This set of Aerodynamics Multiple Choice Questions & Answers (MCQs) focuses on “The Cambered Airfoil – 2”.
1. 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
View Answer
Explanation: 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. 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
View Answer
Explanation: Slope of the camber line \(\frac {dz}{dx}\) is not zero for a cambered airfoil but is some finite value. All the other statements are valid assumptions of thin airfoil theory.
3. The equation \(\frac {1}{2\pi } \int_0^c \frac {\gamma(\xi)d\xi}{x-\xi}\)=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
View Answer
Explanation: The original fundamental equation of thin airfoil theory is \(\frac {1}{2\pi } \int_0^c \frac {\gamma(\xi)d\xi}{x-\xi}\)=V∞(α-\(\frac {dz}{dx}\)). For the symmetric airfoils, \(\frac {dz}{dx}\)=0 and so \(\frac {1}{2\pi } \int_0^c \frac {\gamma(\xi)d\xi}{x-\xi}\)=V∞α is valid. While for the cambered airfoils \(\frac {dz}{dx}\) is non-zero.
4. 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
View Answer
Explanation: 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. 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
View Answer
Explanation: 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. NACA 0023 is______
a) Negatively cambered airfoil
b) Positively cambered airfoil
c) Symmetrical airfoil
d) Thin cambered airfoil
View Answer
Explanation: 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. 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
View Answer
Explanation: 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 \(\frac {dz}{dx}\)=0.
8. Select the statement which is not true for the solution of \(\frac {1}{2\pi } \int_0^c \frac {\gamma(\xi)d\xi}{x-\xi}\)=V∞(α-\(\frac {dz}{dx}\)) 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
View Answer
Explanation: The given equation is the fundamental equation of thin airfoil theory. For a cambered airfoil, the solution is in the form γ(θ)=2V∞(A0\(\frac {1+cos\theta }{sin\theta }\) + Σ\(_{n=1}^∞\)sin 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. For γ(θ)=2V∞(A0\(\frac {1+cos\theta }{sin\theta }\) + Σ\(_{n=1}^∞\)sin 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.
View Answer
Explanation: The solution is valid for all thin airfoils (for symmetric airfoils \(\frac {dz}{dx}\)=0 which makes An=0 and gives the required solution). This is the general solution. Kutta condition is also satisfied (γ(π)=0).
10. The correct formula for the Fourier sine series appearing in the solution of thin airfoil theory is_____
a) An=\(\frac {2}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cosn∅ d∅
b) An=\(\frac {1}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cosn∅ d∅
c) An=\(\frac {2}{\pi }\int_0^{2\pi }\frac {dz}{dx}\) cosn∅ d∅
d) An=α-\(\frac {1}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cosn∅ d∅
View Answer
Explanation: From the general solution of thin airfoil theory we have An=\(\frac {2}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cosn∅ d∅ and A0=α-\(\frac {1}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cosn∅ d∅ where the limits are 0≤∅≤π.
11. 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∞
View Answer
Explanation: From the formula of total circulation Γ=cV∞(πA0+\(\frac {\pi }{2}\)A1) we get Γ=0 upon putting the values given in the question.
12. The lift per unit span for a thin, cambered airfoil with α=5°, A0=0.65, A1=1 is____
a) L’ = cπ\(V_∞^2\)ρ∞ (1.15)
b) L’ = cπ\(V_∞^2\)ρ∞ (1.65)
c) L’ = cπ\(V_∞^2\)ρ∞ (-0.35)
d) L’ = cπ\(V_∞^2\)ρ∞ (0.15)
View Answer
Explanation: For a thin cambered airfoil lift per unit span is given by L’ = cπ\(V_∞^2\)ρ∞ (A0+\(\frac {1}{2}\)A1). Thus, with the given value of A0 and A1 we get L’ = cπ\(V_∞^2\)ρ∞ (1.15).
13. The lift per unit span for a thin, cambered airfoil with Γ=10\(\frac {m^2}{s}\), ρ∞=1.0255\(\frac {kg}{m^3}\), V∞=10\(\frac {m}{s}\) is____
a) 0
b) 102.55\(\frac {N}{m}\)
c) 102.55N
d) 55\(\frac {N}{m}\)
View Answer
Explanation: 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’=102.55\(\frac {N}{m}\) (unit is N/m, not N).
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