Stream Function For 2-D Vortex Flow Calculator

Vortex Stream Function Equation:

\[ \psi_{vortex} = \frac{\gamma}{2\pi} \ln(r) \]

Vortex Stream Function (ψ):

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1. What is the Vortex Stream Function?

The Vortex Stream Function represents the flow patterns associated with rotational motion in fluid dynamics. It quantifies the streamlines around a vortex, providing insight into the velocity field and circulation characteristics of the flow.

2. How Does the Calculator Work?

The calculator uses the Vortex Stream Function equation:

\[ \psi_{vortex} = \frac{\gamma}{2\pi} \ln(r) \]

Where:

\( \psi_{vortex} \) — Vortex Stream Function (m²/s)
\( \gamma \) — Vortex Strength (m²/s)
\( r \) — Radial Coordinate (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \ln \) — Natural logarithm function

Explanation: The equation describes the stream function for an ideal 2-D vortex flow, where the streamlines are concentric circles around the vortex center.

3. Importance of Vortex Stream Function Calculation

Details: Accurate calculation of the vortex stream function is crucial for analyzing rotational flows, predicting flow patterns, and understanding vortex behavior in various engineering applications including aerodynamics, hydrodynamics, and meteorological studies.

4. Using the Calculator

Tips: Enter vortex strength in m²/s and radial coordinate in meters. The radial coordinate must be greater than zero.

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: What does the radial coordinate represent?
A: The radial coordinate (r) represents the distance from the center of the vortex to the point where the stream function is being calculated.

Q3: What are typical values for vortex strength?
A: Vortex strength values vary widely depending on the application, from small-scale laboratory vortices to large atmospheric vortices.

Q4: Are there limitations to this equation?
A: This equation describes an ideal vortex and assumes inviscid, incompressible flow. Real vortices may deviate due to viscosity and other real-world effects.

Q5: What is the physical significance of the stream function?
A: The stream function provides information about flow patterns, with constant stream function values representing streamlines of the flow.