Are you familiar with D'Alembert's paradox,
@PHstud? Thin airfoil theory assumes an inviscid flow, so D'Alembert's paradox applies. You might take a look at the concept of conformal mapping and the Joukowsky transform to illustrate how an airfoil behaves, in many ways, similar to flow around a circle. Perhaps that is more intuitive to think about as a zero-drag shape than an airfoil? Ultimately, though, the drag on a subsonic airfoil comes from two primary sources: viscosity and finite-span wings, both of which are neglected by thin airfoil theory. You need the account for a finite span and viscous drag to get the total drag on a wing.
Regarding singularities, the velocity does go to infinity at a singularity such as a source/sink or point vortex in potential flow, but I fail to see how that intuitively has anything to do with the OP's question. In a potential flow, the drag is zero period. This is D'Alembert's paradox, and the reason why there was a schism between the fields of hydraulics and fluid mechanics for over a century. Theoreticians predicted zero drag, while engineers observed clearly finite drag, so they just stopped talking to one another almost until Prandtl described the boundary layer in the early 20th century.
Murmur79 said:
When you add the boundary layer, the effective volume (area if 2D) in which there is potential flow changes. So a flat plate + boundary layer becomes equivalent to a blunted body whose thickness increases going towards the trailing edge. This changes the pressure distribution and creates pressure drag. So we could say that the pressure drag is "applied" to the border of the boundary layer. My intuition suggests that this pressure drags on the border of the boundary layer, becomes friction drag when "transmitted" to the actual flat plate surface via the boundary layer.
This is... wrong. I mean, sure, adding a boundary layer means there is a nonzero displacement thickness, so you have to account for some finite thickness to get a "correct" answer. Simply adding some thickness wouldn't change the answer according to thin airfoil theory, though, which assumes an infinitely thin airfoil regardless.
More importantly, though, pressure has precisely nothing to do with skin friction drag. The pressure gradient through a boundary layer normal to the surface (or an airfoil or anything) is zero, so the pressure at the edge of the boundary layer is identical to that at the surface. Further, the pressure force always acts normal to a surface, so it cannot create any component that is locally tangent to said surface like skin friction does. Skin friction drag arises purely due to the fact that viscosity requires the no-slip condition, so there is a nonzero velocity gradient at the wall, which means there is a shear stress. Thin airfoil theory cannot predict this. Iniviscid panel methods cannot predict this. No theory based on potential flow can predict this. You must incorporate boundary-layer theory to model it.
