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# MCQs on The Cambered Airfoil – 2

1 - Question

The camber line is not a streamline of flow for a cambered airfoil according to the thin airfoil theory.

a) Always true

b) Always false

c) True only for thin airfoils

d) Depends on the camber distribution

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bExplanation: The thin airfoil theory solution when subjected to the Kutta condition makes the camber line as a streamline of the flow, irrespective of the airfoil being symmetrical or cambered.

2 - Question

Which of the following is incorrect for a thin, cambered airfoil?

a) The angle of attack is small

b) The induced velocity distribution for the camber line is the same for the chord line

c) Vortex sheet is kept at the chord line

d) The slope of the camber line is zero

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dExplanation: Slope of the camber line dzdx is not zero for a cambered airfoil but is some finite value. All the other statements are valid assumptions of thin airfoil theory.

3 - Question

The equation 12π∫c0γ(ξ)dξx−ξ=V∞α is called the fundamental equation of thin airfoil theory for______

a) Cambered airfoils only

b) Symmetric airfoils only

c) All thin airfoils

d) Symmetric and positively cambered airfoils

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bExplanation: The original fundamental equation of thin airfoil theory is 12π∫c0γ(ξ)dξx−ξ=V∞(α-dzdx). For the symmetric airfoils, dzdx=0 and so 12π∫c0γ(ξ)dξx−ξ=V∞α is valid. While for the cambered airfoils dzdx is non-zero.

4 - Question

The extra term appearing in the thin airfoil theory solution for a cambered airfoil is a______

a) Full Fourier series

b) Fourier sine series

c) Fourier cosine series

d) Constant

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bExplanation: The cambered airfoil solution of the thin airfoil theory is different from that of symmetric airfoils with the addition of a Fourier sine series term.

5 - Question

For NACA4313 what is the maximum camber and the position of maximum camber from the leading edge respectively is______

a) 0.04c, 0.4c

b) 0.4c, 0.03c

c) 0.13c, 0.4c

d) 0.04c, 0.03c

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aExplanation: For NACA 4 digit airfoils the first digit gives the maximum camber in 100th parts of the chord length c and the second digit gives the position of maximum camber in 10th parts of the chord length from the leading edge.

6 - Question

NACA 0023 is______

a) Negatively cambered airfoil

b) Positively cambered airfoil

c) Symmetrical airfoil

d) Thin cambered airfoil

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cExplanation: The first two digits in the NACA nomenclature give the maximum camber and position of maximum camber. For a symmetric airfoil, both of these are zero.

7 - Question

For an angle of attack of 5° and slope of camber line being zero, find the value of A0.

a) 0.087

b) 5

c) 0

d) -5

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aExplanation: For zero slope of camber line, the airfoil is symmetrical and A0 is the same as that of the angle of attack. We can also get the same value from the cambered airfoil solution since dzdx=0.

8 - Question

Select the statement which is not true for the solution of 12π∫c0γ(ξ)dξx−ξ=V∞(α-dzdx) for a cambered airfoil.

a) An depends on chord length of the airfoil

b) A0 depends on the slope of the camber line

c) An depends on the slope of the camber line

d) A0 depends on the angle of attack

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aExplanation: The given equation is the fundamental equation of thin airfoil theory. For a cambered airfoil, the solution is in the form γ(θ)=2V∞(A01+cosθsinθ + Σ∞n=1sin nθ An) where An depends on the slope of camber line and A0 depend both on the slope of camber line and angle of attack.

9 - Question

For γ(θ)=2V∞(A01+cosθsinθ + Σ∞n=1sin nθ An) select the statement which is invalid.

a) The solution is valid only for cambered airfoils

b) The solution is valid for all thin airfoils

c) A0 Is the n=0th term for the Fourier series

d) Kutta condition is satisfied at the trailing edge i.e. θ=π.

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aExplanation: The solution is valid for all thin airfoils (for symmetric airfoils dzdx=0 which makes An=0 and gives the required solution). This is the general solution. Kutta condition is also satisfied (γ(π)=0).

10 - Question

The correct formula for the Fourier sine series appearing in the solution of thin airfoil theory is_____

a) An=2π∫π0dzdx cosn∅ d∅

b) An=1π∫π0dzdx cosn∅ d∅

c) An=2π∫2π0dzdx cosn∅ d∅

d) An=α-1π∫π0dzdx cosn∅ d∅

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aExplanation: From the general solution of thin airfoil theory we have An=2π∫π0dzdx cosn∅ d∅ and A0=α-1π∫π0dzdx cosn∅ d∅ where the limits are 0≤∅≤π.

11 - Question

For α=5°, A0=1 and A1=-2 total circulation Γ for a thin cambered airfoil equals______

a) 0

b) 2πcV∞

c) πcV∞

d) 2.5πcV∞

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aExplanation: From the formula of total circulation Γ=cV∞(πA0+π2A1) we get Γ=0 upon putting the values given in the question.

12 - Question

The lift per unit span for a thin, cambered airfoil with α=5°, A0=0.65, A1=1 is____

a) L’ = cπV2∞ρ∞ (1.15)

b) L’ = cπV2∞ρ∞ (1.65)

c) L’ = cπV2∞ρ∞ (-0.35)

d) L’ = cπV2∞ρ∞ (0.15)

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aExplanation: For a thin cambered airfoil lift per unit span is given by L’ = cπV2∞ρ∞ (A0+12A1). Thus, with the given value of A0 and A1 we get L’ = cπV2∞ρ∞ (1.15).

13 - Question

The lift per unit span for a thin, cambered airfoil with Γ=10m2s, ρ∞=1.0255kgm3, V∞=10ms is____

a) 0

b) 102.55Nm

c) 102.55N

d) 55Nm

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aExplanation: The lift per unit span is given by the formula L’=Γρ∞V∞ by Kutta-Joukowski Theorem. Putting the respective values given in the question, L’=102.55Nm (unit is N/m, not N).