The combination of a labyrinth weir with an orifice is a proper solution for floating material to pass over the weir and transfer sediment through the orifice. Additionally, creating a slot in the overflow wing leads to higher discharge. This study examined four discharges (5, 10, 15, and 20 liters per second) with channel width and height of 30 and 40 cm in trapezoidal-orifice, square-orifice, and triangular-orifice labyrinth weirs in the laboratory and using Flow3D with RNG k-epsilon (k-ε) turbulence model, the results were compared with one another. Comparing the discharge flow over weirs and measuring the discharge coefficient among the mentioned models showed that the triangular-orifice labyrinth weir had the highest discharge rate. Moreover, the increased Ht/P ratio (Ht represents total hydraulic head; P denotes weir height) for all models resulted in the increased discharge coefficient. Due to the efficiency of this type of weirs, the highest discharge coefficient was obtained at low Ht/P ratios. At lower ratios, since there was free flow, the coefficient of weir discharge increased, and as the ratio increased, the weir was partially submerged. Furthermore, for the weir design, the best Ht/P ratio was between 0.13 to 0.41, and the maximum discharge coefficient (Cd = 1.2) was within this range.