Incompressible Flow over Airfoils Questions and Answers

Answer: A

Correct answer: 0.88

The lift coefficient is proportional to the angle measured from the zero-lift angle, not from the chord line: \[ c_l = a_0(\alpha - \alpha_{L=0}) = 0.11\,(6 - (-2)) = 0.11 \times 8 = 0.88. \] Measuring from zero incidence instead gives 0.66, which is offered as a distractor. For a cambered section the zero-lift angle is negative, so the effective angle is always the larger of the two.

Answer: B

Correct answer: 0.5

In level flight lift equals weight, so \[ C_L = \frac{W}{qS} = \frac{50\,000}{4000 \times 25} = \frac{50\,000}{100\,000} = 0.5. \] The lift coefficient is therefore not a fixed property of the wing but whatever the flight condition demands: fly slower and \( q \) falls, so \( C_L \) must rise, until it reaches the maximum the section can supply and the aircraft stalls.

Answer: C

The first two are standard results of the theory and agree well with measurement at low incidence. The third is false: the theory is inviscid and gives no drag at all, so profile drag has to come from experiment or from a viscous calculation.

Answer: D

Correct answer: 1 and 2 only

Statements 1 and 2 are both consequences of the symmetry: with no camber the section produces no lift at zero incidence, so its zero-lift angle is zero, and the moment about the quarter chord vanishes. Statement 3 is wrong - a symmetric section lifts perfectly well at any non-zero angle of attack, which is why tailplanes and control surfaces are usually symmetric.

Answer: A

The condition is a subsonic, incompressible construct used to close the potential-flow problem, and it does both of the things the first two statements describe. It has no role in supersonic airfoil theory, where the flow is governed by wave relations instead.

Answer: B

Camber changes the zero-lift angle and introduces a residual moment, but the aerodynamic centre stays near the quarter chord in subsonic flow whatever the camber. Only its position in supersonic flow moves appreciably, and then towards mid-chord.

Answer: C

Camber sets the zero-lift angle, thickness governs the pressure distribution and hence the drag at zero lift, the sharp trailing edge is where the Kutta condition is applied, and the leading edge radius decides whether the section stalls from the leading or trailing edge.

Answer: D

Each result belongs to a distinct step of the classical argument: Bernoulli relates pressure to speed, Kutta-Joukowski converts circulation into lift, Kelvin explains where the circulation comes from, and thin airfoil theory supplies the slope.

Answer: A

Correct answer: A-2, B-1, C-4, D-3

In the NACA four-digit series the first digit is the maximum camber as a percentage of chord, the second its position in tenths, and the last two the thickness as a percentage of chord. So 0012 is symmetric and twelve per cent thick, 2412 has two per cent camber and is twelve per cent thick, 4415 has four per cent camber and fifteen per cent thickness, and 0006 is symmetric and six per cent thick.

Answer: B

Thick sections tend to stall gently from the trailing edge, moderately thick ones abruptly from a bursting leading edge bubble, very thin ones through a long bubble, and transonic separation is caused by the shock rather than by incidence alone.