Drip Irrigation Design Research Articles

APPLICATION OF DRIP IRRIGATION ON COTTON PLANT GROWTH (Gossypium sp.)

The condition of cotton planting in South Sulawesi is always constrained in the fulfillment of water. All plant growth stages are not optimal to increase production, so it is necessary to introduce good water management technology, such as through water supply with drip irrigation system. This study aims to analyze the strategy of irrigation management in cotton plants using drip irrigation system. Model of application by designing drip irrigation system and cotton planting on land prepared as demonstration plot. Observations were made in the germination phase and the vegetative phase of the early plants. Based on the result of drip irrigation design, the emitter droplet rate (EDR) was 34.266 mm/hour with an operational time of 4.08 min/day. From the observation of cotton growth, it is known that germination time lasted from 6 to 13 days after planting, the average plant height reached 119.66 cm, with the number of leaves averaging 141.93 pieces and the number of bolls averaging 57.16 boll.

Application of the DIDAS program for the design and scheduling of drip irrigation

The DIDAS software package assists in drip-irrigation system design and irrigation scheduling. It is based on analytical solutions of the linearized water flow equation. The problem of water flow and uptake is described by superposing solutions for positive sources (on-surface or subsurface emitters) and negative sinks (root systems). Steady water flow is assumed in the design module and unsteady flow in the irrigation-scheduling module. The design tool, based on the relative water-uptake rate (RWUR) criterion, assesses the effects on water-use efficiency of geometrical attributes: distances between emitters along drip lines, separation between drip lines, depth of subsurface emitters, and size and depth of root systems. For design purposes, it is assumed that there is no plant-atmosphere resistance to water uptake, i.e., roots are assumed to apply maximum suction and water-uptake rate depends only on the soil's ability to conduct water from sources to sinks. The RWUR computations require only three parameters describing soil texture, root-zone size, and potential evaporation. The optimizing tool for irrigation scheduling is based on a relative water-uptake volume (RWUV) criterion. The RWUV computations for a given drip-irrigation design require additional information on the diurnal pattern of plant resistance to water uptake and soil hydraulic conductivity. DIDAS also contains a diurnal pattern module to evaluate diurnal water-uptake patterns; it assumes quasi-steady flow, accounts for diurnal variations in plant-atmosphere resistance and evaporation, and serves for fine-tuning the design and in preliminary evaluation of scheduling scenarios. DIDAS was programmed in Delphi, runs on a PC under the Windows operating system, and requires no further software. The drip-irrigation scenario is constructed via a few GUI windows, which also contain a library of the required soil input parameters, and a best-fitting procedure to determine them. The computed RWURs and RWUVs are displayed graphically and the tabulated output results can be exported to, e.g., Microsoft Excel for further processing. An updated DIDAS version can be downloaded freely from http://app.agri.gov.il/didas. From March 2014 through July 2016, 877 people from 94 countries downloaded the first or second DIDAS versions (1.0.1 and 1.1.1, respectively). We briefly introduce drip irrigation and other available programs for its design and scheduling, outline the major DIDAS concepts, and illustrate the operation of the main software modules.

Backpressure effects on the flow-pressure relation of driplines

ABSTRACT For drip irrigation design and management, it is necessary to know the relation between flow and pressure acting on emitters. In the case of subsurface drip irrigation, the backpressure phenomenon may change the hydraulic characteristics of emitters. Thus, this study aimed at determining such relationship between flow and pressure of different driplines in surface and subsurface conditions; aiming to find possible differences in hydraulic behavior. We tested four emitter types; two pressure compensating (D5000 and Hydro PCND) and two non-pressure compensating (TalDrip and Jardiline). Emitter flow rates were attained in atmospheric conditions and submerged in water, in which submergence levels represented backpressure. Assays were performed using inlet pressures of 80, 100, 120, and 150 kPa for the Hydro PCND dripline and 25, 50, 100, and 150 kPa for the other ones; the backpressures were of 0.49, 1.47, 2.45, 4.41 and 6.37 kPa with four replications. The emitters had their proportionality constants and discharge exponents changed in submerged applications, representing backpressure effect. Non-pressure compensating emitters had their discharge exponent decreased, while in pressure compensating ones, it was increased. Backpressure reduced emitter flow rates at all evaluated pressures.

DIDAS – User-friendly software package for assisting drip irrigation design and scheduling

The DIDAS software package, based on analytical solutions of linearized water flow and uptake problems, assists in drip-irrigation system design and irrigation scheduling. Water flow is described by superposition of solutions for positive sources (on-surface or subsurface emitters) and negative sinks (root systems). Steady water flow is assumed in the design module and unsteady flow in the irrigation scheduling module. The design tool, based on relative water uptake rate (RWUR) criterion, assesses the effects on water use efficiency of geometrical attributes: distances between emitters along drip lines; separation between drip lines; depth of subsurface emitters; and size and depth of root systems. Evaluation of the maximum possible RWUR assumes no plant–atmosphere resistance to water uptake, i.e., the roots are assumed to apply maximum suction and the water uptake rate depends only on the soil capability to conduct water from sources to sinks. The RWUR computations require only three parameters describing the soil texture, the root zone size, and the potential evaporation, in accounting also for evaporation from the soil surface. The optimizing tool for irrigation scheduling is based on a relative water uptake volume (RWUV) criterion. The computations of diurnal variations of water uptake rates and RWUV for a given irrigation scenario require additional information on the diurnal pattern of plant resistance to water uptake and on the soil hydraulic conductivity. DIDAS also contains a diurnal pattern module for evaluating diurnal water-uptake patterns; it assumes quasi-steady flow and accounts for the diurnal variations of plant–atmosphere resistance and evaporation in fine-tuning the design and in preliminary evaluation of scheduling scenarios. DIDAS was programmed in Delphi, runs on a PC under the Windows operating system, and requires no further software. The drip irrigation scenario is constructed via a few GUI windows, which contain also a library of the required soil input parameters, and a best-fitting procedure for determining them. The computed RWURs and RWUVs are displayed graphically and the tabulated output results can be exported to, e.g., Microsoft Excel for further processing. An updated DIDAS version can be downloaded freely from http://app.agri.gov.il/didas.

Optimal Irrigation Scheduling, Irrigation Control and Drip Line Layout to Increase Water Productivity and Profit in Subsurface Drip‐Irrigated Agriculture

AbstractA new optimization framework is presented which is able to identify optimal solutions for maximum profit design of subsurface drip irrigation (SDI) systems under limited supply. To solve this complex optimization problem, decomposition is used which splits the problem into three sub‐problems: (i) optimal irrigation control, which maximizes water distribution uniformity and minimizes percolation losses; (ii) optimal irrigation scheduling, which minimizes irrigation water applied in order to meet a high yield with a specified reliability; and (iii) optimal drip line layout, which includes the solutions of the other sub‐problems and maximizes profitability. The multi‐level optimization framework was tested in France with corn cultivated on two SDI plots with drip line spacing of 1.2 m (SDI120) and 1.6 m (SDI160), respectively. HYDRUS simulations estimated adequate irrigation amounts of 20–35 mm per event. For optimal irrigation scheduling, initial schedules were provided at sowing and adapted weekly according to observed weather data and synthetic weather scenarios. The presented framework significantly increased profit and water productivity for deficit SDI designs. The latter was increased up to 30% (SDI120), compared to seven other irrigation experiments. The optimal SDI design was achieved by SDI160, which increased profitability by 27% compared to SDI120. Copyright © 2015 John Wiley & Sons, Ltd.

Design, Introduction, and Extension of Low-Pressure Drip Irrigation in Myanmar

Drip irrigation is used extensively by both large and small commercial horticultural crop growers in most developed countries where benefits include not only high water use efficiency, but also higher yields, improved product quality, and reduced incidence of foliar disease. Drip systems are still relatively new and expensive in Southeast Asia, and it is primarily wealthier farmers who currently enjoy its benefits. There are also significant perceptual barriers to adoption as many farmers are accustomed to applying copious amounts of water to horticultural crops and are unfamiliar with drip or their crops’ actual water requirements. As a nongovernmental organization whose mission is to help boost small farm incomes, International Development Enterprises (IDE) began experimenting with low-pressure, low-cost gravity-fed drip systems in Myanmar (Burma) in 2006. While the basic design was similar to microtube drip systems of the 1960s, local improvements included filters designed for low pressures, easy-to-use fittings, and inexpensive collapsible header tanks. Our system was optimized for operation on small but commercial-scale plots using pressures as low as 1 psi or only ≈1/10th of that used for conventional drip irrigation. Extension support materials included illustrated installation guides, system design software, videos, testing/filtering of dissolved iron, and easy-to-use water requirement calculators. After hundreds of controlled and farmers’ field tests, our locally manufactured drip sets were offered for sale by private dealers throughout Myanmar in 2009. Incremental system improvements coupled with a strong on-farm demonstration and farmer education program resulted in the successful introduction and widespread adoption of drip irrigation in Myanmar.

Effect of Flushing Velocity and Flushing Duration on Sediment Transport in Microirrigation Driplines

<abstract><title><italic>Abstract. </italic></title> Dripline flushing is a maintenance procedure that is recommended for all microirrigation systems. However, flushing velocity and flushing duration, which particularly affect the design and management of subsurface drip irrigation (SDI) systems, have not been studied extensively. For a better understanding of the flushing process in driplines and manifolds, a laboratory study was conducted at Kansas State University with a 10 m transparent pipe simulating an SDI dripline. Three different sediments with sizes up to 500 μm were introduced into the pipeline, and their distribution along the pipeline was analyzed under different flushing velocities over various times. Head loss under the conditions of this study increased exponentially with increased flushing velocity, suggesting that the flow regimes could be characterized between moving beds and heterogeneous flow. The percentage of pipeline blockage was logarithmically related to the flushing velocity, with greater than 30% of the pipeline occupied by larger sand sediments when the flushing velocity was less than 0.3 m s^-1. Although flushing velocities at or near the calculated deposition velocity could remove the majority of the sediments with a short duration of 15 min or less, flushing velocities that were approximately 45% to 65% of the deposition velocity could achieve similar sediment removal with longer flushing duration (up to 180 min). The ASAE EP-405 recommended minimum flushing velocity of 0.3 m s^-1 still appears adequate for most microirrigation systems operating under typical conditions. Designers are encouraged to calculate the deposition velocity for new microirrigation systems and to use it as a flexible guideline to assess the adequacy of flushing. End-users are encouraged to extend the duration of flushing for perhaps as long as 5 min after the initial concentration of sediments are removed to improve overall flushing. Further research is warranted to evaluate flushing velocity, but the results of this study should be representatively instructive of the phenomenon of sediment transport in microirrigation driplines during flushing.

Drip-Irriwater: Computer software to simulate soil wetting patterns under surface drip irrigation

Drip irrigation provides greater efficiency in terms of water usage and energy. These factors are very important in light of the current competition for water resources between the various users, especially in the Mediterranean region due to water scarcity. The shape and dimensions of the volume of wet soil below the emitter are some of the most influential variables in the optimal design and management of drip irrigation systems. This paper presents Drip-Irriwater, a code for determining soil wetting patterns under a single emitter in order to suggest planning factors for a drip irrigation system. The code solves Richards’ equation using the finite difference method subject to appropriate boundary conditions for drip irrigation. The boundary conditions on the surface of the soil allow us to consider forming a pond under the emitter. The user interface enables users to simply enter the input parameters (discharge rate, soil type and horizons, irrigation time, initial water content and total simulation time). The code then displays the soil water content and pressure heads, enabling a visual distinction between the wetted radius and depth, the parameters required for subsequent drip irrigation design. The results obtained with Drip-Irriwater were compared with those obtained with HYDRUS and with results from field tests carried out on three different soil types. The soil water distribution, as well as the wetted radius and depth, calculated from the Drip-Irriwater and HYDRUS code, were very similar. Field tests conducted to verify the results of the code confirmed that Drip-Irriwater gave a good approximation of the wetted radius and depth, and could therefore be used to design a drip irrigation system.

Deep subsurface drip irrigation using coal-bed sodic water: Part I. Water and solute movement

Water co-produced with coal-bed methane (CBM) in the semi-arid Powder River Basin of Wyoming and Montana commonly has relatively low salinity and high sodium adsorption ratios that can degrade soil permeability where used for irrigation. Nevertheless, a desire to derive beneficial use from the water and a need to dispose of large volumes of it have motivated the design of a deep subsurface drip irrigation (SDI) system capable of utilizing that water. Drip tubing is buried 92cm deep and irrigates at a relatively constant rate year-round, while evapotranspiration by the alfalfa and grass crops grown is seasonal. We use field data from two sites and computer simulations of unsaturated flow to understand water and solute movements in the SDI fields. Combined irrigation and precipitation exceed potential evapotranspiration by 300–480mm annually. Initially, excess water contributes to increased storage in the unsaturated zone, and then drainage causes cyclical rises in the water table beneath the fields. Native chloride and nitrate below 200cm depth are leached by the drainage. Some CBM water moves upward from the drip tubing, drawn by drier conditions above. Chloride from CBM water accumulates there as root uptake removes the water. Year over year accumulations indicated by computer simulations illustrate that infiltration of precipitation water from the surface only partially leaches such accumulations away. Field data show that 7% and 27% of added chloride has accumulated above the drip tubing in an alfalfa and grass field, respectively, following 6 years of irrigation. Maximum chloride concentrations in the alfalfa field are around 45cm depth but reach the surface in parts of the grass field, illustrating differences driven by crop physiology. Deep SDI offers a means of utilizing marginal quality irrigation waters and managing the accumulation of their associated solutes in the crop rooting zone.

Influence of geometric design of alternate partial root-zone subsurface drip irrigation (APRSDI) with brackish water on soil moisture and salinity distribution

Abstract in Undetermined In alternate partial root-zone irrigation (APRI) a significant amount of irrigation water can be saved without considerable yield reduction. In this paper, Hydrus-2D/3D was used to investigate the impact of geometric design of alternate partial root-zone subsurface drip irrigation (APRSDI) with brackish water for growing tomato on soil moisture and salinity distribution. Three inter-plant emitter distances (IPED; 20, 30, and 40 cm), two emitter depths (10 and 20 cm), and three irrigation water salinity levels (0, 1, and 2 dS m-1) were used to implement the proposed simulation scenarios in loamy sand soil during a 40-day simulation period. The simulation results showed that higher soil moisture content was found beneath the plant trunk in case of 20 cm (short IPED) and near the domain border in case of 30 and 40 cm IPED. Short IPED guarantees more water in the maximum root density zone. A deeper wetting front occurred for deep emitter depth, while the wetting front reached the soil surface for shallow emitter depth. Salinity results revealed that as irrigation water salinity increased, the salinity in the top soil increased. In addition, the salinity at the soil surface increased as IPED and emitter depth increased. Higher root water uptake rates were recorded in the case of 20 cm IPED while the emitter depth did not show any considerable effect on root water uptake rates. Moreover, the applied irrigation water was fully consumed by the plant in case of short IPED. Emitter depth and salinity of irrigation water had negligible effect on amount of irrigation water extracted by plant roots and percolated amount below the bottom boundary of the flow domain. Overall, short IPED is recommended in APRSDI with or without brackish irrigation water regardless of the emitter depth. (Less)

Aplicação de modelos matemáticos na estimativa do volume de bulbo molhado por gotejamento superficial em diferentes tipos de solo

A informação do volume de solo molhado pela irrigação localizada é importante para o dimensionamento e manejo da irrigação por gotejamento superficial, bem como para a estimativa da quantidade de água disponível para as plantas. Com o objetivo de avaliar cinco modelos para estimar o volume molhado pela irrigação por gotejamento superficial, foram instalados experimentos em seis tipos de solos (Luvissolo Crômico, Argissolo Vermelho-Amarelo, Cambissolo Háplico, Neossolo Quartzarênico, Latossolo Vermelho e Neossolo Flúvico). A partir desses experimentos, constatou-se que, com exceção do modelo proposto por NARDA &amp; CHAWLA, os demais modelos estimam satisfatoriamente o volume de solo molhado pela irrigação por gotejamento superficial. Além disso, concluiu-se que o volume médio molhado para as mesmas combinações entre a vazão do emissor e o tempo de aplicação de água foram maiores para o Argissolo e menores para o Neossolo Flúvico e que, com exceção do Argissolo e do Neossolo Flúvico, o volume molhado do solo pode ser estimado por uma única equação em função do volume de água aplicado e do tempo de aplicação de água.

Simulation of point source wetting pattern of subsurface drip irrigation

Laboratory experiments and calculations were carried out to analyze the effect of subsurface drip irrigation (SDI) design features on soil wetting patterns for a point source. Experimental and simulated soil wetting patterns, using the SWMS-2D (simulating water movement and solute transport in two-dimensional) Galerkin finite element model, were investigated to maximize the efficiency of water saving. The analysis addressed the influence of water pressure head, back pressure and emitter diameter on wetting patterns. Predictions of water content distributions in the soils made with SWMS-2D were found to be in good agreement with the observed data. Results showed that this model provides confidence that model predictions are not too sensitive to back-pressure effects.

Effect of soil water repellency on moisture distribution from a subsurface point source

Wetting and redistribution of water in air‐dried wettable, slightly repellent, and strongly repellent soils was investigated by tracking the spatial and temporal moisture‐content variation in a transparent flow chamber. Water was applied as a subsurface point source. The degree of water repellency had a substantial effect on the plume's shape, dimensions, and internal moisture‐content distribution. The high uniform moisture content in the repellent soil's plume surrounded by a narrow transition layer within which moisture content was sharply decreasing indicates that unstable flow shapes a finger‐like wetting front. Moisture redistribution in the repellent soils was limited and took place mainly in the vertical direction. The repellent soils were wetted immediately, very likely by local positive pressure buildup induced by the hydraulic resistance imposed by the initial &gt;90° contact angle. The plume shape dimensions and internal moisture‐content distribution should be considered in the design and operation of subsurface drip irrigation in water‐repellent soils.

Gravity-fed drip irrigation design procedure for a single-manifold subunit

A simple procedure was developed for the design of low-cost, gravity-fed, drip irrigation single-manifold subunits in hilly areas with laterals to one or both sides of the manifold. The allowable pressure head variation in the manifold and laterals is calculated individually for different pressure zones, and the manifold subunit design is divided into independent processes for laterals and manifold. In the manifold design, a two-stage optimal design method is used. In the first design stage, the pipe cost is minimized and a set of optimal manifold pipe diameters is obtained. In the second design stage, a partial list of available diameters is prepared based on the calculated optimal diameters, and the lengths for available diameters and pressure head of every lateral location along the manifold are calculated. The size of each of the pressure sections is determined according to the pressure head distribution along the manifold. Using the proposed methodology, the minimum manifold pipe cost is obtained, and the target emission uniformity is satisfied for gravity-fed drip irrigation subunits.

Modelo aplicado à dinâmica da água e do potássio no solo sob irrigação por gotejamento: análise de sensibilidade

A compreensão do transporte simultâneo da água e de solutos, a partir de uma fonte pontual, permite desenvolver estratégias eficientes na fertirrigação, sendo importante no dimensionamento, na operação e no manejo de sistemas de irrigação localizada. O presente trabalho teve como objetivo apresentar a análise de sensibilidade de um modelo matemático, desenvolvido para simular o deslocamento simultâneo de água e de potássio na irrigação por gotejamento. A análise de sensibilidade foi realizada com respeito às variações individuais da condutividade hidráulica do solo saturado, umidade inicial e saturada do solo, dispersividade, fator de retardamento e vazão do emissor. Os resultados obtidos revelaram que o modelo matemático, com relação à distribuição de água, é bastante sensível à umidade de saturação e inicial do solo e, em relação à distribuição de potássio, é bastante sensível a variações negativas da condutividade hidráulica do solo saturado e da vazão do gotejador; já em relação aos parâmetros de transporte de solutos no solo, é bastante sensível a variações negativas do fator de retardamento e pouco sensível às variações da dispersividade do solo.

Simulation of soil wetting pattern with subsurface drip irrigation from line source

The information on depths and widths of wetted zone of soil under subsurface application of water plays the great significance in design and management of subsurface drip irrigation (SDI) system for delivering required amount of water and chemical to the plant. A simulation model was developed using semi-empirical approach and dimensional analysis method for determining geometry of wetted soil zone under line sources of water application placed below the soil surface. The predicted values of wetted depth and width were compared with those obtained through field experiments conducted under sandy loam soil. Experimentation included determination of maximum depths and widths of wetted zone after 0.5, 1, 2, 3, 5, and 7 h of water application under laterals, porous pipes, and drip tape placed at 0.05, 0.10 and 0.15 m depths below soil surface. Statistical analysis revealed that there was no significant difference between predicted and observed values of wetted width and depth. The effect of discharge, depths of placement of lateral and duration of water application on wetted width and depth were similar for predicted and observed values. Predictability of model was expressed in terms of model efficiency, which was estimated as 96.4 and 98.4%, respectively, for prediction of wetted width and depth. This shows that developed model can be used to simulate wetting pattern under SDI system with line source of water application.

MODELING OF WATER FLOW AND NITRATE TRANSPORT UNDER SURFACE DRIP FERTIGATION

The knowledge of water and nitrogen dynamics under drip irrigation is essential to the best management of drip fertigation systems, and model simulation is an effective way to obtain such knowledge. A model of water and nitrate transport in soil from a surface point source of ammonium nitrate (NH4NO3) was established and solved numerically by using HYDRUS-2D software. In the model, selected boundary conditions were used to describe the solute transport for a mediumand a coarse-textured soil. Simulated wetting dimensions of soil volume and distributions of water content and nitrate concentrations in soil were compared with data obtained from laboratory experiments conducted on a loam and a sandy soil. An excellent agreement was obtained between the simulated results and the measured data. Then the verified model was used to simulate water and nitrate distributions under various initial conditions and fertigation strategies. The results demonstrated that nitrate accumulated toward the boundary of the wetted volume for selected combinations of initial nitrate concentration, application rate, volume applied, and input concentration. Nitrate distribution was greatly affected by fertigation strategies. A strategy of first applying water for one-fourth of the total irrigation time, then applying fertilizer solution for one-half of the total irrigation time, followed by applying water for the remaining one-fourth of the total irrigation time left the most nitrate close to the source and was therefore recommended. The use of HYDRUS-2D enabled us to implement water and nitrogen transport under surface drip fertigation and to strengthen the conclusions derived from the observations. The information obtained from the simulations is helpful in the design, operation, and management of a fertigation system with drip irrigation.

Distribuição da água no solo para o dimensionamento da irrigação por gotejamento

O objetivo do dimensionamento de um sistema de irrigação por gotejamento é escolher adequadamente o "layout" e os componentes do sistema para promover a distribuição precisa da água (e fertilizante) para todas as plantas, ao longo do campo. Com vistas a este propósito, avaliaram-se as contribuições capazes de fornecer elementos básicos para o dimensionamento da irrigação por gotejamento, utilizando-se sondas de TDR. Assim, o estudo experimental foi dividido em duas partes; na primeira, tem-se o efeito de irrigações sucessivas nas dimensões dos raios horizontal e vertical do bulbo molhado, analisado em condições de laboratório e, na segunda, o processo de distribuição da água na formação do bulbo molhado em campo. Com os resultados apresentados nesta pesquisa pôde-se concluir que: a umidade inicial do solo, o volume aplicado, a vazão do gotejador, o disco saturado e a condutividade hidráulica, são elementos importantes e devem ser conhecidos para o dimensionamento e o manejo adequado da irrigação.

Hydraulic design and performance evaluation of subsurface drip irrigation for coconut in Coimbatore district

Field experiments, conducted during 1993 to 1996 with subsurface drip irrigation (drippers are placed on the surface) for coconut in a farmer's field in Coimbatore showed that application of 112 lit/day/ tree registered 133 nuts/tree/year. The water saving was 63 per cent in the drip over the conventional basin method. The yield increase was 7.25 per cent over the conventional method. In subsurface drip irrigation system, a labour saving of 75 per cent was recorded over the conventional method for irrigation work alone.

Infiltration from a surface point source and drip irrigation: 1. The midpoint soil water pressure

Bresler [1978] proposed a procedure for drip irrigation design which is focused on the midpoint soil water pressure hc. We present a practical field test of this approach in order to evaluate the validity of the underlying assumptions. The simulated hc values were obtained from Raats' [1971] steady state theory for 32 points in the field where the hydraulic conductivity parameters Ks and αwere measured. The hc values were measured at the same locations during microirrigation of a maize crop. Measured hc's appear to be lower than the simulated ones, especially late in the season. The measured spatial variability in hc appeared to be higher than the simulated ones. This could well have been caused by root uptake activity, which is not considered in the analysis, as well as by the large but typical drippers spacing of d = 1.00 m. Thus the tensiometers could have been beyond the practical limit of wetting. Consequences for design and management are important. For design, even if a high hc value is chosen, there is no real guarantee that the wetting would be effective at the midpoint. For irrigation management, tensiometer placement too far from the dripper would lead to overirrigation, so for a large dripper spacing d, the midpoint placement is not judicious.