In the present paper, the effects of side slopes, bed slopes and bed roughness on the flow over free overfalls in triangular channels have been studied experimentally. For this purpose, three models of triangular channels with free overfalls have been constructed and fixed in a 6m length laboratory flume. These three models had length of 244cm with different values of side slopes (Z) (0.8(H):1(V), 1:1 and 1.33:1). Each one of these models had four different bed slopes (S) (0, 0.0041, 0.0082 and 0.0123). For each bed slope, the bed was roughened with three particle sizes of sand (ds) (1.18mm, 2.36mm, and 4.75mm). The experimental testing program included sixteen series of experiments for each model. Four of them were for smooth beds and twelve for rough beds. A total of forty eight experiments were tested for different rates of discharge (Q). Experimental results of all models showed that Froude number (Frb) of flow decreases with the increasing of end depth ratio values (yb/yc) for different bed roughness, different bed slopes. The relations between the brink depth (yb) and the critical depth (yc) were found to be a simple linear formula for various bottom slope and different bottom roughness. An empirical expression was obtained for the flow over the free overfall in triangular channels for different bed slopes and roughness. The results of the present study have been compared with studies were obtained by other investigators, the comparison shows a very good agreement between them.
The critical depth and normal depth computation are essential for hydraulic engineers to understanding the characteristics of varied flow in open channels. These depths are fundamental to analyze the flow for irrigation, drainage, and sewer pipes. Several explicit solutions to calculate critical and normal depths in different shape open channels were discovered over time. Regardless of the complexity of using these explicit solutions, these formulas have a significant error percentage compared to the exact solution. Therefore, this research explicitly calculates the normal and critical depth in circular channels and finds simple, fast, and accurate equations. First, the dimensional analysis was used to propose an analytical equation for measuring the circular channels' critical and normal depths. Then, regression analysis has been carried for 2160 sets of discharge versus critical and normal depths data in a circular open channel. The results show that this study's proposed equation for measuring the circular channels' critical and normal depths overcomes the error percentage in previous studies. Furthermore, the proposed equation offers efficiency and precision compared with other previous solutions.
In present paper, the computational fluid dynamics (CFD - program Flow-3D) was used to analyze and study the characteristics of flow energy dissipation over stepped spillways. Three different spillway heights () (15, 20 and 25cm) were used. For each one of these models, three numbers of steps (N) (5, 10 and 25) and three spillway slopes (S) (0.5, 1 and 1.25) were used. Eight different discharges ranging (600-8500cm³/s) were passed over each one of these models, therefore the total runs of this study are 216. The energy dissipation over these models and the pressure distribution on the horizontal and vertical step faces over some models were studied. For verification purpose of the (CFD) program, the experimental work was conducted on four models of stepped spillway and five different discharges were passed over each model. The magnitude of dissipated energy on models was compared with results of numerical program under same conditions. The comparison showed good agreement between them with standard percentage error ranging between (-2.01 - 11.13%). Thus, the program Flow-3D is a reasonable numerical program which can be used in this study.Results showed that the energy dissipation increases with increased spillway height and decreased number of steps and spillway slope. Also, the energy dissipation decreases with increasing the flow rate. An empirical equation for measuring the energy dissipation was derived using the dimensional analysis. The coefficient of determination of this equation (R2) equals 0.766.
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