Boundary Layer and Drag Questions and Answers

Answer: A

Prandtl's 1904 insight was that at high Reynolds number the viscous terms matter only very near the wall, leaving the rest of the flow effectively inviscid. That division is what makes aerodynamics tractable: potential flow outside, a boundary-layer calculation within, and the two matched at their common edge.

Answer: B

The fluid in contact with the wall moves with the wall, so the relative velocity there is zero. Everything else about the boundary layer follows from reconciling that condition with the free-stream velocity a short distance away, and it is the origin of the velocity gradient that produces skin friction.

Answer: C

Displacement thickness is the distance the wall would have to be moved outward in a frictionless flow to pass the same mass flow that the real layer passes. It quantifies how much the boundary layer thickens the effective body shape, which is why it feeds back into the outer inviscid solution.

Answer: D

Von Karman's momentum integral ties the growth of momentum thickness directly to the wall shear stress, so the momentum thickness at the trailing edge is a direct measure of the friction drag the surface has generated. It is the single most useful of the three thicknesses.

Answer: A

The shape factor compares the two integral thicknesses and so describes how full the velocity profile is. A high value means a profile with little momentum near the wall and impending separation, which is why it is watched as a separation indicator in boundary-layer codes.

Answer: B

As an adverse pressure gradient drains momentum from the fluid nearest the wall, the profile becomes less full and the ratio of displacement to momentum thickness climbs. Values around 2.6 for a laminar layer and about 2.4 for a turbulent one are commonly taken as separation warnings.

Answer: C

Turbulent mixing brings high-momentum fluid down towards the wall, which steepens the velocity gradient there and so raises the shear stress, but that same momentum lets the layer push further into an adverse gradient before separating. Nearly every practical drag decision is a trade between these two effects.

Answer: D

The commonly quoted figure is around five times ten to the fifth based on distance from the leading edge, though the real value depends heavily on surface roughness, free-stream turbulence, pressure gradient and noise. It should be treated as an order of magnitude rather than a constant.

Answer: A

Separation is defined by the wall shear stress vanishing, which happens when the velocity gradient at the surface reaches zero. Beyond that point the flow near the wall reverses and the layer lifts away from the surface, leaving a wake of low-energy fluid behind it.

Answer: B

Fluid near the wall has little momentum, so a pressure rising downstream can bring it to rest and then reverse it. A favourable gradient accelerates the flow and keeps the layer firmly attached, which is why the forward part of a well-designed body rarely separates.