Circulation by Kutta-Joukowski Theorem Calculator

Kutta-Joukowski Theorem:

\[ \Gamma = \frac{L'}{\rho_{\infty} \cdot V_{\infty}} \]

Vortex Strength (Γ):

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1. What is the Kutta-Joukowski Theorem?

The Kutta-Joukowski theorem is a fundamental theorem in aerodynamics that relates the lift generated by a two-dimensional airfoil to the circulation around the airfoil. It provides the mathematical basis for understanding how wings generate lift in inviscid, incompressible flow.

2. How Does the Calculator Work?

The calculator uses the Kutta-Joukowski theorem:

\[ \Gamma = \frac{L'}{\rho_{\infty} \cdot V_{\infty}} \]

Where:

\( \Gamma \) — Vortex strength/circulation (m²/s)
\( L' \) — Lift per unit span (N/m)
\( \rho_{\infty} \) — Freestream density (kg/m³)
\( V_{\infty} \) — Freestream velocity (m/s)

Explanation: The theorem states that the lift per unit span of an airfoil is directly proportional to the circulation around the airfoil, the freestream density, and the freestream velocity.

3. Importance of Circulation Calculation

Details: Calculating circulation is essential for understanding aerodynamic lift generation, designing efficient airfoils, and analyzing flow behavior around aerodynamic bodies in fluid dynamics.

4. Using the Calculator

Tips: Enter lift per unit span in N/m, freestream density in kg/m³, and freestream velocity in m/s. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is circulation in fluid dynamics?
A: Circulation is a scalar quantity that measures the macroscopic rotation of fluid around a closed contour. It represents the line integral of velocity around a closed loop.

Q2: What are typical values for vortex strength?
A: Vortex strength values vary widely depending on the application, from small values for gentle flows to large values for strong vortices in high-speed aerodynamics.

Q3: What are the limitations of the Kutta-Joukowski theorem?
A: The theorem assumes inviscid, incompressible, irrotational flow and is strictly valid only for two-dimensional flow around airfoils with sharp trailing edges.

Q4: How is lift per unit span measured?
A: Lift per unit span is typically measured in wind tunnel experiments using force balances or calculated from pressure distribution measurements around the airfoil.

Q5: Can this theorem be applied to three-dimensional wings?
A: While the theorem is fundamentally two-dimensional, it forms the basis for three-dimensional lifting line theory which extends the concept to finite wings.