For laminar flow over a flat plate, the Blasius result gives δ/x ≈ 5/√Re_x. If the Reynolds number at a point doubles, what happens to the boundary layer thickness at that location?
AIt doubles
BIt halves
CIt decreases by a factor of √2
DIt increases by a factor of √2
Since δ/x ∝ 1/√Re_x, doubling Re_x multiplies δ/x by 1/√2, so δ decreases by a factor of √2. Higher Reynolds number means inertia dominates more strongly over viscosity, confining viscous effects to a thinner region near the wall.
Question 2 True / False
A turbulent boundary layer produces more drag than a laminar boundary layer and is also more likely to separate from a curved surface.
TTrue
FFalse
Answer: False
This is a common misconception. Turbulent boundary layers do have higher skin friction (more drag) than laminar, but they are significantly more resistant to separation. The turbulent mixing brings high-momentum fluid close to the wall, which helps the flow stay attached under adverse pressure gradients. This is why golf balls have dimples — the dimples trigger turbulence to delay separation and reduce pressure drag.
Question 3 Short Answer
What is displacement thickness δ*, and what does it represent physically?
Think about your answer, then reveal below.
Model answer: Displacement thickness is the distance by which the outer streamlines are displaced outward due to the slowing of fluid in the boundary layer. It is defined as δ* = ∫₀^∞ (1 − u/U∞) dy, and it represents the thickness of a zero-velocity layer that would carry the same mass flow deficit as the actual boundary layer.
The boundary layer slows down fluid near the wall, reducing the effective flow area seen by the inviscid outer flow. Displacement thickness quantifies this blockage effect, allowing engineers to correct inviscid calculations for the presence of the boundary layer without solving the full viscous problem.