Introduction:
The replacement of linear weirs with nonlinear types, such as labyrinth weirs, is often considered as an effective alternative for increasing spillway discharge capacity without the need to widen the existing channel. Labyrinth weirs are frequently a desirable design choice for regulating upstream water elevations and enhancing flow capacity. They have been successfully used to increase weir capacity and manage upstream flooding during low-probability storm events. Staged labyrinth weirs (weirs with crest lowering) are employed to safely discharging water under both normal and flood conditions. Their unique shape allows for more efficient energy distribution, minimizing turbulence and potential damage to downstream structures. Furthermore, maintenance requirements for labyrinth weirs are generally lower due to their simple yet effective design. When combined with flood forecasting systems, staged labyrinth weirs offer enhanced operational control, ensuring safety during extreme hydrologic events.
 Methods:
Physical models are used to study the performance of labyrinth weirs under various flow conditions. In this research, labyrinth weirs were analyzed with different crest lowering configurations, including the vertex of the weir (VW), left oblique wall (LW), and left and right straight crests (LRW) near the channel walls. Additionally, different angles, heights, and the presence or absence of a nappe breaker were considered. The experiments were conducted in a metal and glass flume with a rectangular cross section. The flume had a width of 0.25 m, a depth of 0.5 m, and a length of 10 m. In each test, the upstream subcritical depth was measured using point gauges with an accuracy of 0.1 mm. The total head upstream of the weir was measured at a horizontal distance of three to four times the maximum water head at the crest of the weir. Also, the discharge was measured using a triangular sharp-crested weir placed at the end of the flume. The discharge-head relationship (Q-h) for the triangular weir was found in the experiments. The trapezoidal labyrinth weir models were installed three meters from the beginning of the flume. In this study, experimental tests were conducted on trapezoidal labyrinth weirs with one cycle, testing three sidewall angles (15°, 18°, and 23°) and three weir heights (14 cm, 16 cm, and 18 cm), in a rectangular channel. The discharge coefficient of the weirs depends on several factors, including: the hydraulic properties of the passing flow, the weir crest, and the geometric properties of the weir. Based on the effective parameters sidewall angle (α), weir height (p), and hydraulic head (Ht), the discharge coefficient was evaluated.
 Results:
The results showed that for trapezoidal labyrinth weirs without a nappe breaker, the discharge coefficient (C_d) was higher than in the presence of a nappe breaker. In the Ht/p range of 0.1 to 0.5, under conditions without a nappe breaker, flow interference was reduced as the flow adheres more closely to the weir, leading to an increase in discharge. Additionally, the discharge coefficient (C_d) decreased as the hydraulic head ratio (Ht/p) increased. As flow discharge increases, the mixing of flow over the weir also increases, which contributes to a decrease in the discharge coefficient. There is an inverse relationship between the discharge coefficient and the weir length. As the crest angle increases, the weir length decreases, resulting in a higher discharge coefficient. Furthermore, for a given crest angle, the discharge coefficient slightly decreased as the weir height (p) increased. For instance, for a weir with a height of 12 cm, the discharge coefficient was slightly higher than for the 14 cm and 16 cm weirs. The study also revealed that for different conditions in staged weirs, the discharge coefficient for the left oblique wall staged crest (LW) was higher than those for the left and right straight crests (LRW) and the vertex of the weir (VW). At high values of Ht/p, the discharge coefficient decreased due to the collision of the falling jets. Additionally, by increasing the sidewall angle, the decrease of C_d with H_t/P became more significant. Optimizing the crest angle and sidewall angle can lead to a more efficient design by balancing the trade-offs between weir length and flow aeration. The discharge coefficient for trapezoidal labyrinth weirs was the highest for weirs with a sidewall angle of 23°, followed by those with a sidewall angle of 18°, which showed approximately 4.5% and 3% higher performance, respectively, compared with weirs with a sidewall angle of 15°.
 Conclusion:
These findings highlight the significant impact of geometric parameters on the hydraulic performance of trapezoidal labyrinth weirs. The presence or absence of nappe breakers influences the flow pattern and energy distribution, affecting both discharge capacity and stability. A comparison of the results indicated that for a staged trapezoidal weir with a ∆P of 3 cm, the discharge coefficient for the left oblique wall staged crest (LW) was, on average, 30% higher, for the left and right straight crests (LRW) was about 20% higher, and for the vertex of the weir (VW) was 10% higher, compared to normal labyrinth weirs.