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

Step 1: Understanding the Concept.
In thin airfoil theory, the flow around an airfoil is modeled by placing a sheet of vortices (not sources) along the chord line, with an unknown strength distribution \(\gamma(x)\).
Solving the governing integral equation for \(\gamma(x)\) from potential flow alone gives infinitely many mathematically valid solutions, because inviscid theory by itself does not fix the total circulation.

Step 2: Key Formula or Approach.
The Kutta condition is the extra physical requirement that closes this gap: it states that the flow must leave the sharp trailing edge smoothly, so the velocity there stays finite (in practice, \(\gamma(\text{trailing edge}) = 0\) for a cusped or sharp trailing edge).

Step 3: Detailed Explanation.
In a truly inviscid flow with no Kutta condition applied, potential theory would allow the flow to whip around the sharp trailing edge at infinite speed, which is unphysical.
In the real, viscous flow, the boundary layer and the adverse pressure gradient near the sharp trailing edge force the rear stagnation point to sit right at the trailing edge, so the flow leaves smoothly with no infinite velocity.
The Kutta condition mimics exactly this real, viscous behavior by picking out the one circulation value, out of the infinitely many mathematically possible ones, for which the inviscid model also gives a smooth, finite-velocity exit at the trailing edge.
In this sense, the Kutta condition is the one piece of borrowed viscous physics that an otherwise inviscid potential flow calculation needs, to correctly predict lift.

Step 4: Why the other options are wrong.
(A) is wrong because thin airfoil theory (the version producing lift and circulation) uses a vortex sheet, not a source distribution, source strength is a separate topic used for representing thickness, not this condition.
(B) is wrong because the free stream speed is a given input to the problem, not something the Kutta condition determines.
(D) is wrong because induced drag comes from the downwash of a finite, three-dimensional wing, which is outside the scope of 2D thin airfoil theory and has nothing to do with the trailing edge condition.

Final Answer:
The Kutta condition exists to bring the essential, real effect of viscosity, smooth flow off a sharp trailing edge, into the otherwise inviscid potential flow model. \[ \boxed{\text{Option (C)}} \]