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The velocity distribution in natural channels is of considerable interest for streamflow measurements to obtain information on discharge and flow resistance. This study focuses on the comparison of theoretical velocity distributions based on 1) entropy theory, and 2) the two-parameter power law. The analysis identifies the correlation between the parameters of the distributions and defines their dependence on the geometric and hydraulic characteristics of the channel. Specifically, we investigate how the parameters are related to the flow resistance in terms of Manning roughness, shear velocity and water surface slope, and several formulae showing their relationships are proposed. Velocity measurements carried out in the past 20 years at Ponte Nuovo gauged section along the Tiber River, central Italy, are the basis for the analysis. [ABSTRACT FROM AUTHOR]

• Velocity distribution and averaged velocity in gravel-bed streams derivate from seepage flow and mixing length models. • Experiments demonstrate the flow velocity in the gravel layer and surface layer are affected by gravel array spatial density. • The bed context effects are found to be slightly more sensitive parameters for flow velocity than hydraulic effects. The standard exponential and logarithmic laws for flow velocity evaluation cannot be applied for gravel-bed streams due to the effect of large-scale roughness. An analytical model based on a two-layer subdivision approach was developed to predict flow velocity over a gravel array with different densities. The velocity distribution in the gravel layer was derived by solving the Darcy-Forchheimer-Brinkman (DFB) differential equation based on the concept of porous medium flows. The velocity in the surface layer was modeled by the mixing length theory with the length scale modified by taking into account the porous effect of the gravel (ball) arrays. To assess the model, flow velocities over gravel beds simulated by Ping-Pong ball arrays with different densities (or porosities) were measured in a laboratory flume. The results show that the predicted velocities by this subdivision model agree well with experimental data, reflecting that the porosity of the gravel array essentially impacts the flows both in the gravel layer and surface layer. In comparison with the existing models not considering the porous effect of the gravel bed, this model can effectively predict vertical velocity distributions and thereby flow resistances in gravel streams. The permeable interface velocity atop the gravel layer, as the boundary condition for the two-layer model, is sensitive to the bed context effect rather than the hydraulic effect, suggesting that the inflection point of the full velocity profile might be vital in determining the accuracy of the model. Moreover, with other data sources over dense gravel-bed, our model is suitable for data pre-dealt with the spatially averaging, where the spatial non-uniformity effect is great. [ABSTRACT FROM AUTHOR]