Tests of a proposed friction-factor equation have shown it to be accurate for calculating pressure loss in turbulent flow for a pipeline transporting a non-Newtonian fluid, such as most crude oils ...

"In transitional flow, friction varies with no discernible patterns," says Dr. Rory Cerbus, a postdoctoral researcher at the Okinawa Institute of Science and Technology Graduate University (OIST).

I concluded that vibration had no effect on the friction factor except that at Reynolds numbers above about 2,200 flow ... Comments on Effect of Vibrations on the Transition Regime in Pipe Flow.