# Flow Measurements Using a Sluice Gate; Analysis of Applicability

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## Abstract

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## 1. Introduction

- Is it possible to use the given formulas and discharge coefficients determined for the submerged gate outflow for structures with the gate installed in intake canals with trapezoidal cross-sections?
- Where should the downstream water depth measured for the submerged gate be, installed in a canal with rectangular cross-section, to ensure a good fit between measured and calculated flow rates?
- How does the construction of guides necessary for lifting the gate (changing the width of the opening in relation to the width of the channel) affect the values of the flow coefficients for the submerged flow conditions?

## 2. Methods

#### 2.1. One-Dimensional Description of the Sluice Gate Flow

_{z}at the gate outflow is noticeably lower than the water depth h in a downstream channel (h

_{z}< h) or a form of the submerged hydraulic jump (Figure 1b), when the water depth h

_{z}is close to the water depth in the downstream channel (h

_{z}≈ h). The water profile downstream of the gate for the hydraulic jump formed is unstable and wavy (Fig. 1a).

_{1}at depth h

_{z}determined using the equation of energy conservation between Sections 0-0 and 1-1:

_{z}necessary in Equation (1) should be measured, is not clearly defined. With the submerged jump, it is assumed that the depth h

_{z}is equal to the depth of the downstream i.e., h

_{z}≈ h (Figure 1b).

_{d}(2) is defined as follows:

_{d}. In the case of the free flow conditions, the discharge coefficients depended on the upper water depth H and the opening height of the gate a. However, in the case of the submerged outflow, it is necessary to condition its value on the downstream water depth h. Swamee (1992) [15] provided a relationship describing the dependency of the discharge coefficient for the submerged sluice in the following form:

#### 2.2. Studies on Submerged Flow through Irrigation Sluice Gate

^{−1/3}s, 0.034 m

^{−1/3}s and 0.037 m

^{−1/3}s. The values of Manning roughness coefficients were calculated by the relationship given by Gwinn and Ree (1980) [19], which makes their values dependent on grass height, product of water velocity v in the channel, and hydraulic radius vR. The downstream water levels were set up using a weir mounted downstream of the laboratory flume (Figure 4), based on the calculated flow curves for given values of roughness coefficients.

## 3. Results

_{c}and the percentage deviation ΔQ of the measured flow Q from the calculated ($\mathsf{\Delta}Q=\frac{Q-{Q}_{c}}{Q}\cdot 100[\%]$) using relationship (6) were obtained. On this basis, it was possible to determine the downstream water depth h

_{d}, which allowed to obtain a flow rate equal to the measured one, i.e., the percentage deviation was zero ΔQ = 0 (Figure 5). The analysis allowed us to specify the measurement cross-section, where depth h

_{d}was observed at distance L

_{d}from the gate (Figure 5).

_{d}from the gate to the cross-section in which the measured downstream water depth h

_{d}ensures agreement between the calculated and observed flow rates is independent from the roughness coefficient in the downstream channel and increases with the height of the gate opening a. For the opening height a = 0.06 m, the depth h

_{d}should be measured in the cross-section located at a distance L

_{d}≈ 10a downstream of the gate valve. Increasing the sluice gate opening to a height of a = 0.08·m means that the downstream water depths should be measured at a distance of about L

_{d}≈ 15a. Increasing the gate opening to a = 0.10 m shifts the measuring cross-section to a distance of L

_{d}≈ 18a (Figure 7).

_{d}used to calculate the flow Q

_{c}and the depth h measured at the end of the analyzed section, at a distance of 3.035 m from the gate, are small; as a result, the flow rates measured and calculated are equal. The values of the discharge coefficient calculated on the basis of the measured flow rate and flow rate determined on the basis of relationship (5) using the measured depth are also equal. With smaller openings (a = 0.06 m) and large h/a ratios, the differences between h and h

_{d}depths noticeably increase (Figure 8). For example, with the opening height a = 0.06 m and the ratio H/a = 7.85, the depth of the downstream water was h

_{d}= 0.255 m (Figure 8) and should be measured at a distance from the gate L

_{d}= 0.65 m (Figure 7). The calculated ratio of the downstream water depth to the gate-opening height would then be equal h

_{d}/a = 4.25. The measured cross-section at constant distance from the gate at 3.035 m provides a measured downstream water depth equal to h = 0.283 m, changing the value of the ratio h/a = 4.72. Changing this ratio from h

_{d}/a = 4.25 to h/a = 4.72 results in different values of the discharge coefficient as that shown in Figure 3. The discharge coefficient calculated for the depth in the cross-section, in which the measured flow corresponds to the calculated flow, is determined from the curve in Figure 3, given by the ratio h

_{d}/a = 4.25 ≈ 4.0, while the discharge coefficient calculated for the depth h

_{d}measured in a constant measuring cross-section is given by a curve for h/a = 4.72 ≈ 5.0. This means that the discharge coefficients calculated on the basis of the downstream water depth measured in the cross-section located at a constant distance from the valve equal to 3.035 m will be grater. Figure 9 compares the discharge coefficients C

_{d}calculated directly from the measurements and C

_{dc}from relationship (5).

_{d}and depth h measured in the measuring cross-section located at a distance of 3.035 m from the gate (Figure 8), it was assumed that it is possible to calculate the correct flow rate for the submerged outflow of the sluice gate using a correction factor for the discharge coefficient (or flow rate) for depth h measured at the end of the analyzed section.

_{d}and C

_{dc}discharge coefficients calculated for the V1 and V2 experimental cases are shown in Figure 10 as a function of h/a. C

_{d}was calculated using relationship (2) with measured value of the flow rate Q and upper water depth H, while C

_{dc}with relationship (5), based on upper water depth H and downstream h in the cross-section located at a distance of 3.035 m from the gate. The percentage deviation is defined as follows:

_{dcc}for the submerge sluice gate flow.

_{d}and that obtained from the Swamee relationship (5) C

_{dcc}, but corrected it with the factor given in Equation (9). In Figure 11, only exemplary points of C

_{d}and C

_{dcc}were given (as a function of H/a) from selected experiments in the V2 variant. All discharge coefficients determined on the basis of measurements and calculated from relationship (5), with a correction (8,9), show a satisfactory agreement.

_{d}discharge coefficients determined directly by the measurements of those calculated using relationship (11,12), with correction C

_{dcc}in cases V1 and V2, as function h/a, is presented in Figure 12.

_{d}measurements and relationship (5) given by Swamee [15] C

_{dc}are in the range of (−5 ÷ 40)% (Figure 10). The values of the C

_{dcc}discharge coefficients calculated from Equation (5) with the correction ΔC

_{dcc}differ from the discharge coefficients C

_{d}obtained from measurements by ± 9% (Figure 12)

## 4. Conclusions

- As it was not possible to clearly determine the position of the cross-section in which depth h
_{z}should be measured, relationship (1) is not useful for calculating water flow rates on the basis of the depths measured upstream and downstream of the sluice gate. - The location of the cross-section for measuring downstream water depth h, used to calculate downstream discharge coefficients C
_{d}using the Swamme relationship (5), changes with the opening height of the gate a. - It is possible to use the Swamme relationship (5) to calculate the discharge coefficients on the basis of the downstream water depth measured in a fixed cross-section as in the practice of adopting corrections provided in relationships (8), (9). Calculated on the basis of measured depths, upstream H, downstream h and gate opening height a with Equations (11) and (12), the flow factors allow us to achieve compliance between the calculated flow rates and measured rates with accuracy of about 10%, confirming the practical usefulness of this method in estimating flow through the sluice gate, as stated by Boiten (1992) [20].
- This approach might be useful in calibration of other designs of sluice gates for flow measurements.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Submerged flow under the gate: (

**a**) water depth h

_{z}immediately downstream of the gate is noticeably lower than the downstream water depth h (h

_{z}< h), (

**b**) the tailwater curve is always above the jump curve (h

_{z}≈ h).

**Figure 2.**Sluice gate flow: (

**a**) free flow at outflow (unsubmerged); (

**b**) submerged outflow (Swamee, 1992).

**Figure 3.**Values of discharge coefficient for different H/a and h/a ratios in the case of a free and submerged flow through the sluice gate [15].

**Figure 4.**The sluice gate model: (

**a**) the view from the downstream stand in case V1, (

**b**) depth measurement points in case V1, (

**c**) depth measurement points in case V2 (dimensions in meters).

**Figure 5.**Procedure to determine the measurement cross-section for downstream water depth h

_{d}, ensuring that the discharge calculated, using Equation (6), is equal to the observed one; L

_{c}—the distance from the gate to the measurement cross-section.

**Figure 6.**Measured water level profiles downstream of the gate in Case V1 experiments for the submerged sluice gate and constant roughness coefficients in the channel, with percentage deviation ΔQ of the measured flow rate Q from the calculated Qc on the basis of the measured depths.

**Figure 7.**Changes in the L

_{d}distance between the gate and the cross-sections, wherein the measured downstream water depth h

_{d}ensures that calculated flow rate equals the measured one, showed in the function of H/a.

**Figure 8.**Comparison of the water depths h measured in the cross-section 3.035 m downstream of the gate and the depth h

_{d}ensuring agreement between the measured and calculated discharge, according to Equation (6).

**Figure 9.**Discharge coefficients C

_{d}calculated on the basis of measurements in experiments in the V2 case and from the Swamee [15] C

_{dc}relationship (5).

**Figure 10.**Percentage deviation of the C

_{d}discharge coefficients calculated on the basis of measurements from the C

_{dc}obtained using relationship (5): (

**a**) Case V1, (

**b**) Case V2.

**Figure 11.**Discharge coefficients determined from measurements C

_{d}and calculated using relationship (5) with correction (9) for h/a ratios 3, 5, and 7 in the V2 case.

**Figure 12.**Percentage deviation in values of discharge coefficients obtained on the basis of measurements C

_{d}and calculated with correction C

_{dcc}: (

**a**) case V1, (

**b**) case V2.

**Figure 13.**Discharge coefficients obtained from measurements C

_{d}and calculated using Equation (5) with correction (11-12) C

_{dcc}for: (

**a**) case V1; (

**b**) case V2.

**Figure 14.**Nomogram to calculate the discharge coefficients C

_{dcc}developed on the basis of dependence (5), including correction (8-9) for experiments performed in cases V1 and V2.

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**MDPI and ACS Style**

Kubrak, E.; Kubrak, J.; Kiczko, A.; Kubrak, M.
Flow Measurements Using a Sluice Gate; Analysis of Applicability. *Water* **2020**, *12*, 819.
https://doi.org/10.3390/w12030819

**AMA Style**

Kubrak E, Kubrak J, Kiczko A, Kubrak M.
Flow Measurements Using a Sluice Gate; Analysis of Applicability. *Water*. 2020; 12(3):819.
https://doi.org/10.3390/w12030819

**Chicago/Turabian Style**

Kubrak, Elżbieta, Janusz Kubrak, Adam Kiczko, and Michał Kubrak.
2020. "Flow Measurements Using a Sluice Gate; Analysis of Applicability" *Water* 12, no. 3: 819.
https://doi.org/10.3390/w12030819