The impact of design approximations on the operational performance of an irrigation scheme

A method is presented to analyse the impact of the selection of irrigation gates on operational performance of the Sungai Muda Irrigation Scheme in Malayisa. The method examines the discharge capacity of the water control gates at all levels in order to compare the specific water supply (the ratio of supply to command area) with the specific water demand which is the required hydromodule. The term hydromodule is the reciprocal of water duty and thus has units of litres/second/hectare. The greater the deviation between the two, the greater the potential loss of control during the operation of the scheme. The method is relatively simple but is more complex in this particular example as two hydromodules are used for the irrigation of basin rice; one for the presaturation period and one for the normal supply period. The most common cause of loss of water control is found to be provision of oversized turnout gates at the head of secondary and tertiary canals. Such design approximations enable more water to be used in those command areas thus leading to waste and to shortage of water in other areas. It is suggested that during design and rehabilitation of irrigation schemes, the operational implications of design approximations should be examined more carefully.     

Operative irrigation modelling for real-time applications on closed-end furrows

The complexity of physical phenomena in furrow irrigation,where numerous parameters vary with time and space, makeempirical models more operative than mechanistic models forimproving irrigation efficiency. In addition, when theseempirical models are well adapted for real-time calibration onadvance trajectory, they can be considered an efficient toolto predict irrigation performance.In the first section of this paper, the selection of operativefurrow irrigation modelling for real-time applications isdiscussed. Models derived from Horton and linear infiltrationequations through the water balance equation (WBE) arepreferred to those derived from the 2-term Philips equationand to the solution of WBE involving both the power advancefunction and Kostiakovs extended equation.The second section shows that simplified analytical modellingoptions can be added to the basic advance-infiltration modelfor improving irrigation efficiency. The modelling optiondeveloped in this paper concerns the prediction of cutoff timeand irrigation performance for closed-end furrows (CEF).The simplified analytical model for CEF based on the massconservation principle is successfully compared to field testsand numerical simulations.     

On-demand canal operation: Optimally designed

The design of most canal systems requires that they be operated under rigid schedules, rather thanon-demand. Rigid schedule operation results in water wastage through spillage, or users taking their turn even when the water cannot be efficiently used. This paper develops a two step method for optimally designing a canal system so it can be operated effectively under user on-demand requests for water. The first step determines the cross-sectional dimensions of the canal to provide storage capabilities while minimizing costs, by solving an appropriate nonlinear optimization problem. In the second step a hydraulic simulation model finds a near-optimal storage capacity based on construction and right-of-way costs, penalties due to operational water losses, water over supplied to users and supply shortages. The performance is evaluated by a quality index that is defined as the ratio of volume of satisfied demands to total volume of water requested. Results of regression equations from hundreds of computer sensitivity analyses relating variables are summarized in tables.     

Mungbean response to irrigation with waters of different salinities

Summary Experiments were conducted in lysimeters (1985) and field plots (1986) to evaluate changes in soil moisture and salinity status following irrigations with different blends of a saline water, SW (EC_iw = 6.4 dS/m) and non-saline water, NSW (0.3 dS/m) and their effects on the growth and yield of Mungbean (Vigna radiata L. Wilczek). Normalised to the yield of the treatment receiving NSW (100%), relative seed yields (RY) declined to 73, 11 and 3%, respectively, for the treatments receiving SWNSW blends of 12 (2.5 dS/m), 21 (4.7 dS/m) and SW as such. RY increased to 64 and 74% when NSW was substituted for presowing irrigation and 21 SWNSW blend and SW, respectively were used for postsowing irrigations. Due to moderating effect of rainfall (9.8 cm) during the growing season of 1986, valus of RY obtained with 12 and 21 SWNSW blends were 81 and 42% and increased to 96 and 82% when these waters were applied after presowing irrigation with NSW. Irrigation at presowing with non-saline water leached the salts of shallow depths leading to better germination and initial growth. In addition, plants were able to extract greater amounts of water even from deeper soil layers. The RY of Mungbean was related to the weighted time averaged salinity of the 0–120 cm soil depth (EC_e) by RY = 100-20.7 (EC_e-1.8). The study indicated that applying NSW for presowing irrigation to Mungbean is more beneficial than using it after blending with saline water.     

Effects of salinity on germination,seedling growth,and yield of melons

Summary Four melon (Cucumis melo L.) cultivars were tested for salt tolerance at germination, seedling growth stages, and plant maturation. Noy Amid was the most tolerant during germination, achieving 56% germination in 15,000 mg/l NaCl solution. However, this cultivar and Eshkolit Ha 'Amaqim were relatively sensitive during the first 4 days' growth of the radicle and the hypocotyl, and the first 3 weeks' development of the seedling. Their yields were reduced under saline as compared with non-saline field conditions. In contrast, Honey Dew and Rochet had little or no germination in 15,000 mg/l NaCl but showed salt tolerance during seedling growth stages. Yield of Honey Dew was unaffected by saline field conditions, and that of Rochet was not significantly reduced from the non-saline control. Thus, selection for salt tolerance in melons appears feasible during early vegetative growth stages but not during germination.Contribution No. 1032-E, 1984 series, from the Agricultural Research Organization, Bet Dagan, Israel     

Water-conserving wheat irrigation schedules based on climatic records

Summary Correlations between spring rainfall and grain yield were determined for four winter wheat cultivars (Triticum aestivum L. em. Thell. Triumph, Wichita, Concho, and Triumph 64), grown between 1950 and 1977 under dryland conditions at Stillwater, in the East Central region of Oklahoma, and at Goodwell, located in the drier, western part of the state.At Stillwater, all but one of the cultivars exhibited maximum positive correlations between rainfall and yield in the fourth week of March, when stem-extension occurs. Smaller positive correlations were observed in mid-April when flowering. Results at Goodwell were similar except that the correlations between rainfall and yield were lower and occurred earlier than at Stillwater and showed a less marked secondary peak at flowering. These results agree with those of experiments in which irrigation has been applied at different growth stages of wheat, and have shown that both stem-extension and flowering are critical stages of water requirement. As the results of this climatic study show that the peak correlations between rainfall and yield occur at these same two stages, it is suggested that long-term climatic data could be used to determine optimum timing for irrigation of wheat.Such an approach should save water and energy by limiting irrigation to those times when analysis of local records demonstrates the maximum positive correlation between rainfall and yield.     

Pressurised irrigation technologies for smallholders in developing countries – a review

The findings of a study of factors influencing the uptake of pressurised irrigation technologies by smallholders in developing countries are presented. The paper reviews the physical and technical characteristics that determine their suitability for use by smallholders. It also identifies a range of pre-conditions relating to water availability, institutional support and economic opportunity that must be satisfied before smallholders will adopt even low-technology pressurised irrigation systems.The review demonstrates that where physical, economic and institutional conditions are right some forms of pressurised modern irrigation technology permit smallholder irrigation of high value crops where surface irrigation would be inappropriate. However, the paper warns against the danger of wide-scale promotion of such technologies without considering the issues of institutional and technical support. Where pressurised systems are promoted to increase water use efficiency it is essential that they be well designed, installed and operated for savings to be realised.     

Yield and growth responses of kenaf (Hibiscus cannabinus L.) in a semi-arid tropical environment to irrigation regimes based on leaf water potential

Summary The growth response of kenaf (Hibiscus cannabinus L.) to four irrigation schedules based on leaf water potential _l was evaluated in a semi-arid tropical environment. Total dry matter production was unaffected by regimes in which the mean value of leaf water potential _l (mean of solar noon and dawn value) did not fall below –1.26 MPa. Stem elongation was more sensitive than dry matter accumulation to plant water stress. — The economic yield for paper pulp production (i. e. total plant dry matter production minus that of the foliage and upper 60 cm of stem) increased with the frequency of irrigation. — Growth recovery by kenaf following a period of water stress was examined. Alleviation of water stress 10 weeks after irrigation, when _l was –1.60 MPa, produced stem elongation rates that were greater than those of plants previously receiving irrigation. This ability to withstand water stress and partially compensate in growth following alleviation of the stress indicates that the kenaf crop has stress response features suitable for rainfall only production under semi-arid tropical conditions. — Irrigation schedules based on _l resulted in water applications tailored to crop requirements in that water use increased, and the time interval between irrigation decreased, with increasing canopy development as well as with increasing evaporative demand. However, erratic fluctuations in _l between irrigations make scheduling by this method difficult and the use of daily mean, dawn or noon values of _l for scheduling irrigation of kenaf cannot be recommended in environments of high evaporative demand. The factors contributing to these fluctuations in (_l) are discussed.     

Effects of alternative water distribution rules on irrigation system performance: a simulation analysis

Based on a simulation model reflecting physical and economic conditions typically found in rice irrigation systems in Asia, the irrigation performance implications of alternative water distribution rules for dry season irrigation are evaluated under varying degrees of water shortage. The rules examined reflect differing water distribution strategies designed either to maximize conveyance efficiency, economic efficiency, or equity; or to achieve a balance between efficiency and equity objectives. Irrigation performance is evaluated using several efficiency measures reflecting the physical, agronomic and economic productivity of water, and one measure of equity. Economic efficiency and equity among farmers within the portion of the irrigation system that is on in any given season are shown to be complementary, and not competing objectives. Economic efficiency and equity among all farmers within the command area of the irrigation system are largely complementary strategies at the lower levels of water shortage, but with increasing shortage, significant tradeoffs develop between these objectives. An operational rule for water distribution under a goal of maximizing economic efficiency is developed, and the data requirements for its implementation are shown to be modest. Under the model's assumed conditions of dry season rice production dependent solely on surface irrigation for water, the distribution strategy designed to maximize conveyance efficiency results in only modestly lower levels of economic efficiency and equity than could be achieved by the strategy designed to maximize economic efficiency.     

Infiltration and runoff as affected by pitting,mulching and sprinkler irrigation

Summary Changes in infiltration and runoff caused by pitting and mulching under sprinkler irrigation were studied on two soil types. Pitting or diking was done with an implement called a dammer-diker. Five soil treatments were applied: shallow and deep dammer-diker, shallow dammer-diker with mulch, bare, and a mulched soil, combined with two water application rates. Total water infiltration and runoff varied during the experiment. Runoff decreased with area of water storage provided by the pits and the less water was applied. Mulch treatments also reduced runoff. Surface water storage decreased during the season. Changes in soil physical properties due to pitting were more important in controlling runoff than surface water storage.The effective saturated hydraulic conductivity of the soil progressively decreased through the season for all soil treatments and water application rates.A model was developed to simulate the effect of pits on runoff. On a silt loam soil, simulated percent runoff and accumulated runoff over time for the bare and pitted treatments agreed closely to measured values. The agreement of simulated to measured runoff for a silty clay loam soil was not as good probably because of cracking which the simulation model did not take into account.     

Photosynthesis,leaf conductance,and water relations of cowpea under saline conditions

Summary Cowpea (Vigna unguiculata L.), grown widely under both irrigated and dryland conditions, is well adapted to drought and high temperature and is moderately salt tolerant. Data on photosynthetic response and regulation of water relations in cowpea under salinity stress is lacking. Therefore, in conjunction with a field plot experiment to establish the leaching requirement of cowpea, measurements were made of carbon dioxide assimilation rates (A) by ¹⁴CO₂ uptake, leaf conductances to H₂O (g₁) by tritum uptake, and to CO₂ (g), and leaf total water potential (_t ¹) and osmotic potential ( ¹).Cowpeas, grown in field plots containing Pachappa fine sandy loam (mixed, thermic, Mollic Haploxeraff), were irrigated daily with saline water (1,350 mg 1^–1 total salt concentration) to achieve leaching fractions of 0.17, 0.13, 0.09, 0.07, and 0.02. Cowpea maintained high leaf water potentials, high rates of CO₂ assimilation and high leaf conductances under moderately saline conditions (high leaching). Values of _t ¹ and ¹ for high leaching were consistently 50 to 200 J kg^–1 higher than for low leaching throughout the day. Calculating ¹ at full leaf turgor eliminated diurnal variation in ¹. As leaching decreased, however, A, g₁, and g, decreased significantly. About 45% of the 1°C assimilated by the leaf was incorporated rapidly into ethanol insoluble compounds. The relationship between A and g₁ for cowpea was similar to that reported for other crops.Contribution from the US Salinity Laboratory, USDA-ARS, 4500 Glenwood Dr., Riverside, CA. 92501, USA     

Potassium induced improvement of yield response in barley exposed to soil water stress

Summary The interaction of different K status of barley plants (Hordeum vulgare, L.) and water stress on yield and water relations was studied. The plants which were cultivated outdoor in pots and supplied with 0.8, 5.0, 8.5 or 12.0 g K per pot, as KCl, were subjected to increased soil water stress during the early grain filling stage.The water content of the flag leaf tissue was significantly increased from 3.1 to 4.1 g H₂O/g D.M. (dry matter) by K application resulting in maintenance of similar leaf osmotic potentials (–1.5 MPa) at all K levels prior to onset of water stress (Table 2). At the lowest K level Ca contributed essentially to maintenance of the cell osmotic potential (Fig. 2).In fully watered plants grain yield at the lowest K level was reduced 20% (Fig. 5 a) due to a decrease in the number of tillers with ears per plant (Fig. 5 b) and to early commencement of maturity processes (Table 3).Water stress caused grain yield reductions between 15 and 50%. However, by increase of K application yield was maintained to the greatest degree in high K plants (Fig. 5 a) due to improved water status in these plants during the drying cycle (Fig. 4). The production of above ground dry matter (top D.M.) during the grain filling period and the grain yield were highly correlated with the leaf water content at the end of the drying cycles (Fig. 6). The greater yield in high K plants was associated with prolongation of the grain filling period by up to 7 days (Table 3) and with an increase in grain weight by up to 20% (Fig. 5 b) as compared with low K plants. Preanthesis reserves contributed up to 52% of grain yield at low K levels (Fig. 5 c) reducing differences in grain yield between the K levels.Abbreviations RWC predawn relative water content - predawn leaf osmotic potential - WUE water use efficiency - R preanthesis reserves - ear D.M. increase in ear D.M. during the grain filling period - top D.M. increase in top D.M. during the grain filling period - SD standard deviation - LSD least significant difference     

Effect of tillage and furrow irrigation timing on efficiency of preplant irrigation

Summary A field study to determine the efficiency of preplant irrigating with furrow irrigation and the effects of tillage and fall or spring application of preplant irrigation on this efficiency was conducted during 1983, 1984, and 1985 at the Texas Agricultural Experiment Station, North Plains Research Field at Etter, Texas on a Sherm, silty clay loam soil. Sorghum residue from the previous crop was shredded, gravimetric soil samples were taken, and five tillage treatments were imposed in the fall. The tillage treatments consisted of various combinations of disking, chiselling, moldboard plowing, and disk bedding. A preplant irrigation was applied in the fall to half of each tillage plot and in the spring to the other half of each plot. Soil samples were taken from each plot one month after the spring preplant irrigation. Sorghum (Sorghum bicolor L. cv. NC 178) was planted and irrigated similarly on all plots during the growing season. On the average, 237 mm of water were required to irrigate the tillage treatments during fall preplant irrigation and 466 mm were required during spring preplant irrigation. The additional water requirement in the spring was associated with increased water uptake by non-wheel-track furrows. Treatments with chiselling required larger water application during spring preplant irrigation. All treatments had similar soil water contents at planting time. Neither timing of preplant irrigation nor type of tillage had any effect on sorghum grain yield. Therefore, fall preplant irrigation was considerably more efficient than spring preplant irrigation. Averaged over the three years do study and five tillage treatments storage efficiency was 26% for fall application and 17% for springtime.Contribution of the Texas Agricultural Experiment Station, Paper No. 21724     

Potassium-salinity interactions in irrigated corn

Summary Potassium uptake by plants can be affected by high salinity and the Na concentration in the soil solution. There is abundant evidence that Na and the Na/Ca ratio affects K uptake and accumulation within plant cells and organs and that salt tolerance is correlated with selectivity for K uptake over Na. This provides the basis for hypothesis which exists in the literature and was examined in this study, that K application can reduce salinity damage to plants. The main objectives of this study were to: (i) study the effects of salinity and K fertilization interactions on corn yield and nutrient uptake; (ii) test the possibility that salinity damage can be reduced by elevating K fertilization rate; and (iii) study K dynamics in soil as a function of the salinity of the irrigation water, in soils with high and low indigenous potassium. The response of corn (Zea mays (L.) cv. Jubilee) to K fertilization under saline and non-saline conditions was studied by growing corn in two soil types in a pot experiment. Rates of K application to a 3 kg pot were: 0, 15 and 30 mmol K to the Gilat soil and 7.5, 15 and 30 mmol K to the Nordiya soil as KCl. The desired quantity of K was applied in one dose after seedling emergence. The salinity levels of the irrigation water were 4, 20 and 40 mmol charge 1^–1. The irrigation was applied at least every second day and in excess to avoid water stress and to ensure drainage. Increased salinity in the irrigation water significantly decreased yield in both soils. Potassium significantly increased yield at all salinity levels only in the sandy soil which had a low natural level of K, but there was no difference in the relative yield decrease with salinity increase between the lowest and highest K application rates. Potassium fertilization did not eliminate the deleterious effects of salinity on corn yield despite its beneficial effect of increasing K content and reducing the NaK ratio in plant tissue. Potassium uptake by plants was the major factor in K dynamic processes. Potassium adsorption, release and fixation were secondary factors while leaching was an insignificant factor in overall K balance under cropping conditions.     

A model of crop yield response to irrigation water salinity: theory,testing and application

A relationship between crop yield and irrigation water salinity is developed. The relationship can be used as a production function to quantify the economic ramifications of practices which increase irrigation water salinity, such as disposal of surface and sub-surface saline drainage waters into the irrigation water supply system. Guidelines for the acceptable level of irrigation water salinity in a region can then be established. The model can also be used to determine crop suitability for an irrigation region, if irrigation water salinity is high. Where experimental work is required to determine crop yield response to irrigation water salinity, the model can be used as a first estimate of the response function. The most appropriate experimental treatments can then be allocated. The model adequately predicted crop response to water salinity, when compared with experimental data.Abbreviations A Crop threshold rootzone salinity in Equation of Maas and Hoffman (dS/m) - B Fractional yield reduction per unit rootzone salinity increase (dS/m)^–1 - C_i Average salinity of applied water (dS/m) - C_r Average salinity of rainfall (dS/m) - C_s Linearly averaged soil solution salinity in the rootzone (dS/m) - C_se Linearly averaged soil saturation extract salinity in the rootzone (dS/m) - C_w Average salinity of irrigation supply water (dS/m) - C_z Soil solution salinity at the base of the crop rootzone (dS/m) - C Mean root water uptake weighted soil salinity in equation of Bernstein and François (1973) (dS/m) - E_p Depth of class A pan evaporation during the growing season (m) - ET_a Actual crop evapotranspiration during the growing season (m) - ET_m Maximum crop evapotranspiration during the growing season (m) - I The total depth of water applied during the growing season (including irrigation water and rainfall) (m) - K Empirical coefficient in leaching equation of Rhoades (1974) - K_c Crop coefficient for equation of Doorenbos and Pruit (1977) to estimate crop water use - K_y Yield response factor in equation of Doorenbos and Kassam (1974) - LF The leaching fraction - Ro Depth of rainfall runoff during the growing season (m) - R Depth of rainfall during the growing season (m) - W Depth of irrigation water applied during the growing season (m) - Y Relative crop yield - Y_a Actual crop yield (kg) - Y_m Maximum crop yield (kg) - /z Dimensionless depth for equation of Raats (1974), and empirical coefficient for the leaching equation of Hoffman and van Genutchen (1983)     

Verification of impermeable barrier depth and effective radius for drain spacing using exact solution of the steady state flow to drains

The steady-state drainage equation ofHooghoudt (1940) has adrawback that tables for the determination of the so-calledequivalentlayer, d_e are needed. These calculations arecumbersome as d_e is dependenton the unknown spacing. Moreover, additional head islost due to theconvergence of stream lines towards the finite numberof perforations withinthe pipe wall. Therefore, corrections are required byreplacing the actualdrain radius by its effective radius. The designers inEgypt assume that thedepth of impermeable layer is infinity which resultsin an over estimationof drain spacing that will affect the ability of thedrainage system.Van der Molen and Wesseling (1991) have developed aseries solution toreplace the Hooghoudts approximation method for theequivalent depth by anexact solution. A comparison between this solution andthose of Lovell andYoungs (1984) and Hooghoudt (1940) showed that theexact solution proved tobe very accurate and efficient solution. The mainobjective of this study isto verify an accurate depth of the impermeable barrierand an effectiveradius of drain pipes which should be used in thedesign process using theexact solution.A field investigation was conducted in a study area of33,138 ha in theNorthern Delta of Egypt within Daqahliya Governorate.The results indicatethat a 5 m depth instead of infinity for theimpermeable layer in Nile Deltaand an effective radius of 90 mm should be used in thedesign process. Theuse of the exact solution for equivalent depth is acrucial issue especiallywith the high rate of on-going drainage projects inEgypt.     

The Irrigation Management Game: A role playing exercise for training in irrigation management

The development of a role playing exercise for training of irrigation professionals in the management of small holder irrigation schemes is described. The exercise places participants in the position of either agency staff or farmers. As farmers participants are dependent on irrigation water supplies from the agency managed run-of-the-river irrigation system. As agency staff participants are responsible for water allocation between competing demands on the main system. The exercise develops interaction between the participants as they trade in water and negotiate for irrigation supplies.The exercise develops an understanding of the issues involved in managing an irrigation system, though not only on technical matters such as water allocation policy, yield response to water and performance assessment. The exercise also creates an awareness of the whole system, in particular the importance of communication between agency staff and farmers, and between farmers themselves.The Irrigation Management Game is the copyright of the author, Professor Ian Carruthers of Wye College, University of London and consulting engineers Mott MacDonald, Cambridge, UK.     

Farmer participation in irrigation – 20 years of experience and lessons for the future

This article examines trends in the understandingof and policies toward farmer participation in irrigationmanagement over the past 20 years, with special attention toexperiences with induced participation and management transferprograms in the Philippines, Sri Lanka, Pakistan, Senegal,Columbia Basin USA, and Mexico. Key lessons relate to the valueof social organizers as catalysts; the role of the irrigationagency as partner; and the enabling conditions for participation.As levels of income and infrastructure rise, we can expect moreformal organizations that enable farmers to deal with bankaccounts, service contracts, water rights, water markets, andadvanced technology in irrigation systems. The impact ofparticipation on irrigation performance needs to be evaluated notjust in terms of reductions in government costs, but by whetherimprovement in physical structures and farmers control overwater are great enough to offset the farmers costs ofparticipating.     

Rapid field evaluation of drip and microspray distribution uniformity

The Cal Poly ITRC irrigation evaluation programs have been widely used to assess the global distribution uniformity (DU) of drip and microsprayer irrigation systems. The field procedures and formulas used in the program are presented in this paper. The system DU is estimated by mathematically combining the component DU values. DU components include pressure differences, other causes (such as manufacturing variation, plugging, and wear), unequal drainage, and unequal application rates. Results are presented from evaluations by several entities, including Cal Poly ITRC. Cal Poly evaluations of 329 fields provided an average DU_lq of 0.85 for drip and 0.80 for microspray. Approximately 45% of the non-uniformity was due to pressure differences, 52% was due to other causes, 1% due to unequal drainage, and 2% due to unequal application rates. The data show that with good design and management, it is possible to have high system DU values for at least a 20-year system life.     

Procedure for predicting and designing moving sprinkler application patterns

Summary Water application pattern, WAP, is one of the most important factors that determine the instantaneous and the cumulative application rates of moving irrigation machines. The mathematical background of a procedure to predict and design the WAP of moving irrigation machines is introduced. It includes a mathematical analysis of the effect of pressure head, height and spacing between emitters on the WAP, and a nomograph that presents this analysis graphically and illustrates the design procedure of the application pattern of irrigation machines.Abbreviations P()a water application rate at a normalized radial distance from the emitter [m/s] - ka number of linear segments needed to represent the pattern - s/Ra normalized radial distance from the emitter - Ra wetted radius [m] - sa radial distance from the emitter [m] - n _j n _i/ha normalized water application rate at point - j, ha maximum water application rate [m/s] n _j water application rate at point j [m/s] - _j =m _j/Ra normalized radial distance of point j from emitter - m _ja radial distance of point - ja from emitter [m], CWAP - (x)a Cumulative Water Application Pattern: amount of water per unit area applied at a distance - xa from the travel path of the emitter [m³/m²] - xa distance from the travel path of the emitter [m] - T _xa time of application at a distance - xa from the travel path of the emitter [s] - va velocity of propagation of the machine [m/s] - k ₁a the outmost linear segment that its radial distance from the emitter - m _k1a is smaller than the distance of the travel path from the emitter - x, T _ja time at which the - j ^tha linear segment (ring) stops influencing the point located at a distance - xa from the emitter - ₁, ₂, ₃a dimensionless numbers derived by dimensional analysis - ua water jet velocity [m/s] - ga gravity acceleration [m/s²] - da nozzle diameter [m], v kinematic viscosity [m²/s] - Ha emitters height [m] - , a regression analysis coefficients - Paa Pattern fit coefficient for water application - F(r)a normalized desired water application pattern [1/m] - f(r)a normalized actual water application pattern [1/m] - La common distance on which - F(r) and f(r)a are defined [m], SP spacing interval between emitters [m] - DSa dimensionless spacing interval between emitters - DSa variation of dimensionless spacing interval - Paa variation of Pa coefficient - Pa pressure head [kPa]