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In this study, the effects of the gate opening, sill placement with different widths under the gate, and the sill position from under the gate on the discharge coefficient were investigated experimentally. Sills are placed in positions below, tangentially and upstream of the gate at distances of 7.5 and 17.5 cm from the gate. The results of the present study showed that the discharge coefficient increases with increasing sill width and decreasing total area of the flow passing through the gate. The discharge coefficient increases by installing the sill at certain intervals at increasing distance with respect to the upstream of the sluice gate and has a lower value compared to the non-sill state. At the same opening in non-sill and suppressed sill states, with a sill below and tangential to the gate, the discharge coefficient of the sluice gate with the sill has increased compared to the non-sill state. In addition, the discharge coefficient for a tangential sill has the highest value.

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  • Experimental investigation of the sluice gate discharge coefficient without and with sills in different widths and positions has been done.

  • A general equation for calculating the flow rate passing through the sluice gate in suppressed sills was developed for non-suppressed sills.

  • This investigation improves the design of hydraulic control structures.

Graphical Abstract

Graphical Abstract
Graphical Abstract
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discharge coefficient, experimental work, free-flow condition, sill position
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Gates are typically used to regulate discharge and upstream water levels in irrigation channels. Often these gates are sluice gates that move vertically up and down to adjust the opening. The control of the water level upstream of the gate and the accuracy of the flow measurements are based on the extent of gate opening. So far, several analytical and experimental studies have been performed to determine the hydraulic and geometric parameters of sluice gates. Estimating the discharge coefficient and consequently determining the flow rate under gates is a fundamental issue in hydraulic engineering. The sill will reduce the height of the gate design. In order to increase hydraulic proficiency and increase the performance of water distribution in irrigation channels, the use of the gate-sill combined structure should be considered. When the design height of the gate exceeds a certain criterion, double or triple gates are used; however, the use of double or triple gates is economically expensive (Negm et al. 1998).

Von Mises (1917) pioneered the usage of the flow potential theory to estimate the sluice gate contraction coefficient. The research of Albertson et al. (1950), based on experimental data that justify the analysis, provides the necessary coefficients for flow from both slots and orifices. Henry (1950) presented a graph for estimating the sluice gate discharge coefficient in free and submerged flow conditions. Rajaratnam & Subramanya (1967), and Rajaratnam (1977) examined the discharge coefficient of sluice gates and presented a relation. Swamee (1992) obtained the discharge coefficient of sluice gates as a function of upstream depth and gate opening under free-flow conditions. The results of Shivapur & Prakash (2005) showed that by increasing the angle of the sluice gate relative to the vertical position, the discharge coefficient increases. Khalili Shayan & Farhoudi (2013) estimated Cd of a sluice gate using energy and moment relations and determined the mean values of the energy loss factor. The results of Daneshfaraz et al. (2016) showed that the flow contraction coefficient for sharp edges and round-edge gates decreases when the ratio of gate opening to upstream specific energy is less than 0.4 and increases for ratios greater than 0.4. Kubrak et al. (2020) analyze the possibilities of using an irrigation sluice gate to measure fluid discharge. Based on their results, relationships for discharge coefficients of the analyzed sluice gate were developed. Salmasi & Abraham (2020a) conducted a series of experiments to determine the discharge coefficient for inclined slide gates. Their results indicated that the inclination of the slide gates has a progressive effect on discharge coefficient and increases capacity through the gate. Salmasi et al. (2021) used intelligence methods to investigate the inclined gates discharge coefficient. Their results showed that by increasing gate angle, the discharge coefficient increases.

Regarding the existence of the sill and its combination with the gate, an experimental study of the effect of shape and sill height under the vertical gate on the discharge coefficient in free-flow conditions was reported by Alhamid (1999). He reported an increase in the discharge coefficient with a sill compared to the non-sill state. Salmasi & Norouzi (2018) investigated the effect of different geometric shapes of suppressed sills on sluice gate discharge coefficient. Based on their results the triangular sill is one of the best polygonal sills. Karami et al. (2020) performed a numerical simulation using FLOW-3D software. The results showed that the semi-circular sill increases the Cd by 20%. Salmasi & Abraham (2020b) conducted an experimental study on the discharge coefficient of the sluice gates with polygonal and non-polygonal sills. Their results showed that a circular sill has the greatest effect, and trapezoidal sills have the least effect on the discharge coefficient. Ghorbani et al. (2020), by using the H2O method and intelligent models, analyzed the sluice gates discharge coefficient with a sill. Lauria et al. (2020) investigated the sluice gate discharge coefficient on the broad-crested weir with and without weir conditions. Their results, with weirs at different inclination of the wall, allow us to identify the minimum value of the gate opening above which the scale effect due to viscosity is negligible. The study by Daneshfaraz et al. (2022b) showed that increasing the sill length leads to an increase in flow shear stress and consequently a decrease in discharge coefficients of the sluice gate.

Sill-gate combination can be used in irrigation channels or dam gates, which leads to an increase in discharge coefficient and outlet flow. A review of previous research showed that no study has been conducted on the simultaneous use of a sill-gate with different dimensions and the sill in different positions relative to the sluice gate. Also, the use of a non-suppressed sill is one of the new methods to increase the discharge coefficient and prevent the accumulation of sediment behind the gate in the suppressed sill state. In addition in the present study a new method for calculating discharge passing under the sluice gate with a non-suppressed sill will be developed; the discharge coefficients with and without sill with different sluice gate openings and positions will be investigated. This investigation will improve the design of hydraulic control structures.

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Experimental equipment

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A laboratory flume with a rectangular cross-section 5 m long, 0.3 m wide, and 0.5 m deep was fabricated with transparent Plexiglas walls and floors which facilitate observation of the flow; 451 experiments were performed for the discharge range of 0.0025–0.01417 m3/s. The inlet flow to the flume is provided by pumps with a nominal capacity of 0.015 m3/s. To measure the inlet flow, Rotameters installed on the inlet pipe were used with ±2% accuracy. In this research, a point gauge with ±1 mm reading accuracy was used to measure water depth. The experiments incorporated situations with and without a sill and with different gate openings. In this research, experiments using polyethylene sills with constant sill height (3 cm) and relative widths (ratio of sill height to sill width (Z/B)) of 1.2, 0.6, 0.4, 0.3, 0.2, 0.15, 0.12, and 0.1 cm were used. The sills were installed under the gate (X = 0), tangential to the gate (X = 2.5 cm), upstream of the gate at intervals of 7.5 and 17.5 cm relative to the gate, double sill upstream and under the gate, and double sill upstream and tangential to the gate. In double modes, the second sills were as far as the thickness of the sill from the first sill (L = ε = 5 cm). A schematic view of the gate-sills is shown in Figure 1.
Figure 1
Schematic view of the gate and sill (a) 1- Sill under the gate 2- Sill tangential to the gate; (b) Sill upstream of the gate at different distances from the gate; (c) Double sill upstream and under gate; (d) Double sill upstream and tangential to the gate.
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Schematic view of the gate and sill (a) 1- Sill under the gate 2- Sill tangential to the gate; (b) Sill upstream of the gate at different distances from the gate; (c) Double sill upstream and under gate; (d) Double sill upstream and tangential to the gate.

Figure 1
Schematic view of the gate and sill (a) 1- Sill under the gate 2- Sill tangential to the gate; (b) Sill upstream of the gate at different distances from the gate; (c) Double sill upstream and under gate; (d) Double sill upstream and tangential to the gate.
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Schematic view of the gate and sill (a) 1- Sill under the gate 2- Sill tangential to the gate; (b) Sill upstream of the gate at different distances from the gate; (c) Double sill upstream and under gate; (d) Double sill upstream and tangential to the gate.

Close modal
Figure 2 shows a view of the experimental flume and sills with different widths and positions.
Figure 2
Photographs of the experimental flume with the equipment installed on it and some of the models used in the present study.
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Photographs of the experimental flume with the equipment installed on it and some of the models used in the present study.

Figure 2
Photographs of the experimental flume with the equipment installed on it and some of the models used in the present study.
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Photographs of the experimental flume with the equipment installed on it and some of the models used in the present study.

Close modal

Dimensional analysis

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Using the energy equation and for free-flow conditions, the flow rate passing under the sluice gate without a sill is calculated according to Equation (1) (Rajaratnam & Subramanya 1967):
(1)
where, Q is the discharge (L3T−1), Cd is the discharge coefficient (−), W is the channel width (L), G is the gate opening (L), g is the gravitational acceleration (LT−2) and H0 (L) is the fluid depth upstream of the sluice gate.
The discharge rate under the gate for the suppressed sill state is obtained according to Equation (2) (Alhamid 1999; Salmasi & Abraham 2020b):
(2)
In relation (2), Z is the sill height (L) and A=WG is the flow area under the gate (L2). Accordingly, Equation (2) can be extended to Equation (3) for the non-suppressed sill state:
(3)
where, A1, A3 and A2 are the areas of the flow (L2) passing under the gate without the sill and above the non-suppressed sill, respectively.
(4)

In relation (4), Atotal is the total area of the flow through the sluice gate (L2).

The value of Cd without the sill is a function of the upstream water depth and the sluice gate openings (Swamee 1992), so the most important parameter affecting it can be expressed as follows:
(5)
In relation (5), ρ is the specific gravity of water (ML−3), μ is the dynamic viscosity (ML−1T−1) and σ is the surface tension (MT−2). According to the π-Buckingham theorem, the dimensionless parameters are shown in Equation (6):
(6)
In Equation (6), Re and We represent the dimensionless Reynolds number (−) and Weber number (−), respectively. When the liquid is the same and the temperature is constant, in the experimental set-up, Re and We are dependent on each other and vary with the opening of the gate, so one of the two must be eliminated; therefore the effect of Weber number was ignored (Raju 1984; Lauria et al. 2020). Here, the flow is turbulent and 47,222 ≥ Re ≥ 11,111, so the effect of this parameter can be ignored (Madadi et al. 2014; Nasrabadi et al. 2021). Therefore, Equation (6) can be summarized as Equation (7).
(7)
In the present study and with a sill, the most important parameters affecting the discharge coefficient are:
(8)
where, B is the sill width (L), ε is the sill thickness (L) and X is the axis-to-axis distance of the sluice gate to the sill (L). Considering ρ, g and B as iterative variables and using the π-Buckingham theorem, the dimensionless relation (9) can be presented:
(9)

Due to the above description, the effects of Re and We were ignored. In some parameters of Equation (9), such as sill thickness and channel width, the values are constant and the effect of these parameters was ignored. In fact, the discharge coefficient parameter is the same as the Froude number under the gate (Lauria et al. 2020; Salmasi & Abraham 2020b). Carrying out the tests in conditions where the viscosity and the surface tension do not affect the flow, the discharge coefficient becomes a function of the following variables only (Lauria et al. 2020):

The final functional dependence is provided by Equation (10).
(10)

According to White's theorem (2016), dimensionless parameters can be obtained by dividing, multiplying, adding, or subtracting dimensionless parameters from each other.

In this study, statistical indicators of absolute error (AE), percentage relative error (RE%), root mean square error (RMSE) and Kling-Gupta efficiency (KGE) have been used to estimate the capability and accuracy of the proposed equation in estimating Cd. Statistical criteria for estimating the Cd were calculated from Equations (11)–(14), respectively.
(11)
(12)
(13)
(14)
where, n is the total number of data, Cd obs is the observed discharge coefficient, Cd cal is the calculated discharge coefficient from the estimated equation, is the mean value of the observed values, is the mean value of the calculated values, σcal is the standard deviation of calculated values and R is the correlation coefficient.
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Table 1 shows the variation of Cd without a sill and with different sluice gate openings. According to Table 1, the values of Cd vary inversely with the gate opening and with increased opening. One of the parameters affecting the discharge coefficient of the sluice gate is the water depth upstream of the gate. Consequently, with a constant discharge, increasing the gate opening reduces the water depth upstream of the gate and this factor reduces the discharge coefficient. Also, by reducing the gate opening, flow passing under the gate converges and the area of the flow through the gate decreases, which causes an increase in velocity and consequently the coefficient of discharge. Also, by increasing the relative upstream water depth, the discharge coefficient increases. It should be noted that in open-channel flows, bottom and sidewall friction resistance can be neglected as a first approximation (Chanson 2004). In addition, in the present study, transparent Plexiglas with a Manning coefficient of 0.009 has been used, so the effect of sidewall friction has been ignored. But the approximation of frictionless flow is no longer valid for very long channels. Considering a water supply channel extending over several kilometers, the bottom and sidewall friction retards the fluid and, at equilibrium, the friction force counterbalances exactly the weight force component in the flow direction (Chanson 2004).

Table 1

Range of Cd changes at different openings

Gate opening (m)Range of discharge changes (m3/s)Range of H0/G changes ( − )Range of Cd changes ( − )
0.01 0.0033–0.0067 44 ≥ H0/G ≥ 13.6 0.75–0.68 
0.02 0.0050–0.0100 14.94 ≥ H0/G ≥ 4.45 0.68–0.63 
0.04 0.0067–0.0125 3.53 ≥ H0/G ≥ 1.36 0.62–0.53 
Gate opening (m)Range of discharge changes (m3/s)Range of H0/G changes ( − )Range of Cd changes ( − )
0.01 0.0033–0.0067 44 ≥ H0/G ≥ 13.6 0.75–0.68 
0.02 0.0050–0.0100 14.94 ≥ H0/G ≥ 4.45 0.68–0.63 
0.04 0.0067–0.0125 3.53 ≥ H0/G ≥ 1.36 0.62–0.53 
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Examination of downstream streamlines without sill state showed that the supercritical flow continues in parallel conditions after the gate without breaking in streamlines and continues its path by creating a free hydraulic jump with turbulent and eddy flows. To investigate the efficacy of applying the suppressed and non-suppressed sill in the positions under the sluice gate and tangentially to the upstream of the gate, a rectangular sill with a thickness of 5 cm, a height of 3 cm, and different widths was investigated. In Figure 3(a) and 3(b), the effect of the dimensionless parameter of the ratio of upstream depth to sill width (H0/B) is shown. According to Figure 3(a) and 3(b), by increasing the sill width, Cd increases so that the sill with the smallest width has the minimum value of the Cd. It is also observed that by increasing the ratio of the upstream flow depth to the sill width, the discharge coefficient has an increasing trend. It should be noted that the rate of increase in the discharge coefficient has decreased by increasing depth, as long as the discharge coefficient rate is not affected by the depth increase. In the non-suppressed sill state, both sides of the sill are empty of the sill, so the flow through the sides and over the sill takes on a different form due to the different gate openings. There is a high volume of flow around the sill; therefore, the velocity of the flow is lower than the velocity through over the sill, which leads to the formation of V-shaped streams downstream of the gate. Figure 3(c) shows the Cd diagram against the dimensionless parameter (Z−X)/B with a sill height of 0.03 m. The results show that by keeping the sill height constant in all models and increasing the sill width, the discharge coefficient has an increasing trend by increasing discharge, and its highest value occurs when it is tangential with the gate.
Figure 3
Cd changes for tangential and under gate positions.
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Cd changes for tangential and under gate positions.

Figure 3
Cd changes for tangential and under gate positions.
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Cd changes for tangential and under gate positions.

Close modal
In Figure 4, the effect of the gate opening on the sides of the sill and above it, the width of the sill and the total area of the flow through the sluice gate on the coefficient of discharge is presented. As can be seen, by increasing Atotal/B2, Cd decreases. In other words, by increasing sill width, the area of the flow on both sides of the sill decreases. For a larger sill width, the total area of the flow through the gate will be smaller than for a sill with a smaller width, which leads to an increased discharge coefficient. The presence of a sill with a minimum width under the sluice gate compared to no-sill increases the discharge coefficient, so that this increase indicates a decrease in the total area of the flow under the gate.
Figure 4
The area of flow through the gate at different sill widths.
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The area of flow through the gate at different sill widths.

Figure 4
The area of flow through the gate at different sill widths.
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The area of flow through the gate at different sill widths.

Close modal
In Figure 5, a comparison is made between the discharge coefficient of the sluice gate in the no-sill state and suppressed sill state with an opening of 1 cm. It should be noted that the gate opening above the suppressed sill is also 1 cm. The existence of the sill under and tangential to the sluice gate in comparison with the no-sill state increases the discharge coefficient and improves flow rate. On average, the presence of the suppressed sill below and tangential to the sluice gate compared to the no-sill state with a constant gate opening increases the Cd by 7.75% and 9.53%, respectively. The upstream fluid depth in the tangential and below positions is less than the no-sill state; therefore, in the non-sill mode the amount of force applied to the gate is higher than in the sill state. The presence of a sill causes the pressure on the gate to be lower than the no-sill state. On the other hand, this reduction in depth leads to an increase in the discharge coefficient.
Figure 5
Comparison of the Cd between without sill state and suppressed sill state at the same opening.
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Comparison of the Cd between without sill state and suppressed sill state at the same opening.

Figure 5
Comparison of the Cd between without sill state and suppressed sill state at the same opening.
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Comparison of the Cd between without sill state and suppressed sill state at the same opening.

Close modal

In Table 2, experimental discharges with corresponding discharge coefficients for some of the sills with different widths are given. The discharge coefficient with a sill is higher than without a sill and increases with increasing sill width. By comparing the discharge coefficient in different sill positions, the discharge coefficient in the tangential location is higher than when the sill is positioned under the sluice gate. This can be attributed to the placement of the sill. With a tangential position, the entire thickness of the sill is behind the gate. When the sill is under the gate, the sill more effectively acts as a barrier to the flow and increases the flow depth upstream of the gate compared to the tangential position. The deformation of streamlines in different sill positions has a significant effect on the discharge coefficient. Experimental observations showed that the streamlines in the tangential position continue with a smoother state immediately after passing over the sill, while in the below position, the flow passes over the sill as jet and backwater and irregular flow lines are formed in front of the gate.

Table 2

Cd values for various sill positions and widths of single sills

Sill widths (cm)No Sill G = 4 cmB = 5 cm
B = 15 cm
B = 20 cm
B = 25 cm
B = 30 cm
Sill LocationNo SillUnder the gateTangential to the gateUnder the gateTangential to the gateunder the gateTangential to the gateUnder the gateTangential to the gateUnder the gateTangential to the gate
Q (m3/s) 0.0025 Cd (−) – – – – – – – – – 0.7768 – 
0.0029 – – – – – – – – – 0.7760 – 
0.0033 – – – – – – – 0.6691 – 0.7705 0.7732 
0.0038 – – – – – – – – – – 0.7767 
0.0042 – – – – – – – 0.6791 0.6839 0.7749 0.7817 
0.0050 – – – – – – – 0.6880 0.6968 0.7798 0.8039 
0.0054 – – – – – – – – – 0.7797 – 
0.0058 – 0.5554 – 0.5969 0.6051 06515 0.6571 0.6897 0.6987 0.7760 0.8015 
0.0063 – 0.5592 – 0.6083 – 0.6538 0.6571 0.6860 – – 0.8038 
0.0067 0.5377 0.5604 0.5624 0.6143 0.6234 0.6520 0.6621 0.6818 0.7059 – 0.8157 
0.0075 0.5667 0.5820 0.5857 0.6310 0.6368 0.6625 0.6733 0.6868 0.7177 – – 
0.0083 0.5843 0.5975 0.6004 0.6426 0.6477 0.6786 0.6888 0.6902 0.7323 – – 
0.0088 – – – – – – 0.6930 – 0.7407 – – 
0.0092 0.5955 0.6007 0.6041 0.6598 0.6648 0.6823 0.6943 – 0.7469 – – 
0.0096 0.6008 0.6036 – 0.6601 – 0.6857 – – 0.7496 – – 
0.0100 0.6060 0.6095 0.6119 0.6615 0.6671 0.6865 0.6959 – – – – 
0.0104 0.6088 0.6110 0.6128 0.6657 – 0.6796 – – – – – 
0.0108 0.6127 0.6137 0.6166 0.6631 0.6686 0.6830 0.6982 – – – – 
0.0113 0.6167 0.6188 0.6210 0.6656 0.6664 – – – – – – 
0.0116 0.6211 0.6262 0.6281 0.6615 0.6686 – 0.7004 – – – – 
0.0125 0.6263 0.6278 0.6312 0.6653 0.6674 – – – – – – 
0.0133 – – 0.6339 – – – – – – – – 
0.0141 – – 0.6350 – – – – – – – – 
Sill widths (cm)No Sill G = 4 cmB = 5 cm
B = 15 cm
B = 20 cm
B = 25 cm
B = 30 cm
Sill LocationNo SillUnder the gateTangential to the gateUnder the gateTangential to the gateunder the gateTangential to the gateUnder the gateTangential to the gateUnder the gateTangential to the gate
Q (m3/s) 0.0025 Cd (−) – – – – – – – – – 0.7768 – 
0.0029 – – – – – – – – – 0.7760 – 
0.0033 – – – – – – – 0.6691 – 0.7705 0.7732 
0.0038 – – – – – – – – – – 0.7767 
0.0042 – – – – – – – 0.6791 0.6839 0.7749 0.7817 
0.0050 – – – – – – – 0.6880 0.6968 0.7798 0.8039 
0.0054 – – – – – – – – – 0.7797 – 
0.0058 – 0.5554 – 0.5969 0.6051 06515 0.6571 0.6897 0.6987 0.7760 0.8015 
0.0063 – 0.5592 – 0.6083 – 0.6538 0.6571 0.6860 – – 0.8038 
0.0067 0.5377 0.5604 0.5624 0.6143 0.6234 0.6520 0.6621 0.6818 0.7059 – 0.8157 
0.0075 0.5667 0.5820 0.5857 0.6310 0.6368 0.6625 0.6733 0.6868 0.7177 – – 
0.0083 0.5843 0.5975 0.6004 0.6426 0.6477 0.6786 0.6888 0.6902 0.7323 – – 
0.0088 – – – – – – 0.6930 – 0.7407 – – 
0.0092 0.5955 0.6007 0.6041 0.6598 0.6648 0.6823 0.6943 – 0.7469 – – 
0.0096 0.6008 0.6036 – 0.6601 – 0.6857 – – 0.7496 – – 
0.0100 0.6060 0.6095 0.6119 0.6615 0.6671 0.6865 0.6959 – – – – 
0.0104 0.6088 0.6110 0.6128 0.6657 – 0.6796 – – – – – 
0.0108 0.6127 0.6137 0.6166 0.6631 0.6686 0.6830 0.6982 – – – – 
0.0113 0.6167 0.6188 0.6210 0.6656 0.6664 – – – – – – 
0.0116 0.6211 0.6262 0.6281 0.6615 0.6686 – 0.7004 – – – – 
0.0125 0.6263 0.6278 0.6312 0.6653 0.6674 – – – – – – 
0.0133 – – 0.6339 – – – – – – – – 
0.0141 – – 0.6350 – – – – – – – – 
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In Figure 6(a) and 6(b), the effect of the sill distance upstream of the gate on Cd is shown for similar openings. In these models, the gate is in the non-sill state, and the sills are located a certain distance from the gate so they have no effect on the flow area passing under the gate. Changes in the discharge coefficient result from changes to the position of the sill relative to the gate and the volume of the sill within the flow. According to Figure 6(a) and 6(b), it is observed that in all sill modes, by increasing discharge and thus increasing the water depth upstream of the gate, Cd increases. Furthermore, the Cd in the no-sill state is higher compared with an upstream sill. The reason for this is the inverse relationship of the discharge coefficient with the depth upstream of the gate, so that by keeping the total area of the flow through the gate (WG) constant, installing a sill increases the upstream fluid depth. A larger width sill increases eddy released from the sill and by this mechanism, enhances the energy loss. At closer distances to the gate, the sill acts as a barrier and eddies engage more with the gate.
Figure 6
Cd changes in sill application mode upstream of the gate in (a) X = 7.5 cm; (b) X = 17.5 cm.
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Cd changes in sill application mode upstream of the gate in (a) X = 7.5 cm; (b) X = 17.5 cm.

Figure 6
Cd changes in sill application mode upstream of the gate in (a) X = 7.5 cm; (b) X = 17.5 cm.
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Cd changes in sill application mode upstream of the gate in (a) X = 7.5 cm; (b) X = 17.5 cm.

Close modal

In Table 3, the effect of double sills on the discharge coefficient is given. The results indicated that the discharge coefficient in the tangential mode is higher than in the under gate mode. The upstream water depth in the below position is higher than in the tangential position; this increase in depth leads to a decrease in the discharge coefficient. The discharge coefficient in the single sill is higher than the double sill and increases with the increase of the sill width. For the case of single and double sill in the tangential position, the results are very close to each other and unlike the below position, they do not differ much.

Table 3

Cd values in different positions of double sills

Discharge coefficient (−)
Q (m3/s)B = 2.5 cm
B = 5 cm
B = 7.5 cm
B = 10 cm
Under the gateTangential to the gateUnder the gateTangential to the gateUnder the gateTangential to the gateUnder the gateTangential to the gate
0.0058 – – – – – – 0.5525 0.5718 
0.0063 – – – – – – – 0.5742 
0.0067 – – 0.5439 0.5556 0.5514 0.5664 0.5530 0.5741 
0.0075 0.5638 0.5560 0.5578 0.5725 0.5688 0.5831 0.5705 0.5891 
0.0083 0.5679 0.5724 0.5709 0.5939 0.5807 0.5988 0.5842 0.6117 
0.0092 0.5830 0.5828 0.5889 0.5982 0.5966 0.6133 0.5970 0.6159 
0.0100 0.5933 0.5931 0.5941 0.6162 0.6079 0.6226 0.6091 0.6207 
0.0108 0.5985 0.5988 0.6015 0.6150 0.6102 0.6236 0.6064 0.6183 
0.0116 0.5988 0.6019 0.6025 0.6089 0.6062 0.6243 0.6070 0.6283 
0.0125 0.6075 0.6076 0.6012 0.6212 0.6162 0.6302 0.6120 0.6359 
0.0133 0.6044 0.6174 0.6022 0.6208 0.6144 0.6338 – 0.6383 
0.0141 – 0.6178 0.6069 0.6267 0.6137 0.6398 – 0.6465 
B = 15 cm
B = 20 cm
B = 25 cm
B = 30 cm
Q (m3/s)Under the gateTangential to the gateUnder the gateTangential to the gateUnder the gateTangential to the gateUnder the gateTangential to the gate
0.0025 – – – – – – 0.6276 – 
0.0029 – – – – – – 0.6309 – 
0.0033 – – – – 0.5868 – 0.6259 0.7324 
0.0038 – – – – 0.6018 – 0.6325 0.7523 
0.0042 – – – – 0.6145 0.6791 0.6360 0.7647 
0.0046 – – – – – – – 0.7775 
0.0050 0.5739 – 0.6033 – 0.6289 0.6920 0.6444 0.7866 
0.0054 – – – – – – 0.6382 – 
0.0058 0.5777 0.6128 0.6082 0.6572 0.6215 0.6932 – 0.8023 
0.0063 – 0.6169 – 0.6532 0.6202 – – 0.8012 
0.0067 0.5797 0.6172 0.6079 0.6562 0.6145 0.7041 – 0.8177 
0.0075 0.5973 0.6339 0.6234 0.6732 0.6261 0.7135 – – 
0.0079 – – – – 0.6267 – – – 
0.0083 0.6059 0.6497 0.6302 0.6846 – 0.7287 – – 
0.0092 0.6176 0.6599 0.6374 0.6901 – 0.7334 – – 
0.0096 – – – – – 0.7426 – – 
0.0100 0.6267 0.6618 0.6441 0.7050 – – – – 
0.0108 0.6269 0.6592 0.6415 0.7034 – – – – 
0.0116 0.6245 0.6689 – 0.7067 – – – – 
0.0125 – 0.6818 – – – – – – 
Discharge coefficient (−)
Q (m3/s)B = 2.5 cm
B = 5 cm
B = 7.5 cm
B = 10 cm
Under the gateTangential to the gateUnder the gateTangential to the gateUnder the gateTangential to the gateUnder the gateTangential to the gate
0.0058 – – – – – – 0.5525 0.5718 
0.0063 – – – – – – – 0.5742 
0.0067 – – 0.5439 0.5556 0.5514 0.5664 0.5530 0.5741 
0.0075 0.5638 0.5560 0.5578 0.5725 0.5688 0.5831 0.5705 0.5891 
0.0083 0.5679 0.5724 0.5709 0.5939 0.5807 0.5988 0.5842 0.6117 
0.0092 0.5830 0.5828 0.5889 0.5982 0.5966 0.6133 0.5970 0.6159 
0.0100 0.5933 0.5931 0.5941 0.6162 0.6079 0.6226 0.6091 0.6207 
0.0108 0.5985 0.5988 0.6015 0.6150 0.6102 0.6236 0.6064 0.6183 
0.0116 0.5988 0.6019 0.6025 0.6089 0.6062 0.6243 0.6070 0.6283 
0.0125 0.6075 0.6076 0.6012 0.6212 0.6162 0.6302 0.6120 0.6359 
0.0133 0.6044 0.6174 0.6022 0.6208 0.6144 0.6338 – 0.6383 
0.0141 – 0.6178 0.6069 0.6267 0.6137 0.6398 – 0.6465 
B = 15 cm
B = 20 cm
B = 25 cm
B = 30 cm
Q (m3/s)Under the gateTangential to the gateUnder the gateTangential to the gateUnder the gateTangential to the gateUnder the gateTangential to the gate
0.0025 – – – – – – 0.6276 – 
0.0029 – – – – – – 0.6309 – 
0.0033 – – – – 0.5868 – 0.6259 0.7324 
0.0038 – – – – 0.6018 – 0.6325 0.7523 
0.0042 – – – – 0.6145 0.6791 0.6360 0.7647 
0.0046 – – – – – – – 0.7775 
0.0050 0.5739 – 0.6033 – 0.6289 0.6920 0.6444 0.7866 
0.0054 – – – – – – 0.6382 – 
0.0058 0.5777 0.6128 0.6082 0.6572 0.6215 0.6932 – 0.8023 
0.0063 – 0.6169 – 0.6532 0.6202 – – 0.8012 
0.0067 0.5797 0.6172 0.6079 0.6562 0.6145 0.7041 – 0.8177 
0.0075 0.5973 0.6339 0.6234 0.6732 0.6261 0.7135 – – 
0.0079 – – – – 0.6267 – – – 
0.0083 0.6059 0.6497 0.6302 0.6846 – 0.7287 – – 
0.0092 0.6176 0.6599 0.6374 0.6901 – 0.7334 – – 
0.0096 – – – – – 0.7426 – – 
0.0100 0.6267 0.6618 0.6441 0.7050 – – – – 
0.0108 0.6269 0.6592 0.6415 0.7034 – – – – 
0.0116 0.6245 0.6689 – 0.7067 – – – – 
0.0125 – 0.6818 – – – – – – 
View Large

Table 1 presents the range of discharge coefficient changes in different openings of the present study in non-sill state. Accordingly, the maximum value of the discharge coefficient is related to the opening of 1 cm. In this opening, the range of H0/G parameter changes from 13.6 to 44 and includes a wide range. In general and in all studied gate openings, this parameter is in the range of 1.36–44. In Table 4, a comparison was made between the results of the Cd of all openings with the previous studies.

Table 4

Results of the discharge coefficient of the present study with previous studies

GateDischarge coefficient (−)
Present study (integration of all openings)
Rajaratnam (1977) 
Shivapur & Prakash (2005) 
Alhamid (1999) 
Karami et al. (2020) 
Hager (1999) 
MaxMinAvrMaxMinAvrMaxMinAvrMaxMinAvrMaxMinAvrMaxMinAvr
Vertical 0.75 0.53 0.62 0.64 0.60 0.62 0.63 0.52 0.61 0.62 0.53 0.57 0.58 0.53 0.55 0.59 0.53 0.55 
GateDischarge coefficient (−)
Present study (integration of all openings)
Rajaratnam (1977) 
Shivapur & Prakash (2005) 
Alhamid (1999) 
Karami et al. (2020) 
Hager (1999) 
MaxMinAvrMaxMinAvrMaxMinAvrMaxMinAvrMaxMinAvrMaxMinAvr
Vertical 0.75 0.53 0.62 0.64 0.60 0.62 0.63 0.52 0.61 0.62 0.53 0.57 0.58 0.53 0.55 0.59 0.53 0.55 
View Large

In Table 5, the range of the Cd values for the gate with suppressed sill state from the present study are compared with the results of the previous studies including Alhamid (1999), Karami et al. (2020), and Salmasi & Abraham (2020b).

Table 5

Results of the discharge coefficient of the present study compared with previous studies

CaseType of sillRange of (H0-Z)/G ( − )Range of Cd ( − )
Alhamid (1999)  Circular 1.67 ≤ (H0-Z)/G ≤ 14.74 0.65–0.76 
Karami et al. (2020)  Semi-circular 1.19 ≤ (H0-Z)/G ≤ 4.12 0.66–0.69 
Salmasi & Abraham (2020b)  Non-polyhedron 2.00 ≤ (H0-Z)/G ≤ 17.82 0.58–0.70 
Present study (under gate sill) Rectangular 5.86 ≤ (H0-Z)/G ≤ 32 0.77–0.78 
Present study (tangential gate sill) Rectangular 10.53 ≤ (H0-Z)/G ≤ 38.78 0.77–0.82 
CaseType of sillRange of (H0-Z)/G ( − )Range of Cd ( − )
Alhamid (1999)  Circular 1.67 ≤ (H0-Z)/G ≤ 14.74 0.65–0.76 
Karami et al. (2020)  Semi-circular 1.19 ≤ (H0-Z)/G ≤ 4.12 0.66–0.69 
Salmasi & Abraham (2020b)  Non-polyhedron 2.00 ≤ (H0-Z)/G ≤ 17.82 0.58–0.70 
Present study (under gate sill) Rectangular 5.86 ≤ (H0-Z)/G ≤ 32 0.77–0.78 
Present study (tangential gate sill) Rectangular 10.53 ≤ (H0-Z)/G ≤ 38.78 0.77–0.82 
View Large

According to Equation (15), a nonlinear polynomial regression relation was presented to predict the discharge coefficient of the sluice gate in the sill state.
(15)
In Figure 7, the results indicate that the observed discharge coefficient is the same as the values obtained from Equation (15).
Figure 7
Comparison of calculated and observed values of Cd.
View largeDownload slide

Comparison of calculated and observed values of Cd.

Figure 7
Comparison of calculated and observed values of Cd.
View largeDownload slide

Comparison of calculated and observed values of Cd.

Close modal

So that, the maximum RE%, mean RE% and RMSE are 4.96%, 1.48% and 0.0112, respectively. Also, the value of KGE is equal to 0.961, which shows that this index is in the very good range.

In Table 6, a comparison was made between the present study and previous studies (Karami et al. 2020; Salmasi & Abraham 2020b) with Equation (15). As the present study was conducted in a high range of experiments (Table 5), Equation (15) has a suitable coverage. By examining the percentage relative error values, it is possible to realize the smallness of the values, which shows the high accuracy of the presented equation.

Table 6

Comparison of the accuracy of Equation (15) with other researchers' data

Present study (under gate sill)Equation (15)RE (%)Salmasi & Abraham (2020b) Equation (15)RE (%)Karami et al. (2020) Equation (15)RE (%)
1 0.777 0.750 3.446 0.586 0.556 5.127 0.658 0.628 4.566 
2 0.776 0.760 2.064 0.605 0.591 2.258 0.662 0.638 3.618 
3 0.770 0.750 2.675 0.641 0.621 3.120 0.669 0.652 2.509 
4 0.775 0.765 1.273 0.638 0.625 2.038 0.680 0.668 1.694 
5 0.780 0.778 0.226 0.639 0.651 −1.878 0.684 0.674 1.518 
6 0.780 0.784 −0.562 0.660 0.653 0.979 0.684 0.685 −0.089 
7 0.776 0.790 −1.831 0.662 0.668 −0.857 0.692 0.710 −2.572 
Present study (under gate sill)Equation (15)RE (%)Salmasi & Abraham (2020b) Equation (15)RE (%)Karami et al. (2020) Equation (15)RE (%)
1 0.777 0.750 3.446 0.586 0.556 5.127 0.658 0.628 4.566 
2 0.776 0.760 2.064 0.605 0.591 2.258 0.662 0.638 3.618 
3 0.770 0.750 2.675 0.641 0.621 3.120 0.669 0.652 2.509 
4 0.775 0.765 1.273 0.638 0.625 2.038 0.680 0.668 1.694 
5 0.780 0.778 0.226 0.639 0.651 −1.878 0.684 0.674 1.518 
6 0.780 0.784 −0.562 0.660 0.653 0.979 0.684 0.685 −0.089 
7 0.776 0.790 −1.831 0.662 0.668 −0.857 0.692 0.710 −2.572 
View Large

Table 7 describes the details of previous experimental and numerical studies on hydraulic characteristics of flow with gates presented by Daneshfaraz et al. (2022a, 2022b) and the present study.

Table 7

Main characteristics of this study and some past experimental and numerical studies

ReferenceType of gateType of studyMethodology (sill location)Aims of study
Daneshfaraz et al. (2022b)  Non-sill Experimental Non-sill Investigations of hydraulic parameters of flow in gates:
(a) Hydraulic jump
(b) Relative energy dissipation
(c) Relative depth
(d) Discharge and contraction coefficient 
Daneshfaraz et al. (2022a)  With sill Numerical and experimental (a) Single-below gate
(b) Single-tangential to the gate 		Investigations of:
(a) Depth averaged velocity
(b) Shear stress
(c) Stage-discharge
(d) Hydrodynamic force
with sill and their effect on discharge coefficient 
Present study With sill Experimental (a) Single-sill upstream of the sluice gate at different distances from the gate.
(b) Single-below sluice gate.
(c) Single-tangential to the sluice gate.
(d) Double sill-below and upstream position.
(e) Double sill-tangential and upstream position 		Investigations of hydraulic properties of flow with sill:
(a) at different positions with single sill:
  • 1.

    X = 0 cm

  • 2.

    X = 2.5 cm

  • 3.

    X = 7.5 cm

  • 4.

    X = 17.5 cm


(b) at different positions with double sills:

  • 1. Below position: X1 = 0 cm, X2 = 10 cm

  • 2. Tangential position: X1 = 2.5 cm, X2 = 12.5 cm

  • and their effect on discharge coefficient


(c) Presenting a nonlinear regression equation to predict the discharge coefficient with sill with various widths 
ReferenceType of gateType of studyMethodology (sill location)Aims of study
Daneshfaraz et al. (2022b)  Non-sill Experimental Non-sill Investigations of hydraulic parameters of flow in gates:
(a) Hydraulic jump
(b) Relative energy dissipation
(c) Relative depth
(d) Discharge and contraction coefficient 
Daneshfaraz et al. (2022a)  With sill Numerical and experimental (a) Single-below gate
(b) Single-tangential to the gate 		Investigations of:
(a) Depth averaged velocity
(b) Shear stress
(c) Stage-discharge
(d) Hydrodynamic force
with sill and their effect on discharge coefficient 
Present study With sill Experimental (a) Single-sill upstream of the sluice gate at different distances from the gate.
(b) Single-below sluice gate.
(c) Single-tangential to the sluice gate.
(d) Double sill-below and upstream position.
(e) Double sill-tangential and upstream position 		Investigations of hydraulic properties of flow with sill:
(a) at different positions with single sill:
  • 1.

    X = 0 cm

  • 2.

    X = 2.5 cm

  • 3.

    X = 7.5 cm

  • 4.

    X = 17.5 cm


(b) at different positions with double sills:

  • 1. Below position: X1 = 0 cm, X2 = 10 cm

  • 2. Tangential position: X1 = 2.5 cm, X2 = 12.5 cm

  • and their effect on discharge coefficient


(c) Presenting a nonlinear regression equation to predict the discharge coefficient with sill with various widths 

X1 and X2 represent the position of the first and second sill in the double mode, respectively.

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The results showed that without a sill and with different sluice gate openings, the discharge coefficient (Cd) is inversely related to the gate opening. The most important factors for the Cd of the sluice gate in non-sill states are the upstream flow depth and the gate opening. By placing all the sill models below and tangential to the gate, the Cd increases compared to the non-sill state. Comparison of the Cd values obtained with a sill under the gate and tangential to the sluice gate indicates a high value of the Cd in the tangential mode for all discharge rates and widths of the sill. In addition, increasing the width of the sill reduces the total area of the flow through the gate, which causes an increase in the Cd. The comparison of the results of Cd between the suppressed sill state under and tangential to the sluice gate with the non-sill state and for constant opening indicates an increase in the discharge coefficient in the suppressed sill state. The results showed that the Cd increased by increasing the distance of the installation of the sill at certain distances upstream of the gate and has a lower value compared to the without the sill state. Finally, based on the dimensionless parameters obtained from dimensional analysis, a nonlinear polynomial regression relation was proposed to predict the Cd that can be used for suppressed and non-suppressed sills.

One solution to reduce the dimensions of the gate is to use a sill and install the gate on it. The use of the sill increases the discharge coefficient, but the application of suppressed sill also brings with it the problem of accumulation of sediments behind the gate, which had been suggested by previous authors. Therefore, the use of non-suppressed sill is a practical method to simultaneously increase the discharge coefficient and the passage of sediments under the gate.

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The authors would like to thank Professor John Abraham for his help in proofreading in English.

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

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© 2022 The Authors
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).