Boundary Layers, Separation and Drag

No-slip pins the fluid at a wall to zero velocity while the free stream sails past, so the entire velocity change is compressed into a thin layer. Above it there is no gradient, hence no shear, hence nothing for viscosity to do.

Prandtl's 1904 insight was that this lets the flow be split in two: an outer region solved as if inviscid, and a thin inner layer where the hard viscous problem lives. Before that, fluid mechanics had exact equations nobody could solve and experimental results nobody could predict.

δ is conventionally defined where the velocity reaches 99% of the free stream. The choice is arbitrary — the approach is asymptotic — but it gives a usable number.

At the leading edge the layer has zero thickness. Downstream, viscous drag has had longer to act, so more fluid has been retarded and δ grows — as √x while laminar, and faster once turbulent.

Within the layer the flow itself transitions, near Re_x ≈ 5 × 10⁵ on a flat plate. Turbulent mixing flattens the profile and steepens the wall gradient, so skin friction rises. On a flat plate that is straightforwardly bad news. On a curved body it turns out not to be.

Past a body's widest point the outer flow decelerates, so pressure rises in the flow direction — an adverse gradient. Every particle now has to climb a pressure hill.

1. 1The free stream has ample momentum for the climb.
2. 2Fluid near the wall has already lost most of its momentum to friction.
3. 3It runs out first, stops, and then reverses under the pressure gradient.
4. 4The reversed flow wedges the boundary layer off the surface — separation.
5. 5Behind the body sits a broad recirculating wake at low pressure.

That low pressure is never recovered, and the front-to-back pressure difference it creates is pressure drag — which for a bluff body dwarfs skin friction entirely.

A turbulent boundary layer mixes high-momentum fluid down toward the wall, so it can climb further up the pressure hill before running out. Tripping the layer turbulent on purpose moves separation rearward.

Skin friction rises a little, pressure drag falls a great deal, and the trade is strongly worth making. A dimpled ball flies about twice as far. Vortex generators on an aircraft wing are the same trick for the same reason.

Increasing a wing's angle of attack steepens the adverse gradient over its upper surface until the boundary layer separates across it. Lift climbs, peaks at the critical angle, and then collapses.

Note the axis: it is the angle that stalls a wing, not the airspeed. An aircraft can stall at any speed — which is why the recovery is to lower the nose, not to add power.

Total drag is wall shear integrated over the surface, plus the wake's pressure deficit. Which dominates depends entirely on shape.

• Skin friction drag dominates for slender, attached shapes: a flat plate edge-on, an aerofoil at low angle, a ship's hull.
• Pressure drag dominates for bluff bodies: a cylinder, a lorry, a parachute. A flat plate face-on is nearly all pressure drag.
• A streamlined strut can have a tenth the drag of a cylinder with the same frontal area.

Streamlining does not reduce friction — it increases wetted area and therefore skin friction. It wins by spreading the pressure recovery gently enough that the boundary layer never runs out of momentum, so separation is prevented and the wake never forms.