This set of Aerodynamics Multiple Choice Questions & Answers (MCQs) focuses on “The Symmetric Airfoil – 3”.

1. The Kutta condition is not satisfied at the trailing edge where θ=π in transformed coordinates for a symmetrical airfoil.

a) True

b) False

View Answer

Explanation: Directly putting θ=π gives an indeterminate form (γ(π)=\(\frac {0}{0}\)), but using L’Hospital’s rule in the solution for γ(θ) gives a finite value of zero. Thus, the Kutta condition is satisfied.

2. Which of the following is the correct solution of the transformed fundamental equation of aerodynamics for a symmetrical airfoil?

a) γ(θ)=2αV_{∞}\(\frac {sin\theta }{1+cos\theta }\)

b) γ(θ)=2αV_{∞}\(\frac {1+cos\theta }{sin\theta }\)

c) γ(θ)=2αV_{∞}\(\frac {1-cos\theta }{sin\theta }\)

d) γ(θ)=2αV_{∞}\(\frac {cos\theta }{sin\theta }\)

View Answer

Explanation: The solution of the fundamental equation of thin airfoil theory is obtained using the transformation of coordinates. We have α and V

_{∞}and using the standard integrals we can find a solution for γ(x) as γ(θ)=2αV

_{∞}\(\frac {1+cos\theta }{sin\theta }\) where 0≤θ≤π for 0≤x≤c.

3. What is the total circulation around the symmetric airfoil according to the thin airfoil theory?

a) Γ=πα^{2}cV_{∞}

b) Γ=π^{2}αcV_{∞}

c) Γ=2παcV_{∞}

d) Γ=παcV_{∞}

View Answer

Explanation: The total circulation around the symmetric airfoil can be found by integrating the transformed solution γ(θ)=2αV

_{∞}\(\frac {1+cos\theta }{sin\theta }\) using ξ=\(\frac {c}{2}\)(1-cosθ)er 0≤θ≤π i.e. Γ=\(\int_0^c\)γ(ξ)dξ=παcV

_{∞}.

4. Which of these is a wrong expression for the total circulation around a thin symmetric airfoil?

a) Γ=\(\int_0^c\)γ(ξ)dξ

b) Γ=\(\frac {c}{2} \int_0^{\pi }\)γ(θ)sinθ dθ

c) Γ=cαV_{∞}\(\int_0^c\)(1+cosθ)dθ

d) Γ=cαV_{∞}\(\int_0^{\pi }\)(1+cosθ)dθ

View Answer

Explanation: Using the transformation ξ=\(\frac {c}{2}\)(1-cosθ), where 0≤θ≤π, corresponding to 0≤ξ≤c in γ(θ) and integrating gives the total circulation Γ.

5. The lift coefficient for a thin symmetrical airfoil is given by______

a) c_{l} = πα

b) c_{l} = π^{2}α

c) c_{l} = 2πα

d) c_{l} = πα^{2}

View Answer

Explanation: The lift coefficient is given by c

_{l}=\(\frac {L’}{q_∞S}\) where L’ is the lift per unit span and S = c (1). Now, L’=ΓV

_{∞}ρ

_{∞}, according to the Kutta-Joukowski theorem. Putting Γ=παcV

_{∞}we get c

_{l}= 2πα.

6. The lift curve slope for a flat plate is_____

a) 2π rad

b) 2π rad^{-1}

c) π rad

d) 0.11 degree

View Answer

Explanation: The lift curve slope is given by \(\frac {dc_l}{d\alpha }\)=2π rad

^{-1}from the thin airfoil theory for the symmetric airfoils. It is equal to 0.11 degree

^{-1}.

7. Given an angle of attack 5° and c = 5m, the moment coefficient about the leading edge is_____

a) -0.137

b) -0.685

c) -7.8

d) -0.27

View Answer

Explanation: The coefficient of moment about the leading edge is given by c

_{m,le}=-π \(\frac {\alpha }{2}\) where α is in rad. It is independent of chord length.

8. Which of the following is an incorrect relation for a flat plate?

a) c_{m,le}=-π \(\frac {\alpha }{2}\)

b) c_{m,le}=-\(\frac {c_l}{4}\)

c) c_{m,le}=-\(\frac {c_l}{2}\)

d) c_{m,c/4}=c_{m,le}+\(\frac {c_l}{4}\)

View Answer

Explanation: The coefficient of moment about the leading edge is given by c

_{m,le}=-π \(\frac {\alpha }{2}\). Putting c

_{l}= 2πα we get c

_{m,le}=-\(\frac {c_l}{4}\). Finding the moment coefficient about quarter chord we get,

c

_{m,c/4}=c

_{m,le}+\(\frac {c_l}{4}\).

9. The coefficient of moment about the quarter chord is zero for a symmetric airfoil. This implies____

a) Quarter-chord is the center of pressure

b) Quarter-chord is the center of mass

c) Quarter-chord has zero forces acting on it

d) Total lift is zero at quarter-chord

View Answer

Explanation: The coefficient of moment about the quarter chord is zero. By definition, the center of pressure is the point about which the total moment is zero. Hence, quarter-chord is the center of pressure for the symmetric airfoil. Other statements cannot be said conclusively with the given information.

10. Select the incorrect statement for a thin, symmetric airfoil out of the following.

a) Quarter-chord is the aerodynamic center

b) Quarter-chord is the center of pressure

c) Moment about quarter-chord depends on the angle of attack

d) Moment about quarter-chord is zero

View Answer

Explanation: The coefficient of moment about the quarter chord is zero, thereby making it the aerodynamic center (moment coefficient independent of angle of attack) and center of pressure (moment coefficient is zero) for a thin symmetric airfoil.

11. For a flat plate, aerodynamic center and center of pressure coincide.

a) True

b) False

View Answer

Explanation: The flat plate is a thin, symmetric airfoil for which moment about quarter-chord is zero. Thus, quarter-chord acts as both the aerodynamic center and center of pressure.

12. Aerodynamic center and center of pressure coincide for all the airfoils.

a) False

b) True

View Answer

Explanation: Aerodynamic center is the point where the pitching moment remains constant with changing angle of attack. It is generally the quarter-chord for an airfoil. Center of pressure is the point where the resultant of forces act and the moment at that point will change with the change of angle of attack. Thus, the center of pressure will change and may not be the quarter-chord always.

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