Velocity Induced At Point By Infinite Straight Vortex Filament Calculator

Formula Used:

\[ v_i = \frac{\gamma}{2\pi h} \]

Induced Velocity (vᵢ):

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1. What is Velocity Induced at Point by Infinite Straight Vortex Filament?

The velocity induced at a point by an infinite straight vortex filament represents the fluid velocity generated at a specific location due to the presence of a vortex filament. This concept is fundamental in aerodynamics and fluid dynamics, particularly in the study of vortex flows and their effects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ v_i = \frac{\gamma}{2\pi h} \]

Where:

\( v_i \) — Induced velocity (m/s)
\( \gamma \) — Vortex strength (m²/s)
\( h \) — Perpendicular distance to vortex (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the velocity induced at a point located at perpendicular distance h from an infinite straight vortex filament with strength γ.

3. Importance of Induced Velocity Calculation

Details: Calculating induced velocity is crucial for understanding aerodynamic interactions, designing aircraft wings, analyzing wind turbine performance, and studying various fluid dynamic phenomena involving vortex structures.

4. Using the Calculator

Tips: Enter vortex strength in m²/s and perpendicular distance in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is vortex strength?
A: Vortex strength (γ) is a measure of the intensity of a vortex, representing the circulation around the vortex filament per unit length.

Q2: Why is the vortex filament considered infinite?
A: The infinite assumption simplifies the mathematical model and provides accurate results for points not too close to the ends of real finite vortices.

Q3: What are typical values for vortex strength?
A: Vortex strength values vary widely depending on the application, from small-scale laboratory vortices to large atmospheric vortices, typically ranging from 0.01 to 100 m²/s.

Q4: How does distance affect induced velocity?
A: Induced velocity decreases inversely with distance from the vortex filament - doubling the distance halves the induced velocity.

Q5: What are practical applications of this calculation?
A: This calculation is used in aircraft wing design, helicopter rotor analysis, wind turbine performance prediction, and understanding weather patterns involving vortices.