Friction factor of drag-reducing flow with presence of polymers in a rough pipe has been investigated based on the eddy diffusivity model, which shows that the ratio of effective viscosity caused by polymers to kinematic viscosity of fluid should be proportional to the Reynolds number, i.e. uR/ν and the proportionality factor depends on polymer\u27s type and concentration. A formula of flow resistance covering all regions from laminar, transitional and fully turbulent flows has been derived, and it is valid in hydraulically smooth, transitional and fully rough regimes. This new formula has been tested against Nikuradse and Virk\u27s experimental data in both Newtonian and non-Newtonian fluid flows. The agreement between the measured and predicted friction factors is satisfactory, indicating that the addition of polymer into Newtonian fluid flow leads to the non-zero effective viscosity and it also thickens the viscous sublayer, subsequently the drag is reduced. The investigation shows that the effect of polymer also changes the velocity at the top of roughness elements. Both experimental data and theoretical predictions indicate that, if same polymer solution is used, the drag reduction (DR) in roughened pipes becomes smaller relative to smooth pipe flows at the same Reynolds number.
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