Experimental Study of Chezy Coefficient in Open Channels with Bed Forms

Accurate estimation of flow resistance, such as Chezy coefficient, is important for calculating the hydraulic flow conditions and sediment transport in open channels. Chezy coefficient is affected by various factors: bed particles size, vegetation, irregularity of waterway cross-section, irregularity of waterway path, scour and sedimentation, presence of obstructions, suspended and bed load, and bed form (Bahrami Yarahmadi & Shafai Bejestan, 2010, 2011). Previous researches, Talebbeydokhti et al. (2006), Omid et al. (2010), Nasiri Dehsorkhi et al. (2011), Chegini & Pender (2012), Kabiri et al. (2014), and Kwoll et al. (2016), have shown that the bed forms can affect the hydraulic or sediment transport characteristics. However, there is a lack of study to investigate the effect of bed forms with different sediment sizes on the Chezy coefficient. Therefore, the present study aims to conduct experiments on a straight channel whose bed is covered with the artificial bed forms made from P.V.C sheet, and on its surface is glued sediment of different sizes in the range of 0.51 and 2.18 mm.

The experiments were performed in a straight flume of 12 m in length and 0.30 m wide (Figure 1). In this study, different flow discharge of 10, 15, 20, 25, and 30 l/s and different bed slopes of 0, 0.0001, 0.0005, 0.001, and 0.0015 were tested. Two series of experiments were carried out: plane bed or bed without form and bed covered with form. Each form was made in a triangular shape with a P.V.C sheet. The form's length and height were equal to 20 and 4 cm, respectively, and the angles of its upstream and downstream to the horizon were selected as 16.4 and 32 degrees, respectively. After each form was built, the desired sediment size was glued to their surface. This study used two types of uniform granulation with average sizes (d50) of 0.51 and 2.18 mm. The total number of experiments in the present study was 100. Since in alluvial rivers with bed form, the resistance Chezy coefficient includes the grain Chezy coefficient and the form Chezy coefficient. A formless bed, covered with the same sediment size, was tested to determine the grain Chezy coefficient ((C_b ) ́). The bed with the form was used to determine the total Chezy coefficient (C_b) and the form Chezy coefficient (C_b^''). Ripple and dune form is formed in a lower flow regime, in which the Froude number of the flow is less than 1 (Shafai Bajestan, 2008). In this study, the Froude number values in all tests with bed form were 0.435 to 0.6, indicating a lower flow regime.

Figure 3 shows the changes in the total Chezy coefficient (C_b) against Froude number for sediment-covered substrates of 0.51 and 2.18 mm. It can be seen that as the Froude number increased, the total Chezy coefficient (C_b) increased. In addition, increasing the longitudinal slope of the bed decreased C_b.Figures 4, 5 and 6 illustrate the effect of sediment particles size on (C_b ) ́, C_b^'', and C_b. These figures show that (C_b ) ́, C_b^'', and C_b decreased with increasing particles size. In addition, Figures 5 and 6 show that with increasing R/∆, the total Chezy coefficient (C_b) and the form Chezy coefficient (C_b^'') increased. Calculations showed that the value of C_b^'' in beds with a sediment size of 0.51 mm for slopes of 0, 0.0001, 0.0005, 0.001, and 0.0015 was, on average, 14, 12, 12, 15, and 16.4% more than 2.18 mm sedimentary beds, respectively. In addition, the value of C_b in beds with a sediment size of 0.51 mm for slopes of 0, 0.0001, 0.0005, 0.001, and 0.0015 was, on average, 15, 13, 13, 16, and 16.5% more than 2.18 mm sedimentary beds, respectively.The results of Table 1 shows that the grain Chezy coefficient ((C_b ) ́) for particles with sizes of 0.51 and 2.18 mm was, on average, 98 and 93% more than the total Chezy coefficient (C_b), respectively. In addition, The form Chezy coefficient (C_b^'') for particles with sizes of 0.51 and 2.18 mm was, on average, 16 and 17% more than the total Chezy coefficient (C_b), respectively.

The results of this study shows that generally with increasing the bed slope and the bed particle size of movable bed sediment channel, the flow resistance increases or the total Chezy coefficient , the form Chezy coefficient and the grain Chezy coefficient decreases. Increasing the bed particle size from 0.51 to 2.18 mm reduced the coefficients of Cb ́, Cb'', and Cb by 15.14, 12, and 12.9%, respectively. Moreover, the value of Cb ́, Cb'', and Cb in sedimentary beds with particles of 0.51 mm were, on average, 18, 14 and 15% more than sedimentary beds with particles of 2.18 mm, respectively.