Stream Function For 2-D Incompressible Source Flow Calculator

Stream Function Formula:

\[ \psi_{source} = \frac{\Lambda}{2\pi} \times \theta \]

Source Stream Function (ψ_source):

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1. What Is The Stream Function For 2-D Incompressible Source Flow?

The Stream Function for 2-D Incompressible Source Flow describes the flow pattern where fluid emanates uniformly from a point source in a two-dimensional plane. It is a fundamental concept in fluid dynamics used to analyze potential flow fields.

2. How Does The Calculator Work?

The calculator uses the stream function formula:

\[ \psi_{source} = \frac{\Lambda}{2\pi} \times \theta \]

Where:

\( \psi_{source} \) — Source Stream Function (m²/s)
\( \Lambda \) — Source Strength (m²/s)
\( \theta \) — Polar Angle (radians)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The equation represents the stream function value at any point in the flow field, which depends on the source strength and the angular position relative to the source.

3. Importance Of Stream Function Calculation

Details: The stream function is crucial for analyzing fluid flow patterns, visualizing streamlines, and solving potential flow problems in fluid mechanics and aerodynamics.

4. Using The Calculator

Tips: Enter source strength in m²/s and polar angle in radians. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What Is Source Strength In Fluid Dynamics?
A: Source strength represents the volumetric flow rate per unit depth emanating from a point source in two-dimensional flow.

Q2: What Is The Physical Significance Of The Stream Function?
A: The stream function represents lines of constant stream function value are streamlines, and the difference between stream function values gives the flow rate between streamlines.

Q3: Can This Formula Be Used For Sink Flow?
A: Yes, for sink flow the formula is similar but with negative source strength, representing flow converging to a point.

Q4: What Are The Limitations Of This Model?
A: This model assumes ideal, inviscid, incompressible flow and is most accurate for potential flow analysis rather than real viscous flows.

Q5: How Is Polar Angle Measured?
A: Polar angle is measured in radians from a reference direction (typically the positive x-axis) in the counterclockwise direction.