Radial Velocity For 3d Incompressible Source Flow Calculator

Formula Used:

\[ V_r = \frac{\Lambda}{4 \pi r^2} \]

Radial Velocity (Vr):

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

The Radial Velocity for 3D Incompressible Source Flow describes the velocity component in the radial direction for fluid flow originating from a point source in three-dimensional space. It represents how quickly fluid particles move away from or toward the source point.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_r = \frac{\Lambda}{4 \pi r^2} \]

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 calculates the radial velocity component for an incompressible source flow in three dimensions, where the velocity decreases with the square of the distance from the source.

3. Importance of Radial Velocity Calculation

Details: Calculating radial velocity is essential for understanding fluid dynamics in various engineering applications, including aerodynamics, hydrodynamics, and the study of potential flows around sources and sinks.

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 physically representing?
A: Source strength represents the volumetric flow rate per unit depth from the source, physically indicating how much fluid is being emitted from the source point.

Q2: Why does radial velocity decrease with r²?
A: The velocity decreases with the square of the distance because the same amount of fluid flows through increasingly larger spherical surfaces as we move away from the source.

Q3: What are typical applications of this calculation?
A: This calculation is used in fluid mechanics for modeling point sources in potential flow theory, environmental studies of pollutant dispersion, and various engineering applications involving radial flows.

Q4: Are there limitations to this formula?
A: This formula assumes ideal incompressible flow, point source geometry, and neglects viscous effects and other real-world complexities.

Q5: How does this differ from 2D source flow?
A: In 2D source flow, velocity decreases with 1/r, while in 3D source flow, velocity decreases with 1/r² due to the different geometry of flow expansion.