Introduction
Weirs are usually made of impermeable materials such as concrete. These impermeable structures prevent the longitudinal movement of aquatic organisms and physical and chemical substances in the water, thereby preventing sediment accumulation behind the weir and negative impacts on the water ecosystem (Mohamed, 2010). According to the Francis equation, increasing the discharge coefficient or the effective length of the weir can enhance its hydraulic performance (Crookston, 2012). Various studies have been conducted on impermeable weirs. Using an arc-shaped and zigzag plan can increase the effective length of the weir, thereby improving its performance. The main idea of this research was to investigate the performance of a porous weir with an arc-shaped plan. Firstly, due to its porous nature, the weir increases the discharge coefficient (due to the presence of flow through and over it). Secondly, the arc-shaped plan increases the effective length of the weir, resulting in significant hydraulic performance. The flow through and over the weir and their mutual effects combine flow within an open channel and a porous medium, significantly increasing the subject's complexity.
This research aims to experimentally investigate the discharge reduction factor (DRF) in submerged flow conditions in a porous weir with an arc-shaped plan under different hydraulic and geometric conditions.

Methodology
In the present study, two impermeable weir models of plexiglass were compared with corresponding porous weir models, and four porous weir models were constructed. The stone materials used in the porous weirs included five sizes ranging from approximately 7.13 to 31.75 mm in diameter, which were uniform and sharp-edged. In this research, various weir models were tested at different flow rates, and a total of 1704 experiments were conducted in the submerged flow condition and analyzed. To achieve this, the gate at the end of the flume was used to gradually increase the depth of submergence by reducing the gate opening, and the results were obtained for different submergence depths.
As the weir became submerged, the water depth upstream was influenced by the downstream depth. The discharge through the weir in submerged flow conditions was smaller than the discharge in free flow conditions, and it is usually extracted using a discharge reduction factor from the free flow discharge as follows:
Q_s=DRF × Q→DRF=Q_s/Q (1)
The first step in the dimensional analysis is identifying the potential parameters affecting the hydraulic flow in a submerged arc porous weir. A general relationship consisting of dimensionless parameters has been derived by dimensional analysis and based on previous studies. This study neglected the number of weirs with a flow depth greater than 3 cm, considering the range of hydraulic conditions and flow depth over the weir (Horton, 1907; Novak & Cabelka, 1981). Although the flow conditions in this study were turbulent, the Reynolds number (Re) was used as an effective parameter in the relationship for the discharge reduction factor (DRF) based on the correlation between DRF and Reynolds number and by the studies by Mohamed (2010). Therefore, the final relationship for DRF can be simplified as follows.
DRF=f(ξ,L_c/L_Arc,R_e,d_50/P,n) (2)

Results and Discussion
With an increase in flow rate, the value of the DRF decreases with a steep slope. At lower flow rates, the slope of the DRF is steep and gradually decreases with increasing flow rates. In the submerged condition, the discharge coefficient reduces the free-state coefficient by up to 68 percent. In other words, the discharge coefficient in the submerged condition is 68 percent less than the corresponding free-flow discharge coefficient. By increasing the materials' size, the DRF's value decreases, and the model becomes submerged earlier. Comparing the results of each model with the corresponding solid model, it is evident that impermeable weirs have less sensitivity to lower depths and take longer to become submerged compared to porous weirs. The results indicate that the linear porous weir model becomes submerged later and is less sensitive to lower depths than arc-shaped models. Despite the similar values, comparing arc-shaped models shows that with an increase in arc length, the sensitivity of the weir to submergence decreases.
With an increase in flow rate, the DRF increases. With an increase in flow rate, the head over the weir crest increases, meaning the energy over the weir crest has increased. With increased energy over the crest, more energy is required for the weir to become submerged. Therefore, the weir becomes submerged at a greater depth and less sensitive to the submergence depth. The equation derived using the SPSS model has statistical parameter values of R2 = 0.78, RMSE = 0.074, and MAE = 0.068. Furthermore, the equation derived using the GEP model has statistical parameter values of R2 = 0.95, RMSE = 0.035, and MAE = 0.027.

Conclusion
In comparison with impermeable models, porous models consistently have a lower DRF. In impermeable models, the DRF decreases as the size of the materials increases. As the intensity of flow increases, the reduction in the DRF decreases. The results show that the discharge coefficient in the submerged condition is at most 68% less than the corresponding free condition. The investigation of the effect of arc shape on the DRF showed that the linear porous weir model becomes submerged later compared to models with arc and has less sensitivity to lower depths. The accuracy of the extracted relationship based on the GEP model is more suitable. It predicts about 95% of the data with an error of less than 10%.