Introduction
Flow measurement in an open channel is a fundamental principle in the advanced management and regulation of irrigation networks. Currently, the principle of critical flow conditions in an open channel is used in the design of flow measurement flumes. A method for creating a flow cross-section, known as a control section, has been implemented, allowing for a definite correlation between flow depth and discharge to be expressed. The Venturi flume was a pioneer in recognizing the effect of local constriction in a channel on the pressure and velocity distribution (Hager 1985; Ferro 2002). Flumes that operate by locally changing the channel width are common, and in various European countries, the throat flume, characterized by a gradual change in width, is used. On the contrary, the Parshall flume, known as a throatless flume, is widely used in Anglo-Saxon countries (Blaisdell 1994; Parshall 1926). Hager (1988) used a moving circular flume to measure flow through channels, which consists of a circular column positioned vertically in the center of a pipe to achieve the required constriction. Hager (1986) and Samani and Magallanez (1993) recommended quantifying flow rate by integrating a circular column into a trapezoidal channel. Samani et al. (1991) conducted laboratory studies to investigate the hydraulic properties of various circular flumes. A review of the research background shows that the flumes used are either partial flumes or flumes with a central baffle. In partial flumes, part of the cross-section is reduced, and sometimes they have a bottom protrusion. In central baffle flumes, the baffle is also non-submerged, and in addition to increasing the possibility of blockage, the high-speed flow passing through both sides of the structure has high shear stress on both sides. In the flume proposed in this study, the goal is to utilize the entire cross-section, especially at high discharges, and, additionally, the flow submerges the baffles. One of the hypotheses of this study is that due to the use of multiple baffles, the shear stress created downstream of the baffles is likely to be reduced compared to flumes with single central baffles. This is especially important in erodible beds. The goal of this study is to conduct a hydraulic evaluation of a new flume with a structure consisting of cylindrical baffles. For this purpose, the effect of the percentage of obstruction (or diameter), and the effect of the height of the cylinders at different discharges have been tested. Additionally, using dimensional analysis, the appropriate discharge relationship for this flume has been extracted, and this relationship has been determined through nonlinear multivariate regression.

Methodology
The modeling of this research will be carried out in a rectangular flume with a length, width, and height of 15, 0.8, and 0.6 meters, respectively, in the hydraulic laboratory of Shahid Chamran University of Ahvaz. In general, 11 models were built with geometric variables, including different heights (P) and diameters (D). Hydraulic variables also include different discharges. At each discharge in free-flow conditions, the downstream valve is fully open. Considering the hydraulic variables, a total of 190 experiments were conducted for free conditions.

Results and discussion
As the height of the baffles increases, the structures are submerged at a higher discharge. Additionally, as the diameter of the baffles increases, due to the increased obstruction, the structures are submerged at a lower discharge rate. Determining the threshold discharge of the obstruction submersion is especially important in waterways that include debris flows, such as tree branches or debris. Because this debris can obstruct the structure, it can also lead to errors in the discharge estimate. In this type of flume, the relationship between discharge and eschel is a logarithmic function. Given that the obstruction of the structure increases with the diameter of the baffles, for a specific discharge, the eschel value is higher for baffles with larger diameters. The results show that for a given upstream depth, the discharge index value decreases with increasing height and increasing obstruction. With the same reasoning used for the height of the baffles, increasing the diameter and increasing obstruction, for a given upstream height, the discharge index is higher for smaller diameter baffles. Based on the dimensionless relationship presented in the dimensional analysis section, as well as the laboratory data, an empirical relationship derived from nonlinear multivariate regression has been established. This relationship has been extracted using SPSS 16 software. For this purpose, the laboratory data were divided into two categories: training data (75% of the data) and calibration data (25% of the data). The training data was used to extract the relationship, and the calibration data was used to evaluate the accuracy of the extracted relationship.

Conclusion
This study experimentally investigated the hydraulic performance of a flume with cylindrical baffles, focusing on how baffle height and diameter affect flow under free conditions. Results show that discharge changes logarithmically with these variables. Reducing the height or increasing the diameter of the baffles causes the flume to become submerged at lower discharges. Also, increasing the height and diameter of baffles reduces the discharge index due to greater flow obstruction. An empirical formula for the discharge index was developed using dimensional analysis and nonlinear regression, achieving high accuracy (R² = 0.90 for training data and 0.96 for calibration data) and a relative error of approximately 9% for the calibration data.