Stream Function For 2-D Doublet Flow Calculator

Stream Function Formula:

\[ \psi = \frac{\kappa \cdot \sin(\theta)}{2 \pi r} \]

Stream Function (ψ):

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1. What is the Stream Function for 2-D Doublet Flow?

The Stream Function for 2-D Doublet Flow describes the flow pattern created by a doublet in a two-dimensional fluid flow field. A doublet is formed by combining a source and sink of equal strength placed infinitesimally close together, creating a specific flow pattern.

2. How Does the Calculator Work?

The calculator uses the stream function formula:

\[ \psi = \frac{\kappa \cdot \sin(\theta)}{2 \pi r} \]

Where:

\( \psi \) — Stream function (m²/s)
\( \kappa \) — Doublet strength (m³/s)
\( \theta \) — Polar angle (radians)
\( r \) — Radial coordinate (m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The stream function describes the flow pattern around a doublet, with streamlines forming circles tangent to the doublet axis.

3. Importance of Stream Function Calculation

Details: The stream function is crucial for analyzing potential flow fields, visualizing flow patterns, and understanding the behavior of ideal fluids around doublet configurations in various engineering applications.

4. Using the Calculator

Tips: Enter doublet strength in m³/s, polar angle in radians, and radial coordinate in meters. All values must be positive (doublet strength > 0, radial coordinate > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is a doublet in fluid mechanics?
A: A doublet is a combination of a source and sink of equal strength placed infinitesimally close together, creating a specific flow pattern used in potential flow theory.

Q2: What are the physical interpretations of stream function?
A: Stream function represents the flow rate between streamlines, with constant values along streamlines and differences representing volumetric flow rates.

Q3: When is the 2-D doublet flow model applicable?
A: This model is applicable for ideal, incompressible, irrotational flows and is commonly used in aerodynamics and hydrodynamics for flow visualization and analysis.

Q4: What are the limitations of this model?
A: The model assumes ideal fluid conditions (no viscosity, incompressible flow) and may not accurately represent real fluid behavior with boundary layers and separation.

Q5: How does doublet strength affect the flow pattern?
A: Doublet strength determines the intensity of the flow pattern, with higher strengths creating stronger flow velocities and more pronounced streamline curvature.