## 1 Introduction  
Vegetation has an important hydrological role at the basin scale because it reduces erosion and floods and increases infiltration [1; 2; 3; 4; 5]. On the other hand, vegetation along watercourses plays an important role in the river ecosystem, enhancing the landscape. In relation to the river ecosystem, aquatic plants can improve water quality by producing oxygen, consume excess nutrients, decrease the suspended solids, provide a habitat for aquatic animals by creating low-flow areas and prevent fertilizers and pollutants from reaching the watercourses [6; 7; 8; 9]. Projects for the renaturalization and rehabilitation of watercourses are currently underway worldwide [10; 11; 12; 13; 14]. From the hydrodynamic viewpoint, vegetation increases the flow resistance, changes the backwater profiles, modifies the sediment erosion and deposition [15] and influencesthe river morphology [16]. These phenomena have a mutual interaction whose analysis becomes very complex owing to the various physical mechanisms involved and the biomechanical properties characterizing different types of vegetation [17; 18]. Resistance due to vegetation varies in the main channel and the flood plains as a result of the vegetation flexibility, submergence, foliage and side-branching, type, height, density and spatial distribution of plants [19; 20; 21]. The effects that vegetation can exert on stream flow processes are further complicated by the temporal and spatial variations of flow stage, uniformity and steadiness [22]. As for river hydraulics, vegetation may occupy part of the river cross section [23; 24; 25], increasing the roughness and reducing the flow velocity: these result in increased flow levels and a reduced water conveyance. Moreover, while, on the one hand the lower average flow velocity reduces the erosion of the riverbed and banks [26], on the other hand it causes an increase of the sediment deposition, making the flow cross section smaller and, consequently, raising the flooding risk. At the scale of the hydrographic network, the general velocity reduction influences the travel time of water particles, making easier the peak flow to control [27]. With reference to the hydraulic aspects, the focus of researchers, in addition to the flow resistance, is on the analysis of turbulence characteristics [28; 29; 30; 31; 32] and solid transport [15; 18; 33; 34; 35]. Commonly, in the literature, vegetation is considered to be rigid or flexible and, according to the flow depth, as emergent or submerged. In laboratory experiments, rigid vegetation is usually represented by rigid cylinders of various materials and sizes [36]. The aim of this study is to recognize how the drag coefficient varies in the case of emergent rigid vegetation in a gradually varied flow (GVF) profile, which apparently differs from the cases of uniform or quasi-uniform flow. To this end, in Section 2, references are made to the methods used for the calculation of the free surface profiles in open-channel flow and to the different drag coefficient predictors, with particular emphasis on the approach proposed by [PERSON] et al. [1]. Thus, Section 3 illustrates the equipment used to perform the experiments in the presence of rigid and emergent vegetation (simulated with cylindrical wooden sticks). In Section 4, considering 26 experimental profiles with linear patterns, the results of both literature predictors and the methodology proposed by [PERSON] et al. [1] are shown. When following the approaches proposed by these authors, the relationship between drag coefficient and Reynolds number appears to be puzzling, showing in some cases a maximum and a minimum value, and in some other cases increasing or decreasing linear trends. To solve this problem, first of all, the experimental profiles were simulated, each one with the appropriate Manning coefficient, to compute the relevant drag coefficient. Dimensional analysis was then applied to obtain, from data for 16 experimental tests, a relationship allowing the drag coefficients to be estimated.