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Updated: Feb 22, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Phenomenological friction equation for turbulent flow of Bingham fluids
H R Anbarlooei1, D O A Cruz1, F Ramos2
1Mechanical Engineering Program, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Rio de Janeiro 21941-450, Brazil.
Abstract:
Most discussions in the literature on the friction coefficient of turbulent flows of fluids with complex rheology are empirical. As a rule, theoretical frameworks are not available even for some relatively simple constitutive models. In the present work, a formula is proposed for the evaluation of the friction coefficient of turbulent flows of Bingham fluids. The developments combine a fresh analysis for the description of the microscales of Kolmogorov and the phenomenological turbulence model of Gioia and Chakraborty [G. Gioia and P. Chakraborty, Phys. Rev. Lett. 96, 044502 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.044502]. The resulting Blasius-type friction equation is tested against some experimental data and shows good agreement over a significant range of Hedstrom and Reynolds numbers. Comments on pressure measurements in yielding fluids are made. The limits of the proposed model are also discussed.
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