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# Aerodynamics – The Symmetric Airfoil – 3

1 - Question

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

a) True

b) False

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Answer: bExplanation: Directly putting θ=π gives an indeterminate form (γ(π)=00), 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 - Question

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

a) γ(θ)=2αV∞sinθ1+cosθ

b) γ(θ)=2αV∞1+cosθsinθ

c) γ(θ)=2αV∞1−cosθsinθ

d) γ(θ)=2αV∞cosθsinθ

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Answer: bExplanation: 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∞1+cosθsinθ where 0≤θ≤π for 0≤x≤c.

3 - Question

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

a) Γ=πα2cV∞

b) Γ=π2αcV∞

c) Γ=2παcV∞

d) Γ=παcV∞

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Answer: dExplanation: The total circulation around the symmetric airfoil can be found by integrating the transformed solution γ(θ)=2αV∞1+cosθsinθ using ξ=c2(1-cosθ)er 0≤θ≤π i.e. Γ=∫c0γ(ξ)dξ=παcV∞.

4 - Question

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

a) Γ=∫c0γ(ξ)dξ

b) Γ=c2∫π0γ(θ)sinθ dθ

c) Γ=cαV∞∫c0(1+cosθ)dθ

d) Γ=cαV∞∫π0(1+cosθ)dθ

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Answer: cExplanation: Using the transformation ξ=c2(1-cosθ), where 0≤θ≤π, corresponding to 0≤ξ≤c in γ(θ) and integrating gives the total circulation Γ.

5 - Question

The lift coefficient for a thin symmetrical airfoil is given by______

a) cl = πα

b) cl = π2α

c) cl = 2πα

d) cl = πα2

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Answer: cExplanation: The lift coefficient is given by cl=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 cl = 2πα.

6 - Question

The lift curve slope for a flat plate is_____

a) 2π rad

b) 2π rad-1

c) π rad

d) 0.11 degree

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Answer: bExplanation: The lift curve slope is given by dcldα=2π rad-1 from the thin airfoil theory for the symmetric airfoils. It is equal to 0.11 degree-1 .

7 - Question

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

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Answer: aExplanation: The coefficient of moment about the leading edge is given by cm,le=-π α2 where α is in rad. It is independent of chord length.

8 - Question

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

a) cm,le=-π α2

b) cm,le=-cl4

c) cm,le=-cl2

d) cm,c/4=cm,le+cl4

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Answer: cExplanation: The coefficient of moment about the leading edge is given by cm,le=-π α2. Putting cl = 2πα we get cm,le=-cl4. Finding the moment coefficient about quarter chord we get, cm,c/4=cm,le+cl4.

9 - Question

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

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Answer: aExplanation: 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 - Question

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

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Answer: cExplanation: 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 - Question

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

a) True

b) False

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Answer: aExplanation: 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 - Question

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

a) False

b) True

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Answer: aExplanation: 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.