Freestream Density By Kutta-Joukowski Theorem Calculator

Kutta-Joukowski Theorem Formula:

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

Freestream Density (ρ∞):

Unit Converter ▲

Unit Converter ▼

From:	To:

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 freestream density. It forms the basis for calculating lift in inviscid, incompressible flow.

2. How Does the Calculator Work?

The calculator uses the Kutta-Joukowski theorem formula:

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

Where:

\( \rho_{\infty} \) — Freestream Density (kg/m³)
\( L' \) — Lift per Unit Span (N/m)
\( V_{\infty} \) — Freestream Velocity (m/s)
\( \Gamma \) — Vortex Strength (m²/s)

Explanation: The formula calculates the freestream density by dividing the lift per unit span by the product of freestream velocity and vortex strength.

3. Importance of Freestream Density Calculation

Details: Freestream density is a crucial parameter in aerodynamics as it affects lift, drag, and other aerodynamic forces. Accurate calculation helps in aircraft design, performance analysis, and understanding fluid flow behavior.

4. Using the Calculator

Tips: Enter lift per unit span in N/m, freestream velocity in m/s, and vortex strength in m²/s. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is lift per unit span?
A: Lift per unit span is the lift force generated per unit length of a two-dimensional airfoil, measured in Newtons per meter (N/m).

Q2: How is vortex strength defined?
A: Vortex strength (circulation) quantifies the rotational intensity of a vortex and is measured in square meters per second (m²/s).

Q3: What are typical values for freestream density?
A: At sea level, standard atmospheric density is approximately 1.225 kg/m³. Density decreases with altitude according to the atmospheric model.

Q4: When is the Kutta-Joukowski theorem applicable?
A: The theorem applies to inviscid, incompressible flow around two-dimensional bodies with circulation, particularly airfoils with sharp trailing edges.

Q5: Can this calculator be used for compressible flow?
A: No, the Kutta-Joukowski theorem is specifically derived for incompressible flow. Compressible flow requires different aerodynamic models.