Field Calibration of Submerged Sluice Gates in Irrigation Canals

Four rectangular sluice gates were calibrated for submerged-flow conditions using nearly 16,000 field-measured data points on Canal B of the B-XII irrigation scheme in Lebrija, Spain. Water depth and gate opening values were measured using acoustic sensors at each of the gate structures, and the data were recorded on electronic data loggers. Several gate calibration equations were tested and it was found that the rectangular sluice gates can be used for accurate flow measurement. The Energy-Momentum (E-M) equations proved to be sound. The calibration of the contraction coefficient, to be used in the energy equation, allowed good estimations of the discharge for three of the four gates studied. The gate for which the E-M method did not perform satisfactorily was located at the head of the canal with a unique nonsymmetric approach flow condition. Alternatively, we investigated the performance of the conventional discharge equation. The variation of the discharge coefficient, Cd, with the head differential, Δh, and the vertical gate opening, w, suggests that Cd be expressed as a function of these two variables. For the sluice gates considered in this study, the best empirical fit was obtained by expressing Cd as a parabolic function of w, although an exponential expression tested previously by other writers also produced satisfactory results. The greatest uncertainty in the variables considered in this study was in the calculated coefficient of discharge, and based on the uncertainty analysis, it is possible to quantify the uncertainty in the estimated discharge through a calibrated sluice gate. The discharge uncertainty in each of the four gates in this study decreases with increasing gate opening, and it decreases slightly with increasing head differentials.     

Refined Energy Correction for Calibration of Submerged Radial Gates

The energy-momentum (E-M) method for calibrating submerged radial gates was refined using a large laboratory data set collected at the Bureau of Reclamation hydraulics laboratory in the 1970s. The original E-M method was accurate in free flow, and when the gate significantly controls submerged flow, but for large gate openings with low head loss through the gate, discharge prediction errors were sometimes large (approaching 70%). Several empirical factors were investigated with the laboratory data, including the combined upstream energy loss and velocity distribution factor and the submerged flow energy correction. The utility of the existing upstream energy loss and velocity distribution factor relation was extended to larger Reynolds numbers. The relation between the relative energy correction and the relative submergence of the vena contracta was shown to be sensitive to the relative jet thickness. A refined energy correction model was developed, which significantly improved the accuracy of submerged flow discharge predictions. Although the focus of this work was radial gates, the energy correction concept and these refinements potentially have application to all submerged sluice gates.     

Energy and Momentum Velocity Coefficients for Calibrating Submerged Sluice Gates in Irrigation Canals

There is renewed interest in developing calibration methods for gates operating in submerged conditions in irrigation canals. In the present study, a new method based on a generalization of the standard energy-momentum method that accounts for variations in the energy and momentum velocity coefficients is proposed, for the following reasons. First, it was found that the assumption of uniform submerged jet velocity to account for the kinetic energy head and momentum flux is in reality equivalent to assuming a parabolic relationship between the Coriolis and Boussinesq coefficients. Second, literature investigations showed that the coefficients for the downstream side of submerged gates are notably greater than unity, and the implicit parabolic relationship between these coefficients in the standard energy-momentum method is inadequate, at least for high submergence conditions. The proposed energy-momentum method was evaluated using the data obtained from four gates operating in an irrigation canal in Southern Spain. Improvements in accuracy compared to the standard energy-momentum method (with a constant contraction coefficient Cc = 0.61) were obtained. The results indicate that the calibration of coefficient approach provides a means to improve the energy-momentum method by (indirectly) accounting more accurately for nonuniform velocity effects in the energy-momentum equations.     

Calculation of Contraction Coefficient under Sluice Gates and Application to Discharge Measurement

The contraction coefficient under sluice gates on flat beds is studied for both free flow and submerged conditions based on the principle of momentum conservation, relying on an analytical determination of the pressure force exerted on the upstream face of the gate together with the energy equation. The contraction coefficient varies with the relative gate opening and the relative submergence, especially at large gate openings. The contraction coefficient may be similar in submerged flow and free flow at small openings but not at large openings, as shown by some experimental results. An application to discharge measurement is also presented.     

Role of Energy Loss on Discharge Characteristics of Sluice Gates

A theoretical method was used to derive an equation for the discharge coefficient of sluice gates in rectangular channels under orifice-flow (both free and submerged) conditions. The proposed equation allows for the effects of energy dissipation between the upstream section of the gate and the vena contracta. The hydraulic energy loss in the upstream pool is attributable to the induced turbulence by the recirculating region and to the growth of bottom boundary layer. For the submerged-flow condition, turbulent shear-layer entrainment is also responsible for the energy loss. This energy loss is introduced into the equations through a coefficient k that has been conventionally assumed to be negligible. Experimental data from the literature were used to validate the equation, which showed good agreement with the measured values. It is also shown that the magnitude of the energy-loss factor is a function of the geometry of the gate and can modify the discharge coefficient. An equation for the distinguishing condition between free and submerged flows is also presented. The new equations can be used to predict the performance of sluice gates with different edge shapes under free- and submerged-flow situations.     

Dimensionless Stage–Discharge Relationship in Radial Gates

Dimensional analysis was used to obtain stage–discharge relationships under submerged and free flow conditions in radial gates to develop a management tool. Experimental data from a laboratory flume and the indicial method of dimensional analysis were used for this purpose. The resulting equation relates the discharge (or critical depth) to upstream and downstream water depth and gate opening. These equations were then validated by experimental data obtained from field radial gates and compared with the conventional gate equation. Results showed that there was a good agreement between dimensionless equations and field and laboratory data under submerged or free flow conditions. Dimensionless equations are more general and accurate than the conventional ones when there is not an accurate estimation of discharge coefficients.     

Conversion from Discharge to Gate Opening for the Control of Irrigation Canals

The paper reviews several methods to convert discharge into gate opening. A control algorithm for one or several reaches of an irrigation canal sometimes uses a discharge as the control action variable even though the device to be manipulated is a gate or a weir. In this case a slave controller has to convert the discharge into a gate opening or a sill elevation in the case of a weir. This is usually done by inverting the static relation between discharge and gate opening. An improved method can be based on the characteristics theory to estimate the deviations of the water levels. However, both methods underestimate the gate opening deviations required to deliver a desired discharge deviation, because water levels vary continuously over time when the gate is operated. The paper proposes a method to take into account this dynamic behavior of the pool-gate interaction by using a simple linear model for the pools’ dynamics, the integer delay zero model. The proposed method enables us to better estimate the gate opening necessary to get a desired average discharge. The method is evaluated in simulation and on a gate of the Gignac Canal, located in the South of France. A dimensionless analysis of the problem is finally performed to evaluate the methods’ applicability.     

Performance of Submerged Ogee-Crest Weir Head-Discharge Relationships

Submergence is defined as the ratio of the tailwater to the headwater, both measured relative to the weir crest. The performance of published submerged ogee-crest head-discharge relationships was investigated in this study. Four submerged and one free-flow head-discharge relationship were evaluated relative to a submerged ogee-crest data set covering a range of tailwater elevations, discharges, and weir geometries. For submergence levels <0.70, the head-discharge relationship was relatively independent of the tailwater elevation, but at higher submergence levels, this was not the case. For submergence values <0.8, the submergence head-discharge data were best predicted using the free-flow head-discharge relationship. For submergence values >0.8, the accuracies of all but one of the head-discharge relationships were very poor. For such high submergence levels, more accurate methods are needed for predicting submerged ogee-crest head-discharge relationships.     

Analytical Solution for Circular Gates as Flow Metering Structures

Water measurement in irrigation canals is frequently hindered by low head availability and high capital investment costs associated with construction of compatible hydraulic structures. Often irrigation systems have circular sliding gates in place used as diversion and flow control structures. The Fresno Irrigation District investigated the feasibility of using such circular gates (Armco Model 101) as flow metering stations in the 1920s. This early work demonstrated that circular gates could be used simultaneously for both flow control and as flow measurement structures. The original work is compiled by USBR as 10,500 data points and is presented in tabular fashion for gate diameters varying from 20.3?to?121.9?cm (8–48?in.). An analytical equation of the form Q = CD(y,D)yD, [where CD(y,D) is a discharge function which depends on the gate displacement y and the nominal gate diameter D, g represents the gravitational acceleration, and H is the hydraulic headloss through the crescent-shaped orifice] accurately predicts most tabulated values. Equations are provided to compute the discharge function for nominal gate diameters varying from 20.3?to?121.9?cm (8–48?in.) for gate displacements between 5.1?cm (2?in.) and fully open conditions. The precision of the proposed algorithms are excellent (predicted values are within ±5% of the corresponding reported values 95% of the time) for gates greater than 30.5?cm (12?in.).     

Discharge Relation for Cutthroat Flume under Free-Flow Condition

A cutthroat flume is commonly used as flow measuring device for open-channel flow due to ease of fabrication and installation. In most of the cases it is difficult to calibrate the flume in the field. Therefore, accurate relation between discharge and upstream head applicable for all sizes of cutthroat flume is needed. Seven different sizes of cutthroat flumes, having different length to throat width ratios, are fabricated and tested in the laboratory under free-flow condition. Selecting groups of different variables describing flow through a cutthroat flume number of dimensionless parameters are formed. Regression analysis of experimental data is carried out between all possible combinations of pairs of dimensionless parameters and the pair giving the best correlation is selected. Using the selected pair, relation between dimensionless parameters of discharge and head is developed. The relation is simple and convenient to use and, at the same time, more accurate compared to methods available in literature for prediction of discharge.     

Simulation of Automatic Canal Control Systems

Simulation models for unsteady open channel flows have been commercially available for more than 2 decades. Most of these models are now available for personal computers and can be used to study the control of irrigation canals. Studies on automatic control methods and algorithms have been performed on at least half a dozen of the available unsteady-flow simulation models. Although, many of these automation studies have been conducted by the institution that created the simulation model, these simulation models were not created with automatic gate control in mind, and thus one has to be intimately familiar with the source code in order to implement sophisticated control features. Three commercially available unsteady-flow simulation software packages that allow automatic control of gates based on algorithms written by users are: CanalCAD from the Univ. of Iowa, Hydraulics Lab; Mike 11 version 3.2 from the Danish Hydraulic Institute; and Sobek from Delft Hydraulics. In this paper, we describe the various features of these unsteady-flow simulation packages and how they interface to control engineering software/code. There are a number of tradeoffs between simplicity and functionality. All these models present difficulties and have limitations. The hope is to provide guidance on the next generation of unsteady-flow canal simulation models so that control functions can be routinely applied.     

Conditional Assessment of Flow Measurement Accuracy

A study conducted by the Utah Water Research Laboratory assessed the accuracies of a wide variety of flow measurement devices currently in service. During the study, a wide variety of flow measurement devices, including flumes, weirs, and rated sections in open channel systems, were evaluated; magnetic and ultrasonic meters in closed-conduit systems were also tested. The specified design accuracies for each device are presented. Actual flow measurements were determined at 70 sites and were compared with the theoretical discharges of each device. Comparison of actual and theoretical flow indicates that only 33% of the measurement devices tested currently measure flow within manufacturer-designed specifications. Field data is presented, and possible reasons for the flow measurement errors and their corrections are discussed.     

New Method for Estimation of Discharge

A new technique for drawing isovel patterns in an open or closed channel is presented. It is assumed that the velocity at each arbitrary point in the conduit is affected by the hydraulic characteristics of the boundary. While any velocity profile can be applied to the model, a power-law formula is used here. In addition to the isovels patterns, the energy and momentum correction factors (α and β), the ratio of mean to maximum velocity (V/umax), and the position of the maximum velocity are calculated. To examine the results obtained, the model was applied to a pipe with a circular cross section. A comparison between the profiles of the proposed model and the available power-law profile indicated that the two profiles were coincident with each other over the majority of the cross section. Furthermore, the predicted isovels were compared with velocity measurements in the main flow direction obtained along the centerline and lateral direction of a rectangular flume. The estimated discharge, based on measured points on the upper half of the flow depth away from the boundaries was within ±7% of the measured and much better in comparison to the prediction of one- and two-point methods. The prediction of the depth-averaged velocity values for the River Severn in the United Kingdom shows a good agreement with the measured data and the best analytical results obtained by the depth-averaged Navier–Stokes equations.     

Supervised Gain-Scheduling Multimodel versus Linear Parameter Varying Internal Model Control of Open-Channel Systems for Large Operating Conditions

In this paper, two internal model control (IMC) controllers using gain-scheduling techniques are proposed and compared for open-channel systems that allow to deal with large operating conditions. In particular, in one side, a linear parameter varying (LPV) model for an open-flow channel system based on a second-order delay Hayami model is proposed. This model will allow one to design a classic gain-scheduling strategy for the IMC controller. On the other side, the LPV model is discretized in a set of linear time invariant (LTI) models corresponding to different operating points. For each LTI model a LTI IMC controller is designed off-line. Then, a supervised gain-scheduler detects on-line which is the LTI model that represents better the open-flow channel system at the current operating point and decides which is the LTI controller that should be used. Finally, both approaches will be applied to a simulated open canal: the Lunax gallery located at Gascogne, France.     

Multiple-Model Optimization of Proportional Integral Controllers on Canals

Canals or open channels that convey water often consist of pools in series separated by control structures. Successful implementation of water-level control with these structures using decentralized proportional integral (PI) controllers depends heavily on the tuning of the control parameters. These parameters are hard to determine due to the interactions between the pools and the varying flow conditions in the canal. This paper presents a procedure for tuning any linear controller (including decentralized PI controllers) that guarantees stability of the controlled canal. It minimizes a cost function that weights the water-level deviations from the target level against control efforts at both low- and high-flow conditions. The procedure is tested on a model of the Umatilla Stanfield Branch Furnish Canal in Oregon. The tests show the capability of the procedure to deal with the pool interactions. The results of a realistic turnout schedule applied to the controlled canal show the high performance of the controllers (small water-level deviations in all pools) over varying flow conditions.     

Evaluation of the Water Delivery Performance of the Menemen Left Bank Irrigation System Using Variables Measured On-Site

This study determines the water delivery performance at secondary and tertiary canal level of the Menemen Left Bank Irrigation system, an open canal irrigation system located in Turkey, for the irrigation seasons of the years 2005–2007. At secondary canal level, water supply ratio was used, and at tertiary level, the indicators of adequacy, efficiency, dependability, and equity were used. In calculating these indicators in this study, the amounts of water diverted to the canals, efficiency of water conveyance, and of water application were measured. Of these indicators, the water supply ratio was determined for the secondary canal, and the other indicators were determined for a total of six selected tertiary canals at the head, middle, and lower end of the secondary. At secondary level, the water supply ratios obtained to total irrigation water requirements for the months of July and August, when requirement for irrigation water is at a maximum, was determined to be less than one, while the water supply ratios obtained to net irrigation water requirement was found to be more than one. With regard to water delivery performance at tertiary level, adequacy, efficiency, dependability, and equity were found to be poor for each of the three years of the study, with efficiency rising to “fair” level only in 2005. In order to raise the water delivery performance of the system, it is necessary to reduce water conveyance losses to increase the water application efficiency, to prepare water distribution plans which take in tertiary canals, and to measure and monitor the water diverted to the canals.     

Backwater Prediction due to the Blockage Caused by a Single, Submerged Spur Dike in an Open Channel

A method is proposed for predicting the backwater effect due to a single, submerged spur dike located within an open channel flow. A theoretical analysis based on the momentum principle relates the backwater effect to the drag force exerted by the spur dike on the flow. Experimental data obtained in laboratory flumes having subcritical flow conditions throughout the flow field have been used in developing predictive relationships for the spur dike drag coefficient, which is found to be strongly correlated to the blockage created by the spur dike within the flow cross section. The predictive relationships provide a means of obtaining a first-level estimate of the backwater effect due to a single, submerged spur dike in an open channel flow.     

General Characteristics of Solutions to the Open-Channel Flow, Feedforward Control Problem

A dimensionless formulation of the open-channel flow equations was used to study the feedforward control problem for single-pool canals. Feedforward inflow schedules were computed for specified downstream demands using a gate-stroking model. The analysis was conducted for various design and operational conditions. Differences in the shape of the computed inflow hydrographs are largely related to the volume change resulting from the transient, the time needed to supply this volume, and the time needed by the inflow perturbation to travel down the canal. The gate-stroking method will fail to produce a solution or the solution will demand extreme and unrealistic inflow variations if the time needed to supply the canal volume change is much greater than the travel time of the upstream flow change. As an alternative, a simple feedforward-control flow schedule can be developed based on this volume change and a reasonable delay estimate. This volume compensating schedule can deliver the requested flow change and keep water levels reasonably close to the target under the range of conditions tested.