Radial Velocity For 2-D Incompressible Source Flow Calculator

Formula Used:

\[ V_r = \frac{\Lambda}{2 \pi r} \]

Radial Velocity (Vr):

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1. What is Radial Velocity For 2-D Incompressible Source Flow?

The Radial Velocity for 2-D Incompressible Source Flow represents the velocity component in the radial direction for fluid flow emanating from a point source in a two-dimensional incompressible flow field. It describes how fast fluid particles are moving away from or toward the source point.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_r = \frac{\Lambda}{2 \pi r} \]

Where:

\( V_r \) — Radial Velocity (m/s)
\( \Lambda \) — Source Strength (m²/s)
\( r \) — Radial Coordinate (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula shows that radial velocity decreases inversely with distance from the source, following the conservation of mass principle for incompressible flow.

3. Importance of Radial Velocity Calculation

Details: Calculating radial velocity is essential for analyzing potential flow fields, designing fluid systems, and understanding flow patterns around singularities in fluid mechanics applications.

4. Using the Calculator

Tips: Enter source strength in m²/s and radial coordinate in meters. Both values must be positive numbers greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is source strength in fluid mechanics?
A: Source strength represents the volumetric flow rate per unit depth (for 2D flow) emanating from a point source, measured in m²/s.

Q2: Why does radial velocity decrease with distance?
A: Due to conservation of mass in incompressible flow, as the flow spreads out radially, the velocity must decrease to maintain constant flow rate through increasing circumferential areas.

Q3: What are typical applications of this calculation?
A: This calculation is used in potential flow theory, aerodynamics, hydrodynamics, and analyzing flow around objects using the method of singularities.

Q4: Does this formula work for sink flow as well?
A: Yes, the same formula applies to sink flow, but with negative source strength values, indicating flow toward the point rather than away from it.

Q5: What are the limitations of this model?
A: This model assumes ideal, inviscid, incompressible flow and is most accurate for potential flow applications rather than real viscous flows with boundary layers.