Abstract
An upper bound λmax on the friction factor λ is found for transitional pipe flow up to Reynolds numbers of Re=4000. This bound corresponds to the laminar Hagen–Poiseuille value until the energy stability point of Re=81.52 (where λmax=0.7851) after which it decreases monotonically to approach a viscosity-independent asymptote of 0.27±0.01 as Re→∞. Comparison is made with the friction factors associated with recently discovered, finite-amplitude traveling waves in rotating and nonrotating pipe flow as well as experimental data.
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