Drag reduction (DR) agents are used in several ppm concentrations to accelerate significantly the flow through conduits in oil pipelines, oil well operations, flood water disposal, fire fighting, field irrigation, transport of suspensions and slurries, sewage systems, water heating and cooling systems, airplane tank filling, marine systems, and also in biomedical systems including blood flow. The drag reduction agents are typically high molecular mass polymers; in industrial applications they undergo mechanical degradation in turbulent flow. We provide an equation that describes quantitatively the degradation, thus predicting drag reduction as a function of time and of the concentration of the drag reduction agent. We report how grafting a polymer on the backbone of a different polymer affects the drag reduction efficacy. Our grafted polymer undergoes degradation by flow turbulence more slowly and also provides high levels of drag reduction efficacy at much lower concentrations than homopolymers do.