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Previous studies showed that integrating a power velocity profile, deduced applying dimensional analysis and the incomplete self-similarity condition, the flow resistance equation for open channel flow can be obtained. At first, in this paper the relationship between the Γ function of the power velocity profile, the channel slope and the Froude number, which was already empirically introduced in a previous paper, is now theoretically deduced. Then this relationship is calibrated using the field measurements of flow velocity, water depth and bed slope carried out in 101 reaches of gravel bed rivers available by literature. The proposed relationship for estimating Γ function and the theoretical flow resistance equation are also tested by an independent dataset of 104 reaches of some gravel bed rivers (Fiumare) in Calabria region. Finally, the theoretically-based relationship for estimating the Γ function is calibrated by the overall available database (205 reaches). In this way the three coefficients of the theoretically based Γ function are estimated for a wide range of slopes (0.1%-6.19%) and hydraulic conditions (Froude number values ranging from 0.08 to 1.25). In conclusion, the analysis shows that the Darcy-Weisbach friction factor for gravel bed rivers can be accurately estimated by the approach based on a power-velocity profile and the theoretically-based relationship proposed for estimating Γ function. The analysis also points out a performance in estimating mean flow velocity better than that obtained in a previous study carried out by the authors.