. Using the Calculator

Tips: Enter vortex strength in m²/s and radial coordinate in meters. The radial coordinate must be greater than zero. Negative vortex strength values are acceptable and indicate clockwise rotation.

5. Frequently Asked Questions (FAQ)

Q1: What is vortex strength?
A: Vortex strength (γ) is a measure of the intensity or circulation of a vortex, representing the total angular momentum per unit density in the flow field.

Q2: Why does tangential velocity decrease with radial distance?
A: In an ideal vortex flow, angular momentum is conserved, resulting in tangential velocity decreasing inversely with distance from the center to maintain constant circulation.

Q3: What are typical values for vortex strength?
A: Vortex strength values vary widely depending on the application, from small laboratory vortices (0.01-1 m²/s) to large atmospheric vortices (1000+ m²/s).

Q4: Can this formula be used for 3-D vortex flows?
A: This specific formula applies to 2-D potential vortex flow. For 3-D vortices, additional factors like axial velocity and vortex core size need to be considered.

Q5: What does a negative tangential velocity indicate?
A: A negative tangential velocity typically indicates clockwise rotation when using the standard mathematical convention where positive rotation is counterclockwise.