Irrigation Offtake Sensitivity

This article is an attempt to develop an analytical framework to address sensitivity of irrigation offtakes. The perturbation of water depth and the deviation of the setting are considered for analysis. Sensitivity of delivery takes into account the impacts of the perturbations on the delivery (to the command area of the offtake). Sensitivity of conveyance assesses the effects on the conveyance discharge of the parent canal. Analytical formulations of six sensitivity indicators are provided. The concept of head loss equivalent is introduced to explicitly take into account the hydraulic behavior in the dependent canal downstream of the offtakes. Hydraulic perturbations are considered either as upstream deviations in the parent canal or downstream perturbations in the dependent canal.     

Offtake Sensitivity, Operation Effectiveness, and Performance of Irrigation System

Analytical relationships between the control of canal water depth, the sensitivity of irrigation delivery structures, and the resulting internal performance are established at the system level. One system sensitivity indicator is derived for both adequacy and efficiency, and two for equity (coefficient of variation and Theil information index). The level of precision which reflects the effectiveness in controlling water depth is defined as a permissible variation of water depth at the cross-regulator (±ΔHR) about the target. The degree of influence exercised by the cross-regulator on offtakes is accounted for through an influence factor between zero and one. The behavior of three different irrigation systems in Sri Lanka and Pakistan is studied with both analytical system indicators and numerical hydraulic simulations. It shows good agreement for a range of precision between 0.02 and 0.2 m. These global system indicators can be used to define the precision level required to achieve a given performance, to estimate actual performance from recorded precision at regulators, and to diminish the system sensitivity, improving the performance for a given precision. Practical operating policies can be inferred from sensitivity information of irrigation systems without the necessity of a complex irrigation operation model.     

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.).     

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.     

Reducing Detention Volumes with Improved Outlet Structure

To reduce required detention volume, a detention basin outlet structure (DBOS) was tested that can control the maximum allowable outlet discharge rate independent of the upstream driving head. Unlike traditional outlet control structures, such as culverts, orifices, and weirs, whose maximum discharge represents a single point in time on the outflow hydrograph, the DBOS can discharge at the maximum allowable discharge for an extended period of time, thus reducing the required detention volume. Data are presented and methods discussed regarding techniques for altering the head–discharge characteristics of the DBOS in order to meet various head–discharge requirements.     

Allocation of Flow to Plots in Pressurized Irrigation Distribution Networks: Analysis of the Clément and Galand Method and a New Proposal

This article reviews the method for allocating flow to irrigation plots proposed by Clément and Galand in (1979). Mention is made of its shortcomings, such as the lack of consideration given to the specific technical and economic factors governing current pressurized (drip or sprinkler) irrigation systems and how they provide water to plots. We propose a method for fixed irrigation systems, which takes into account the irrigation method on the plot and the existence of an optimum block area. The result is to allocate a constant flow of water to plots up to an established value of maximum surface area. From there on, we propose applying linear increases related to the total plot area. We also present a formula for calculating the maximum number of blocks based on variables that are easily obtainable during the project phase.     

Influence of Regulators in Controlling Upstream Water Depth

Control of irrigation canals usually consists of control of water levels upstream from regulators or check structures. Regulators provide the necessary head to offtakes. Generally, influence factor is used to express the extension of the backwater curve effect within the controlled reach. This factor shows how a change in water depth exercised by a regulator can influence the water surface profile along an irrigation canal. No direct equation is available in the technical literature up until now for calculating this factor on the basis of the steady gradually varied flow theorem. In current research, using the steady gradually varied flow equation for a prismatic canal, an elegant algebraic equation for this factor is derived. Control of water levels upstream from regulators is an important application of this equation in irrigation networks.     

Irrigation Scheduling Using Mixed-Integer Linear Programming

A mixed-integer program is presented for scheduling canal irrigation among a group of users where the duration of flow of each outlet and a target start time is specified by the users. Two models are developed. The first is a single-period model which uses as input a minimized demand at the head of the canal. This will allow the discharge at the head of the canal to be set once at the beginning of the irrigation period. Within this constraint, the single-period model minimizes the sum over all outlets of the difference between the scheduled start time of flow to each user and the requested target start times. The second model is a multiperiod model. This model favors those users who had been disadvantaged in the previous irrigation periods by giving them priority in scheduling their actual start times with target start times for the subsequent irrigation period. The proposed models can be used to support decisions in irrigation schemes operating on an arranged demand.     

Simple Water Level Controller for Irrigation and Drainage Canals

A simple water level controller for irrigation and drainage canals is proposed; the proposed controller has a master-slave structure where the slaves control the flow rates through the control structures. The master controller consists of PI-based controllers for feedback, and a decoupler and feedforward controller that are based on the inversion of a simple dynamic model of the canal system. The applicability of the controller is demonstrated in field experiments.     

Equivalent Friction Factor Method for Hydraulic Calculation in Irrigation Laterals

A simplified method for the resolution of lateral hydraulic problems in laminar and turbulent flow is presented. In the first stage, the head losses are calculated by applying the Darcy–Weisbach equation with a discrete and constant outflow model, which leads to a correction parameter equivalent to Anwar’s Ga factor. The difficulty that arises from variation of the friction factor along the lateral (due to discharge flow) is overcome by means of an equivalent friction factor (feqN). In the second stage, this head loss model is used together with a variable discharge model based on Taylor polynomials to make a better estimate of the flow rate distribution by means of a successive-approximations scheme. This new approach directly allows the computation of the real mean lateral’s outflow and the minimum and maximum discharges. In the third stage, the previous results can be improved (if desired) by taking into account the nonconstant outflow distribution model developed in the previous stage. The method proposed is useful to work out the hydraulic computation of laterals with the inlet segment at full or fractional outlet spacing, and complex laterals when a different pipeline diameter, slope, flow regime, or emitter gap has to be considered. The results are comparable to those obtained in the literature.     

Discharge Formulas of Crump-De Gruyter Gate-Weir for Computer Simulation

One of the problems of interest to professionals in the field of irrigation and drainage is the computer simulation of discharge or level control structures. Particularly troublesome are structures that display a marked change of behavior when the downstream water level exceeds a certain limit. The Crump-de Gruyter gate displays several such changes of behavior. Not only does it exhibit a transition from free to drowned flow when the downstream water level rises, it can also go from weir to gate flow. A series of experiments in a laboratory flume provided the basic data to test a simple mathematical model of this structure. The model assumes the structure is located between two reaches with sub-critical flow in the upstream and downstream reach.     

Field-Scale Assessment of Uncertainties in Drip Irrigation Lateral Parameters

Grass establishment on railway embankment steep slopes for erosion control in Central Queensland, Australia, is aided by drip lateral irrigation systems. The effective field values of the lateral parameters may be different from the manufacturer supplied ones due to manufacturing variations of the emitters, environmental factors, and water quality. This paper has provided a methodology for estimating drip lateral effective parameter values under field conditions. The hydraulic model takes into account the velocity head change and a proper selection of the friction coefficient formula based on the Reynolds number. Fittings and emitter insertion head losses were incorporated into the hydraulic model. Pressure measurements at some locations within the irrigation system, and the inlet discharges, were used to calibrate the lateral parameters in a statistical framework that allows estimation of parameter uncertainties using the Metropolis algorithm. It is observed that the manufacturer’s supplied parameters were significantly different from the calibrated ones, underestimating pressures within the irrigation system for a given inlet discharge, stressing the need for field testing. The parameter posterior distributions were found to be unimodal and nearly normally distributed. The emitter head loss coefficient distribution being very significant suggests the need to incorporate it into the hydraulic modeling. Although the example given in this paper relates to steep slopes, the methodologies are general and can be applied to any use of drip laterals.     

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.     

Pumping Selection and Regulation for Water-Distribution Networks

Because of the increasing importance of on-demand irrigation systems, a support system for general use has been developed to aid in selecting and regulating pumping stations. This innovation will improve the balance between total costs (project and energy) and operation quality. The procedure first determines the maximum and minimum system head curves, followed by the evolution of demand curves to obtain the maximum discharge needed. Once this discharge is determined, it is possible to carry out the dimensioning and regulation of the pumping station. An easy tool to select the number of variable and fixed speed pumps has also been developed Excel and Visual Basic can be used. The results demonstrate the importance of selecting pumps that are best adapted to the system head curve. The minimum total cost solution has been obtained by using one variable-speed pump in conjunction with another operating at fixed speed.     

Analytical Equation for Variation of Discharge in Drip Irrigation Laterals

Statistical uniformity of discharge variation is an important parameter in designing drip irrigation laterals. A simple analytical equation is derived to determine the coefficient of variation of discharge. This equation is used to determine the coefficient of variation of discharge for a numerical problem. The result is compared with the energy gradient line approach. Both the methods give the same result. For any required coefficient of variation of discharge, the diameter of a lateral can be designed directly for a known lateral length, slope, emitter discharge exponent, pressure head at the start of the lateral, and discharge rate through the lateral, by writing the analytical equation in quadratic form.     

Modeling the Behavior of Flow Regulating Devices in Water Distribution Systems Using Constrained Nonlinear Programming

Currently the modeling of check valves and flow control valves in water distribution systems is based on heuristics intermixed with solving the set of nonlinear equations governing flow in the network. At the beginning of a simulation, the operating status of these valves is not known and must be assumed. The system is then solved. The status of the check valves and flow control valves are then changed to try to determine their correct operating status, at times leading to incorrect solutions even for simple systems. This paper proposes an entirely different approach. Content and co-content theory is used to define conditions that guarantee the existence and uniqueness of the solution. The work here focuses solely on flow control devices with a defined head discharge versus head loss relationship. A new modeling approach for water distribution systems based on subdifferential analysis that deals with the nondifferentiable flow versus head relationships is proposed in this paper. The water distribution equations are solved as a constrained nonlinear programming problem based on the content model where the Lagrangian multipliers have important physical meanings. This new method gives correct solutions by dealing appropriately with inequality and equality constraints imposed by the presence of the flow regulating devices (check valves, flow control valves, and temporarily closed isolating valves). An example network is used to illustrate the concepts.     

Sensitivity Analysis of Soil Hydraulic Properties on Subsurface Water Flow in Furrows

Knowledge of the sensitivity of various soil hydraulic properties is beneficial for model development and application purposes. It can lead to better estimated values, better understanding, and thus reduced uncertainty. In the present study, an extensive sensitivity analysis was performed to investigate the effects that various soil hydraulic properties have on subsurface water flow below furrows during two successive irrigation events to see which irrigation event was more sensitive and to analyze the effect of spatial variations in the initial soil water contents within the soil profile. Testing the sensitivity of the various soil hydraulic parameters in the van Genuchten-Mualem expression was carried out using the HYDRUS-2D model for two irrigation events 10?days apart. Results showed that the first irrigation event was clearly more sensitive than the second one. The latter event was mainly associated with the nonuniformity of the initial soil water contents within the soil profile. Pressure heads in the soil profile were more sensitive than cumulative outlet fluxes and soil water contents. Sensitivity analysis results for pressure heads, cumulative fluxes, and water contents indicated that in every case the most sensitive parameter was the hydraulic property shape factor (n) followed by the saturated water content (θs), the saturated hydraulic conductivity (Ks), the residual water content (θr), and the shape factor in the soil water retention curve (α), with the pore-connectivity parameter (l) the least sensitive parameter during both irrigation events. Pressure head sensitivity analysis for all parameters studied showed that the least sensitivity was linked with the wetting front as it gradually moved deeper with time, and the highest sensitivity was observed in those regions where the initial soil water contents were lower. Similarly, for water contents, higher sensitivity occurred in the drier regions during the first irrigation event and near the moisture front in the second irrigation event. Both pressure heads and water contents showed some sensitivity near the soil surface during both irrigation events, suggesting the importance of evaporation from the soil surface.     

Modified Hazen–Williams and Darcy–Weisbach Equations for Friction and Local Head Losses along Irrigation Laterals

In previous analytical approaches, the direct calculation of friction loss along a lateral is usually based on empirical power-form flow resistance equations, such as the Hazen–Williams and Blasius equations. The more generalized Darcy–Weisbach resistance equation is not usually applied since its friction coefficient varies along the lateral. In this paper, initially, the Darcy–Weisbach and Hazen–Williams equations are systematically compared, leading to a correction form for the Hazen–Williams coefficient. In addition, a more accurate procedure assuming a power function form for the Darcy–Weisbach equation along irrigation laterals is also proposed. The systematic analysis of various typical flow pipe irrigation situations (e.g., sprinkler irrigation laterals of linear or radial-center pivot displacement, trickle irrigation laterals, and manifolds) indicates that the friction loss along laterals calculated using the Darcy–Weisbach equation closely follows a discharge-power form function. The two empirical parameters of the power function depend on the specific pipe characteristics as well as the specific range of discharge values along the lateral. The proposed analytical solution is extended to incorporate the local head loss, the velocity head variation, and the outflow nonuniformity along sprinkler and trickle irrigation laterals. The suggested direct computation solution is demonstrated in two application examples of sprinkler and trickle irrigation laterals and compared with accurate numerical solutions.     

Water Distribution in Laterals and Units of Subsurface Drip Irrigation. II: Field Evaluation

The performance of drip irrigation and subsurface drip irrigation (SDI) laterals has been compared. Two emitter models (one compensating and the other noncompensating) were assessed. Field tests were carried out with a pair of laterals working at the same inlet pressure. A procedure was developed that recorded head pressures at both lateral extremes and inlet flow during irrigation. Both models showed similar behavior and soil properties affected their discharge. On the other hand, the performance of a field SDI unit of compensating emitters was characterized by measuring pressures at different points and inlet flow. Finally, the distribution of water and soil pressure in the laterals and the unit were predicted and irrigation uniformity and soil pressure variability were also determined. Predictions agreed reasonably well with the experimental observations. Thus, the methodology proposed could be used to support the decision making for the design and management of SDI systems.     

Discharge Coefficient for a Water Flow through a Bottom Orifice of a Conical Hopper

Discharge coefficients for water flow through a vertical, circular orifice at the bottom of a conical hopper were experimentally studied in the present paper. The conical hopper consists of a cylindrical hopper of inside diameter of 48 cm and a bottom cone of side slope of 45°. Experiments were carried out under different orifice diameters and water heads. The dependence of the discharge coefficient on the orifice diameter and water head was analyzed, and then an empirical relation was developed by using a dimensional analysis and a regression analysis. The results show that the larger orifice diameter or higher water head have a smaller discharge coefficient and the orifice diameter plays more significant influence on the discharge coefficient than the water head does. The discharge coefficient of water flow through a bottom orifice is larger than that through a sidewall orifice under the similar conditions of the water head, orifice diameter, and hopper size.