A model is described which explains drag reduction (DR) in dilute polymer solutions in terms of solvation of macromolecular chains and formation of relatively stable domains. The domains partly suppress the vortex formation, act as energy sinks, and also play a role in mechanical degradation in flow (MDF). We report ultrasonically determined solvation numbers for a series of copolymers with the same chemical structure but differing widely in their intrinsic viscosities. The solvation numbers confirm the model. Thus, we have a criterion for selection of DR agents with low MDF for: oil well operations; crude oil transport, fire fighting; high sewer throughput; irrigation; hydrotransport of solids; marine applications; and biomedical applications including the arteriosclerosis prevention.