Analytical Expressions for Hydraulic Calculation of Trapezoidal Drip Irrigation Units

Analytical expressions have been developed relating water distribution indexes in trapezoidal drip irrigation units to design variables which define these units: lengths and diameters of pipes, emitter and lateral spacing, slopes, emitter flow equation parameters, and equivalent lengths characterizing local losses. The proposed expressions are founded in classical hydraulics. They are more accurate than predictions in irrigation practice and are easier to handle than the simulation models frequently proposed to irrigation technicians. Unit design and irrigation decision making and evaluation can thus be furthered. An example for the application of the proposed expressions is presented. First, lateral and submain diameters are determined for different shapes of irrigation units to achieve a given water application uniformity. The irrigation time to supply the desired irrigation depth is then calculated. Results are finally compared with values obtained by simulations that take into account hydraulic and manufacture variations in the unit.     

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. 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.     

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.     

Procedures for Determining Maximum Emitter Discharge in Subsurface Drip Irrigation

One problem associated with subsurface drip irrigation (SDI) is the reduction in discharge resulting from soil-water back-pressure at the emitter outlets. An experimental setup was made to measure emitter discharge and pressure at the emitter outlet in different soils. Experiments were carried out with 2–24??L/h noncompensating and compensating emitters, operating at a constant lateral pressure of 10?m. Emitter discharge was reduced to a range of 2–10% for noncompensating models and to less than 1% for compensating models. Soil pressure ranged from 0.15–2.07?m. Laboratory conditions were simulated with HYDRUS-2D/3D. Experimental values of discharge and soil pressure showed good agreement with estimated values. Finally, maximum emitter discharge to limit the decrease of discharge was determined for an operating pressure of 10?m. For a 10% decrease, considering a constant radius of the spherical cavity in the soil, maximum emitter discharge was 2.35??L/h for loamy soil and 12.44??L/h for sandy soil for noncompensating emitters, and 10.73 and 54.51??L/h, respectively for compensating emitters. These values increased when considering a cavity radius variable with emitter discharge.     

Wetting Pattern Models for Drip Irrigation: New Empirical Model

Reliable information about the wetted dimensions of soil under drip irrigation helps designers to determine optimal emitter flow rates and spacings to reduce system equipment costs and provide better soil water conditions for the most efficient and effective use of water. This study presents a new empirical formula that predicts soil wetted dimensions around a drip emitter. The coefficients were obtained by using regression analysis on the results of field experiments done on the Pardis Agricultural Farm of Tehran University in Karaj, Iran. These data were also used to evaluate the semiempirical model of Zur and Schwartzman, the empirical model of Amin and Ekhmaj, and the analytical model WetUp. Statistical comparisons (mean error, root mean square error, and model efficiency) are made of the simulated data with the observed data. To evaluate the models, published experimental data by Risse et?al. and Li et?al. were also used. The results demonstrate that the suggested equations can be used for a wide range of discharge rates and soil types. The best result was obtained from the new empirical model proposed in this investigation. The lowest mean error for the wetted radius and wetted depth was 8.21 and 8.62?cm, respectively.     

Comparison of Crop Contamination by Microorganisms during Subsurface Drip and Furrow Irrigation

This study was conducted to compare subsurface drip irrigation (SDI) with furrow irrigation (FI) in crop contamination with microbial-contaminated water irrigation. Escherichia coli, Clostridium perfringens, and coliphage PRD-1 were added to water used to irrigate cantaloupe, lettuce, and bell pepper. Samples of produce, surface, and subsurface (10?cm) soil for each irrigation system were collected on Days 1, 3, 5, 7, 10, and 14 after the application of the study microorganisms. Overall, greater contamination of produce occurred in FI plots than in SDI plots. The microorganisms were detected on the surfaces of cantaloupe and lettuce, but were never recovered on the bell peppers. The greatest amount of contamination occurred with PRD-1 on cantaloupe. The study microorganisms survived longer in the subsurface soil than the soil surface. PRD-1 showed greater persistence than E. coli in soil, while C. perfringens experienced little inactivation during the experiment periods. This study showed that subsurface drip irrigation has great potential to reduce health risks when microbial-contaminated water is used for irrigation water.     

Soil Hydraulic Properties Affecting Discharge Uniformity of Gravity-Fed Subsurface Drip Irrigation Systems

The use of subsurface drip irrigation (SDI) is increasing for many reasons, including its many agronomic advantages and the ability for safe application of wastewater to crops. In contrast to surface drip irrigation, soil hydraulic properties may affect SDI performance, particularly for new SDI systems designed to operate under low pressure (e.g., 2?m of head). This work introduces a new approach for solving problems of predicting discharge in SDI laterals. We accomplish this by coupling models of head loss in laterals and soil impacts on dripper discharge. The coupled model enables an evaluation of the performance of SDI laterals while changing inputs, such as the lateral diameter, length and slope, dripper nominal discharge and exponent, inlet pressure head, soil hydraulic properties, and soil spatial variability. This model is used to determine the coefficient of variation of discharge for two numerical comparisons.     

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.     

Experimental Study on the Multisegment Regime of the Water Flow in Drip Emitters

The flow exponent greatly determines the hydraulic performance of drip emitters. The objective of this study is to reveal the change of flow exponents with different water pressures. Laboratorial experiments of the relationship between discharges and water pressures were conducted with five types of drip emitters used for surface drip irrigation systems. The regression for calculating flow exponents was done with different segment pressures. The results showed that the flow exponent reduced gradually with the increase of the pressure segment except a brief increase in the early stage of pressure increasing due to the channel expansion. The eddy drip-arrow is most suitable for the pressure ranges of 2–8 and 8–14?mH2O. The effect of the use of the small diameter drip-tube is best in the high-pressure range of 17–25?mH2O. The relation between average flow velocities and water pressures is characterized by the flow exponent, the same as that between emitter discharges and water pressures. The eddy drip-arrow and the in-line drip-tape with a low discharge but a high flow velocity can meet the requirements of both prominent anticlogging and long-distance use. The Reynolds numbers of the five types of drip emitters range from 200 to 1,800, below the critical value of the turbulent transition of a conventional scale flow. The small diameter drip-tube needs the lowest Reynolds number required for full turbulence transition which assures a lower flow exponent when the emitter runs with a relatively low discharge.     

Experimental Determination of the Hydraulic Properties of Low-Pressure, Lay-Flat Drip Irrigation Systems

The hydraulics of IDEal low-pressure drip irrigation system components were analyzed under controlled laboratory conditions. The hydraulic loss coefficient for the lateral-submain connector valves was determined based on laboratory measurements. It was found that the hydraulic loss due to friction in the lay-flat laterals can be accurately estimated with standard friction loss equations using a smaller effective diameter based on the wall thickness and inlet pressure head. The equivalent-length barb loss, expressed as an equivalent length of lateral, was calculated for button emitters, as well as for microtubes inserted to lengths of 5 and 10 cm. The head-discharge relationship and coefficient of manufacturer’s variation of prepunched lateral holes (without emitters), button emitters, and microtubes were determined. It was found that most of the head loss occurs in the connector valve, which has a relatively small hole through the hollow stopcock. The presence of manufacturing debris in the valve also increases the head loss and contributes to variability in the valve loss coefficient. The lateral cross-sectional area in the creases does not greatly impact the effective diameter for the 125-, 200-, and 250-μm wall thickness laterals. However, the use of the lateral height as effective diameter for the 500-μm sample resulted in significant overestimation of friction loss. The prepunched holes and the button emitters had very low manufacturer’s variation coefficients, but the microtube emitters showed excellent uniformity and are the emitter of choice among the tested alternatives. However, the microtube flow rate is relatively high and is more sensitive to pressure variation than the other emitter types.     

Compatibility Assessment of Drip Irrigation Laterals

Emitters inserted in drip irrigation laterals cause local head loss, generally estimated as a product of a coefficient and the velocity head. This local head loss coefficient and the emitter discharge curve hydraulic parameters may exhibit considerable variability attributable to the manufacturing process. This paper provides a framework for assessing whether the variability in the hydraulic parameters could lead to significant differences in the performance of rolls of drip irrigation laterals from the same manufacturing batch. A system approach with inlet pressure as input, pressure distribution along the drip lateral and inlet discharge as outputs (or responses), and a drip lateral hydraulic model as the transfer function is explored. Within a Bayesian statistical framework of parameter uncertainty based on the Metropolis algorithm, the hydraulic parameters of pressure-compensating drip lateral rolls from the same manufacturing batch were inferred (calibrated). Overlapping of the space (region) of the hydraulic parameters of different drip laterals give an indication of compatibility (similarity) of the drip laterals. Results indicated that half of the drip lateral rolls tested were strongly compatible, a third were weakly compatible, and the remainder were not compatible with any other. This finding has significant ramifications in the design of drip irrigation lateral networks. Therefore, it is essential to closely examine the hydraulic properties of drip laterals for the design of drip irrigation networks to avoid poor performance of the system.     

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.     

Bacteriophages MS2 and PRD1 in Turfgrass by Subsurface Drip Irrigation

The contamination of turfgrass by bacteriophages MS-2 and PRD-1 was assessed in the field under sprinkler irrigation (SI) and subsurface drip irrigation (SDI). No contamination of turfgrass by MS-2 was observed using SDI in the summer or winter seasons. In the summer, PRD-1 was detected in low numbers in SDI turfgrass; however, at significantly lower numbers than in SI turfgrass (p<0.05). In contrast, SI turfgrass was readily contaminated with MS-2 and PRD-1 during both seasons. Column experiments showed that viral migration was greater in sandy soil than in clay soil. Descending viral transport was more pronounced than upward migration, but only significantly greater (p<0.05) in sandy soil. The survival in soil of MS-2 and PRD-1 was compared with that of poliovirus 1 and enteric adenovirus 40. MS-2 showed shorter survival in comparison to the other viruses (p<0.05). The results obtained in this study suggest that SDI used to irrigate turfgrass with wastewater may effectively reduce the risk of contamination by potential viral pathogens.     

Improved Pressurized Pipe Network Hydraulic Solver for Applications in Irrigation Systems

GESTAR is an advanced computational hydraulic software tool specially adapted for the design, planning, and management of pressurized irrigation networks. A summary is given of the most significant characteristics of GESTAR. The hydraulic solver for quasi-steady scenarios uses specific strategies and incorporates several new features that improve the algorithms for pipe network computation, overcoming some of the problems that arise when attempting to apply drinking water software, using the gradient method, to irrigation systems. It is shown that the gradient method is a nodal method variant, where flow rates are relaxed using head loss formula exponents. Although relaxation produces a damping effect on instabilities, it is still unable to solve some of the numerical problems common to the nodal methods. In this contribution the results of the research on computational strategies capable of dealing with low resistance elements, hydrant modelling, multiple regulation valves, numerous emitters, and pumps with complex curves are presented, obtaining accurate results even in conditions where other software fails to converge. GESTAR incorporates all these computational techniques, achieving a high convergence rate and robustness. Furthermore, GESTAR’s solver algorithm was easily adapted to incorporate inverse analysis options for optimum network control and parameter calibration. Illustrative examples are provided, documenting the improved numerical techniques and examples of GESTAR’s performance in comparison with EPANET2, a widely used gradient method-based hydraulic solver.     

Comparison of HYDRUS-2D Simulations of Drip Irrigation with Experimental Observations

Realizing the full potential of drip irrigation technology requires optimizing the operational parameters that are available to irrigators, such as the frequency, rate, and duration of water application and the placement of drip tubing. Numerical simulation is a fast and inexpensive approach to studying optimal management practices. Unfortunately, little work has been done to investigate the accuracy of numerical simulations, leading some to question the usefulness of simulation as a research and design tool. In this study, we compare HYDRUS-2D simulations of drip irrigation with experimental data. A Hanford sandy loam soil was irrigated using thin-walled drip tubing installed at a depth of 6 cm. Three trials (20, 40, and 60 L?m?1 applied water) were carried out. At the end of each irrigation and approximately 24 h later, the water content distribution in the soil was determined by gravimetric sampling. The HYDRUS-2D predictions of the water content distribution are found to be in very good agreement with the data. The results support the use of HYDRUS-2D as a tool for investigating and designing drip irrigation management practices.     

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.     

Analytical Relationships for Designing Multiple Outlets Pipelines

In this paper an analytical procedure taking into account the nonuniform outflow profile for hydraulic analysis and design of multiple outlets pipelines, is presented. Energy relations are improved based on the average friction drop approach with a simple exponential function, to express the nonuniform outflow concept. To determine friction head losses, the Darcy-Weisbach formula is used here; and the kinetic head change is considered whereas minor head losses are neglected. Several mathematical relationships are also derived for computing extreme pressure heads and their locations of occurrence along the pipeline. The presented method also provides specific lengths of the segments in which the different flow regimes occur along its length. This method simulates pressure and outflow profiles along trickle and sprinkler irrigation laterals and manifolds, as well as gated pipes. The presented technique was applied to several computational examples to clarify its precision for trickle and sprinkler lateral design and the analytical results were compared with those obtained using the numerical step-by-step method. The comparison test for the various design combinations indicated that, the proposed method is found to be sufficiently accurate in all design cases for both trickle and sprinkler lateral design. The analytical development is simple, direct, and easily adaptable to solve hydraulic design problems of various types of single-diameter mutiple-outlet pipelines in different flow regimes and uniform line slope cases. It is preferred to the numerical techniques which need large amounts of execution time and complex computer operations.