This paper deals with the velocity distribution and friction factor of polymer drag reducing flows in smooth pipes. By applying the concept of elastic shear stress or the Reynolds shear stress deficit, the equations of velocity distribution and friction factor in turbulent drag reducing flows are derived. Based on the derived equations, the onset Reynolds number for drag reduction is discussed which shows that the onset of drag reduction depends on the polymer type and its concentration. The optimal polymer concentration for Maximum Drag Reduction (MDR) is obtained, and it depends only on the polymer species. The effect of polymer mechanical degradation is discussed in the current paper. (C) 2013 Elsevier Ltd. All rights reserved.