"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.
Best Answer
No it cannot in the general case. The formulas giving the pressure loss in a duct are always given by a form P = K.geometry.rho.V² where K is an empirical friction coefficient, geometry contains geometrical parameters (diameter, length etc), rho is the density and V the velocity.
Now K depends typically on the Reynolds number and on the roughness of the duct wall. Once the nature of the fluid and the geometry of the duct fixed, the pressure loss depends only on K.V².
What does it mean "increasing turbulence" in the duct? Only 2 possible answers :
1) Increasing the velocity. As this increases both K and V², it increases the pressure loss. Bad.
2) Increasing the roughness of the duct. This increases K without changing V. The pressure loss increases again. Bad.
Of course very low velocity laminar flows are also very bad pressure loosers but then they move so little fluid that they are not used anyway. Going from laminar to turbulent may be better or worse depending on the rougness but one has generally no choice because the flow (kg/s) is a constraint and the turbulent flow is the result. Once the turbulent flow given, best is to reduce the roughness as far as it goes.
You have an excellent calculator here and you can play with all kinds of possible flows : http://www.engineeringtoolbox.com/colebrook-equation-d_1031.html
As a bonus there is also a chart for Darcy friction coefficients depending on Reynolds and roughness.