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Vegetation on the banks and flooding areas of watercourses significantly affects energy losses. To take the latter into account, computational models make use of resistance coefficients based on the evaluation of bed and walls roughness besides the resistance to flow offered by vegetation. This paper, after summarizing the classical approaches based on descriptions and pictures, considers the recent advancements related to the analytical methods relative both to rigid and flexible vegetation. In particular, emergent rigid vegetation is first analyzed by focusing on the methods for determining the drag coefficient, then submerged rigid vegetation is analyzed, highlighting briefly the principles on which the different models are based and recalling the comparisons made in the literature. Then, the models used in the case of both emergent and submerged rigid vegetation are highlighted. As to flexible vegetation, the paper reminds first the flow conditions that cause the vegetation to lay on the channel bed, and then the classical resistance laws that were developed for the design of irrigation canals. The most recent developments in the case of submerged and emergent flexible vegetation are then presented. Since turbulence studies should be considered as the basis of flow resistance, even though the path toward practical use is still long, the new developments in the field of 3D numerical methods are briefly reviewed, presently used to assess the characteristics of turbulence and the transport of sediments and pollutants. The use of remote sensing to map riparian vegetation and estimating biomechanical parameters is briefly analyzed. Finally, some applications are presented, aimed at highlighting, in real cases, the influence exerted by vegetation on water depth and maintenance interventions.

A new discharge computational model is proposed on the basis of the integration of the velocity profile across the flow cross-section in an internally corrugated pipe flowing partially full. The model takes into account the velocity profiles in the pressurised pipe to predict the flow rate under free-surface flow conditions. The model was evaluated through new laboratory experiments as well as a literature datasets. The results show that flow depth and pipe slope may affect the model accuracy; nevertheless, a prediction error smaller than 20% is expected from the model. Experimental results reveal the influence of the pipe slope and flow depth on the friction factor and the stage-discharge curves: the friction factor may increase with pipe slope, while it reduces as flow depth increases. Hence, a notable change of pipe slope may lead to the variation of the stage-discharge curve. A part of this study deals with numerical simulation of the velocity profiles and the stage-discharge curves. Using the Reynolds-Averaged Navier-Stokes (RANS) equations, numerical solutions were obtained to simulate four experimental tests, obtaining enough accurate results as to velocity profiles and water depths. The results of the simulated flow velocity were used to estimate the flow discharge, confirming the potential of numerical techniques for the prediction of stage-discharge curves.Reference [4]. On the other hand, there are few studies on the friction factor and velocity profiles of corrugated pipes under free-surface flow conditions. The following paragraphs point to the previous studies on the hydraulics of corrugated pipes under free-surface flow conditions. An earlier study on flow resistance of three relatively large corrugated pipes under both full-pipe and free-surface flow conditions was performed by Webster and Metcalf [5]. The employed pipes were 3, 5, and 7 ft in diameter. That study mainly focused on the velocity profile and friction factor of the selected pipes under full-pipe flow conditions with less attention to the flow resistance of the pipes under free-surface flow. Nevertheless, the finding of Webster and Metcalf [5] about the value of Manning's n when the pipes convey the flow under free-surface conditions is quite interesting: they concluded that Manning's n for free-surface flow is almost independent of the flow depth and is around the value of 0.024 s/m 1/3 obtained for full-pipe flow conditions.Ead et al. [6] derived empirical equations to predict the flow velocity pattern within a steel corrugated pipe. The measurement of the velocity profiles was conducted at the pipe centreline axis as well as at the different lateral distances from the central vertical plane. Ead et al. [6] reported that the well-known Prandtl equation for the rough wall is valid to predict the velocity profile at a region near the corrugations, whereas, after a certain distance from the corrugations, there would be a deviation from the logarithmic line. The proposed equations by Ead et al. [6] may be used to predict the location w...

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