Q_Goest said:
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Also, what seems interesting to me is that surface roughness is not part of the equation in the laminar flow range. I presume the single equation used for laminar flow makes the assumption that the walls are smooth. Thoughts?
I think it is completely coherent. Maybe the problem is to understand what is laminarity. IFF the walls would have a non negligible roughness in laminar flow the flow would not be longer laminar, how can one write a parameter which destroys the theory?. Fluid magnitude variations in laminar flow only depend on MACROSCALES. As Re increases, the convection plays a more important role instabilizing flow field, depending magnitude variations on (Kolmogorov)MICROSCALES.
In fully turbulent flow f=f(\epsilon/D) only because inertia does not play any role, but an slight modification of wall geometry has an extraordinary effect on fluid magnitudes. The characteristic length scale induced by the wall rugosity affects eddy reflecting phenomena and dumping properties. As you may know, there are a couple of interesting boundary layers in turbulent flow: the boundary layer itself dominated by molecular viscosity, the buffer layer in which reflection-dumping of eddies is important, and the external turbulent layer dominated by the turbulent viscosity (Reynolds Stresses). The buffer layer has an extraordinary dependence on the wall geometry (if you have coped with CFD you will know about wall functions, Karman universal constant----not as universal as I thought after the Barenblatt seminar I attended a week ago---), and it is because the characteristic eddy length (Kolmogorov \eta microscale) is comparable to the characteristic rugosity. For that reason, an small variation on \epsilon would have a great impact in \eta, and this last dimension is vital in the development of a turbulent flow because it is the responsible of transporting and dissipating the kinetic energy into heat.
In laminar flow, the perturbations induced by wall rugosity are literally dumped by viscosity, because the flow (the convective terms) are stable enough for allowing such dumping. It is for that reason that \epsilon must not appear in any formulation of laminar flow. On the other hand, altering the wall geometry such that provoking boundary layer separation etc is made via macroscale alteration, and would have a great impact in flow, producing perhaps the transition to turbulence (the flow is unable to dump such a perturbation).
I think I have never talked about this, but this is a great place for doing so. The laplacian terms in N-S equations \nabla^2 \overline{u} come from the viscous stresses. These terms have an Elliptic-Parabolic behavior, such that are afraid about what is happening in all the flow domain, intercepting information of what happens both upstream, downstream, up and down. The viscous terms generate stability via diffusion-dissipation of perturbations. On the other hand, the convective terms \overline{u}\nabla\overline{u} are instable per se. These terms have an Hyperbolic behavior, such that they only transmit information along priviledged lines (characteristic lines). This terms are responsible of setting up shock waves and sharp discontinuities of fluid variables, because they don't intercept the information multidirectionally. As Re is increased the convectives terms become stronger. Ideally one may assume \mu=0 (Ideal flow) but that's not physically realizable. In fact the viscous terms are negligible at very high Re but --->not just zero<----. One needs to incorporate laplacian terms in turbulent flow besides an additional viscosity generated by turbulent shear stresses which come precisely from the convective terms. The molecular viscosity (the laplacian terms) gives an small dosis (but real) stability to the flow. Finally, when the flow is laminar, the laplacian terms enhance enough stability because they are not negligible compared with the convective instabilizers. Any microscopic variation is instantaneously dumped and dissipated by the laplacian term.
Hope everybody (included me) understood the big picture.
Javier.
Let me play that back to you in my own words: The point is that if Re is low enough to maintain laminar flow, any turbulence which might be generated near the walls due to surface roughness is dampened (you said "dumped" and a few other things) by the fluid's viscosity such that any minor turbulence, if it could develop, would remain at or very near the wall and not propagate into the flow stream. 
