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Flow measurement and water level control in open channels are vital to water management. Lateral intake structures are commonly used for different purposes in civil and environmental engineering applications. Flow characteristics of rectangular, triangular, and semi-circular shapes were experimentally investigated using 357 runs under subcritical flow conditions. Correlation analysis was conducted to determine the effect of various parameters on the discharge coefficient. Upstream Froude number (F1), the ratio of the gate opening to the upstream flow depth, and the gate length to flow depth ratio are influential for all side gates. However, the ratio of the gate opening to the gate length is also influential for triangular side gates. Discharge coefficient of the semi-circular side gate is relatively higher than that of the other tested gates within the range of 0.05<F1<0.40; the discharge coefficient of the triangular side gate is relatively higher than that of the other shaped gates for 0.40<F1<0.98 and the efficiency of the triangular side gate decreases more than that of the other gates as the downstream Froude number value increases. A reliable equation for side gates was developed. Good agreements were obtained between the proposed equations and the experimental data.

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  • Discharge performance of side sluice gates was investigated for different types with the same cross-sectional area in lateral flows in detail.

  • Side sluice gate flow in a straight channel was experimentally investigated using different shapes with the same cross-sectional area for different Froude numbers and different flow depths under free flow conditions and a subcritical flow regime.

correlation test, discharge coefficient, gate, lateral flow, open channel
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a

gate opening length (L)

α

kinetic energy correction coefficient (M0L0T0)

b

gate and weir length (L)

B

main channel width (L)

Cd

discharge coefficient (M0L0T0)

Δhs

friction loss (L)

E1

specific height at the upstream (L)

E2

specific height at the downstream (L)

F1

upstream Froude number (M0L0T0)

F2

downstream Froude number (M0L0T0)

g

acceleration due to gravity (L T−2)

K

correction factor for side gate shape

η

discharge efficiency (M0L0T0)

S0

channel slope (M0L0T0)

Sf

friction slope (M0L0T0)

μ

dynamic viscosity (M1L−1T−1)

ρ

mass density of water (M L−3)

Q

discharge (L3/T−1)

q

unit discharge (L2T−1)

Qg

side gate discharge (L3T−1)

Q1

main channel discharge (L3T−1)

Q2

downstream discharge of main channel (L3 T−1)

Re

Reynolds number (M0L0T0)

σ

surface tension (M1T−2)

V1

upstream flow velocity (L T−1)

We

Weber number (M0L0T0)

y1

upstream flow depth (L)

y2

downstream flow depth (L)

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The control and regulation of water date back to the beginning of human history, and efforts to manage it have significantly influenced the development of great civilizations. Efficiently using, evaluating, and operating water resources and simultaneously minimizing the risks associated with existing hydraulic facilities are vital for sustaining life, particularly human life. In the early 20th century, there was an increase in studies focused on the development of water resources hydraulic structures. Consequently, many hydraulic structures, such as dams, weirs, river regulation structures, and open channels, have made a significant contribution to the development of societies. However, it is also necessary to control water structures with appropriate methods and to ensure the safety of these hydraulic structures. To build reliable structures, it is essential to base designs on reliable experimental data. In lateral flows, the flow rate of the main channel gradually decreases as water is discharged from the main channel along the length of the side weir or gate. Lateral flows are classified as spatially varied flows with a decreasing discharge. In other words, ∂Q/∂x ≠ 0 indicates a non-uniform flow condition. Gates have long been used in open channel flows as both control structures and flow measurement devices (Henderson 1966). Side gates are widely used for various applications, including distributing water from the source to irrigated areas (Vatankhah & Mirnia 2018), serving as head regulators for canals, branches, and silt flushing in power canal forebays (Swamee et al. 1993), regulating the head of distributaries (Esmailzadeh et al. 2015), controlling and regulating flow in irrigation systems (Jamei et al. 2021), and managing flow in farmlands, urban wastewater treatment plants, and drainage networks (Azimi et al. 2017).

The literature contains numerous studies on sluice gate flow in open channels. However, research on gate flow in open channels has focused more on frontal flows than on lateral flows. A side gate, in the context of lateral flow, is a sluice gate and flow-measuring structure placed on the side of the channel that allows a portion of the flow to be diverted. A side gate is an opening in the side of a channel that facilitates a lateral discharge into a side channel (Swamee et al. 1993). The flow through a side gate represents a typical case of spatially varied flow with a decreasing flow rate (Figure 1). Despite the importance of side gates in hydraulic engineering, research on the flow characteristics of these structures remains limited in the literature. Side gates serve as essential hydraulic structures in various applications, including irrigation, land drainage, urban sewerage systems, combined sewer systems, flood relief, and distribution networks.
Figure 1
Sketch of gate flow in a rectangular channel: (a) plan view, (b) frontal view of different shapes of side gates.
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Sketch of gate flow in a rectangular channel: (a) plan view, (b) frontal view of different shapes of side gates.

Figure 1
Sketch of gate flow in a rectangular channel: (a) plan view, (b) frontal view of different shapes of side gates.
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Sketch of gate flow in a rectangular channel: (a) plan view, (b) frontal view of different shapes of side gates.

Close modal
Panda (1981) investigated the characteristics of the flow under side gates for both free and submerged flow conditions. Using the De Marchi approach, the researcher determined the discharge coefficient of the side gates. Panda (1981) concluded that the discharge coefficient decreases with an increasing Froude number. The author proposed Equation (1) to obtain the rectangular side gate discharge coefficient for flow conditions, where 0.06 < F1 < 0.40.
(1)
where Cd is the discharge coefficient (-) and F1 is the upstream Froude number.

Gill (1987) conducted a theoretical analysis of lateral flow through side orifices. The researcher neglected both friction losses along the length of the side orifice in the main channel and the main channel's slope, considering both free surface and pressure flow conditions. Simple mathematical solutions were obtained for nearly frictionless flows and near-horizontal channels. It is noted that these simplifications are valid for orifices with relatively short lengths.

Vatankhah & Mirnia (2018) experimentally and analytically investigated flow through the lateral equilateral triangular orifice in open channels under free-flow conditions. Hussain et al. (2011) conducted experiments on side orifices with different side lengths and varying crest heights under free-flow conditions. During the experiments, they observed that when the water height above the orifice was relatively small, or the velocity in the main channel was low, a vortex formed in the main channel in the vicinity of the orifice. However, they did not conduct further investigations under these conditions. Downstream of the orifice, they observed a slight decrease in the water level in the main channel for all experimental runs, but the specific energy in the main channel remained constant.

Swamee et al. (1993) reported that the discharge coefficient can be obtained by taking the differential of a small cross-section of the gate length to calculate the discharge of the side gate. The discharge coefficient of the side gate for free-flow conditions was found to be a function of the ratio of the flow depth in the channel to the gate opening, similar to that observed in frontal flow. They also stated that under submerged flow conditions, the discharge coefficient depends on the ratio of the tailwater depth to the gate opening. For a broad-crested side gate, they stated that the discharge coefficient also depends on the plate thickness ratio to the gate opening. Swamee et al. (1993) proposed the following equation to calculate the discharge coefficient of rectangular side gates.
(2)
where a is the height of the gate (m) and y is the flow depth (m).
Ojha & Subbaiah (1997) studied the side orifice flow. Their analysis was formulated using assumptions for both small and large orifice lengths. Ghodsian (2003) conducted an experimental study to investigate the hydraulic properties of side gates. The author also used the De Marchi approach to determine the discharge coefficients of these side gates. As a result of the study, it was found that the specific energy remained constant along the side gates. Ghodsian reported that the discharge coefficient of the side gate depends on the Froude number in the main channel and the ratio of flow depth to gate opening under free-flow conditions. Ghodsian (2003) proposed the following equation for side gates under free-flow conditions.
(3)
in which y1 is the upstream flow depth (m).

Kianmehr et al. (2020) investigated a sharp-edged rectangular side gate's water surface profile and flow characteristics under free and submerged flow conditions in a subcritical flow regime. This study also presents some approaches to distinguish between free or submerged flow conditions. For this purpose, two approaches to solving the flow equation through the side gate were used. The direct solution of the discharge equation and the gradually varying flow of the side gates were experimentally investigated to determine the flow characteristics of the side gates in a subcritical flow regime.

The researchers also proposed Equation (4) for free-flow conditions.
(4)
Kartal & Emiroglu (2022) experimentally investigated the hydraulic characteristics of combined side weir-gate structures. They used the De Marchi approach to obtain the rectangular side gate discharge coefficient. The authors proposed the following equation for predicting a rectangular side gate.
(5)
where B is the main channel depth and b is the width of the gate (m).

Furthermore, Kartal & Emiroglu (2022) investigated the hydraulic characteristics of combined weir-gate structures by experimentally investigating rectangular side gates and presented nonlinear equations to determine the combined flow rate.

The use of side sluice gates for lateral flows is very limited in the literature. These studies were generally conducted for side orifices. In the literature, triangular and semi-circular shapes are used for side orifice. The same is not valid for the side sluice gates. The current study presents comprehensive experimental runs for the side sluice gate flows with different geometric shapes, the same cross-sectional area for different Froude numbers, and flow depths under subcritical and free flow conditions. This study aims to contribute to hydraulic engineering by examining the hydraulic characteristics of side gates with the same cross-sectional area in lateral flows in detail. This study investigated the effect of flow characteristics and gate geometric shape on discharge capacity with a wide range of experiments for rectangular, triangular, and semi-circular side gates. The results obtained are aimed to contribute to the limited literature on the topic and fill the gaps in the related field.

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The experimental study was carried out at the Hydraulic Laboratory of Firat University, Türkiye. Experiments were conducted in a rectangular channel (Figure 2). The present study evaluated the discharge capacity of side sluice gates and flow characteristics. Dimensional analysis was performed for rectangular, triangular, and semi-circular side gates. Thus, the dimensionless parameters were determined using the Buckingham-Pi theorem. The experimental setup has a pumping station with a recirculation system, which supplies a horizontal rectangular main channel with a length of 12 m, width of 0.40 m, and depth of 0.50 m. The schematic views of the experimental setup are shown in Figure 2. The present experimental setup consists of a main channel and a collection channel. In the present study, 357 experimental runs were conducted for different geometric shapes of the side sluice gates with the same cross-sectional area in the range 0.307 ≤ b/B ≤ 0.75 under free and subcritical flow conditions. To test the gates in lateral flow, eight cross-sectional areas (i.e., 0.06, 0.075, 0.08, 0.09, 0.010, 0.012, 0.0125, and 0.015 m2) and three geometric shapes (i.e., rectangular, triangular, and semi-circular) were used in the study. As mentioned above, their cross-sectional areas were taken equally.
Figure 2
Experimental setup.
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Experimental setup.
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Experimental setup.

The flow discharge was measured using an electromagnetic flowmeter (Krohne brand, ± 0.01 L/s accuracy). The depth of the flow was measured by the digital limnimeter (Mitutoyo brand name, ± 0.1 mm accuracy) placed in the gauge car (see Figure 2). At the end of the main channel and the collection channel, there is a 90° V-notch weir. A V-notch weir was placed in both the main channel and the collection channel. A V-notch weir was used to verify the value of the discharge. The flow in the main channel was a subcritical flow regime (0.08 ≤ F1 ≤ 0.97). In each experimental run, the upstream flow rate at the main channel (Q1) and the discharge of the side gate (Qg) were determined by measuring the piezometric head over the 90° V-notch weir at the end of the collection channel. Flow depths at the upstream and downstream sections of the side gate in the main channel were measured to analyze the discharge coefficient.

De Marchi approach for side gates

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The side gate flow is a spatially varied flow with decreasing discharge across the direction of flow. Therefore, the side gate flow is conducted by a spatially varied flow equation. The general spatially varied flow equation (see Figure 1) was written in the following equation (Chow 1959):
(6)
in which Sf is the slope of friction (-); x is the distance along the side gate from upstream to downstream (m); S0 is the slope of the main channel, Q is the discharge of the main channel (m3/s); α is the kinetic energy correction coefficient (-); dQ/dx represents the unit discharge (m3/s/m); A is the cross-sectional area of flow (m2); g is the acceleration due to gravity (m/s2); B is the width of the main channel (m).
Assuming the coefficient of kinetic energy correction as unity and ignoring friction losses (Sf = 0) for a horizontal (S0 = 0), Equation (6) is reduced as:
(7)
in which; y is the flow depth (m).
Swamee et al. (1993), Ojha & Subbaiah (1997), and Ghodsian (2003) gave the unit discharge for gate flow in lateral flows as follows:
(8)
in which Cd is the discharge coefficient of the gate, a is the opening of the gate (m).
By assuming that specific energy (E) is constant along the length of the side gate, the discharge at any section is (Chow 1959):
(9)
Substituting Equations (8) and (9) into Equation (7):
(10)
Equation (10) becomes (Panda 1981; Ghodsian 2003) integrating between the limits x = 0 and x=b (1 and 2 sections) in Figure 1:
(11)
where ϕ is the varied flow function similar to the De Marchi function, given as (Panda 1981; Ghodsian 2003), and b is the distance between 1 and 2 sections (Figure 1):
(12)
Equations (11) and (12) are combined [3, 8]:
(13)

Subscripts 1 and 2 refer to upstream and downstream sections, respectively.

The functional relationship between the discharge coefficient of a side gate (Cd) and the effective variables expected to influence it can be written as follows:
(14)
in which K is the correction factor for side gate shape (K = 1 for rectangular, K = 2 for triangular, and K = 3 for semi-circular gate), a is gate opening (m); b is the length of the side gate (m); V1 is the upstream flow velocity of the main channel (m); B is the width of the main channel (m); ρ is the mass density of water (kg/m3); y1 is the upstream flow depth of the main channel (m); σ is the surface tension (kg/s2); μ is the dynamic viscosity of water (kg/m s); S0 is the slope of the main channel (-).
The dimensionless parameters obtained from the dimensional analysis of the discharge coefficient of the gates in lateral flow can be written as follows:
(15)
where We, Re, and F1 are Weber number, Reynolds number, and upstream Froude number of the side gate, respectively. S0 was neglected since the main channel slope is constant (Henderson 1966). Similarly, We and Re numbers were ignored due to the limited effect on the flow through the side gate. If the neglected variables are removed, the parameters affecting the discharge coefficient of the gate in the lateral flows can be written as follows:
(16)

De Marchi's approach was used to obtain the flow coefficient for the side gates. The physical and hydraulic conditions of the experiments are shown in Table 1.

Table 1

The physical and hydraulic conditions of the experiments

ParametersValue(s)
Main channel Width, B (m) 0.40 
Height, z (m) 0.50 
Slope, (-) 0.001 
Rectangular side gate Length, b (m) 0.20–0.25, 0.30 
Opening, a (m) 0.03, 0.04, 0.05 
Cross-sectional area 0.06–0.015 
Triangular side gate Length, b (m) 0.20–0.25, 0.30 
Opening, a (m) 0.06, 0.08, 0.10 
Cross-sectional area 0.06–0.015 
Semi-circular side gate Length, b = D (m) 0.12361, 0.1382, 0.14273, 0.15139, 0.15958, 0.17481, 0.17841, 0.19544 
Cross-sectional area 0.06–0.015 
ParametersValue(s)
Main channel Width, B (m) 0.40 
Height, z (m) 0.50 
Slope, (-) 0.001 
Rectangular side gate Length, b (m) 0.20–0.25, 0.30 
Opening, a (m) 0.03, 0.04, 0.05 
Cross-sectional area 0.06–0.015 
Triangular side gate Length, b (m) 0.20–0.25, 0.30 
Opening, a (m) 0.06, 0.08, 0.10 
Cross-sectional area 0.06–0.015 
Semi-circular side gate Length, b = D (m) 0.12361, 0.1382, 0.14273, 0.15139, 0.15958, 0.17481, 0.17841, 0.19544 
Cross-sectional area 0.06–0.015 
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Rectangular side gate

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In the present study, the problem under study was analyzed using the effective dimensionless parameters obtained in the dimensional analysis. The De Marchi approach, available in the literature, was used to obtain the discharge coefficient for lateral gates (Panda 1981; Ghodsian 2003; Kartal & Emiroglu 2022).

Figure 3 shows the variation of upstream and downstream specific energy of different gates (⁠⁠) with the same cross-sectional area in a straight channel under the subcritical flow regime and free-flow conditions. As shown in Figure 3, it is seen that the specific energy at the upstream and downstream are almost equal to each other and perfectly correlated (⁠⁠). Therefore, it was observed that the assumption of the De Marchi approach used to obtain the gate discharge coefficient, that the specific energy is constant along the main channel, is correct. Borghei et al. (1999) and Emiroglu et al. (2014) estimated a 3.7% for rectangular side weir and 1% for trapezoidal labyrinth side weir, respectively. Ghodsian (2003) reported that the average energy difference between upstream and downstream sections is 1.13% for free-flow conditions. The average difference between E1 and E2 is about 2.8% in the present study. Hence, the assumption of constant specific energy was taken into account for further analysis. As a result, the fact that the specific energy upstream and downstream are almost equal to each other shows that the De Marchi approach can be safely used for lateral gates (⁠⁠).
Figure 3
The variation of upstream and downstream specific energy of different gates with the same cross-sectional area: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.
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The variation of upstream and downstream specific energy of different gates with the same cross-sectional area: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.

Figure 3
The variation of upstream and downstream specific energy of different gates with the same cross-sectional area: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.
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The variation of upstream and downstream specific energy of different gates with the same cross-sectional area: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.

Close modal

Table 2 shows the statistical values of the relationship between upstream and downstream specific energy. Mean absolute error (MAE), root mean squared error (RMSE), coefficient of determination (R²), and mean absolute percentage error (MAPE) were used to assess the differences between upstream and downstream specific energy. As shown in Table 2, all error values are acceptable values.

Table 2

The statistical evaluation of the relationship between upstream and downstream specific energy

ParameterSemi-circular gateTriangular gateRectangular gate
R² 0.993 0.995 0.980 
MSE 0.00001 0.00001 0.000011 
RMSE 0.004 0.002 0.003 
MAPE 1.958 1.027 1.916 
ParameterSemi-circular gateTriangular gateRectangular gate
R² 0.993 0.995 0.980 
MSE 0.00001 0.00001 0.000011 
RMSE 0.004 0.002 0.003 
MAPE 1.958 1.027 1.916 
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Figure 4 shows the lateral gate discharge coefficient variation with upstream Froude number for different geometries and shapes with the same cross-sectional area. As seen in Figure 4, the gate discharge coefficient decreases with the increase in the upstream Froude number. In other words, the change between Cd and the upstream Froude number is a function of y=ax2+bx+c. Although the coefficients a, b, and c in the equation y=ax2+bx+c vary for different geometries, in all cases, the coefficients a and b take negative values, and therefore, Cd behaves as a decreasing function of the upstream Froude number. Consequently, decreasing the flow velocity or increasing the flow depth increases the Cd value. As a result of the increase in the flow depth behind the gate, the velocity of the flow passing under the gate increases; therefore, the amount of water discharged is higher. At the same time, with the decrease in the flow depth behind the gate, the amount of water discharged decreases and with the increase in the upstream Froude number, deviations in the jet trajectory of the under-gate flow begin to occur.
Figure 4
The variation of discharge coefficient with upstream Froude number for different shapes with the same cross-sectional area: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.
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The variation of discharge coefficient with upstream Froude number for different shapes with the same cross-sectional area: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.

Figure 4
The variation of discharge coefficient with upstream Froude number for different shapes with the same cross-sectional area: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.
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The variation of discharge coefficient with upstream Froude number for different shapes with the same cross-sectional area: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.

Close modal
Figure 5 shows the lateral gate discharge coefficient variation with y1/a for different geometry and hydraulic conditions. As shown in Figure 5, it is seen that significant discharge coefficients are obtained at large y1/a values. As the upstream flow depth increases, the total load behind the gate increases, and therefore, the velocity of the flow discharging from the under-gate flow increases. At large values of y1/a, more flow is discharged, and the discharge coefficient also increases.
Figure 5
The variation of Cd with y1/a: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.
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The variation of Cd with y1/a: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.

Figure 5
The variation of Cd with y1/a: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.
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The variation of Cd with y1/a: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.

Close modal
Figure 6 compares the discharge coefficients obtained in the present study for rectangular, triangular, and semi-circular gates with the same cross-sectional area and the discharge coefficients obtained from the equations proposed by researchers in the literature. The present study was compared with the studies of Panda (1981), Ghodsian (2003), Kianmehr et al. (2020), and Kartal & Emiroglu (2022). Compared with the present study, all the studies were conducted for rectangular side gates. In this study, in addition to the rectangular side gate, experiments were also carried out for triangular and semi-circular gates with the same cross-sectional areas, unlike the literature. Kianmehr et al. (2020) investigated the lateral gate discharge coefficient under 056 ≤ F1 ≤ 0.32.
Figure 6
The comparison of the present study and literature.
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The comparison of the present study and literature.

Figure 6
The comparison of the present study and literature.
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The comparison of the present study and literature.

Close modal

Similarly, Panda (1981) stated that the proposed equation is valid for 0.06 < F1 < 0.40 conditions. Panda (1981), Ghodsian (2003), and Kartal & Emiroglu (2022) used the De Marchi approach, which is also used in the present study, to obtain the lateral gate discharge coefficient. It should be noted that the dimensionless parameters b/y1 and b/B obtained from the dimensional analysis are not considered in the proposed equations, or a single gate width is used in the a/y1 and b/B on the lateral gate discharge coefficient was also investigated by using different gate widths. Kartal & Emiroglu (2022) conducted a study for 0 < F1 < 1 and 0.10 ≤ b/B ≤ 0.40 and rectangular side gates. In the present study, experiments were conducted for different a/y1 (0.15–1.75) and b/B (0.309–0.75) ranges. When the graph is analyzed, it is seen that the coefficient of flow decreases with increasing upstream Froude number in accordance with the literature. It is seen that the present study is in full agreement with the study of Kartal & Emiroglu (2022). The difference in this changing trend may be a result of the geometric and hydraulic conditions of the present study, or the use of different gate shapes, or the effect of the secondary current occurring at large b/B values. As seen in Table 4, the present study was conducted in different b/B and a/b values compared with the literature.

Correlation analysis was conducted for rectangular, triangular, and semi-circular gates and all data at a 95% confidence interval. As a result, the bold values in Table 3 show significant correlation coefficients at the 95% confidence interval. It was determined that the upstream Froude number, the ratio of the gate opening to the upstream flow depth, and the gate length to flow depth ratio are effective for all side gates. Still, the ratio of the gate opening to the gate length is also effective for triangular side gates.

Table 3

Correlation results

(a) Correlation matrix for all data
VariablesCdTypeF1b/y1a/y1b/ab/B
Cd 1       
Type 0.134 1      
F1 − 0.937 −0.057 1     
b/y1 − 0.455 − 0.607 0.533 1    
a/y1 − 0.344 0.608 0.482 0.017 1   
b/a −0.087 − 0.909 0.037 0.681 − 0.668 1  
b/B −0.002 − 0.669 0.051 0.789 − 0.235 0.751 1 
(b) Rectangular side gates
 
Variables Cd F1 b/y1 a/y1 b/a b/B  
Cd 1       
F1 − 0.958 1      
b/y1 − 0.467 0.579 1     
a/y1 − 0.531 0.584 0.469 1    
b/a 0.076 −0.031 0.443 − 0.509 1   
b/B 0.064 0.014 0.655 0.071 0.56 1  
(c) Triangular side gates
 
Variables Cd F1 b/y1 a/y1 b/a b/B  
Cd 1       
F1 − 0.956 1      
b/y1 − 0.564 0.677 1     
a/y1 − 0.708 0.709 0.447 1    
b/a 0.193 −0.092 0.409 − 0.583 1   
b/B 0.019 0.064 0.634 −0.025 0.554 1  
(d) Semi-circular side gates
 
Variables Cd F1 b/y1 a/y1 b/B   
Cd 1       
F1 − 0.929 1      
b/y1 − 0.799 0.901 1     
a/y1 − 0.799 0.901 1 1    
b/B 0.031 0.066 0.391 0.391 1   
(a) Correlation matrix for all data
VariablesCdTypeF1b/y1a/y1b/ab/B
Cd 1       
Type 0.134 1      
F1 − 0.937 −0.057 1     
b/y1 − 0.455 − 0.607 0.533 1    
a/y1 − 0.344 0.608 0.482 0.017 1   
b/a −0.087 − 0.909 0.037 0.681 − 0.668 1  
b/B −0.002 − 0.669 0.051 0.789 − 0.235 0.751 1 
(b) Rectangular side gates
 
Variables Cd F1 b/y1 a/y1 b/a b/B  
Cd 1       
F1 − 0.958 1      
b/y1 − 0.467 0.579 1     
a/y1 − 0.531 0.584 0.469 1    
b/a 0.076 −0.031 0.443 − 0.509 1   
b/B 0.064 0.014 0.655 0.071 0.56 1  
(c) Triangular side gates
 
Variables Cd F1 b/y1 a/y1 b/a b/B  
Cd 1       
F1 − 0.956 1      
b/y1 − 0.564 0.677 1     
a/y1 − 0.708 0.709 0.447 1    
b/a 0.193 −0.092 0.409 − 0.583 1   
b/B 0.019 0.064 0.634 −0.025 0.554 1  
(d) Semi-circular side gates
 
Variables Cd F1 b/y1 a/y1 b/B   
Cd 1       
F1 − 0.929 1      
b/y1 − 0.799 0.901 1     
a/y1 − 0.799 0.901 1 1    
b/B 0.031 0.066 0.391 0.391 1   
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Table 4

Experimental conditions of literature for rectangular side gates

The shape of the side gateb/Ba (m)y1 (m)F1 (-)Qg (m3/s)Q1 (m3/s)Author(s)
Rectangular 0.60–1.00 0.01–0.08 0.30–0.75 0.05–0.40 0.005–0.097 0.016–0.129 Panda (1981)  
Rectangular 1.00 0.01–0.10 0.07–0.37 0.105–0.948 0.003–0.090 0.010–0.097 Swamee et al. (1993)  
Rectangular 1.00 0.01–0.10 0.05–0.78 0.02–0.94 0.005–0.099 0.01–0.098 Ghodsian (2003)  
Rectangular 0.60 0.02–0.07 0.13–0.57 0.056–0.32 0.011–0.081 0.065–0.154 Kianmehr et al. (2020)  
Rectangular 0.10–0.40 0.02–0.04 0.05–0.22 0.09–0.98 0.0002–0.0081 0.0034–0.0041 Kartal & Emiroglu (2022)  
Rectangular, triangular, and semi-circular 0.309–0.75 0.03–0.10 0.082–0.347 0.044–0.986 0.00357–0.02038 0.0812–0.04305 Present study 
The shape of the side gateb/Ba (m)y1 (m)F1 (-)Qg (m3/s)Q1 (m3/s)Author(s)
Rectangular 0.60–1.00 0.01–0.08 0.30–0.75 0.05–0.40 0.005–0.097 0.016–0.129 Panda (1981)  
Rectangular 1.00 0.01–0.10 0.07–0.37 0.105–0.948 0.003–0.090 0.010–0.097 Swamee et al. (1993)  
Rectangular 1.00 0.01–0.10 0.05–0.78 0.02–0.94 0.005–0.099 0.01–0.098 Ghodsian (2003)  
Rectangular 0.60 0.02–0.07 0.13–0.57 0.056–0.32 0.011–0.081 0.065–0.154 Kianmehr et al. (2020)  
Rectangular 0.10–0.40 0.02–0.04 0.05–0.22 0.09–0.98 0.0002–0.0081 0.0034–0.0041 Kartal & Emiroglu (2022)  
Rectangular, triangular, and semi-circular 0.309–0.75 0.03–0.10 0.082–0.347 0.044–0.986 0.00357–0.02038 0.0812–0.04305 Present study 
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In the present study, the following equation was obtained to estimate the discharge coefficient of lateral gates (i.e., rectangular, triangular, and semi-circular) in a straight channel under free-flow conditions and subcritical flow by the least squares method using the data obtained from the experimental study by considering the effective parameters because of the dimensional analysis performed for the lateral gates. The coefficient of determination value of the equation obtained is relatively high (R2 = 0.91). Therefore, it can be said that the proposed equation is safe to be used to estimate the discharge coefficient for lateral gates under the conditions of free flow, subcritical flow, 0 < F1 < 1 and 2 ≤ b/a ≤ 10 and 0.309 ≤ b/B ≤ 0.75.
(17)
The Taylor diagram clearly and concisely visualizes the similarities and differences between multiple contexts (Taylor 2001). Taylor diagrams of the prediction model are shown in Figure 7. The Taylor diagram is used to visualize the relationship between actual data and predicted data, standard deviation, and error level. Figure 7 presents the evaluation of actual (measured) and predicted discharge coefficient values from the recommended equation (Equation (17)) based on the Taylor diagram. As demonstrated in Figure 7, it can be seen that the data have a compatible pattern.
Figure 7
Evaluation of predicted and measured values: (a) Taylor diagram, (b) scatter diagram.
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Evaluation of predicted and measured values: (a) Taylor diagram, (b) scatter diagram.

Figure 7
Evaluation of predicted and measured values: (a) Taylor diagram, (b) scatter diagram.
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Evaluation of predicted and measured values: (a) Taylor diagram, (b) scatter diagram.

Close modal

Table 4 shows the literature's experimental conditions of studies on side gates. As seen in Table 4, the present study has more details than the literature.

Discharge efficiency (⁠⁠) is expressed as the ratio of the discharge (⁠⁠) discharged under the side gate to the total discharge in the main channel (⁠⁠). Figure 8 shows the variation of the discharge efficiency of lateral gates (Qg/Q1 = η) with downstream Froude number. Maranzoni et al. (2017), Kilic & Emiroglu (2022), and Kartal & Emiroglu (2022) calculated the discharge efficiency of the hydraulic structures by dividing the flow through the structure by the total flow. Unlike the literature, the researchers compared the efficiency obtained with the downstream Froude number. Similarly, the efficiency of the lateral gates obtained in the present study was compared with the downstream Froude number. As seen in Figure 8, the discharge efficiency of the lateral gates with different shapes and the same cross-sectional area decreases with increasing downstream Froude number. At small Froude numbers, the discharge efficiency takes the highest values. In this study, the results are compatible with the studies of Maranzoni et al. (2017), Kilic & Emiroglu (2022), and Kartal & Emiroglu (2022).
Figure 8
The variation of the discharge efficiency (η) with the downstream Froude number (F2): (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.
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The variation of the discharge efficiency (η) with the downstream Froude number (F2): (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.

Figure 8
The variation of the discharge efficiency (η) with the downstream Froude number (F2): (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.
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The variation of the discharge efficiency (η) with the downstream Froude number (F2): (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.

Close modal
Figure 9 shows the variation of discharge efficiency (η) with the discharge coefficient of lateral gates. As mentioned above, Maranzoni et al. (2017), Kilic & Emiroglu (2022), and Kartal & Emiroglu (2022) calculated the efficiency of the side weir structure by dividing the flow through the weir by the total discharge. Figure 9 shows that the discharge coefficient values increase with discharge efficiency. In the present study, small discharge coefficient values were obtained at small efficiency values for all shapes with the same cross-sectional area.
Figure 9
The variation of discharge efficiency with discharge coefficient: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.
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The variation of discharge efficiency with discharge coefficient: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.

Figure 9
The variation of discharge efficiency with discharge coefficient: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.
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The variation of discharge efficiency with discharge coefficient: (a) rectangular side gate, (b) triangular side gate, (c) semi-circular gate.

Close modal
Figure 10 compares upstream (Cd1) and downstream (Cd2) discharge coefficients obtained from upstream and downstream flow depths for triangular side gates. The discharge coefficients obtained in the De Marchi approach were obtained by substituting the upstream and downstream flow depths. As proven in Figure 10, there is almost no difference between the discharge coefficients obtained when both upstream and downstream flow depths are used. There is perfect agreement between the discharge coefficient data obtained using different flow depths (R2 = 0.996). Similarly, this situation was observed for the other side gates (rectangular and semi-circular).
Figure 10
The comparison of Cd values obtained based on upstream (y1) and downstream (y2) flow depths for the triangular side gate.
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The comparison of Cd values obtained based on upstream (y1) and downstream (y2) flow depths for the triangular side gate.

Figure 10
The comparison of Cd values obtained based on upstream (y1) and downstream (y2) flow depths for the triangular side gate.
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The comparison of Cd values obtained based on upstream (y1) and downstream (y2) flow depths for the triangular side gate.

Close modal

The statistical values of the equation proposed in the present study for estimating the side gates are given in Table 5. As seen in Table 5, it can be concluded that there is a good agreement between observed and predicted values. Therefore, it can be deduced that the proposed equation can be safely used to predict the discharge coefficient of the lateral gate flows.

Table 5

The statistical values of the proposed equation (Equation (17)) for lateral flow

Eq. No.Min.Max.MeanStd. deviationRMSEMAEAPE (%)Scatter index (SI)R2
Equation (17) 0.243 0.546 0.414 0.085 0.0250 0.0186 4.8839 0.0602 0.91 
Eq. No.Min.Max.MeanStd. deviationRMSEMAEAPE (%)Scatter index (SI)R2
Equation (17) 0.243 0.546 0.414 0.085 0.0250 0.0186 4.8839 0.0602 0.91 
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The comparison of side rectangular, triangular, and semi-circular gate

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Figure 11 shows the side gate discharge coefficient (Cd) variation with upstream Froude number (F1) for all types with the same cross-sectional area. As seen in Figure 11, the gate discharge coefficient decreases with the increase in the upstream Froude number. In other words, the variation of Cd with the upstream Froude number is a function of y=ax2+bx+c. Although the coefficients a, b, and c in the equation y=ax2+bx+c vary for different geometries, the coefficients a and b take negative values. Therefore, Cd behaves as a decreasing function of the upstream Froude number. The trend of Cd with F1 for all shapes has a high determination coefficient value (R2 = 0.891). Therefore, it can be stated that the results can be safely used to predict the discharge coefficient.
Figure 11
The variation of Cd with F1 for all shapes.
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The variation of Cd with F1 for all shapes.

Figure 11
The variation of Cd with F1 for all shapes.
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The variation of Cd with F1 for all shapes.

Close modal
Figure 12 demonstrates the variation of discharge efficiency with downstream Froude number for all types with the same cross-sectional area. As shown in Figure 12, the discharge efficiency decreases with the increase of downstream Froude number. In other words, the variation of Cd with the upstream Froude number is a function of y=aebx+c. The trend of η with F2 for all shapes has high accuracy (R2 = 0.891). Therefore, it can be stated that the results can be safely used.
Figure 12
The variation of η with F2 for all shapes.
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The variation of η with F2 for all shapes.

Figure 12
The variation of η with F2 for all shapes.
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The variation of η with F2 for all shapes.

Close modal
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In this study, the flow characteristics of rectangular, triangular and semi-circular side gate structures with the same cross-sectional area were investigated experimentally for free and subcritical flow conditions. The hydraulic performances of different-side sluice gates with the same cross-sectional areas were analyzed for 357 experimental runs. The results obtained for the rectangular side gate are consistent with the literature. This study showed that the discharge coefficient values of rectangular, triangular, and semi-circular gates with the same cross-sectional area did not differ significantly. It was determined that the upstream Froude number, the ratio of the gate opening to the upstream flow depth, and the gate length to flow depth ratio were effective for all side gates. Still, the ratio of the gate opening to the gate length was also effective for triangular side gates. The results showed that the discharge coefficient of the semicircular side gate was relatively higher than that of the other gates under 0.05 < F1 < 0.40; the discharge coefficient of the triangular side gate is relatively higher than that of the other shaped gates for 0.40 < F1 < 0.98 and the efficiency of the triangular side gate decreases more than that of the other gates as the downstream Froude number value increases. It was determined that the De Marchi approach can be applied to different side gate shapes. This study proposed reliable equations for rectangular, triangular, and semi-circular side gates. The APE, RMSE, and scatter index (SI) values of the proposed equation (Equation (17)) are 4.88, 0.025, and 0.0602%, respectively; thus, the experimental and calculated results are in good agreement.

Similarly, it can be studied for rectangular, triangular, and semi-circular gates with different lengths for supercritical flow regimes.

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The experiments were conducted in the Hydraulic Laboratory of Firat University. The authors are greatly thankful to Firat University, Türkiye.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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M.F.Y. performed in experiments; V.K., M.E.E., M.F.Y. provided statistics, validated the project, conceptualized the study, developed the methodology, contributed in multiple regression analysis. All authors contribute to investigation, resources, wrote the original draft preparation, and visualized the work. All authors have read and agreed to the published version of the manuscript.

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There is no funding source.

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Data cannot be made publicly available; readers should contact the corresponding author for details.

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The authors declare there is no conflict.

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