LABYRINTH WEIRS are one of the kind of nonlinear crest WEIRS causing the increase of discharge capacity for specified height of water level in canals and dams. In this study, the effects of dentate and orifice LABYRINTH WEIRS on increasing the discharge capacity were investigated. Experiments were conducted in a laboratory flume with length of 12 m and width of 0.8 m. The nine experimental models with 15 cm height were used. The results showed that for L/W=2 and H/P=0.2, the discharge coefficient of the orifice-dentate LABYRINTH weir and the dentate LABYRINTH weir are 75.6% and 17.5%, more than the simple LABYRINTH weir, respectively. However, dent and orifice may decrease their efficiency in high heads and the discharge coefficient will be close to simple LABYRINTH weir. The reason for these changes was increasing the flow interference in downstream of LABYRINTH weir between dents, orifices and weir with increasing discharge. Also, the result showed the efficiency of orifice and dentate on LABYRINTH WEIRS will decrease with increasing the weir magnification (L/W) and they lose their effect.

WEIRS are used in different ways to control water levels and flow measurement. One of the most effective and economical way to increase the effective length of weir is using LABYRINTH spillways. The direction of flow of the LABYRINTH spillways is not perpendicular to the edge of the weir and it is oblique. On the upstream and downstream of the weir, the flow direction of the symmetry axis of LABYRINTH WEIRS is parallel. This phenomenon is more common in the downstream overflow because of flow stacking and, thus efficiency of weir is reduced (Hay the Taylor, 1970). Since, study about the using of upstream guide vanes in the direct channel has not been yet published, in this paper, flow guide vanes were used in the upstream of the triangular LABYRINTH spillway with vertex angles of 45o or 90o. The main purpose is guiding flow on weir wall perpendicularly and study of discharge coefficient.The experiments were conducted in a canal with a length of 7 m, width of 0.32 m and height of 0.36m. The two triangular LABYRINTH spillways with vertex angle of 45o and 90o were used. The models were made of galvanized sheet with 1 mm thickness and smooth overflow threshold edge. According to previous researchers (w/P³2.5, in this case P is weir height and w is canal width), the height of the weir was considered equal to 12 cm. A direct spillway with the same width was used to calculate the equivalent discharge. Guide vanes were made from galvanized steel plates. The height of guide vanes was 12 cm and their widths were 2, 3, 4 and 5 cm. The width of guide vanes was a coefficient of the length of one side spillway. Spillways were installed at a distance of 4.5 meters from the beginning of the canal. The reason of choosing this distance is that the flow completely developed from 3.5 to 4.5 meters from the beginning of the canal. Height and velocity of upstream water flow were taken at 5 discharges. The upstream depth of water, above the weir and longitudinal profile of the water surface was measured by a depth meter. Acoustic Doppler Velocimeter was used to measure the flow velocity. The tests were conducted in 3 groups: Group I at vertex angle of 45 or 90o, the width of guide vanes were 2, 3, 4 or 5 cm at a direct distance of 8 cm from the weir with 45o wall angle. Group II at vertex angle of 45 or 90o, wall angle guide vanes with weir of 35, 45, 65 or 90 degrees at direct distance of 8 cm from the weir. Group III at vertex angle of 90o, direct distance of 8, 22 or 33 cm from the center.In this study, Group I on the weir at vertex angle of 90 degrees and direct distance of 8 cm from the upstream weir does not positive effect on overflow efficiency, because efficiency in all tests were less than simple triangular LABYRINTH spillway with vertex angle of 90 degrees. The comparison shows that the highest efficiency occurred on weir with vertex angle of 45 degrees with guide vane width of 2 cm and on weir with vertex angle of 90 degrees without guide vane. In group II at the weir with vertex angle of 90 degrees, existence of guide vanes at direct distance of 8 cm from the weir with all angles of 35, 45, 65 and 90 degrees is reduced efficiency of flow. It is determined by comparing the curve of models, the maximum of efficiency occurred with vertex angle of 45 degrees and wall angle of 35 degrees, and on weir with vertex angle of 90 degrees and wall angle of 35 degrees. In group III, efficiency in all tests were less than simple triangular LABYRINTH spillway with vertex angle of 90 degrees and adistance of 8, 22 and 33 cm. In triangular LABYRINTH spillway with small vertex angle, using guide vanes could affect on vertical velocity component and this component could be increased. So at the same time, the flow is passed more quickly from weir crest, discharge is increased then for the same height water, the discharge coefficient increased. It was found that the triangular LABYRINTH weir with less vertex angle had very disturbance flow with increasing of discharge. These vanes could be guided flow perpendicularly on wall weir and then efficiency was improved.

Flow water passing through spillways of dams has a high level of kinetic energy, which can lead to extensive damage to downstream facilities and bring about severe erosion of river beds. Energy dissipation would usually be accomplished by creating structures such as still basins at downstream of WEIRS, flip buckets, or steps in WEIRS. Stepped spillways are one of the common structures for energy dissipation, as well as reduction of the dimensions of still basins. The effects of LABYRINTHs on total energy dissipation at downstream of the stepped spillways with slopes of 1: 1, 1: 2 and 1: 3 was investigated; the height of LABYRINTHs was 0. 5 and 0. 75 of the height of steps (h), working interspaces were equal to two times of the height of steps, and three roughness heights on the step face were 0. 002, 0. 004 and 0. 006 m. The results showed that in first case, 1: 1 slope of the stepped spillway, a LABYRINTH with height of 0. 5h, working interspaces of 2h and equal length of the steps caused an increase of 12. 7 percent in dissipation of relative energy. The comparison of results showed that for slope of stepped weir of 1: 2, installation of a LABYRINTH with a height of 0. 75h, interspaces of 2h and equal length to the height of the steps, the relative energy dissipation increased by 8. 4 percent. When stepped WEIRS with slopes equal to1: 3 were used, results indicated that installation sill with a length h, a height of 0. 5h instead of LABYRINTHs on steps, caused an increase of 4. 7 percent in relative energy dissipation. Result showed that increase surface roughness of studied WEIRS reduced the relative energy dissipation by 3. 6 percent.

Nonlinear WEIRS are among the hydraulic structures that, despite their great importance and application, so far, no general method for estimating their discharge capacity has been accomplished. Laboratory or numerical modelling is commonly used to achieve nonlinear weir discharge capacity. It should be noted that employing the design equation from one geometric family of nonlinear WEIRS to another is impractical. The utilization of numerical or laboratory models in the preliminary stages of the design of these structures is a time and cost-consuming process, which is highlighted by the variety of nonlinear weir geometry. In this research, a general method for estimating the nonlinear WEIRS discharge capacity is presented. The proposed method analyzes nonlinear weir discharge capacity using energy and discharge equations for discretized solution fields. Furthermore, the local submergence in nonlinear WEIRS, which has a tangible effect on their discharge capacity, has been corrected. Results of laboratory models performed on the oblique weir, arced LABYRINTH weir, and Isabella dam weir have been used to evaluate the efficiency of the proposed method. The proposed method with high correlation and accuracy has estimated the discharge capacity of these WEIRS. The maximum error observed was 12 percent for the oblique weir,15 percent for the arced LABYRINTH weir, and 15 percent for the Isabella Dam weir.

WEIRS are among the structures used in water transfer channels, hydraulic structures, irrigation and drainage channels, and they are used to regulate the water level and control the flow. WEIRS are flow diversion tools that are widely used in irrigation and drainage systems and urban sewage systems. Increasing the capacity of each WEIRS in a certain width is one of the important issues. These changes cannot be implemented in all structures because limiting factors such as topographical conditions and construction materials may not allow. The use of WEIRS with non-linear crests is one of the ways to increase the capacity of each weir. During the construction of dam structures, due to the high cost, they are looking for a solution to optimize costs, and one of the best ways to build a dam is to use a weir with a non-linear crest. One of the advantages of non-linear weir is to increase the flow rate capacity. Simulation using various software including Flow3d to investigate the flow pattern has become very popular in recent years. The most important reason for using simulation software, in addition to cost reduction, is the possibility of creating different forms of LABYRINTH WEIRS in the software. Meanwhile, in the laboratory, it is not possible to investigate the LABYRINTH WEIRS of different shapes and dimensions. In this research, the hydraulic model was tested inside a glass flume with a length of 10 meters, a height of 80 cm and a width of 80 cm. This flume has a pump with a maximum flow rate of 90 lit/s. The flow rate is measured using an ultrasonic flow meter. To measure the water level, several rail gauges points that can move along the flume are used. The LABYRINTH weir is triangular with 4 mm thick and height of 15 cm. The length of the model is 126 cm and the L/W ratio is 1.58. At first, the laboratory model was compared with the simulated model with the same magnification ratio. For this purpose, 9 discharges with a head ratio of 0.2 to 0.7 were investigated in the laboratory. The purpose was to check the accuracy of the model used in the simulation compared to the laboratory model. Then, three triangular and three arched LABYRINTH WEIRS models were simulated with 2, 3 and 4 magnifications. K-Ɛ RNG turbulence model was used to solve the turbulence flow. This model has an additional term compared to other turbulence equations, which will give us a more accurate solution for solving and discretizing the turbulence equations. In the current research, the flow depth boundary conditions were used in the flow entry, the exit flow boundary conditions were used in the exit sections, the wall boundary conditions were used in the walls and the floor, and the symmetry boundary conditions were used in the water surface. In order to validate the model, comparison of numerical and laboratory of discharge coefficient (Cd) was used. The results showed that RMSE is equal to 3.9% and MSE is equal to 0.16%. Therefore, the error is acceptable and the model will be used in the simulation of triangular and arched LABYRINTH WEIRS. The results showed that the discharge coefficient increased at first and then decreased. At first, gradually increasing the flow over the WEIRS, the amount of air trapped under the nappe decreases. This has caused a decrease in the amount of momentum introduced by the rotating air under the nappe, as well as a decrease in the negative pressure in that area, and as a result, it has resulted in an increase in the discharge coefficient. Investigations showed that with the increase of the water head ratio (HT⁄P) and magnification ratio (L/W), the nappe interference and local submergence increased and caused a decrease in the discharge coefficient. Thus, in the triangular and arched LABYRINTH weir, the discharge coefficient decreases up to 38% and 39% with the increase of the water head ratio from 0.1 to 1 and up to 29% and 37% with the increase of the magnification ratio from 2 to 4. On the other hand, arched LABYRINTH WEIRS have a lower discharge coefficient of up to 14% at a same magnification ratio than triangular LABYRINTH WEIRS. The reason for this problem is the smaller angle of the arched LABYRINTH weir with the channel wall compared to the triangular LABYRINTH weir, which causes the nappe interference to hit the channel wall and also cause more local submergence in the arched weir. Also, the impact angle of the flow jets at the top of the arched weir is higher than that of the triangular weir, which will cause more disturbance of the flow and decrease the flow coefficient.

Side weir is used as a regulator structure to control discharge and water level in rivers and channels. A LABYRINTH side weir is a kind of WEIRS which does not  have a direct and smooth edge in the plan view. When the opening length is limited, these side WEIRS can divert more water out of the channel by increasing the effective length. To evaluate performance of the side weir and estimate the rate of flow passing through it, the discharge coefficient should be determined. In this research, hydraulic behavior of a LABYRINTH side weir with a trapezoidal plan in the single-cycle has been studied experimentally. Upstream Froude number of the side weir was modified in each test and the effects of opening length, height and side angels on the discharge coefficient were investigated. The results of the tests were analyzed to find out the effect of defined dimensionless parameters such as length, height and angle on the discharge coefficient in subcritical flow. The results obtained showed that in comparison with the normal side WEIRS the discharge coefficient of the trapezoidal LABYRINTH side weir increased about 15-30 percent. Also, the discharge coefficient decreased with increasing the Froude number and side angles and increased with increasing the opening length and height of the weir. In the range of experiments, the angle of 30 degrees gives the highest discharge coefficient that is approximately 1.5 times the other angles.

In the article, through the adaptive neuro-fuzzy inference system (ANFIS), a sensitivity analysis is conducted on the variables affecting the discharge capacity of the weir. To this end, the variables affecting the discharge capacity of LABYRINTH WEIRS are initially identified. Then, using these input parameters, seven ANFIS models are developed for conducting the sensitivity analysis. After that, the most optimal membership function number for the ANFIS model is chosen. In other words, by conducting the trial and error process, the best number of the membership functions in terms of time and modeling accuracy are selected. Then, the sensitivity analysis is performed for the ANFIS models and the superior ANFIS model is chosen finally. The accuracy of the superior model in both the validation and testing artificial intelligence (AI) methods is in an acceptable range. For example, the scatter index (SI), correlation coefficient (R) and the Nash-Sutcliff efficiency coefficient (NSC) for the model in the testing mode are obtained 0. 049, 0. 964 and 0. 924, respectively. It should be noticed that the outcomes of the sensitivity analysis show that the ratio of the weir head to the weir crest and the Froude number are introduced as the most effective input parameters. Eventually, a computer code is proposed to estimate the discharge capacity of LABYRINTH WEIRS by this model.

LABYRINTH WEIRS are of the non-linear WEIRS whose discharge coefficient is higher than similar linear WEIRS. These WEIRS have a simple structure. They are mainly made in rectangular, trapezoidal, triangular and semicircular shapes. Investigating the amount of energy loss in these high-efficiency WEIRS has become very important for engineers in recent years. The experiments were carried out in a flume with a length of 10 meters, a width of 0.6 meters and a height of 0.8 meters. The flow is fed by a pump with an error of 0.01% by three surface tanks and after passing through the flow relaxers into the flume. In this research, four sinusoidal LABYRINTH WEIRS were used to check the amount of energy loss. The first spillway has a crown length of 1.3 meters, the second spillway has a crown length of 1.5 meters, the third spillway has a crown length of 1.55 meters, and the fourth spillway has a crown length of 1.6 meters. Also, the first and second WEIRS have a height of 0.15 meters and the width ratio of the inlet to the outlet is 6.86, and the third and fourth WEIRS have a height of 0.18 meters and the width ratio of the inlet to the outlet is 7.67. The flow depth in the upstream and downstream of the weir was taken by a point gauge with an error of 1 mm. WEIRS are installed at a distance of 5.5 meters from the beginning of the channel. The downstream depth of the spillway was not artificially adjusted by the end valve of the laboratory flume. The WEIRS are made of wood and wood glue was used for their impermeability. The flow is transferred downstream over the sinusoidal edges of the weir like a curved slide or similar to peak WEIRS. Also, due to the sinusoidal nature of the WEIRS, the flow will be transferred downstream faster next to the walls. At the edge of the keys, a local vacuum is created. As the flow rate increases, the available air volume increases. At the downstream of the inlet and outlet keys, a vortex and rotation of the flow is formed, which increases in strength as the flow speed increases. The reason for the formation of vortices is the interference of the falling flow from each sinus. Due to the sinusoidal nature of the flow and the indentations and protrusions in the weir, the flow enters the downstream with a curve and the outflow from each sinus is mixed with the outflow from the other sinus. Also, at the beginning of the outlet keys, a small submerged area is formed, which increases in length and moves downstream as the flow rate increases. In front of the inlet keys, two relatively strong hydraulic jumps are formed, and after that the flow is transferred downstream more calmly. The results were that by increasing the flow rate or increasing the depth of the flow upstream of the weir, the energy loss decreased. Also, the amount of energy loss increases with the effective length of WEIRS. By increasing the ratio of the width of the input keys to the width of the weir output keys, the amount of energy loss increases. Also, by increasing the ratio of flow depth plus height, such as kinetic energy upstream of the weir to the height of the weir, the amount of energy loss decreases. The amount of energy loss is the highest in the fourth weir and the third weir, respectively. On average, with a 20% increase in the height of the weir, the amount of energy loss increases by 23.2%. Also, the average energy loss in type A, B, C, and D WEIRS is 42.3, 47.2, 57.9, and 58.6, respectively.

In this research, an evolutionary based Neuro-fuzzy technique was utilized to estimate the discharge coefficient of LABYRINTH WEIRS. In order to optimize the parameters of the adaptive Neuro-fuzzy inference system (ANFIS), the Firefly Algorithm (FFA) was implemented. In modeling the ANFIS-FFA and ANFIS methods, the Monte Carlo simulation was used to evaluate uncertainty of the model. Furthermore, several models with significant flexibility and generalizability were provided using the k-fold cross validation method. First, the input dimensionless parameters including the Froude number (Fr), ratio of the head above the weir to the weir height (HT/P), cycle sidewall angle (α ), ratio of length of the weir crest to the channel width (Lc/W), ratio of length of the apex geometry to the width of a single cycle (A/w) and the ratio of width of a single cycle to weir height (w/P) were defined. After that, seven different models were introduced for ANFIS and ANFIS-FFA. Then, using a sensitivity analysis, the superior models (ANFIS-FFA 5 and ANFIS 5) and the most effective input parameter (Froude number) were identified. In addition, the error distribution results showed that about 70% of the superior model (ANFIS-FFA 5) results had an error less than 5%. In other words, the superior model had a high statistical significance. Ultimately, the uncertainty analysis for the superior models was carried out.

Side WEIRS are among important hydraulic structures that used in various projects such as water conveyance, flood control, and diversion of excess water in sewer networks. One of the most effective and economical ways to increase the efficiency of these WEIRS is application of LABYRINTH side weir. Using LABYRINTH side WEIRS, the flow discharge is increased by changing the plan geometry and increasing the weir length. Due to complicated calculations related to the determination of the discharge equation for LABYRINTH side WEIRS, extracting simple discharge relation for different conditions is necessary. Therefore, in this study, the discharge relations for rectangular side WEIRS having two opening values of 0. 3, 0. 5 m and for LABYRINTH side WEIRS having 90, 60 and 45 apex angle with opening values of 0. 3, 0. 5 and 0. 6 m were extracted. Comparison of the simulation results with these relations indicated that the accuracy of the relations was within ± 15% which was acceptable for practical purposes. Also due to the results of LABYRINTH side weir, with decreasing the weir effective length, the flow discharge reduced when the apex angle of LABYRINTH side weir was increased for a constant water head. Decreasing the effective width also caused the flow discharge to be reduced when opening was decreased for a constant water head.