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# Aerodynamics – Laminar Flow – 2

1 - Question

The defining assumption for finding the skin- friction drag on an airfoil is____

a) Airfoil is new low-speed airfoil

b) Skin- friction acts due to shear force

c) Airfoil has a zero angle of attack

d) Airfoil is considered a flat plate at zero angle of attack

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Answer: dExplanation: The essential assumption made for finding skin- friction drag on the airfoil is that it is considered as a flat plate with zero angle of attack. It need not be low-speed airfoil only. Skin friction is caused by shear force and it is not an assumption.

2 - Question

The essential assumption of airfoil being a flat plate with a zero angle of attack gives accurate results always.

a) False

b) True

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Answer: aExplanation: This assumption is a first order approximation and the results become more accurate as the airfoil gets thinner and angle of attack approaches zero. It gives good results but the level of accuracy varies.

3 - Question

The Reynolds number for a fluid with density d, free-stream velocity V, viscosity u at a distance x from the leading edge is_____

a) R = Vdux

b) R = xVdu

c) R = Vxdx

d) R = xduV

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Answer: bExplanation: Reynolds number is an important quantity in the study of fluid dynamics and aerodynamics. The correct formula is R = xVdu. It is important to remember that it is a dimensionless quantity.

4 - Question

For a Reynolds number Rec=9×104 and chord length 1m, what is the laminar boundary layer thickness at the trailing edge (in cm)?

a) 2.34

b) 3

c) 1.5

d) 1.67

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Answer: dExplanation: The laminar boundary layer thickness is given by δ=5xRex√, where in our question x is the chord length. Solving this we get the thickness to be 5/3 cm (1.67 cm).

5 - Question

The boundary layer thickness for an incompressible, laminar flow at a distance x with Reynolds number Rex is δ. Which is____

a) Directly proportional to √x

b) Inversely proportional to x

c) Directly proportional to Rex

d) Inversely proportional to Rex2

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Answer: aExplanation: The boundary layer thickness for an incompressible, laminar flow over a flat plate at zero angle of attack, at a distance x where Reynolds number is Rex is given by δ=5xRex√. Here Reynolds number is Rex=xVdu. Thus, the thickness is directly proportional to √x.

6 - Question

For finding the skin- friction drag we need to only measure shear-stress at the top or bottom surface.

a) Always true

b) Always false

c) True for flat plate, which is a symmetric airfoil

d) Depends on the Reynolds number

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Answer: cExplanation: The shear stress distribution on the airfoil is the same at the top and bottom surface for a flat plate. And we can just integrate the local shear stress on one side and double the result to get the total skin-friction drag.

7 - Question

The coefficient of skin-friction drag coefficient Cf, as conventionally defined, when used gives half the value of total drag.

a) True

b) False

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Answer: aExplanation: The skin- friction coefficient Cf, has been defined for the skin-friction drag over one surface only. So in order to calculate total drag, we need to multiply the result by 2.

8 - Question

The constant which is present while establishing a relationship for Cf and Rec for a laminar flow is_____

a) 2.65

b) 0.664

c) π

d) 1.33

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Answer: dExplanation: The coefficient of skin-friction drag is related to Reynolds number as Cf=1.328Rec√ where Rec is the Reynolds number at the trailing edge and the coefficient gives half the total skin-friction drag. The required constant is 1.328 for the case of a laminar flow.

9 - Question

The total skin-friction drag coefficient for laminar flow with Reynolds number at the trailing edge being Rec=40000 and chord length is 1m, is _____

a) 0.01328

b) 0.00664

c) 0.02656

d) 0.664

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Answer: aExplanation: The total skin-friction drag coefficient for laminar flow is twice the value of the skin-friction drag coefficient for laminar flow, Cf=1.328Rec√. Putting the given values, we get the answer as 0.01328.

10 - Question

We can get the skin-friction drag coefficient for a laminar flow for a flat plate by using x as chord length in local skin- friction drag coefficient calculation.

a) True

b) False

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Answer: bExplanation: The skin-friction drag coefficient is Cf=1.328Rec√ and the local skin-friction drag coefficient is Cf=0.664Rex√. Cf is calculated by integrating cf over the whole airfoil chord and as visible by the formula, we cannot get it directly by putting x = c.

11 - Question

The laminar boundary layer for a thin airfoil is maximum at_____

a) Leading edge

b) Trailing edge

c) Quarter-chord

d) We can’t say without calculating

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Answer: bExplanation: The boundary layer thickness increases parabolically with the distance measured from the leading edge (denoted by x) for incompressible, laminar flow. Therefore, it is largest at the trailing edge.

12 - Question

Select the flow which is not laminar all over the thin airfoil at α=0°.

The given values are for Rec.

a) 7×105

b) 9×104

c) 2×103

d) We can’t say with just this information

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Answer: aExplanation: For a flat plate, the turbulent flow starts for Rec>5×105 and flow is laminar for Rec<1×105. A thin airfoil with α=0° can be essentially considered a flat plate. So the turbulent flow is the one with Rec=7×105.