"The velocity gradient in turbulent flows is steeper close to the wall and less steep in the center of the pipe than it is for laminar flows (Blatt p.97)."
Does this mean that some degree of turbulence near the wall of a pipe may actually improve the energy efficiency of pumping a fluid? I realize that turbulence tends to increase the energy required, but perhaps just the minimum amount in the right place might prove advantageous. Have surface modifications to increase turbulence been investigated for potential efficiency?
"The eddy viscosity is generally much larger than the dynamic viscosity (Blatt p.111)." This would suggest that larger diameter pipes would be better candidates for turbulence assisted flow, since the volume to surface area ratio is larger.
Icebreakers bubble air past their hulls to lubricate the ice scraping against their hulls. Specially tailored turbulence might be able to lubricate the sliding the bulk of the fluid as virtually "extruded" past controlled turbulence. The efficiency of the turbulence would likely be velocity dependent.
Relevant Information: The Darcy-Weisbach equation is used to describe the pressure loss over a given segment of pipe.
Blatt, Middleton, and Murray, "Origin of Sedimentary Rocks," 2nd Ed.