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RESEARCH PRODUCT

Overland flow hydrodynamic characteristics in rough beds at low Reynolds numbers

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This paper considers overland flow resistance at low Reynolds numbers through analysis of experimental runs carried out using water only and water/glycerol mixtures. We first examined the power relationship between the Darcy–Weisbach friction factor f and the Reynolds number Re to obtain the values of the K coefficient and b exponent. These results confirmed the applicability of the values of b suggested in literature, while K required a specific calibration for laminar open-channel flows. The analysis revealed that transition from a laminar to turbulent flow regime for water only flows occurred at a threshold value of Re equal to 500 as described historically. The estimate of f by the power relationship and the calibrated b and K values were reliable for water only runs when Re ≥ 500. The measurements were also used to test a theoretical flow resistance law based on a power-velocity distribution. The calibrated theoretical relationship between the velocity profile parameter Γv, bed slope, flow Froude number and Re enabled a good estimate of f for water flows. For mixed fluid flows, the effect of the velocity profile shape was considered calibrating this relationship by two datasets obtained setting a threshold Reynolds number equal to 7. For flows with Re < 7, the shape of the velocity profile can be linear or convex while for flows at Re ≥ 7 the shape of the velocity distribution is always concave. The theoretical flow resistance allowed an accurate estimate also for mixed fluid flows, even at Re < 7. The different shape of the power-velocity distribution highlighted that mixed flows behave differently as compared to water only flows.