Velocity Induced At Point By Semi-Infinite Straight Vortex Filament Calculator

Formula Used:

\[ v_i = \frac{\gamma}{4\pi h} \]

Induced Velocity (v_i):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Velocity Induced by Semi-Infinite Straight Vortex Filament?

The velocity induced at a point by a semi-infinite straight vortex filament represents the fluid velocity generated at that specific location due to the presence of a vortex filament that extends infinitely in one direction. This concept is fundamental in aerodynamics and fluid dynamics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ v_i = \frac{\gamma}{4\pi h} \]

Where:

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

Explanation: The formula calculates the velocity induced at a point perpendicular to a semi-infinite straight vortex filament, with the velocity magnitude inversely proportional to the distance from the vortex.

3. Importance of Induced Velocity Calculation

Details: Accurate calculation of induced velocity is crucial for analyzing aerodynamic interactions, vortex dynamics, and flow field characteristics in various engineering applications, particularly in aircraft wing design and rotor dynamics.

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.

Q2: How does distance affect induced velocity?
A: Induced velocity decreases inversely with distance from the vortex filament - doubling the distance halves the induced velocity.

Q3: What's the difference between finite and semi-infinite vortex filaments?
A: A semi-infinite vortex extends infinitely in one direction, while a finite vortex has both ends bounded. The induced velocity formulas differ accordingly.

Q4: Where is this concept applied in real-world engineering?
A: This concept is widely used in aircraft wing design, helicopter rotor analysis, and wind turbine aerodynamics to calculate induced velocities from trailing vortices.

Q5: Are there limitations to this formula?
A: This formula assumes ideal fluid conditions, negligible viscosity effects, and applies specifically to semi-infinite straight vortex filaments in unbounded flow.