State the Kutta-Joukowski lift theorem and its applicability.

• A. L' = ρ V Γ per unit span; lift is proportional to circulation for inviscid, incompressible, steady flows.
• B. L' is proportional to velocity squared times area.
• C. L' is independent of circulation.
• D. L' = ρ V Γ per unit length.

Answer: (D)

The lift produced by a wing in a two-dimensional, inviscid, incompressible, steady flow is directly tied to the circulation around the wing. The Kutta–Joukowski lift theorem states that the lift per unit span is L' = ρ V Γ, where ρ is the fluid density, V is the freestream speed, and Γ is the circulation around the airfoil. This means lift grows with density, speed, and the amount of circulation around the wing, and it does not depend on area in the simple form.

The option that matches this idea uses the expression L' = ρ V Γ per unit length (i.e., per unit span). This wording is consistent with the concept that L' is lift per length along the wing and that the product ρ V Γ yields the correct units for lift per unit length.

Regarding applicability: the theorem assumes inviscid, incompressible, steady flow and a two-dimensional (or spanwise-invariant) situation. It neglects viscous effects, so it’s most accurate for high-Reynolds-number, subsonic cases where boundary-layer losses don’t dominate the lift, and for flows where compressibility and unsteadiness are either small or treated separately. It can be extended conceptually to finite wings via lifting-line theory, which distribu

tes Γ along the span.