  We extend the analysis of the friction factor for turbulent pipe flow
reported by G. Gioia, P. Chakraborty and N. Goldenfeld (GCG) (G. Gioia and P.
Chakraborty, Phys. Rev. Lett. 96, 044502 (2006), N. Goldenfeld, Phys. Rev.
Lett. 96, 044503 (2006)) to the case where drag is reduced by polymer
additives.
