Friction factor for turbulent flow in rough pipes from Heisenberg's closure hypothesis.

We show that the main results of the analysis of the friction factor for turbulent pipe flow reported by Gioia and Chakraborty [Phys. Rev. Lett. 96, 044502 (2006)] can be recovered by assuming the Heisenberg closure hypothesis for the turbulent spectrum. This highlights the structural features of the turbulent spectrum underlying the analysis of Gioia and Chakraborty.