Changes in drag reduction due to flow-assisted destruction of polymer molecules is investigated using a rotational apparatus with geometrically similar operating units of different sizes. Aqueous solutions of poly(ethylene oxide) (PEO) and solutions of polyisobutylene (PIB) in kerosene were used. For not-too-small concentration. it was found that not only the initial value of the friction coefficient but also its variations in the course of degradation are independent of the Weissenberg number. For this asymptotic regime, the curves describing the variation with time of the ratio between current and maximal for given Reynolds number values of drag reduction are similar. The shape of the curves is independent of the Reynolds number. the length scale of the flow, solution temperature, and polymer molecular weight. The curve shape is identical for the PEO and PIB solutions. These asymptotic curves can be reduced to a single master curve by the choice of a divisor of the time co-ordinate. The half-degradation time, i.e. the time required for decreasing the value of the initial asymptotic polymeric effect on drag by one-half, was taken as the divisor. The theoretical considerations which can be used for calculating the dependence of the half-degradation time on the hydrodynamic and network characteristics are proposed.