Determination of flow characteristics over sharp-crested triangular plan form weirs using numerical simulation

ABSTRACT Triangular plan form weirs are one type of long-crested weirs. Therefore, they can pass more discharge capacity than weirs at the given channel width. This study aims to investigate the effects of different number of teeth (3, 4, and 5 teeth), angle of the weir tip (90, 60, 120, and 150 degrees), and the amount of different discharges (0.009–0.0063 m3/s) of sharp-crested triangular plan form weirs on the hydraulic parameters by using the Finite Volume Method (FVM). It was found that, increasing the effective length of the crest, increases the discharge coefficient up to 95% in the case with 5 teeth (L/B = 4.14 and h/W = 0.128), 45% in the case with 4 teeth (L/B = 3.71 and h/W = 0.168) and 39% for 3 teeth (L/B = 3.28 and h/W = 0.188) compared to the simple triangular plan weir (without teeth). Also, Results indicated that the discharge coefficient has an inverse relationship with the h/w ratio. In contrast, the investigations showed that the velocity in the flow jet is affected by the effective length of the triangular plan crest, and the increase in the effective length results in a decrease in the average velocity of the flow jet. So that these disturbances caused the highest dissipation of energy to occur in the triangular plan crest with 5 teeth (27% compared to the upstream section (Section 1) and 37% compared to the downstream section (Section 2)).


Introduction
Weirs can be divided into linear, diagonal, and congressional weirs based on how they are placed in the plan.Nonlinear weirs are among the major structures used in water transfer.Thus, these structures have been the subject of various studies.Aghashirmohammadi, Heidarnejad, Purmohammadi, and Masjedi (2023) A weir is a structure used to avoid excessive storage of water in the reservoir and transfer the excess water, especially during the flood times, from upstream to the downstream areas and rivers Ghanbari and Heidarnejad (2020).The first studies on the design criteria and hydraulic performance of multifaceted weirs was done by (Hay & Taylor, 1970) on models with triangular, rectangular, and trapezoidal geometry plans with a sharp edge crest shape.In linear plan weirs, the site of the weir must be widened to increase the effective length.However, for triangular plan weirs, the crest axis of the weir is non-linear, and at a given width, the crest length is greater than that of conventional linear weirs.Due to the increase in the effective length of the triangular plan weir, it has a higher discharge coefficient compared to a normal weir (Carollo, Ferro, & Pampalone, 2012;Crookston and Tullis, 2013).Ackers, Bennet, and Zamesky (2011) proposed a congressional weir with downstream bed subsidence for the Lake Holiday dam.First, using the data of Tullis, Amanian, and Waldron (1995), they performed numerical simulations and compared the results with their experimental findings.The results showed that the upstream head obtained from the simulation is 5-6% higher than the laboratory results.The impact of the flow downstream of the weir on the upstream water head was investigated and it was found that as the downstream water depth decreases, the upstream water head also decreases.More recently, Di Stefano and Ferro (2013) obtained the discharge Eschel relationship for a sharp edge triangular plan weir using the flow process over the weir.The hydraulic model experiments were scaled down by a 1:40 factor.The experiments were conducted to verify the numerical results and to compare the weirs phases and discharges of the linear labyrinth weirs and the curved labyrinth weirs with the linear peak weir.Results indicated that the discharge of the labyrinthine weir is 71% higher than the discharge of the linear peak weir at low reservoir height because the labyrinth has a longer effective length.However, with the increase in the water level, the discharge slope of the labyrinth weir became gentler due to submersion and back interference in the side channel, and lowering the bed height of the side channel became the most effective option (Seo, Do Kim, Park, & Song, 2016).Gupta, Kumar, and Ahmad (2014) investigated the discharge characteristics of a sharp crested contracted triangular planform weir under free flow conditions in a rectangular channel.The efficiency of the triangular planform weirs is found better than the normal weir.Shaghaghian and Sharifi (2015) investigated the characteristics of flow in triangular labyrinth weirs through FLUENT Software.Results showed that numerical model of FLUENT is highly able to simulate flow field in labyrinth weirs.Idrees, Al-Ameri, and Das (2016) investigated 15 physical models that discussion the effect of sidewall angle of labyrinth weir on discharge coefficient of flow over and through the compound trapezoidal one cycle Labyrinth weir.Results showed that the compound coefficient of discharge firstly increases when the head reaches maximum value and then decreases gradually.Akhbari, Zaji, Azimi, and Vafaeifard (2017) identified the effective parameters in the prediction of the discharge coefficient.Then by combining the input parameters, for each of the RBNN and M5' methods, six different models are introduced.The mean absolute percentage error (MAPE) and correlation coefficients (R2) values for the preferred model in the test mode were calculated 2.774 and 0.831, respectively.Results showed that the parameters of the ratio of head over the weir to channel width (h/B) and Froude number (Fr) were the most effective parameters in the prediction of the discharge coefficient.To investigate the energy loss and evaluate the characteristics of the flow downstream of a rectangular labyrinth weir and to establish a relationship between the drop height, discharge, and the amount of wasted energy, laboratory studies were conducted.The physical experiments were used to construct a still basin with various discharge and downstream water levels.Results showed that for the given conditions, a simple concrete apron or a rip fence corresponding to the length of the hydraulic jump is sufficient for managing erosion of the river bed for low downstream water levels.Energy loss occurs in a fixed hydraulic jump depending on the weir.By raising the downstream water level, the hydraulic jump becomes submerged and little energy is wasted.Due to its geometric shape, the labyrinth weir can generally guarantee effective energy dissipation.Norouzi, Daneshfaraz, and Ghaderi (2019) investigated the discharge coefficient of trapezoidal concourse weirs using neural networks and support vector machines.Their research showed that the neural networks predicted the discharge coefficient with an acceptable error and there was a good agreement between the experimental data and the predictions of the vector machine.
Yousif and Karakouzian (2020) investigated the effects of corner shape on the hydraulic performance of rectangular labyrinth weirs.They tested five rectangular meandering vault weirs with five different corner shapes made of high-density polyethylene plastic (HDPE) in a rectangular flume.The results showed that the shape of the corners is an effective factor for rectangular labyrinth weirs.Rounding or beveling the corners can significantly increase the discharge capacity of rectangular labyrinth weirs.However, the rounded corner shape was slightly better than the beveled corner shape.Among all the labyrinth weir models tested in this study, the rectangular labyrinth weir with a semi-circular apex provided the highest hydraulic efficiency, while the model with an acute angle corner shape showed the lowest hydraulic efficiency.Idrees, Al-Ameri, and Das (2022) simulate the flow over the compound labyrinth weir into the critical regions that cannot be observed when using an experimental test.The CFD results demonstrated that the hydraulics behavior of the compound labyrinth weir was similar to the oblique and linear weirs in high discharges.Idrees and Al-Ameri (2022) used the artificial ventilation approach to improve the performance of the compound labyrinth weirs.This study proposes artificial ventilation techniques to mitigate the pressure behind nappe flow and to improve the coefficient of discharge.The results indicated that the pressure distribution behind nappe flow was not similar for all tested points.Also, a slight negative pressure was observed when H′t/P′ was measured between 0.1 and 0.2.Ben Said and Ouamane (2022) conducted an experimental and numerical study to improve the performance of a rectangular labyrinth weir.They conducted experiments and performed numerical modeling using Open FOAM.Their laboratory model was tested with four scenarios, three of which corresponded to rectangular labyrinth weirs with a round inlet and one with a flat inlet.The experiments allowed the effect of the inlet shape and width on the discharge capacity to be elucidated.The results indicate that the round inlet increases the weir efficiency by 5%.In Hussain, Hassan, and Jamel (2022) the hydraulic characteristics of the flow through a triangular labyrinth weir with a sharp crest were studied.Their efficiency was compared with that of rectangular weirs.The experiments were performed in a laboratory flume with 12 models, 9 models of triangular labyrinth weirs, and three models of rectangular weirs with apex angles of 60, 90, and 120 degrees.The results showed that compared to linear weirs, triangular labyrinth weirs are hydraulically more efficient.Also, the weir height, P, has an effect on the discharge coefficient, where (C d ) increased with the decrease of P. Also, the apex angle of the triangular labyrinth weirs, θ, has a major effect on the discharge coefficient and the weir performance.The discharge coefficient increases with the decrease of θ.In other words, when the angle decreases, it increases the discharge coefficient.The discharge reaches its maximum value by increasing the apex angles at 90° and 120° and this leads to an increase in the flow capacity or performance for the weir.Idrees and Al-Ameri (2023a) studied the labyrinth weir to increase the discharge capacity.The data was obtained from the quarter-round crest and different sidewall angles ranging from 8 to 35°.Results showed that the compound discharge coefficient initially increased at low water head ratios and decreased at higher values of water head ratios.Idrees and Al-Ameri (2023b) investigated the energy loss from zigzagging the side wall of congressional weirs.The tests included 16 models with angles of 6-35º and 90º in the side walls.The results showed that the discharge coefficient yielded the highest value for the side-wall angle of 35º and the lowest value for the side-wall angle of 6º.
From this prior research, it is clear that various studies have been conducted in relation to the triangular plan weir discharge coefficient, but the effective of the triangular plan weir lengths on the jet velocity and pressure have not been discussed.Here, the single cycle triangular plan weir with serrated wings to increase the effective length of the weir crest and its effect on the discharge coefficient, velocity profile, flow pattern, pressure, and energy dissipation were investigated using numerical simulation.

Materials and methods
To validate the numerical simulation, the experimental results of Kumar, Ahmad, and Mansoor (2011) are used.The simulation of flow around a triangular plan weir has been performed by using the turbulence equations and solving the equations of the free flow surfaces by the finite volume (VOF) method.This research was carried out in a flume with a length of 12 meters and a width of 0.28 meters with walls 0.41 meters high.The walls and floor were made of mild steel plates with sharp edges.Schematic views of the triangular plan weir and the flow direction are shown in Figure 1.
In Figure 2a, a simple triangular plan weir with a channel length of 2.5 meters, a width of 0.28 meters, a floor thickness of 0.01 meters, a weir thickness of 0.005 meters, weir height of 0.101 meters, and an effective length of the weir crest of 0.56 meters with a vertex angle of 60 degrees is shown.Figure 2b shows the jagged triangular plan weir, which is similar to the simple triangular plan weir in terms of channel length, width, floor thickness, weir thickness, weir height, and also the apex angle.The weir of the toothed triangular plan is shown in three parts based on the number of teeth.Figure 2 shows the triangular plan weir with three teeth on each wing, the length of each tooth is 0.06 meters, its height is 0.03 meters, and the distance between the teeth is 0.05 meters.The crown of this weir is 0.92 meters, which is marked with L a .Figure 2 also shows a triangular plan weir with four teeth 0.04 meters long, 0.03 meters high, and 0.04 meters distance between the teeth.The effective length of the weir crown is 1.04 meters and L b is shown.As a third example, Figure 2 shows a triangular plan weir with five teeth, the length of the first and last teeth are 0.03 meters and the middle teeth are 0.02 meters, the height of the teeth is 0.03 meters, the distance between them is 0.04 meters, and the length of its effective crow (Lc) is 1.16 meters.
Table 1 geometric and hydraulic parameters of flow in simple triangular plan weir, toothed triangular plan weir and triangular plan weir with vertex angles of 60, 90, 120 and 150 degrees and effective length 0.56, 0.396, 0.323 respectively and 0.29 meters, it also shows the weir height of 0.103, 0.106 and 0.108 meters, respectively.

Dimensional analysis
The relation of discharge coefficient for free flow and ejection over a weir is as follows (Tullis, Amanian, & Waldron, 1995): where Q is the flow rate.The effective factors for the weir discharge coefficient of the toothed triangular plan are shown here: where C d is the discharge coefficient (dimensionless), g is gravitational accelerationðLT À 2 Þ, ρ is the density of water (ML −3 ), µ is the dynamic viscosity (ML −1 T −1 ), σ indicates surface tension (MT −2 ), v is the velocity (LT −1 ), w is weir height (L), h is the water depth above the weir crest (L), and B is the channel width and the weir vertex angle θ is (dimensionless).
According to П-Buckingham's theorem, certain parameters were selected as repeated variables and the dimensionless parameters for the triangular plan weir were presented as shown in Equation (3).
Re represents the Reynolds number, which in this research is between 22,436 and 32,142; the flow is turbulent so the effect of this parameter can be ignored (Daneshfaraz et al., 2022a).Considering that the depth of water above the weir is more than 3 cm, the effect of surface tension can be ignored and the effect of Weber's number can also be ignored (Norouzi, Daneshfaraz, & Ghaderi, 2019).Also, Fr represents the Froude number of the serrated triangular plan weir (Salmasi and Norouzi, 2020).In this research, considering that the upstream flow is subcritical and the Froude  number is in the range of 0.17 < Fr 1 <0.13, it can be ignored.Due to the stability of some geometric parameters including w, B, and θ, the effect of dimensionless parameters and θ can be ignored.The final dependent dimensionless parameters are obtained based on independent dimensionless parameters according to Equation (4).
The energy dissipation is calculated from: The effective parameters for energy dissipation in a triangular plan weir are in the form of Equation ( 6): Where: y 1 and y 2 are the water depth in sections 1 and 2, respectively, and E 1 and E 2 are the flow energy in sections 1 and 2 respectively.By using the П-Buckingham theorem and considering (ρ, v, y 1 ) as repeating variables, the relation ( 7) was obtained: By combining and simplifying the dimensionless ratios, the dependent dimensionless parameters can be presented based on the independent dimensionless parameters according to relation (8): E 2 ; ΔE 12 E 1 are respectively, the energy dissipation relative to the downstream and upstream locations, and Fr 1 is the Froude number downstream of the weir.

Definition of the solution network and boundary condition
The optimal mesh using the experimental data of Kumar, Ahmad, and Mansoor (2011) was calculated with a flow rate of 0.0063 m 3 /s.To determine the optimal mesh, simulations were first performed with a large mesh, and then, simulations were performed with progressively smaller meshes until mesh independence was achieved.Therefore, by reducing the cell size, the relative error percentage (RE%) was minimized.According to Table 2, the optimal mesh of 1,859,880 was selected.To check the performance of the model and compare it with the laboratory results, the absolute error percentage (AE%) and relative error percentage (RE%) statistical indicators were used from Equations ( 9) and (10), respectively.
In equation ( 9) and ( 10), H (num) is the flow depth in the numerical solution and H (exp) is the experimental flow depth.Figure 3 shows the mesh.

Choice of turbulence model and definition of boundary conditions
The RNG turbulence model was selected for the simulations.Among the reasons for choosing this type of turbulence model are its accuracy in solving the equations, showing the details of the flow accurately, and adequately dealing with turbulence (Daneshfaraz, Norouzi, & Ebadzadeh, 2022a).
For the boundary conditions, the input flow boundary condition is used for the flow input and the standard outflow boundary condition were used for the downstream boundary.No-slip conditions are enforced at all fluid-wall interfaces and symmetry conditions are used on symmetry planes.In the second mesh block, symmetry is used for the input and output.As mentioned earlier, no-slip conditions are used at all walls, and symmetry conditions are also employed as shown in Figure 4.

Scale effect
Hydraulic models are very useful tools to better understand the hydrodynamic behavior of flow.However, the effects of scale in the hydraulic modeling process led to the deviation of the results from the prototype.The results of the scale difference in the physical models showed that the smaller the scale, the greater the influence of fluid properties such as viscosity and surface tension.Therefore, in order to ignore the effect of viscosity, the Reynolds number in the models was chosen between 22,436 and 32,142.When the liquid is the same and the temperature is constant, in the numerical set-up, R e and W e are dependent on each other, so one of the two must be eliminated; therefore, the effect of the Weber number was ignored.In order to check the effect of scale in the walls as well as possible, the experiments should be repeated for different widths of the flume and the results should be compared with the prototype.This research was conducted in a constant flume width in the laboratory and there was no prototype for this research.Therefore, the effect of scale has not been investigated, so the results can be correct for the flow conditions in this research (

Numerical model validation
This study, a method for the hydraulic design and analyses of triangular plan form weirs is presented.First of all numerical model were validated.After choosing the optimal mesh and turbulence model, the discharge coefficient at different flow rates was compared with the experimental data for calibration.The results are described in Table 3. Table 3 shows the results of the comparison of experimental and numerical discharge coefficient in constant weir vertex angle.Different flow rates were investigated in order to calibrate the numerical model.The results indicate that  there is an acceptable agreement between the numerical and experimental data.
In Figure 5, the discharge coefficient of the numerical solution results is compared with the discharge coefficient from the experiments.By comparing numerical and experimental data, it can be concluded that the ability of numerical solutions in estimating experimental results with a correlation coefficient of 0.9452 is acceptable.
As indicated earlier, a simple triangular plan weir with 60, 90, 120, and 150-degree vertex angles were simulated using Flow-3D software.Increasing the angle of the simple triangular plan weir leads to a decrease in its effective length.Then, by serration of the control mode (triangular plan weir with a 60degree vertex angle) with three, four, or five teeth on each wing, the effective length of the weir crest increased.
In Figure 6, the three-dimensional depiction of the flow with a flow rate of 0.009 m 3 /s, vertex angle of 60 degrees, and free flow is shown for both a simple and a toothed triangular plan with five teeth.By increasing the effective length of the triangular plan weir, the water depth above the weir crest decreases at a constant discharge.

The effect of the effective length of the weir crest on discharge coefficient
In this research, the discharge coefficient for control and toothed weirs with crest lengths L c = 1.16,L b = 1.04,L a = 0.92, and L = 0.56 meters, and for angles of 90, 120, and 150 degrees, crest lengths respectively of 0.396, 0.323 and 0.29 meters have been investigated.For a constant flow rate, increasing the effective length of the weir crest has led to a decrease in the water depth above the weir crest and, as a result, an increase in the discharge coefficient.For example, at a constant flow rate of 0.0063 m 3 /s, the discharge coefficient for a simple triangular plan weir is 0.635, and at the same flow rate with three, four, and five teeth, the discharge coefficients are 0.885, 0.925, and 1.240, respectively, which indicates an increase the discharge coefficient of 39%, 45%, and 95% compared to the simple triangular plan weir.In Figure 7a, the discharge coefficient of the control is compared with the discharge coefficient of the triangular plan weir with different angles.According to Figure 7b and by examining a constant flow rate, it can be seen that as the number of teeth increases, the flow rate increases.Figure 8a shows the discharge coefficient of the triangular plan weir with vertex angles of 60, 90, 120, and 150 degrees.Increasing the angle reduces the effective length of the weir crest and increases the water depth above the weir.According to Figure 8b, increasing the independent dimensionless number h/ w (h is the depth of water above the weir and w is the height of the weir) results in a decrease in the discharge coefficient.The reason for this is that the effective length of the weir crest increases as a result of its serrations.It has been shown that this parameter has an inverse relationship with the water depth above the weir and the decrease in the depth above the weir causes an increase in the discharge coefficient.In the simple triangular plan weir at the flow rate of 0.006 m 3 /s, the ratio h/w = 0.32, and in the triangular plan weir with three, four, and five teeth, this ratio is 0.188, 0.168, and 0.128, respectively.With the increase of flow rate, this ratio also increases, so that at a flow rate of 0.0078 m 3 /s, this ratio is equal to 0.38, 0.24, 0.22, and 0.17 for simple triangular plan weirs and with three, four, and five teeth, respectively.It is clear from Figure 8 that the discharge coefficient has an inverse relationship with the h/w ratio.In a simple triangular plan weir for a flow rate of 0.0063 m 3 /s and for h/w = 0.32, the discharge coefficient has a value of C d = 0.635, in a triangular plan weir.With three, four, and five teeth for the same flow rate, the results are: for h/w = 0.188, C d = 0.88; for h/w = 0.168, C d = 0.92; and for h/w = 0.128, C d = 1.24.
In Figure 9a, the changes in the discharge coefficient for the triangular plan weir with 60, 90, 120, and 150-degree vertex angles and the flow rates ranging from 0.0063 to 0.009 m 3 /s are displayed.Reducing the angle of the weir head increases the length of the crest, so the maximum length of the crest occurs with an angle of 60 degrees.Figure 9b shows the relationship between the discharge coefficient and the ratio of water head to the effective length of the weir crest in the plain and toothed triangular plan weir.In a constant flow, by reducing the effective length of the triangular plan weir crest by reducing the number of its teeth, the discharge coefficient decreases.In other words, with the reduction of the effective length of the weir crest, the dimensionless ratio h/L increases and the discharge coefficient according to the relation (1) has the opposite ratio and decreases with the water depth above the weir.
To investigate the relationship between the water head and flow rate in the triangular plan weirs, the flow rate obtained from the numerical solution was related to the corresponding water head.In Figure 10, the discharge-water head diagram for the triangular plan weir with a vertex angle of 60 degrees and different effective lengths is shown.According to the flowwater head diagram, the water depth increases with the increase of the flow rate.Also, as the effective length increases, the water upstream depth decreases, which means that at a constant flow rate, a lower water depth is needed.

The effect of the effective length of the weir crest on the velocity profile and streamlines
Velocity is one of the important parameters for hydraulic structures because controlling the velocity can reduce damage to the structure.The presence of teeth in the weir crest affects the velocity and their pattern.First, the velocity profile for a simple triangular plan weir with a vertex angle of 60 degrees and a jagged one with the same angle at a flow rate of 0.009 m 3 /s was investigated.Figure 11 shows the velocity of the flow passing over the weir of a simple and toothed triangular plan.As the jet passes over the weir, the average velocity increases, which is shown in the blue color in the figure.At the foot of the weir, due to the collision of the falling current with the bottom of the channel and the change of the direction of some of the flow, eddies are formed which cause a decrease in the speed in that area.The orange color in the figure also represents the flow with low speed.Downstream of the weirs, the flow has left the turbulent state and has also become more uniform.The average speed is shown in green in the figure .For a better comparison of the average velocity in the flow jet and the region of vortex formation at the foot of the weir, Figure 12 is presented.In general, the average speed of the jet flow is higher than the average speed where the vortex is formed.Figure 12a shows the average velocity at the foot of the weir where the highest velocity occurs in the middle of the channel and the lowest velocity occurs near the channel walls.By comparing the average speed of the flow jet, (Figure 12b), it can be seen that the highest velocity is in the middle of the channel width and belongs to the simple triangular plan weir.The average speed of the jet decreases with the increase in the number of teeth and as a result, the effective length of the weir decreases as shown in Figure 12b.
Figure 13 shows the flow pattern for triangular plan weirs.The flow lines in a simple triangular plan weir are compared with a triangular plan weir with five teeth at a flow rate of 0.009 m 3 /s.The streamlines before the weir are parallel and regular, and after passing the weir downstream of the channel, there is no disturbance or break in the lines.
The streamlines on the weir of a simple triangular plan, because there is no roughness in the crest of the weir, can be seen symmetrically in two wings, Figure 13a.
In the serrated triangular plan weir, the presence of the serrations in the wings has caused the flow lines to bifurcate.One part passes between the serrations and the other over the serrations, as seen in Figure 13b.At the foot of both weirs, there are simple and jagged triangular plan return currents which causes the flow lines in that area to exhibit a vortex pattern.Turbulence at the head of the weir is due to the fact that the flow tends to become supercritical as the discharge increases, But there is a subcritical flow upstream, and for this reason, when the flow falls over the weir, a weak hydraulic jump is formed upstream (weir) at the foot of the weir due to the swirling currents that exist.
The rotating currents and the interference of the flow lines in the head above the passing stream downstream of the congress weirs are the limitations of this type of weir, these formed eddies reduce the coefficient of flow in the congress weirs.

The effect of the effective length of the weir crown on the pressure
Figure 14a shows the two-dimensional distribution of pressure in simple and toothed weirs at a flow rate of 0.009 m 3 /s.With increasing distance from the bottom of the channel, the pressure is reduced and at the free surface, the pressure is equal to the atmospheric pressure.At the location of x = 1.148 m, the flow pressure at the bottom of the channel has suddenly increased due to the falling currents.One of the important issues in the design of a weir is to consider the consumption of flow energy in this area to prevent erosion of the channel floor.Negative pressure is created in the return flow toward the body at the foot of the weir.In the flow falling from the top of the weir, the pressure is low due to the interaction of water with air.As shown in Figure 14b, with the increase of the effective length of the weir crest from L to L c respectively, the pressure decreases due to the decrease of the water depth above the weir.Also, in a case of an weir, for example, a simple triangular plan weir, with the increase in flow rate, the depth of the water upstream of the weir increases and this leads to an increase in the pressure on the bottom and the walls of the channel.

The effect of the effective length of the weir crest on energy dissipation
Figure 15a shows the percentage of relative energy consumption in section 1, i.e. the place where the water jet hits, compared to the effective length of the weir crest.Figure 15b shows the percentage of relative energy dissipation in section 2, i.e. the end of the channel, compared to the effective length of the weir crest.The increase in the effective length of the weir crown has increased energy consumption, the reason for this is the collision of the flow jet with the bottom of  the channel.Since the energy of the jet in the weir of the triangular toothed plan decreases by hitting the teeth, the energy consumption is higher in the weir of the triangular toothed plan, which further increases with the impact of the jet flow with the bottom of the channel.The highest energy consumption is related to the triangular plan weir with five teeth and for a flow rate of 0.0063 m 3 /s, which is 27% compared to the upstream and 37% compared to the downstream.
In Figure 16, the depreciation of the weir energy of the triangular plan in simple and toothed weirs are shown for various Froude numbers.According to Figure 16, energy consumption decreases with the increase of the Froude number.The reason for this decrease is that the increase in the Froude number leads to a decrease in depth, and this decrease in depth has caused a decrease in energy consumption compared to the two sections.
According to Figure 16, the greatest energy dissipation is related to the weir of the triangular plan with five teeth.The weir with the largest effective length has the maximum energy dissipation, which is 27% and 37% compared to sections 1 and 2, respectively.

Conclusion
This research has investigated the effect of increasing the effective length of the triangular plan weir crown by serrating its crown, with three crown lengths of 1.16, 1.04, and 0.92 meters and with a fixed vertex angle (60 degrees), as well as reducing its length by increasing the vertex angle.Angles of 90, 120, and 150 degrees were also studied.The impact of the effective length of the weir crown on discharge coefficent, average velocity, streamlines, pressure, and energy dissipation were obtained.The results showed that the increase in the angle of the triangular plan weir led to a decrease in the effective length of the weir crest, which caused an increase in the discharge coefficient.Results indicated that discharge coefficient for a simple triangular plan weir is 0.635, and at the same flow rate with three, four, and five teeth, the discharge coefficients are 0.885, 0.925, and 1.240, respectively, which indicates an increase the discharge coefficient of 39%, 45%, and 95% compared to the simple triangular plan weir.So the highest discharge coefficient for the triangular plan weir occurs with five teeth and is equal to 1.24.This is a 95% increase compared to the simple triangular plan weir.The highest average velocity of the jet flow corresponds to the simple triangular plan weir and the lowest is for the triangular plan weir with five teeth.In the investigation of the pressure between simple and toothed triangular plan weirs, the triangular plan weir with five teeth showed the lowest pressure due to the greater length of the crest and less water upstream of the weir.Also, due to the interaction of water with air, a negative pressure was created in the flow jet and the place of vortex at the foot of the triangular plan weir.The energy dissipation in two sections of the jet and the end of the channel showed that the highest energy dissipation occurs with the triangular plan weir with five teeth, which is 27% compared to the upstream and 37% compared to the downstream.
Future research in this field can be done using the results of this study, such as investigating the changes in the depth of the pool, investigating the flow pattern in the downstream, the effect of the shape of the teeth on the hydraulic parameters.

Highlights
• This study investigated triangular paln weirs hydraulic parameters.• Simulations were done energy dissipation by flow-3D software.
• The length of triangular plan form weir affects the discharge coefficient.

Figure 1 .
Figure 1.Schematic views of the triangular plan weir studied in this research.

Figure 2 .
Figure 2. Schematic view of simple triangular plan weir and triangular plan weir with three, four, and five teeth on the weir edges and their geometrical parameters.

Figure 4 .
Figure 4.The applied boundary conditions of the present study.

Figure 7 .
Figure 7.The relationship between discharge and discharge coefficient for the control and a) simple triangular plan weirs with different angles, b) serrated triangular plan weirs.

Figure 9 .Figure 11 .
Figure 9. Changes in discharge coefficient according to the ratio of head to effective length in a) triangular plan weir with 60, 90, 120, and 150 degrees vertex angle, b) serrated triangular plan weir.

Figure 12 .
Figure 12.The average velocity of the weir of a simple and jagged triangular plan at: the vortex formation area, b) in the jet.

Figure 13 .Figure 14 .Figure 15 .
Figure 13.a) Flow lines in a simple triangular plan weir b) Flow lines in a jagged triangular plan weir.

Figure 16 .
Figure 16.Percentage of relative energy consumption compared to Froud number of section 1 compared to: a) section 1, b) section 2.

Table 1 .
Hydraulic and geometric characteristics of the models.

Table 3 .
Calibration of numerical solution data.