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Boundary Layer and Drag Questions and Answers

51.

Assertion (A): Displacement thickness feeds back into the outer inviscid solution.

Reason (R): It measures how far the external streamlines are pushed out by the velocity deficit.

Select the correct answer from the options below.

Answer: C

Both statements are true and the second explains the first. Because the layer thickens the effective body, the outer flow must be recomputed about that enlarged shape, and iterating between the two is how viscous-inviscid interaction methods work.

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52.

Assertion (A): Boundary-layer suction is widely used on production transport aircraft.

Reason (R): Suction removes the low-momentum fluid and leaves a fuller velocity profile.

Select the correct answer from the options below.

Answer: D

The assertion is false and the reason is true. Suction works well aerodynamically, but the ducting, pumping power, weight and the risk of the porous surface clogging have kept it out of routine service. It remains a research and special-purpose technique.

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53.

Assertion (A): The drag crisis causes a sphere's drag to fall even though its skin friction rises.

Reason (R): The transition to turbulence delays separation and narrows the wake.

Select the correct answer from the options below.

Answer: A

Both are true and the second explains the first. For a bluff body the pressure drag from the wake dwarfs the friction term, so narrowing the wake outweighs the extra shear many times over. The drag coefficient can drop by a factor of five through the transition.

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54.

Consider the following statements about a turbulent boundary layer:

1. Its skin friction is higher than that of a laminar layer at the same Reynolds number.

2. It resists separation better than a laminar layer.

3. It grows more slowly along the surface than a laminar layer.

Which of the statements given above is or are correct?

Answer: B

The first two are correct and between them define the standing trade. The third is reversed: a turbulent layer thickens roughly as distance to the four-fifths against the laminar half-power, so it grows considerably faster.

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55.

Consider the following statements about boundary-layer separation:

1. It occurs where the velocity gradient at the wall falls to zero.

2. It requires an adverse pressure gradient.

3. It always occurs wherever the pressure gradient is adverse.

Which of the statements given above is or are correct?

Answer: C

The first two are correct. The third overstates the case: an adverse gradient is necessary but not sufficient, and a turbulent layer often negotiates a mild pressure rise without separating at all. The gradient must be steep enough to drive the wall shear to zero.

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56.

Consider the following statements about the three boundary-layer thicknesses:

1. Displacement thickness measures the outward shift of the external streamlines.

2. Momentum thickness is directly related to the skin-friction drag.

3. The shape factor is the ratio of momentum thickness to displacement thickness.

Which of the statements given above is or are correct?

Answer: D

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: displacement thickness is the distance the external streamlines are pushed outward by the retarded flow, and momentum thickness is directly proportional to the skin-friction drag through the momentum integral. Statement 3 inverts the definition - the shape factor is the *displacement* thickness over the *momentum* thickness, running about 2.6 for a laminar layer and 1.3 to 1.4 for a turbulent one, which is what makes it a useful indicator of impending separation.

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57.

Consider the following statements about the drag crisis on a sphere:

1. It is caused by transition of the boundary layer to turbulence.

2. The drag coefficient falls sharply as it occurs.

3. The skin friction falls as it occurs.

Which of the statements given above is or are correct?

Answer: A

The first two are correct. The third is false: the skin friction actually rises when the layer goes turbulent. What falls, and falls far more, is the pressure drag, because the separation point moves aft and the wake narrows.

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58.

Consider the following statements about laminar-flow aerofoils:

1. They hold a favourable pressure gradient over much of the chord.

2. Their low-drag advantage is confined to a band of lift coefficient.

3. Their advantage is robust to surface contamination.

Which of the statements given above is or are correct?

Answer: B

The first two are correct and describe the drag bucket. The third is the opposite of the truth: insects, rain and manufacturing waviness readily trip the layer, and the measured in-service benefit is often a fraction of the wind-tunnel figure.

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59.

Consider the following statements about drag on a bluff body:

1. Pressure drag dominates over skin friction.

2. Streamlining reduces the total drag despite increasing the wetted area.

3. The drag coefficient is independent of Reynolds number at all speeds.

Which of the statements given above is or are correct?

Answer: C

The first two are correct. The third ignores the drag crisis, at which the coefficient of a sphere or cylinder falls abruptly by a factor of several as the layer goes turbulent. Far from being independent, it is strongly Reynolds-number dependent there.

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60.

Consider the following statements about boundary-layer control:

1. Suction removes low-momentum fluid from near the wall.

2. Vortex generators mix high-momentum fluid down towards the wall.

3. Both techniques work by making the boundary layer laminar.

Which of the statements given above is or are correct?

Answer: D

The first two describe the two mechanisms correctly. The third is wrong: neither aims at laminarisation. Both work by giving the near-wall flow more momentum so it can survive a steeper adverse gradient, and vortex generators positively rely on turbulent mixing.

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