Velocity Potential For 3d Incompressible Source Flow Calculator

Formula Used:

\[ \text{Source Velocity Potential} = \frac{-\text{Source Strength}}{4 \times \pi \times \text{Radial Coordinate}} \]

Source Velocity Potential:

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1. What is Velocity Potential For 3D Incompressible Source Flow?

The Velocity Potential for a 3D incompressible source flow represents a scalar function whose gradient gives the velocity field. For a source flow, fluid emanates radially outward from a point source, and the velocity potential quantifies this flow behavior mathematically.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Source Velocity Potential} = \frac{-\text{Source Strength}}{4 \times \pi \times \text{Radial Coordinate}} \]

Where:

Source Strength (Λ) — Physically the rate of volume flow from the source, per unit depth perpendicular to the page (m²/s)
Radial Coordinate (r) — Distance from the source point (m)
π — Archimedes' constant (approximately 3.141592653589793)

Explanation: The negative sign indicates that the potential decreases radially outward from the source, consistent with the flow direction.

3. Importance of Velocity Potential Calculation

Details: Calculating velocity potential is crucial in fluid dynamics for analyzing irrotational flows, solving potential flow problems, and modeling various engineering applications such as aerodynamics and hydrodynamics.

4. Using the Calculator

Tips: Enter source strength in m²/s and radial coordinate in meters. Both values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of source strength?
A: Source strength represents the volumetric flow rate per unit depth emanating from the source, characterizing the intensity of the source flow.

Q2: Why is the velocity potential negative for source flow?
A: The negative sign convention ensures that the velocity vector (gradient of potential) points radially outward from the source, consistent with the flow direction.

Q3: Can this formula be used for sink flow?
A: Yes, for a sink (which is a negative source), the source strength would be negative, resulting in a positive velocity potential value.

Q4: What are the limitations of this model?
A: This model assumes ideal, irrotational, incompressible flow and may not accurately represent real fluids with viscosity or compressibility effects.

Q5: How is this different from 2D source flow?
A: For 3D source flow, the velocity potential varies inversely with radial distance (1/r), while for 2D source flow it varies logarithmically with radial distance (ln r).