# Aerodynamics Questions and Answers – Laminar Flow – 2

This set of Aerodynamics Multiple Choice Questions & Answers (MCQs) focuses on “Laminar Flow – 2”.

1. 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

Explanation: 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. The essential assumption of airfoil being a flat plate with a zero angle of attack gives accurate results always.
a) False
b) True

Explanation: 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. 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 = $$\frac {Vd}{ux}$$
b) R = $$\frac {xVd}{u}$$
c) R = $$\frac {Vx}{dx}$$
d) R = $$\frac {xdu}{V}$$

Explanation: Reynolds number is an important quantity in the study of fluid dynamics and aerodynamics. The correct formula is R = $$\frac {xVd}{u}$$. It is important to remember that it is a dimensionless quantity.

4. 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

Explanation: The laminar boundary layer thickness is given by δ=$$\frac {5x}{\sqrt{Re_x}}$$, where in our question x is the chord length. Solving this we get the thickness to be 5/3 cm (1.67 cm).

5. 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

Explanation: 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=$$\frac {5x}{\sqrt{Re_x}}$$. Here Reynolds number is Rex=$$\frac {xVd}{u}$$. Thus, the thickness is directly proportional to √x.
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6. 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

Explanation: 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. The coefficient of skin-friction drag coefficient Cf, as conventionally defined, when used gives half the value of total drag.
a) True
b) False

Explanation: 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. 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

Explanation: The coefficient of skin-friction drag is related to Reynolds number as Cf=$$\frac {1.328}{\sqrt{Re_c}}$$ 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. 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

Explanation: The total skin-friction drag coefficient for laminar flow is twice the value of the skin-friction drag coefficient for laminar flow, Cf=$$\frac {1.328}{\sqrt{Re_c}}$$. Putting the given values, we get the answer as 0.01328.

10. 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

Explanation: The skin-friction drag coefficient is Cf=$$\frac {1.328}{\sqrt{Re_c}}$$ and the local skin-friction drag coefficient is Cf=$$\frac {0.664}{\sqrt{Re_x}}$$. 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. The laminar boundary layer for a thin airfoil is maximum at_____
b) Trailing edge
c) Quarter-chord
d) We can’t say without calculating

Explanation: 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. 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

Explanation: 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.

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