Abstract
Empirical formulae describing the Darcy-Weisbach friction factor remain indispensable for applications in sciences and engineering dealing with turbulent flows. Despite their practical significance, these formulae have remained without theoretical interpretation for many decades. To close this knowledge gap we provide, using a co-spectral budget model, a clarification of the link between spectral properties of velocity fluctuations and the scaling of friction factors in turbulent pipe flows in the hydraulically smooth and fully rough regimes.
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