Question

The fundamental purpose of the Kutta condition in the thin airfoil theory is .

• A. to determine the total strength of the source distribution
• B. to determine the speed of the uniform flow
• C. to incorporate the essential effect of viscosity in the potential flow theory
• D. to incorporate the concept of induced drag in the inviscid theory

Hint:

Think about why inviscid theory alone cannot fix circulation at a sharp trailing edge without an extra, physically motivated condition.

Answer 1

The Correct Option is C

Thin airfoil theory is an inviscid model, but it still needs to predict the correct, real-world circulation and lift. The Kutta condition is the rule that makes this possible. Check what each option claims it does.

1. To determine the total strength of the source distribution: circulatory thin airfoil theory (the part responsible for lift) is built from a vortex sheet, not sources. Sources are used elsewhere, for modeling thickness, and are unrelated to this condition.
2. To determine the speed of the uniform flow: the free stream speed is always given as part of the problem statement (from flight condition or wind tunnel setting), it is never something solved for using the Kutta condition.
3. To incorporate the essential effect of viscosity in the potential flow theory: without any extra condition, the inviscid equations allow infinitely many circulation values, including ones that let flow race around the sharp trailing edge at infinite speed, which never happens in reality. In real, viscous flow, the boundary layer forces the rear stagnation point to sit exactly at the trailing edge, giving a smooth, finite exit velocity. The Kutta condition selects the one circulation for which the inviscid model reproduces this same smooth exit. It is how the theory borrows this one real, viscous fact.
4. To incorporate the concept of induced drag in the inviscid theory: induced drag is caused by wingtip vortices and downwash on a finite wing in 3D, a completely different topic from the 2D trailing-edge condition used in thin airfoil theory.

Only option (C) correctly describes why the Kutta condition is needed, it fixes the circulation so a purely mathematical, inviscid flow model still behaves the way a real, viscous flow does near the trailing edge.

Let's summarize:

• Inviscid theory alone cannot fix circulation, it needs one more physical rule.
• The Kutta condition supplies that rule by enforcing smooth, finite-velocity flow off the trailing edge, standing in for the effect of viscosity.

So the correct option is (C).