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Boundary Layer and Drag Questions and Answers

61.

Consider the following statements about the Reynolds number:

1. It compares inertial with viscous forces.

2. Matching it between model and full scale is a central difficulty in wind-tunnel testing.

3. Transition on a smooth flat plate occurs at a fixed value of about five hundred thousand.

Which of the statements given above is or are correct?

Answer: A

The first two are correct. The third treats a rough guide as a constant: the transition Reynolds number depends heavily on roughness, free-stream turbulence, noise and pressure gradient, and can vary by an order of magnitude.

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62.

Match each boundary-layer quantity in List I with its meaning in List II.

List I

A. Displacement thickness

B. Momentum thickness

C. Shape factor

D. Wall shear stress

List II

1. Directly related to the friction drag accumulated so far

2. The outward shift of the external streamlines

3. Viscosity times the velocity gradient at the surface

4. The ratio of the first two thicknesses, watched as a separation indicator

Select the correct match.

Answer: B

The three integral quantities each answer a different question -- how much the body is effectively thickened, how much drag has been generated, and how close the profile is to separating -- while the wall shear stress is the local quantity from which the friction drag is built up.

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63.

Match each flow-control device in List I with how it works in List II.

List I

A. Vortex generator

B. Boundary-layer suction

C. Golf ball dimple

D. Streamlining

List II

1. Removes the slowest fluid through the surface

2. Stirs faster air down towards the wall

3. Tapers the rear so the pressure rise is gentle

4. Trips the layer turbulent to bring on the drag crisis

Select the correct match.

Answer: C

All four attack separation, but by different routes: two add momentum near the wall, one removes the fluid that has lost it, and streamlining reduces the demand instead by easing the pressure gradient the layer must survive.

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64.

Match each body in List I with the drag component that dominates it in List II.

List I

A. A flat plate aligned with the flow

B. A circular cylinder in crossflow

C. A well-streamlined strut

D. A parachute canopy

List II

1. Almost entirely pressure drag from a very broad wake

2. Almost entirely skin friction

3. Pressure drag, from separation near the shoulder

4. Mostly skin friction, with a modest pressure contribution

Select the correct match.

Answer: D

The sequence traces the whole range from a body that never separates to one designed to separate as violently as possible. Where a given shape falls on that scale is largely a question of how gently its rear allows the pressure to recover.

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65.

Match each Blasius laminar result in List I with its value in List II.

List I

A. Boundary layer thickness coefficient

B. Displacement thickness coefficient

C. Momentum thickness coefficient

D. Shape factor

List II

1. 1.721

2. 5.0

3. 2.59

4. 0.664

Select the correct match.

Answer: A

Each coefficient multiplies the distance from the leading edge divided by the square root of the local Reynolds number. The shape factor is the ratio of the second to the third, and 1.721 divided by 0.664 gives 2.59 as it should.

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66.

Match each surface condition in List I with its consequence in List II.

List I

A. Roughness buried in the laminar sublayer

B. Roughness protruding through the sublayer

C. A favourable pressure gradient

D. A steep adverse pressure gradient

List II

1. Skin friction rises sharply

2. The surface behaves as hydraulically smooth

3. Separation

4. Transition is delayed and the layer stays attached

Select the correct match.

Answer: B

The first pair shows that roughness matters only in relation to the sublayer's own thickness, not in absolute terms. The second pair shows the pressure gradient acting as the other main lever, holding the layer on in one direction and tearing it off in the other.

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Answer: C

A steeper adverse gradient is the very thing that causes separation, so it can only hasten it. The other three all give the near-wall fluid more momentum, or remove the fluid that has lost it, and so postpone separation.

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Answer: D

Skin friction rises, not falls, because the fuller profile gives a steeper gradient at the wall. The other three are all genuine consequences, and the first two together are why the choice between laminar and turbulent is never obvious.

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Answer: A

Skin friction rises through the crisis. What collapses is the pressure drag, because the separation point moves aft and the wake narrows, and for a bluff body that term is so much larger that the total still falls sharply.

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Answer: B

Below the critical Reynolds number a polished surface keeps the layer laminar, so it separates early and the wake stays broad. Roughening it, counter-intuitively, reduces the drag. The other options all narrow the wake by easing or delaying separation.

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