Lift Per Unit Span By Kutta-Joukowski Theorem Calculator

Kutta-Joukowski Theorem:

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

Lift Per Unit Span (L'):

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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, the freestream velocity, and the fluid density. It forms the basis for the calculation of lift in inviscid, incompressible flow.

2. How Does the Calculator Work?

The calculator uses the Kutta-Joukowski theorem:

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

Where:

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

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

3. Importance of Lift Per Unit Span Calculation

Details: Accurate calculation of lift per unit span is crucial for aircraft design, wing performance analysis, and understanding aerodynamic behavior of airfoils in various flow conditions.

4. Using the Calculator

Tips: Enter freestream density in kg/m³, freestream velocity in m/s, and vortex strength in m²/s. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is circulation in aerodynamics?
A: Circulation is a measure of the rotational component of the flow around an airfoil, representing the net effect of vorticity in the flow field.

Q2: When is the Kutta-Joukowski theorem applicable?
A: The theorem applies to two-dimensional, inviscid, incompressible flow around airfoils with sharp trailing edges that satisfy the Kutta condition.

Q3: What are typical values for vortex strength?
A: Vortex strength values vary significantly depending on airfoil shape, angle of attack, and flow conditions, typically ranging from 0.1 to 10 m²/s for practical applications.

Q4: How does air density affect lift?
A: Lift is directly proportional to air density - higher density results in greater lift for the same velocity and circulation, which is why aircraft performance varies with altitude.

Q5: Can this theorem be used for three-dimensional wings?
A: While the theorem is fundamentally for two-dimensional flow, it forms the basis for lift calculation in three-dimensional wings through lifting-line theory and other extensions.