The aim of the current research is to investigate the effect of geometry and different angles (180°, 150°, 120° and 90°) of the edge of a vertical drop with a height of 0.15 m with and without a vertical screen on energy dissipation. The finding showed that the triangulation plane forms a vertical drop at different angles of 180°, 150°, 120° and 90° without a screen that increases the energy dissipation of the drop, which is highest at an angle of 90°, by 50.5%. In the vertical drop with a screen, reducing the angle also leads to a decrease in energy dissipation, so the highest energy dissipation occurs at an angle of 180° with a 45.2% increase in energy dissipation compared to the vertical drop without a screen. The relative depth of the edge and the relative depth of the vertical drop pool of the triangular plane are different at the angle vertex and its wings, in such a way that the relative depth of the edge at the vertex is less than the wings and the relative depth of the pool at the vertex is greater than the wings.

  • This study investigated the hydraulic parameters of a triangular plan forming a vertical drop.

  • The energy dissipation is different at different angles in the triangular plan forming a vertical drop.

  • The length of the edge of the triangular plan forms a vertical drop that affects the energy dissipation.

  • The simultaneous use of the screen affects the hydraulic parameters of the triangular plan that forms a vertical drop.

It is very important to depreciate the kinetic energy of water when the slope in its bed is high, in order to prevent possible damages to the downstream. The vertical drop is one of the structures that dissipate the destructive energy of water and prevents damage. Also, researchers have used additional structures such as screens to increase the energy dissipation (ED) in the vertical drop. Rajaratnam & Hurtig (2000) were the first to use vertical screens to improve ED, they found that the screen with a porosity of 40% had higher ED. These structures are placed perpendicular to the flow and create a hydraulic jump in the flow regime and cause an increase in ED (Abbaszadeh et al. 2024). Rouse (1936) was one of the first to study the drop, using the results obtained from the edge depth measurements. He presented an equation to estimate the discharge, which was later used by Blaisdell (1980) and was corrected by Rajaratnam & Chamani (1995). Rajaratnam & Chamani (1995), Akram Gill (1979) and Chamani et al. (2008) by conducting studies on ED in the vertical drop found that the impact of the falling jet with the bottom of the channel and creating turbulence in the pool are the main factors of ED. Hong et al. (2010) studied the impingement force of the flow jet and the drop length in the presence of a positive slope at the downstream bed of the drop. The result of their research is an equation to estimate the jet force and the length of the drop. Liu et al. (2014) investigated the effect of positive slope upstream of the vertical drop on the hydraulic parameters of the flow, according to the results obtained from their research, the edge depth, pool depth, and falling jet angle decrease due to the presence of the upstream slope. Parsaie & Haghiabi (2019) using the M5 algorithm and Multilayer Perceptron Neural Network (MLPNN), investigated the ability of staircase overflows in terms of ED. Their results showed that, based on the M5 algorithm, Drop and Froude numbers play an important role in ED modeling and approximation. Also, the evaluation of the results of both applied methods showed that the accuracy of MLPNN is slightly lower than the M5 algorithm.

Daneshfaraz et al. (2020) studied the effect on the hydraulic parameters of the flow by placing double horizontal screens on the edge of the vertical drop. Their results showed that the distance between the two screens did not affect the relative depth and downstream residual energy and also the increase in the relative length of the drop resulted in the decrease of the relative depth of the downstream. Parsaie & Haghiabi (2021) experimentally investigated the hydraulic properties of the finite crested stepped spillway (FCSS) including discharge coefficient (Cd) and energy dissipation ratio (EDR). The results showed that Cd in FCSS varies between 0.9 and 1.2, while the ratio of upstream depth to crown length (hup/Lc) varies between 0.25 and 1.8. FCSS performance in relation to EDR varies between 40 and 95%. With the increase in the flow rate and the formation of skimming flow, the performance of FCSS related to ED decreases dramatically.

Daneshfaraz et al. (2021) investigated the effect of a vertical drop at three different heights and a horizontal screen with two porosity ratios on the hydraulic parameters of the flow. According to the results of their experiments, the relative depth of the pool, the relative depth of the downstream and the ED increase in the drop equipped with a horizontal screen. They also found that the use of a horizontal screen in a vertical drop reduces the downstream Froude number and increases the percentage of porosity of the horizontal screen, causing a decrease in the relative mixing length and the wetted relative length of the horizontal screen. Norouzi et al. (2021) investigated the performance of the ability of artificial intelligence methods including ANN, ANFIS, GRNN, SVM, GP, LR, and MLR to predict the relative ED for vertical drops equipped with a horizontal screen. The results showed that the performance of ANFIS_gbellmf is more acceptable than all the models. Daneshfaraz et al. (2022a) experimentally researched the hydraulic parameters of vertical gabion drops with different heights and lengths. The results of their research showed that at a constant relative length, increasing the relative height of the gabion drop causes an increase in the flow through the porous medium and results in an increase in ED. Daneshfaraz et al. (2022b) studied the effect of the screen downstream of the vertical drop at different distances and porosity percentages and investigated its effect on ED. According to their findings, the downstream relative depth, the relative depth of the pool, and the relative ED increase in the drop equipped with a vertical screen compared to the drop without a vertical screen. Haghiabi et al. (2022) studied triangular and trapezoidal overflows with one and two cycles. Their results showed that labyrinth overflows can reduce the flow energy by between 70 and 85%.

Shamsi et al. (2022) have investigated the discharge coefficient (Cd) of cylindrical weirs, its flowability and ED in it. The results showed that in the range of relative height (ratio of flow depth on the crown to weir diameter: H/D) between 0.15 and 2.0, Cd is variable between 1.0 and 1.4. At the same H/D range, such structures can dissipate flow energy between 15 and 80%. The optimum value (Cd) for economic design purposes is about 1.3, which occurs in the H/D range between 0.5 and 0.7.

Parsaie et al. (2023) used the group data processing method (GMDH) to estimate the energy loss of flow passing over labyrinth weirs with triangular and trapezoidal planes. Examining the GMDH network structure shows that ho/P, Ncy and Mr play more significant roles in the development network.

Afaridegan et al. (2023) evaluated and modified the performance of semi-cylindrical weirs (SCWs) considering a downstream ramp. Modified semi-cylindrical weirs (MSCWs) in 12 variations, with four different slopes (θ) and three radii (R) were fabricated and tested through laboratory experiments. The findings show that the discharge coefficient (Cd) of MSCWs is dependent on R (negative correlation) and independent of θ. When the ratio of the depth of upstream flow (yup) to R changes from 0.306 to 1.36, the value of Cd changes in the range of 1.1–1.45. Investigating the bed pressure distribution on MSCW models shows that decreasing θ effectively controls the negative pressure on the crown surface.

Yonesi et al. (2023) investigated the vertical drop equipped with a horizontal screen embedded in the edge in two states of rough and smooth bed, according to their results, at a critical depth of more than 0.3, the length of the drop in the drop equipped with a horizontal screen with a rough bed is more than the drop with a smooth bed.

Reviewing the literature has shown that the vertical drop consumes water energy and the use of screen significantly increases the ED. So far, there has been no research that can be used to increase the ED by changing the geometry of the vertical drop and also using the screen. This research is focused for the first time with the aim of increasing the ED in the vertical drop by creating the edge of the triangular plan.

Experimental setup

Experiments were carried out in a laboratory flume with a rectangular cross-section of 5 m in length, 0.328 m in width and 0.45 m in height with plexiglass walls. The flow was controlled by two pumps, each of which has a capacity of 450 L/min, by two rotameters with a relative error (RE) of ±2% that were installed for each of the pumps to read the flow rate. Also, the water depth was measured by a point gauge with an accuracy of ±1 mm. The vertical drop structure was also made of plexiglass with a height of 0.15 m, the same width as the channel and a length of 1.2 m in simple modes (with an angle of 180°) and angles of 150°, 120° and 90°. The tests were first performed for the drop without an additional structure and creating a hydraulic jump using a slice gate in a certain location of the channel. Then, data collection was done by installing a 0.01-m-thick polyethylene screen with circular openings with a diameter of 0.01 m with a zigzag design and a porosity of 50% vertically at a distance of 1.50 m from the end of the drop. Figure 1 shows the laboratory equipment and the way through which the current passes through the channel, and Figure 2 shows the vertical drop at different angles.
Figure 1

Schematic of an experimental setup.

Figure 1

Schematic of an experimental setup.

Close modal
Figure 2

Vertical drop at the vertex angles of 180°–90°.

Figure 2

Vertical drop at the vertex angles of 180°–90°.

Close modal

Table 1 shows the range of parameters measured in the laboratory for four drops, with an angle of 150°, 180°, 120° and 90°, without screen and with screen.

Table 1

The range of parameters measured in the laboratory

Measured variablesVertical plane drop
θ = 150̊
θ = 120̊
θ = 90̊
Without screenWith screenWithout screenWith screenWithout screenWith screenWithout screenWith screen
Q (L/min) 150–600 150–600 150–750 150–600 150–750 150–600 150–750 150–600 
y0 (m) 0.0213–0.0545 0.0213–0.0545 0.022–0.055 0.022–0.0515 0.0221–0.0532 0.0221–0.0526 0.0235–0.058 0.0235–0.0503 
y1 (m) 0.0055–0.0202 0.0404–0.0906 0.0048–0.0295 0.0406–0.0886 0.0039–0.0385 0.0414–0.09 0.021–0.0452 0.0414–0.0903 
y2 (m) 0.019–0.0768 0.028–0.0603 0.0192–0.0822 0.0285–0.0555 0.0233–0.0798 0.0284–0.0582 0.0252–0.0615 0.0281–0.0588 
Measured variablesVertical plane drop
θ = 150̊
θ = 120̊
θ = 90̊
Without screenWith screenWithout screenWith screenWithout screenWith screenWithout screenWith screen
Q (L/min) 150–600 150–600 150–750 150–600 150–750 150–600 150–750 150–600 
y0 (m) 0.0213–0.0545 0.0213–0.0545 0.022–0.055 0.022–0.0515 0.0221–0.0532 0.0221–0.0526 0.0235–0.058 0.0235–0.0503 
y1 (m) 0.0055–0.0202 0.0404–0.0906 0.0048–0.0295 0.0406–0.0886 0.0039–0.0385 0.0414–0.09 0.021–0.0452 0.0414–0.0903 
y2 (m) 0.019–0.0768 0.028–0.0603 0.0192–0.0822 0.0285–0.0555 0.0233–0.0798 0.0284–0.0582 0.0252–0.0615 0.0281–0.0588 

Calculation of ED

One of the important parameters in the vertical drop is ED. In the current research, ED occurs due to factors such as the presence of a vertical drop, hydraulic jump, and the presence of a vertical screen against the flow. To obtain the ED of the vertical drop, the total energy in the upstream and the specific energy in the downstream (before the jump and screen) is calculated and then subtracted from each other. The equations related to total upstream energy, downstream specific energy, and specific energy after the hydraulic jump and screen are expressed in the order of Equations (1)–(3).
formula
(1)
formula
(2)
formula
(3)
where in Equations (1)–(3), E0, E1 and E2, respectively, represent the upstream total energy, the specific energy downstream of the drop (before the hydraulic jump and the screen) and the specific energy after the hydraulic jump and the screen, and y0, y1 and y2 is the depth in the upstream, the depth in the downstream (before the hydraulic jump and screen) and the depth after the hydraulic jump and screen, also q shows the discharge per unit width. The equation related to the total ED, drop ED is also according to Equations (4) and (5).
formula
(4)
formula
(5)

ΔETotal and ΔEDrop show the total ED and ED of the vertical drop.

Dimensional analysis

To check the ED in the vertical drop with the edge of the triangular plan, without the additional structure, the effective parameters are presented in Equation (6):
formula
(6)
where ρ is the density of the fluid, g is the gravitational acceleration of the earth, μ is the dynamic viscosity of the fluid, Q is the inlet flow rate, h is the height of the drop, θ is the angle of the drop, y0 is the depth upstream of the breakwater, yc is the critical depth, yb is the depth at the edge of the drop, yp is the depth of the drop pool, y1 is the depth downstream and the primary depth of the jump, y2 is the depth downstream and the secondary depth of the jump, E0 is the total energy upstream of the drop, E1 is the specific energy downstream and before the hydraulic jump, E2 is the specific energy downstream the drop and after of the hydraulic jump and ΔETotal represents the total ED.
By using the π–Buckingham theory and considering ρ, g and h as repeated variables, the independent dimensionless parameters are obtained according to Equation (7).
formula
(7)

In relation (7), Re0 is the Reynolds number upstream of the drop, Fr0 is the landing number upstream of the drop, is the relative initial depth, is the relative critical depth, is the relative depth of the edge of the drop, is the relative depth of the pool, is the relative primary depth of the hydraulic jump, is the relative depth of the secondary hydraulic jump, is the energy relative upstream, is the relative energy downstream and before the hydraulic jump, is the relative energy downstream and after the hydraulic jump, is the relative ED and θ represents the angle of the drop edge.

In the present research, considering that the Reynolds number upstream of the drop is in the range of (26,978 < Re0 < 115,296), the flow is turbulent, and as a result, the effect of viscosity is neglected (Daneshfaraz et al. 2021). The upstream Froude number is also in the range of (0.76 < Fr < 0.95), which can be ignored due to the non-change of the flow regime and being in the range of insignificant changes (Bagherzadeh et al. 2022), as a result of the dimensionless parameter dependent on the relative ED, based on independent dimensionless parameters, they are obtained according to Equation (8).
formula
(8)
The effective parameters of the vertical drop equipped with a vertical screen can be seen in Equation (9):
formula
(9)
In this relation, p is the percentage of porosity of the screen, t is the thickness of the screen, d is the distance of the screen from the drop, y1 is the depth downstream and the depth before the screen, y2 is the depth downstream and the depth after the screen, E1 is the specific energy of the water before the screen, E2 shows the specific energy of water after the screen and ΔETotal shows the total ED. Due to the constancy of the thickness, percentage of porosity and the distance of the screen from the drop, their influence can be ignored, according to this Equation (10) is obtained from the theory of π–Buckingham.
formula
(10)
Considering that the Reynolds number (26,978 < Re0 < 115,296) shows the turbulent flow, the effect of viscosity is ignored. Also, because in this experiment, a screen with a type of porosity percentage was used, the effect of p can be ignored. The thickness of the screen also has no effect in the experiments because it is constant (Çakir 2003; Balkış 2004). After simplifying the dimensionless parameters for the drop equipped with a screen according to Equation (11):
formula
(11)

Evaluation criteria

To evaluate the results according to Equations (12)–(14), three criteria, root mean square (RMSE), correlation coefficient (R2) and RE have been used.
formula
(12)
formula
(13)
formula
(14)

In Equations (12)–(14), n parameters show the number of laboratory data, Xexp the laboratory values and Xcal the calculated values for the X parameter.

Energy dissipation

One of the goals of building a vertical drop in the flow path is to deplete the destructive energy of water, which is realized in the vertical drop in the form of a falling jet hitting the bottom of the channel, the formation of a pool at the foot of the drop, and the return currents in it. As can be seen in Figure 3, the downward trend in all research shows the reduction of ED with the increase of the relative critical depth. At the lowest flow rate, due to the small volume of water entering the channel and the falling flow pattern, the intensity of the impact of the flow jet on the bottom of the channel is higher, and as a result, the ED is high compared to higher flow rates. In high flow rates, due to the increase in the volume of water entering the channel, the jet flow hits the pool instead of the bottom of the channel and causes a decrease in ED with the increase in the flow rate. According to Figure 3, the experimental data of the current research is closer to the experimental data of Chamani et al. (2008), which fluctuates around linear regression.
Figure 3

Comparing the results of previous researchers with the results of the present study.

Figure 3

Comparing the results of previous researchers with the results of the present study.

Close modal
Figure 4 shows the ED between sections (0,1) and (0,2) in vertical drops without screen and with screen at the vertex angles of 180°, 150°, 120° and 90° relative to the relative critical depth. Figure 4(a) shows the ED of a vertical drop without a screen, in this figure, as the angle of the drop head decreases, the ED increases, because the angularity of the drop edge has increased the length of its edge. Increasing the length of the drop edge also increases the amount of water passing through the drop edge to reduce the energy of the water by increasing the contact surface and increasing the falling jets. In addition, falling jets at the foot of the drop from the pool, which is another factor of ED. The highest relative ED in Figure 4(a) is related to the angle of 90° and relative critical depth of 0.093–0.845. The increase in ED compared to the simple drop is 50.5%, and this increase in ED compared to the simple drop is very significant. Also, with an increase in the relative critical depth, ED has a downward trend because an increase in the critical depth means an increase in flow rate, and with an increase in flow rate, because the depth of the pool increases, the falling jet in the pool hits the water in the pool instead of the bottom of the channel., less energy is consumed, so that the ratio of the highest and lowest flow rate (for example) at an angle of 150° shows a 68% reduction in ED. In Figure 4(b), the ED in the drop along with the screen can be seen. The reduction of the angle in this diagram results in the reduction of ED. The reason for the decrease in ED is that the jump resulting from the presence of the screen collided with the pool and caused the depth of the pool to increase, and considering that the increase in the depth of the pool causes the falling jets to collide with the water in the pool and in fact the jets with the bottom they do not collide, reducing the angle causes a reduction in ED. In the vertical drop with a screen, the highest ED of the drop is 0.763 in the case of a simple drop and a relative critical depth of 0.114, which is 45.2% higher than the vertical drop without a screen. In Figures 4(c) and 4(d) it is shown the total ED in the vertical drop without screen and with screen between two sections (0,2), where the reduction of ED decreases with the decrease of the viewing angle. Decreasing the angle of the drop increases the downstream depth and this factor reduces ED according to Equation (15). The total ED in the drop without a screen in the simple drop mode and relative critical depth of 0.11 has the highest value of 0.847, and in the drop with the screen, the total ED in the simple drop mode and the relative critical depth of 0.11 has the highest value of 0.821.
formula
(15)
Figure 4

ED in the triangular plan forms a vertical drop.

Figure 4

ED in the triangular plan forms a vertical drop.

Close modal

The relative depth of the drop edge

Considering that changes have been made in the edge of the vertical drop of the triangular plan, its investigation is of great importance in terms of the distribution of depth in different points of the channel width and identifying the areas subject to erosion. Figure 5 shows the relative depth of the edge of the vertical drop at angles of 180°–90°, which is different due to the angularity of the edge of this depth at the vertex and wings. In general, the relative depth of the edge increases with the increase of the relative critical depth. Also, according to Figure 5(a), the relative depth of the edge at the angle vertex decreases with the decrease of the angle, so that the maximum relative depth of the edge at the vertex of the angle corresponds to an angle of 180°, the relative critical depth is 0.272 and 0.226, which has a greater relative depth than other angles. Figure 5(b) also shows the relative depth of the edge in the wings, where the relative depth of the edge at angles of 150°, 120° and 90° is slightly higher than the relative depth of the edge at 180°. The maximum relative depth of the edge in the wings is also at an angle of 150°, the relative critical depth is 0.25 and 0.23, which is 10.14% more than the simple drop. The reason for the depth of the edge at the wings compared to the vertex is that the flow passing over the vertical drop of the triangular plan immediately falls from it upon reaching the wings of the angle, and there is less water left for the vertex of the angle to pass, so most of the volume of water is concentrated at the wings.
Figure 5

The relative depth of the edge of the drop in (a) the vertex of the angle and (b) the wings.

Figure 5

The relative depth of the edge of the drop in (a) the vertex of the angle and (b) the wings.

Close modal
Figure 6 compares the relative depth of the edge of the vertical drop of the triangular plan in the wing and vertex with the case without angle. As can be seen, decreasing the angle causes the relative depth of the edge to be gradually separated and different at the wing and vertex of the angle. The relative depth at the wings is more and at the vertex of the angle is lower than the relative depth of the edge in the vertical drop without angle, and the decrease in the angle causes an increase in the depth at the wing and a decrease in the depth at the vertex.
Figure 6

Comparison of the relative depth of the edge at the wing and vertex of the angle in the case without the angle of the vertical drop.

Figure 6

Comparison of the relative depth of the edge at the wing and vertex of the angle in the case without the angle of the vertical drop.

Close modal

Relative depth of the pool

Increasing or decreasing the relative depth of the pool has a great impact on the amount of ED and is also very important from an economic point of view. The depth measurement of the vertical drop pool of the triangular plan showed that due to the triangular nature of the edge, the depth is different at the wing and the vertex of the angle, this issue was also raised in the depth measurement of the drop edge. Figure 7 compares the relative depth of the pool at the vertex and wing of the drop angle with a simple drop. Figure 7(a) shows that with the decrease of the angle of the drop, the relative depth of the pool at the foot of the vertex gradually increases, so that the maximum depth of the pool corresponding to the angle of 90° at the relative critical depth of 0.236, is 0.61. It is 0.47% which is 11.47% higher than the simple vertical drop. Figure 6(b) also shows the depth of the edge on the wings of the drop. It can be seen in Figure 7(b) that the relative depth of the pool in the drop of the triangular plan at the foot of the wings is very close to the relative depth of the pool in the simple drop and has not changed much.
Figure 7

The relative depth of the pool in the vertical slope of the triangular plan.

Figure 7

The relative depth of the pool in the vertical slope of the triangular plan.

Close modal

Figure 7(c) is a comparison of the relative depth of the pool between the present research and the research of researchers such as Rajaratnam & Chamani (1995), Chamani et al. (2008) and Moore (1943), according to Figure 7(c), the present study has the process of the previous researchers.

Figure 8 shows the relative depth of the pool in the vertical drop of the triangular plan combined with the vertical screen at a distance of 1.5 m from the drop. Figure 8(a) shows the relative depth of the pool at the vertex of the drop, in which the relative depth of the pool at the vertex has gradually increased with the decrease of the angle of the vertex, and this increase is at an angle of 90°and the relative critical depth is 0.11 by 33.3% was more than a simple drop. Figure 8(b) also shows the relative depth of the pool at the wing of the drop, in Figure 8 the decrease in the vertex angle results in an increase in the relative depth of the pool. This issue is caused by the fact that the jump from the screen occurred at the foot of the drop. Figure 9 is given for a better comparison of the relative depth of the pool in the case of a drop without a screen and with a screen. As can be seen, the relative depth of the pool at the vertex of the angle in all angles in the drop with the screen is greater than the drop without a screen, also the conditions of the pool at the wings also have the trend of the angle vertex, that is, it is more in the drop with the screen. This issue is also caused by the fact that the jump from the screen occurred at the foot of the drop, and the impact of the jump on the pool caused its depth to increase.
Figure 8

The relative depth of the pool in the triangular plan that forms a vertical drop in the presence of a screen at a distance of 1.5 m from the vertical drop.

Figure 8

The relative depth of the pool in the triangular plan that forms a vertical drop in the presence of a screen at a distance of 1.5 m from the vertical drop.

Close modal
Figure 9

Comparison of the relative depth of the pool in the drop with and without the screen.

Figure 9

Comparison of the relative depth of the pool in the drop with and without the screen.

Close modal

Relative depth of the downstream

Figure 10 shows the relative depth of the downstream in the triangular plan from vertical drop in the state without screen and with screen. According to Figure 10(a) which shows the diagram of the relative depth downstream in the case of a drop without the screen, the maximum relative depth of downstream at an angle of 120° and the relative critical depth of 0.246 is 3.7% more than the simple vertical drop. Figure 10(b) also shows the vertical drop of a triangular plan with a screen, as can be seen, the decrease in the angle of the drop head leads to an increase in the relative depth of the downstream. The maximum relative depth downstream at the angle of 90° and the relative critical depth of 0.206 is 5.1% more than the simple vertical drop.
Figure 10

The relative depth of the downstream in the triangular plan forming a vertical drop.

Figure 10

The relative depth of the downstream in the triangular plan forming a vertical drop.

Close modal
Figure 11 compares the relative depth downstream of the simple vertical drop and the triangular plan in the presence and without the presence of the screen, as it can be seen that the relative depth downstream in the presence of the screen is more than the case without the screen. The relative depth of the downstream in the simple vertical drop without screen is between 0.126 and 0.341, while the relative depth of the downstream in the simple vertical drop with screen is between 0.187 and 0.326.
Figure 11

Comparison of the relative depth of the downstream in the triangular plan forming a vertical drop with and without the screen.

Figure 11

Comparison of the relative depth of the downstream in the triangular plan forming a vertical drop with and without the screen.

Close modal

Increasing the ED in the areas with greater slope has been considered, for this purpose, the change in the geometry of the drop combined with the hydraulic jump, as well as the use of the screen in the downstream, has been to achieve this goal. Changing the geometry of the edge of the drop and its triangular plan at angles of 150°, 120° and 90° has increased the ED of the drop compared to the simple drop, in such a way that ED has increased with the decrease of the angle. The highest ED occurred in the drop with a 90-degree angle with an increase of 50.5% in the relative critical depth of 0.093. By examining the total ED, it can be seen that in both cases of drop with screen and without screen, the total ED decreases with the decrease of the angle. The reason for this is the increase in the downstream depth due to the triangular plan of the drop edge, because the decrease in the angle leads to an increase in the length of the edge, as a result, an increase in the volume of passing water. Finally, the triangular plan forms a vertical drop with a vertex angle of 90°, with the highest ED of the drop, which is the most favorable mode of the vertical drop for ED. According to the present research, the relative depth of the edge of the drop is different at the vertex of the angle and its wings, so that it is less at the vertex of the angle than at the wings and also less than the depth of the edge in the simple drop. Also, the relative depth of the edge of the drop at the vertex of the angle has decreased with the decrease of the angle of the drop, and it has also increased slightly at the wings compared to the simple drop. The relative depth of the pool is also different due to the triangular plan of the drop at the vertex of the angle and its wings, and on the contrary, the relative depth at the edge is more at the vertex than at the wings. The relative depth of the pool at the vertex of the angle increases with the decrease of the angle, and at a 90-degree angle, it is 11.47% more than the simple drop, while at the wings, the decrease of the angle does not have much effect on the relative depth of the pool. The relative depth downstream of the vertical drop without a screen at an angle of 120° has increased by 3.7% compared to the simple drop, and in the vertical drop with a screen, the relative depth downstream has increased with the decrease of the angle, and the maximum relative depth of the downstream at the angle of 90° and happens with an increase of 5.1% compared to the simple vertical drop. In future research, it is possible to study different types of drop edge geometry (trapezoidal, semicircular and congressional), and simultaneously with the change of the drop edge geometry, the effect of the presence of a slope in the bottom of the channel on the hydraulic parameters can be investigated. Investigating the effect of the supercritical flow upstream of the drop on the hydraulic parameters of the flow in the triangular plan form vertical drop is one of the other studies that can be done.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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