Simplified Procedure to Evaluate Head Losses in Drip Irrigation Laterals

The lateral lines of a drip irrigation system consist of pressurized pipelines with inline or online emitters. Proper hydraulic design of drip laterals usually requires the accurate evaluation of the total head losses, represented by friction losses along the pipe and the emitters, and local losses due to the emitter connections. This paper extends the local loss evaluation procedure, previously obtained for coextruded laterals, on the basis of new experiments. In addition, a simplified procedure was proposed based on the constant outlet discharge assumption for a quick evaluation of total head losses in drip irrigation lines, taking into account the total local loss due to the emitter connections. Total head loss values measured on 15 commercially available coextruded laterals were then compared with those obtained by using the nowly proposed methodology. Relative errors on the pressure head estimation for the examined cases were always ±2.4%, and therefore the proposed methodology could serve for a quick, approximate evaluation of the total head losses along the laterals.     

Determining Minor Head Losses in Drip Irrigation Laterals. II: Experimental Study and Validation

Values of friction coefficient K and equivalent length le were determined for various emitter models using analytical and experimental procedures developed in the companion paper by Juana et al. in 2002. Flow contraction coefficient Cc for water jets discharging through orifices with angle α=45° is suggested when the emitters have hydrodynamic geometry at the insertion. Otherwise, α=90° or, as an extreme value, α=180° is preferred. Both criteria K and le showed a reasonable agreement for minor losses evaluation produced at emitter insertions along drip laterals. Accuracy on their determination was analyzed. Larger dispersion of K and le values was observed when lateral head losses were small. Inlet head, Reynolds number, and emitter spacing did not show a clear effect on K and le values, whereas the effect of obstruction ratio r of the pipe cross-sectional area at the emitter location was of practical significance. Parameters of the emitter discharge equation determined with lateral tests were comparable to those obtained on an emitter testing bench using the International Standard procedure.     

Determining Minor Head Losses in Drip Irrigation Laterals. I: Methodology

Minor head losses at emitter insertions along drip laterals were predicted by a derivation of Bélanger’s theorem and analyzed by the classic formula that includes a friction coefficient K multiplied by a kinetic energy term. A relationship was established for K as a function of some emitter geometric characteristics. These take into account the flow expansion behind the reduction of the cross-sectional area of the pipe due to obstruction by the emitter. Flow constrictions at emitter insertions were estimated by analogy with contraction produced by water jets discharging through orifices. An experimental procedure was also developed to determine minor losses in situ, in the laboratory or in the field. An approach is suggested to calculate either K or the emitter equivalent length le as a function of lateral head losses, inlet head, and flow rate. Internal diameter and length of lateral, emitter spacing, emitter discharge equation, and water viscosity must be known. Approximate analytical relations to study flow in laterals were developed. They may be used to design and evaluate drip irrigation units. Analytical and experimental procedures are validated in the companion paper by Juana et al.     

New Computational Fluid Dynamic Procedure to Estimate Friction and Local Losses in Coextruded Drip Laterals

The design of trickle irrigation systems is crucial to optimize profitability and to warrant high values for the emission uniformity (EU) coefficient. EU depends on variation of the pressure head due to head losses along the lines and elevation changes, as well as the water temperature, and other parameters related to the emitters (manufacturer’s coefficient of variation, number of emitters per plants, emitter spacing). Trickle irrigation plants are usually designed using small diameter plastic pipes (polyethylene or polyvinyl chloride). The design problem, therefore, needs to consider head losses along the lines as well as emitter discharge variations due to the manufacturer’s variability. Variations in the hydraulic head are a consequence of both friction losses along the pipe and local losses due to the emitters’ connections, whose importance has been recently emphasized. Since each local loss depends on the emitter type (in-line or on-line) as well as on its shape and dimensions, the morphological variability of the commercially available emitter requires experimental investigations to determine local losses in drip laterals. On the other hand, local losses can be estimated by the mean of computational fluid dynamics (CFD) models, allowing analysis of velocity profiles and the turbulence caused by the emitters’ connections. FLUENT software can be considered a powerful tool to evaluate friction and local losses in drip irrigation laterals, after the necessary validation has been carried out by means of experimental data. The main objective of this study was to assess a CFD technique to evaluate friction and local losses in laterals with in-line coextruded emitters. The model was initially used to choose the turbulence model allowing the most accurate estimation of friction losses in small diameter polyethylene pipes, characterized by low Reynolds number. Second, the possibility of using CFD to predict local losses in drip irrigation laterals with a commercially available coextruded emitter was investigated. Simulated local losses were obtained as difference of the total and friction losses along a trunk of pipe, where one single emitter was installed, not considering the emitter outflow. The proposed procedure allows to evaluate local losses for other different emitter models, avoiding tedious and time-consuming experiments.     

Simple Method for the Design of Microirrigation Paired Laterals on Sloped Fields

In this study, a method for designing paired laterals that meet with required water application uniformity on sloped fields was developed using the energy gradient line approach based on the definition of the best submain position locations in which the same minimum pressure exists in uphill and downhill laterals. The best equation form of best submain position was determined. Also, the solution procedure was introduced to get the final solution to avoid the phenomena of no convergence or slow convergence. In this method, the required water application uniformity was used directly as a computational parameter in designing. When the designed emitter discharge, required water application uniformity and one parameter (either length or diameter) of a paired lateral are provided; the system developed here enables another parameter and the best submain position to be determined for any field slope conditions. Taken together, the results of this study show that final solutions can be obtained quickly and reasonably.     

Linear Solution for Hydraulic Analysis of Tapered Microirrigation Laterals

A simplified analytical solution that takes into account the effect of the emitter discharge exponent on the hydraulic computations of tapered microirrigation laterals, is presented. The hydraulic analysis is evaluated based on the spatially variable discharge function approach. A simple power equation was used to express distribution of the variable outflow delivered from the each emitter along the lateral. An analytical solution is developed for the case of a linear relationship between the emitter discharge and pressure head, namely, the emitter discharge exponent equals to unique, y = 1.0. In this procedure, the analytical derivations can be applied for uphill, downhill, and zero slope conditions. Results are comparable to those obtained from the literature.     

Real Local Losses Estimation for On-Line Emitters Using Empirical and Numerical Procedures

This paper presents a procedure based on a lateral, where the flow rate of all the emitters and the pressure every 10?m were measured. Our goal was to obtain a general formula for directly calculating the local losses of on-line emitters as a function of the number of emitters, the average emitter discharge, and the ratio between the protrusion area and the pipe cross-sectional area. A total friction factor, including the local losses and the Blasius friction factor, was obtained as well. Both approximations accurately predict the local and total losses for the experimental data obtained in an irrigation loop system placed in the Rural Engineering Laboratory. Finally, an estimation of these local losses using a computational fluid dynamics model was carried out by the writers. Our numerical approach accurately predicts the local losses and allows the use of this technique to obtain a better estimation of the local turbulence originated by the emitter’s connection.     

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.     

Explicit Hydraulic Design of Microirrigation Submain Units with Tapered Manifold and Laterals

The optimum hydraulic design problem for microirrigation submain units of specified dimensions is solved analytically. New algebraic equations were derived to calculate explicitly the optimum values of the design variables. The design variables are the lengths of two given pipe sizes for the laterals as well as the appropriate lengths of the available pipe sizes for the manifold. Tapered laterals and manifold are selected in such a way that the sum of the costs of the laterals and the manifold is minimized, while the hydraulic design criterion is ensured. The case of a single-diameter lateral with tapered manifold pipeline is also examined. The design procedure can be also applied in sprinkle irrigation tapered laterals. The explicit optimum design solution is demonstrated in two cases studied.     

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.     

Determining Operating Inlet Pressure Head Incorporating Uniformity Parameters for Multioutlet Plastic Pipelines

An important objective of a microirrigation system is to determine the proper operating inlet pressure head, ensuring the desired level of water application uniformity as well as the allowable pressure head variation along the multioutlet pipeline. This paper offers, simple, direct, but sufficiently accurate, relationships incorporating different microirrigation uniformity parameters, such as Christiansen uniformity coefficient, coefficient of variation of emitter discharge, and allowable pressure head variation, to determine the operating inlet pressure head (i.e., pressure head and outflow profiles) for multioutlet plastic pipelines. In this analysis some mathematical expressions were deduced to relate three uniformity parameters; then the operating inlet pressure head is simply reformulated by taking into account a multiplying factor α to the required average outlet pressure head, in terms of three uniformity parameters. Resulting, the influence of different uniform pipe slopes on the water application uniformity and the operating inlet pressure head for various emitter discharge exponents, was evaluated. In addition, to cover various design combinations an extensive comparison between the proposed equations and those of the previous studies was also presented. Examination of the results from this research indicated that, the performance of the proposed technique is sufficient in comparison to those of the recent analytical and numerical procedures.     

Hydraulic Analysis of Multidiameter Center-Pivot Sprinkler Laterals

Analytical equations for direct hydraulic analysis of a multidiameter center-pivot lateral with and without an end gun were developed. The pressure head profile along the multidiameter center-pivot lateral is described by simple analytical functions. The analysis is based on both continuous outlet and discrete outlet approaches. Friction losses can be calculated using the Darcy–Weisbach or the Hazen–Williams formulas. The proposed equations simplify important practical applications such as the economic design and evaluation of a multidiameter center-pivot system. A comparison test with a numerical stepwise method indicates that the proposed analytical approach is sufficiently accurate for practical applications.     

Integrated Emitter Local Loss Prediction Using Artificial Neural Networks

This paper describes an application of artificial neural networks (ANNs) to the prediction of local losses from integrated emitters. First, the optimum input-output combination was determined. Then, the mapping capability of ANNs and regression models was compared. Afterwards, a five-input ANN model, which considers pipe and emitter internal diameter, emitter length, emitter spacing, and pipe discharge, was used to develop a local losses predicting tool which was obtained from different training strategies while taking into account a completely independent test set. Finally, a performance index was evaluated for the test emitter models studied. Emitter data with low reliability were removed from the process. Performance indexes over 80% were obtained for the remaining test emitters.     

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.     

Water Distribution in Laterals and Units of Subsurface Drip Irrigation. I: Simulation

A complete methodology to predict water distribution in laterals and units of subsurface drip irrigation (SDI) is proposed. Two computer programs have been developed for the hydraulic characterization of SDI; one for laterals and the other for units. Emitter discharge was considered to depend on hydraulic variability, emitter’s manufacture and wear variation, and soil pressure variation. A new procedure to solve the hydraulic calculation of SDI looped network has been established. Moreover, spatial distribution of soil variability was estimated by a geostatistical modeling software that is coupled with the computer programs. Thus the evaluation and performance of laterals and units of SDI can be addressed by changing input variables such us: length and diameters of laterals; coefficients of emitter’s discharge equation; coefficient of variation of emitter’s manufacture and wear; local losses at the emitter insertion; inlet pressure; and soil hydraulic properties and its spatial variability. Finally, the methodology has been applied to different scenarios, and some recommendations are outlined for the selection of emitter discharge and inlet pressures.     

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.