Optimum Design of Drip Irrigation System using Microtubes as Emitters

Transcription

1 Optiu Design of Drip Irrigation Syste using Microtubes as Eitters A thesis subitte in fufient of the requireents for the egree of Master of Engineering Air Keshtgar B. Eng (Irrigation an Drainage Engineering) Schoo of Civi, Environenta an Cheica Engineering Coege of Science, Engineering an eath RMIT University February 2012

2 DECLARATION I certify that except where ue acknowegeent has been ae, the work is that of the author aone; the work has not been subitte previousy, in whoe or part to quaify for other acaeic awar; the content of the thesis is the resut of work which ha been carrie out since the officia coenceent ate of the approve research progra; an, any eitoria work, pai or unpai, carrie out by a thir party is acknowege. Air Keshtgar 20 February 2012 ii

3 ACKNOWLEDGEMENTS In the first pace, I wou ike to recor y gratitue to Dr Muhae Bhuiyan for his supervision, avice an guiance fro the very eary stage of this research. e provie e unfinching encourageent an support to iprove this work in various ways; I a inebte to hi for his patience an scientific inspirations. Many thanks go in particuar to Dr Sujeeva Setunge for a her support an avices. I wou ike to express y sincere gratitue to Ehsan Keshtgar an Ai Muhaa Baie, postgrauate stuents of IT for their precious tie spent on teaching e Visua Basic. I a gratefu to Cheica, Civi an Environenta Engineering staff ebers for their assistance through the course of stuy. I greaty owe y success to y beove parents an wife for their kinness, continuous encourageent an patience. iii

4 ABSTRACT Drip irrigation is a syste in which water is suppie irecty to pant roots with a pressure an fow rate to eet the crop water requireent. Drip irrigation systes are in extensive use aroun the wor since its acceptance for easy contro of the appie water voue an thus to irrigation anageent. These systes are copatibe for a wie range of crop variety, soi type, ciate an an surface espite of few potentia constrains. Cogging an eission non-unifority, for a ong tie, have been the ajor obstaces in the eveopent of rip irrigation. It wou be a serious probe in areas with brackish water where the probes of precipitation of caciu carbonate, organic aterias an suspene sans are severe. Instaation of fiter equipents before suppy to the syste has sove a part of the probe but cou not eiinate it entirey so far an thus irrigators have to use ifferent ethos to reove the precipitations by aci, which has averse infuence on soi an crops. In orer to obtain the best eission unifority (EU) in uneven ans the pressure reguators an pressure copensating eitters (a gaget) have been use. owever, pressure copensating eitters ten to be ore copex an costy than noncopensating eitters an are not easy to appy. In this stuy, the possibiity of utiizing sa iaeter pipes approxiatey 2 to 4 cae icrotubes have been iscusse for enhancing the ischarge unifority of the rip irrigation an ecreasing the ifficuties encountere by those eitters ue to cogging an bockage. Microtubes have any avantages copare to other types of eitters in ters of cost an practica appications. As these sa size pipes are ae of fexibe aterias, can be ajuste in shape an ength without ifficuty. By ajusting the icrotube engths at ifferent points aong the atera accoring to energy hea eveope, an equa outfow can be eivere to eveny space pants in the fie. ere icrotubes act as eitters. The variation of the icrotube engths is ae for issipating the extra heas above a thresho vaue. This thresho energy hea vaue has been set, at the very ast icrotube of the en-atera in a given anifo (or subunit), equa to the frictiona an other inor iv

5 energy heas ost for that iniu ength icrotube require to reach the pant uner consieration. A subunit consists of a anifo fro where ateras are eerging at a reguar interva. As such, ateras can aso be iagine as arger eitters aong the anifo of an irrigation subunit. These arger eitters wou have a characteristic pressure-ischarge reationship, for a hyrauicay cacuate set of icrotube engths that are eitting equa ischarges aong the en-atera, to estabish a base energy hea at the en point of the anifo. At this juncture there wou have two options for the esign of the succeeing ateras. In one option cae Pre-efine Eission Unifority, the ength of a the icrotubes in the succeeing ateras wi have the sae set of engths as has been cacuate for the en-atera. This configuration of the icrotube setup wi eiver variabe ischarges, which cou be ajuste within the eission unifority (EU) assigne by the esigner. In other option cae Fu Eission Unifority, the esigner wi vary a the icrotube engths in a the successive ateras so as to eiver equa ischarges an thereby to achieve fu eission unifority (EU). In the first option on Pre-efine EU, as the sae set of icrotube engths wi be fitte to the other successive ateras, the characteristic pressure-ischarge reationship fro the en-atera can be appie to these other ateras to extrapoate their corresponing ischarges. The energy hea in the en-atera can be ae with the energy require in the preceing reach of the anifo to obtain the energy in the inet of the foregoing atera. The variation of ischarge in anifo ine has been efine by eission unifority (EU) of the syste an can be assigne by the esigner to fin the optiu anifo ength to have the EU within that range. In this research two progras eveope to esign an optiu rip syste with certain eission unifority. The first progra is a stanaone progra that can be run for ifferent ischarges, the outcoe of this progra is the set of icrotube engths, nuber of cois an the pressure heas of the very ast atera. When a set of ischarges an corresponing pressure heas are known, the reationship an hyrauic paraeters of pressure-ischarge reationship cou be obtaine. Severa case scenarios for three typica icrotube iaeters of 2, 3 an 4 have been perfore within four noina atera sizes of 10, 12, 14 an 16, an the esign charts an tabes are eveope for three terrain sopes of 0, 0.25 an 0.5%. At the secon step these resuts an hyrauic characteristics of arger eitters (ateras) appie to a anifo v

6 ine to esign a copete syste. The outcoe of the secon progra is the nuber of ateras require to eterine the Pre-efine EU an finay cacuate the pressure hea of the syste. In the other option on Fu EU, in orer to ake a fow rates of the ateras equa (EU = 100%), ajustent of the icrotube engths corresponing to the tota inet heas are appie for a successive ateras. For this option ike the Pre-efine EU, aso three typica icrotubes an three atera sizes appie aong with three terrain sopes of 0, 0.25 an 0.5%. The resuts of a those ayout cobinations show that correation between icrotube ength variation an energy rop ratio can be generaize for a icrotube an atera sizes in a given sope. To eveop the generaize equations for icrotube ength an energy rop ratio, Energy Grae Line approache has been consiere. Therefore, the set of esign tabes an graphs incorporate with a genera equation as the outcoe of this option, are provie for esigners to avoi any coputer siuation. When the require ischarge an iaeters of icrotube, atera an anifo an soe groun conitions are given, the ength of the icrotubes, the pressure heas, eission unifority (in percentage) an the best subunit iensions can be obtaine. The resuts of stuy show that arger sizes icrotubes have higher variation of ength, whie appying arger fow rates can ecrease the ength variation aong the atera. Few exapes are prepare to eonstrate the rip irrigation esign paraeters in typica subunit sizes. vi

7 Tabe of Contents DECLARATION.ii ACKNOWLEDGEMENTS.iii ABSTRACT.iv Tabe of Contents.vii List of Figures ix List of Tabes.. x Abbreviations an Notations xi Chapter 1 Introuction Drip Irrigation Avantages of Drip Irrigation Probes of Drip Irrigation Objectives of the Propose Stuy Scope of Stuy Thesis Outine 6 Chapter 2 Literature Review Microtubes an Eitters Design Consierations for Eitter aong the Lateras Pressure Distribution aong the Latera Manifo Design Chapter Suary. 15 Chapter 3 Theoretica Deveopent Layout of a Typica Irrigation Subunit Basic yrauics Pressure-Discharge Reationship Eission Unifority (EU) Pre-efine EU Syste Fu EU Syste Chapter Suary. 28 Chapter 4 Moe Deveopent Microtube Eitter Design Design for Pre-efine EU Design for Fu EU Deveopent of Moe Agorith Progra Progra Progra Chapter Suary. 36 vii

8 Chapter 5 Resuts an Discussion Microtube Design for the En-atera Microtube Design for a Pre-efine EU Microtube Design for Fu EU Energy Graient Line Anaysis Microtube Length Coputation Chapter Suary. 58 Chapter 6 Typica Design Exapes Irrigation Design Paraeters Syste Design Exapes on Pre-efine EU Exapes on Fu EU. 68 Chapter 7 Concusions an Recoenations Concusions Design using Pre-efine Eission Unifority (EU) Design using Fu Eission Unifority (EU) Recoenations for Future Works 71 References 73 Appenices Appenix A Output Tabes fro Progra Appenix B Output Graphs fro Progra viii

9 List of Figures Figure 1.1 A typica rip irrigation syste 2 Figure 3.1 Scheatic ayout of a rip irrigation subunit using icrotubes as eitters.17 Figure 3.2 Scheatic ayout of a singe atera aong with varying engths of icrotubes; etais A an B shows the instaation ethos for aking cois.18 Figure 3.3 Energy grae ine an hea osses in one sie of the atera ( h e = entrance oss, h v = veocity oss, h c = coi hea oss, h f (n) = icrotube friction hea oss at n, an h f (n) = atera friction hea oss between n an n 1)...21 Figure 3.4 Scheatic ayout of a typica subunit with Fu EU..7 Figure 4.1 Fow chart of Progra 1 to cacuate the icrotube engths, inet pressure hea an nuber of cois in the en-atera...32 Figure 4.2 Fow chart of Progra 2 to ajust the nuber of ateras require for a pre-efine EU..34 Figure 4.3 Fow chart of Progra 3 to copute the new set of icrotube engths for successive ateras to achieve fu eission unifority.35 Figure 5.1 Pressure-ischarge reationships for ateras as arge eitters ( = 10, in = 1.25, n = 10, = 1 an S = 0 %) 40 Figure 5.2 Coparison between siuate ( i vs i ) an Eq (5.2) erive energy graient ines 47 Figure 5.3 Siuate energy graient ines for typica ateras; a) for = 12, S 0%, b) 16, S 0%, c) 12, S 0.25% an ) 16, S 0.25% (there are 10 trees pace at an interva of 1 space aong the ateras) 49 Figure 5.4 Figure 5.5 Figure 6.1 Microtube tota ength ifference for typica ateras; a) for 12, S 0%, b) for 14, c) for 16 S 0%, ) for 12, S 0.25%, e) for 14, S 0.25% an f) for 16, S 0.25% (there are 10 trees pace at an interva of 1 space aong the atera) Microtube ength ifference istribution for any ischarge, an icrotube an atera size (this graph is erive for 10 trees pace at an interva of 2 space aong the atera).54 Scheatic ayout of the pot use for grape.64 ix

10 List of Tabes Tabe 5.1 Tabe 5.2 Tabe 5.3 Tabe 5.4 Tabe 6.1 Tabe 6.2 Tabe 6.3 Tabe 6.4 Tabe 6.5 Longest ength icrotube ax (), an i, i 5 (), nuber of cois c an inet pressure hea require T () for the given icrotubes an ischarges ( = 10, in = 1.25, n = 10, = 1 an S = 0 %; the shae ces are consiere as unreaistic range of tota heas) 38 Pressure-ischarge reationships for ifferent ateras with in = 1.25, n = 10, an = 1 ; a) for S = 0%, b) for S = 0.25%, an c) for S = 0.50%...41 EU an nuber of ateras in one subunit with in = 1.25, n = 10, an = 1; a) for S = 0%, b) for S = 0.25%, an c) for S = 0.50%...43 Coefficients of Eq (5.4) for iniu possibe engths of icrotube in; a) for =12 an b) for =16 (these tabes are erive for ateras at an interva of 1 space aong the anifo, where 10 trees are pace at an interva of 1 space aong each of the atera) 55 Input ata reate to pot, irrigation piping syste an soi for case stuies...61 Assue an output ata reate to irrigation to Grape...62 Output ata for siuation of Case Stuy on Grape 62 Assue an output ata reate to irrigation to Grape...65 Output ata for siuation of Case Stuy on Toato..66 x

11 ABBREVIATIONS AND NOTATIONS c - nuber of cois D - iaeter of coi () - iaeter of the pipe () - iaeter of atera () - iaeter of icrotube () - iaeter of anifo () g - acceeration ue to gravity ( 2 ) s - tota hea rop up to the en of the atera i - tota hea rop at a ength ratio i sub - pressure hea of sub-unit T - anifo hea () h e - entrance hea oss () h v - veocity hea oss () h c - coi hea oss () h f - frictiona hea oss () h f (n) - icrotube frictiona hea oss at icrotube position n () i x / X - a ength ratio for a given position x fro the atera inet to the tota atera ength X k - ischarge coefficient that characterizes icrotube eitters - ength of the pipe () in - iniu icrotube ength () - ength of the icrotubes () - nuber of ateras n - icrotube nuber Q - anifo ischarge (itre/hr) Q - average of owest ¼ of the atera fow rates (itre/hr) Q a - average of a the atera fow rates in the syste (itre/hr) xi

12 q R e - icrotube ischarge (itre/hr) - Reynos nuber R i - hea rop ratio aong a atera S - sope of atera ine - istance between icrotubes () v - veocity of fow (/s) X - tota ength of the atera () x - ischarge exponent that characterizes the eitter fow regie; given position fro the inet atera xii

13 Chapter 1 Introuction 1.1 Drip Irrigation Drip or tricke aso cae icro or ocaize irrigation is a pressurize syste to irrigate the crops an orchars, consists of an extensive network of pipes usuay of sa iaeters that eiver water irecty to the soi near the pant. The syste usuay possesses fertiizer injection syste, suppying pants with neee nutrients. In rip irrigation the objective is to provie each pant with a continuous reaiy avaiabe suppy of soi oisture, which is sufficient to eet transpiration eans (Keer an Karei, 1974). A fiter is use to reove suspene aterias, organic atter, san an cay to reuce bockage of the eitters. Aong with puping station, contro vaves are instae to provie require pressure heas to the syste (ensen et a., 1980; Brats an Wu, 1979b). The syste contains eitters, ateras, anifo an ainine, which suppies water fro the source to pant root zone. The ainine eivers water to anifo an anifo eivers water to ateras. The eitters, which are attache to ateras, istribute water to pant root zones. Lateras are noray one size pipes, ae of poyethyene (PE) with iaeters 10 to 16 in range, proviing better fushing, easy instaation an aintenance characteristics (ensen et a., 1980, Pero, 1977). Manifo an ainine are either in eiu ensity poyethyene (PE) or rigi PVC with iaeters 20 to 100 in range (Wu an Gitin, 1977b). Eitters are pant s point sources of water an esigne to provie sa an argey equa aount of ischarges of pant requireent. Eitters are of any kins, such as, orifices, nozzes, porous pipes, icrotubes, etc to issipate the pressure in the pipe istribution networks by eans of a narrow nozze or ong fow path, an thereby ecreasing the water pressure to aow ischarges of ony a few itters per hour (Vereiren an Jobing, 1980, Brats an Wu, 1979). Then water is istribute by its nora oveent through the soi profie. Figure 1.1 shows an exape of a typica rip irrigation syste consisting of eitters, ateras, anifo, ainine an fiter equipents. 1

14 Figure 1.1 A typica rip irrigation syste (source: Avantages of Drip Irrigation Drip irrigation offers unique agronoica an econoica avantages for the efficient use of water. It is consiere as the ost water saving etho of irrigation, thus very iea for use in areas with iite water resources. It is aso beneficia in teperate areas where other surface irrigations such as foo an furrow irrigations or pressurize systes such as sprinker are subject to big water oss ue to evaporation. Since the syste s eission can be controe by tie anageent or using ifferent types of eitters, the probe of eep percoation an oss in the sois can be reuce an saves water in root zone an subsequenty appication efficiency cou be achieve. This syste can be appie very efficienty to sa trees an wiey space pants such as toatoes, citrus an grapes (Benai an Ofen, 1984) (Wu an Gitin, 1977b). In ari regions with goo anageent the ratio of transpire to appie water is usuay at east 0.9 (ensen et a., 1980). Water appication efficiencies approach 100 percent an water savings of 30 to 50 percent over other irrigation ethos are obtaine for crops an conitions favouring rip irrigation (ensen et a., 1980). Insect, isease an fungus probes are reuce by iniizing the wetting of the soi surface. Fewer wees, ess soi crusting, reuce cutivation an thus ess soi copaction interference with harvesting are other benefits of rip irrigation (ensen et a., 1980). 2

15 The possibiity of appying the fertiizer an pesticie by injection into irrigation water an eiver to pant root zone can hep to ecine the eep percoation of this iportant input an increase their efficiency. Use of saine water is not recoene in sprinker systes, which cause eaf burn. owever, saine water can be appie in rip irrigation systes. Saine water shou be appie with caution because sats ay cause eitter cogging an require frequent soi eaching to prevent sat accuuation in the soi (Vereiren an Jobing, 1980) Probes of Drip Irrigation Cogging of the sa conuits in the eitters is the ost serious probe of rip irrigation syste. San an cay partices, ebris, cheica precipitants an organic growth can bock fows through eitters. The cogging occurs grauay an reuces the fow rates of eitters an causing poor water istribution (Vereiren an Jobing, 1980). This probe wi ea to poor prouctivity in fars or orchars because soe parts of the an obtain ore water whie other parts o not eet the iniu requireent of pants ue to evaporation. Cogging occurs ainy ue to passage of water through the very fine pores of the eitters. Thus, eitters with saer passages are ore susceptibe to bockage. The eivere water contains suspene partices, sats an issove fertiizers which create severe probes that require teious efforts an skie an-power to resove. Using aci injection an/or repacing new eitters are the ain coon soutions for cogging probe which both are tie consuing an ipose huge running cost to the syste (Gibert et a., 1981). Moreover, uneven fow rate ue to pressure hea oss is another ajor probe of this syste. Drip irrigation systes o not appy water with perfect unifority aong the crop rows. Soe of the variabiity is cause by anufacturing iperfection in the eitters, but the ajor probe crops up fro the stance of the syste esign, in ters of the frictiona oss in the irection of fow through the atera pipe or tubing where eitters are attache (Myers an Bucks, 1972). Drip irrigation usuay operates uner ow pressure (ess than 100 kpa). Pressure istribution insie a atera or anifo wi be greaty affecte by the friction an sope of the pipe aying. This variation of pressure wi change the ischarge of eitters aong the ine. owever, an iea rip irrigation wi be one which can irrigate unifory that each eitter eivers equa ischarge as require by the pant per irrigation (Wu an Gitin, 3

16 1973). Severa anufacturers have esigne eitters to reuce ischarge variations cause by friction-inuce pressure changes in the atera pipes. These eitters are copex an susceptibe to cogging to ipose huge initia an operationa costs to the syste. In another instance, a graphica proceure was eveope by Wu an Gitin (1973) using sipe eitters of ifferent iaeters aong the atera pipe to copensate its frictiona osses, which in practice is very har to insta. In ters of econoica consieration, rip irrigation requires high capita cost as we as aintenance. Researches showe that ue to big initia an running costs, the syste has iite appication in sa pots of the eveoping countries (Singh et a., 2009). 1.2 Objectives of the Propose Stuy Microtubes aso cae spaghetti tubes are sa bore poyethyene tubes, in the range of 1 to 4 in interna iaeters, are use as eitters in rip irrigation syste. These sabore tubes can be use as pressure copensating eitters in rip irrigation syste. Utiizing these fexibe tubes as an aternative to oern ripping eitters wi reuce the risk of cogging significanty as they have siper passages than those eitters. Microtubes have been successfuy use as eitters in rip irrigation syste with the benefit of having equa fow rates at a outets aong the ateras without significant probe of cogging (Vereiren an Jobing, 1980). The varie tota heas aong the ateras can be copensate by using a set of varie icrotube engths to provie requisite frictiona osses an thereby to eiver equa fow rates to pants. Otherwise, ateras wou have ischarge varying fow rates accoring to its varying inet tota heas. These inet heas, inee vary ue to frictiona osses in the succeeing anifo reaches for its ensuing ischarges. When each icrotube works as an eitter an ischarges equay (eission unifority, EU = 100%) at ifferent points aong a particuar atera, the atera at that tie can aso be iagine as an eitter aong the given anifo (Keer an Karei, 1974). Thus on the other han, if we want to stanarize a set of varie icrotube engths for an inet hea of a given atera, it wou eiver proportionatey varying ischarges accoring to the inet heas of the successive ateras. Because this stanarize set of icrotube engths are erive base on an inet hea of a given atera to eiver equa ischarges, the given 4

17 atera wou have a characteristic pressure-ischarge reationship, which can subsequenty be appie for successive ateras with varying inet heas to prouce consequentia ischarges. These ischarges as wou vary aong the anifo ine, a iiting eission unifority (EU) set by the esigner, wou ictate the resuting ength of the anifo with the nuber of ateras to ecie about the iensions of the irrigation subunit. Coputes coes are written to cacuate the icrotube engths an tota heas aong the ateras within a subunit for a given ischarge or ischarges set through EU. These ischarges are projecte accoring to the ean of the pants an the iiting percent of EU. The iaeters of the icrotube an atera, groun sope, an spaces between pants are use to copute the tota heas of the syste an the ength of anifo require to fufi the consiere EU. In one coe the ateras are iagine as arge eitters aong the anifo an the set of icrotube engths are propose to be sae for a the ateras, thus eission unifority wou ictate the subunit iensions. In the other coe, for a given subunit, varying icrotube engths aong each atera are cacuate to prouce equa ischarge throughout the syste to achieve 100 percent EU. Therefore, the specific objectives of this research are as foows: 1. To eveop coputer progras, one is for pre-efine EU (EU = 90%) set by the esigner an the other one is for a Fu EU syste. 2. To use the above coputer progras for severa typica scenarios, specific esign tabes an graphs wou be eveope to eterine appropriate icrotube an anifo engths. 3. To appy the propose techniques to few typica esign exapes. 1.3 Scope of the Stuy A suit of coputer coes have been written using Visua Basic as a graphic user interface (GUI) progra which can easiy be run by orinary hoe coputers. In orer to achieve the best accuracy using the progra, the esigner shou consier soe constraints that wi be iscusse ater. The progras that have been eveope to siuate the syste are as foow: 5

18 i. Deterination of icrotube engths an inet pressure hea of the en-atera in this coe the icrotube an atera iaeters an icrotube spacing an nuber shou be known. ii. Deterination of ength an inet pressure hea of the anifo assuing each atera in the anifo works as a arge eitter in this part the fow rates of a successive ateras have been copute for a given EU using the resuts fro first coe an the corresponing pressure-ischarge reationship. This coe has been eveope base on the practice of convenience that the entire syste appies the sae set of icrotube engths as obtaine in en-atera. iii. Design an iea rip syste with 100 percent EU using varie icrotube ength a over the syste this coe aso works base on the resuts of first coe to initiate an create new series of icrotube engths for each atera separatey. Design tabes an graphs have been generate for irect cacuation of icrotube engths. iv. To eonstrate the functionaity of the above two agoriths, reevant esign paraeters for rip irrigation syste are appie to few case stuies. These case stuies prepare with the reevant soi an an paraeters for toato an grape pants, appropriate to appy in rip syste. 1.4 Thesis Outine This thesis consists of seven chapters an few appenices after the ist of references. Chapter 1 escribes backgroun inforation about rip irrigation, its avantages an probes, sets the objectives of the stuy an provies scope of work of this research. The ain purpose of Chapter 2 is to fin the ost reevant works an stuies to iprove the unerstaning of the probe, an then getting faiiarity with techniques an anaysis. 6

19 In Chapter 3 the basic hyrauic principes are iscusse to estabish the theoretica eveopent of the propose rip irrigation syste esign. The chapter gives the unerpinning agorith of two anticipate approaches to siuate typica rip irrigation systes. The concept fro previous chapter is unertaken here in Chapter 4 to eveop few coputer progras/coes to sove the two approaches of rip irrigation syste esign. The two esign approaches eveope are: i) a syste with Pre-efine Eission Unifority, an ii) a syste with Fu Eission Unifority. The progra can be operate sipy to copute the pressure istribution, icrotube engths aong the ateras, an eission unifority (EU) of the syste. The resuts of the siuation for typica rip irrigation syste are suarize in Chapter 5. The chapter introuces few esign graphs an tabes using the concept of energy graient ine schee to show how the new process of coputation works. A typica ayout aong with soi, eteoroogica an reaistic irrigation paraeters is consiere in Chapter 6 to eonstrate fie esign exapes. The resuts of the exapes obtaine to evauate the functionaity of the propose agoriths. Finay Chapter 7 presents the concusions an recoenations for future research. 7

20 Chapter 2 Literature Review 2.1 Microtubes an Eitters During recent years, nuerous rip irrigation eitters with varying characteristics have becoe avaiabe in the arket. To have the best eission unifority an iniu fow rate fuctuation ue to pressure istribution, soe of the eitters have been esigne as pressure copensating eitter. Soe of the are sef ceaning or fushing to reuce the cogging but others can be cogge easiy an require sophisticate water fitration. Sooon (Sooon, 1979)) an (Keer an Karei, 1974) aong others have iste the esire quaities of those eitters in rip irrigation systes. Drip or tricke irrigation researchers have chosen two approaches to sove the cogging probes (Bucks et a., 1979). The first approach is to focus attention on iproving the quaity of water before it reaches the eitters. The secon approach is to eveop eitters or evices to reain free fro cogging. Extensive researches were one by Bucks et a. (1979) using 8 types of eitters an 6 ifferent treatent processes for water fro various sources. The stuy inicate that a cobination of suitabe physica an cheica treatents is neee to keep the eitters free fro cogging. Particuary fitration aong with p ajustent was essentia in orer to contro the cheica precipitation an bacteria growth. Furtherore, it showe that the expanabe iaphrag eitters treate by cheicas for bockage probes, afunction in its ong ter operations (Bucks et a., 1979). In a hyrauic perforance anaysis on various kins of eitters, ezarjaribi et a., (2008) cacuate the anufacturing variation coefficient, eitter ischarge coefficient an eitter ischarge exponent in orer to estabish fow sensitivity to pressure an copare anufacturers specifications. The resuts inicate that for the chosen eitters the anufacturers suppie ata are not reiabe for esign purposes. Reiabe fie tests are require prior to esign of a rip syste. In fact using the anufacturer s ata wi ea to non-unifority of ischarge throughout the syste (Özekici an Snee, 1995, ezarjaribi et a., 2008). 8

21 Recent stuies inicate that in eveoping countries the size of fars have been ecining ay-by-ay uner continuous popuation increase. Sa an hoers are not abe to utiize oern technoogies for those sa fars. The efforts to fin cheap an efficient etho of irrigation for such sa fars were investigate to raise the prouctivity without neeing to use sophisticate technoogies. In any of these works, icrotube has been recoene as a ow cost an easy to insta eitters. Researchers inicate that the cost is substantiay ess than conventiona eitter systes (Singh et a., 2009; Bhatnagar an Srivastava, 2003; Ea et a., 2009; Poak, 1998). When icrotube is use as an eitter in a rip syste this sa tube itsef issipates energy to fow a certain ischarge. The ost iportant variabe in its esign is the cacuation of energy osses ue to friction at the inner wa of the tube an other inor coponents ike entrance, exit, vaves, bens, etc. These energy osses aso represent the inet pressure of the icrotube since the outet pressure is zero (Khatri et a., 1979); (Bhuiyan, 1990) Use of icrotube as eitter was first conceptuaise by Vereiren an Jobing (1980). The sizes of the tubes were ess than 0.9 an suppose to be the sipest an cheapest aong a the water istributor evices. Microtubes as sa bore poyethyene tubes can be any sizes between 0.6 an 4.0 interna iaeters. The ischarge fro a icrotube varies accoring to the operating pressure, interna iaeter an ength of the tube. In other wors, for a given interna iaeter, the ischarge of a icrotube ay be kept constant uner various pressure conitions by ajusting its ength. Therefore, if the pressure istribution aong a atera is known, unifor istribution of water can be achieve by using appropriate engths of the icrotubes. In this ine of concept, Bhuiyan et a. (1990) propose an agorith to obtain a variabe set of icrotube engths as an eitter to eiver unifor ischarge aong a typica atera ine. Nowaays icrotubes are wiey use as an extension for icro-sprinker or icro-jet systes to increase the outet pressure an therefore to cover arger areas. These sa tubes are aso suitabe for unuating ans where the pressure of the syste varies consieraby accoring to ifferences in eevation. Thus their engths can be ajuste accoring to pressure heas to eiver a unifor ischarge. 9

22 Recenty Internationa Deveopent Enterprises (IDE), a non-profit organization base in Coorao, USA has suggeste the use of this sa iaeter poy tubes in ow cost rip irrigation kits. They beieve that by connecting icrotubes to pastic tape ro ateras an then to ow-height tank wou provie an easy to insta an cheap ow-pressure rip irrigation syste, speciay for eveoping countries in Africa an Southeast Asia (Ea et a., 2009). An experienta project was unertaken to use icrotube as eitter to irrigate ans with various sopes. The resuts showe a wie variation in eission unifority (EU) particuary with increasing upans. The reason of this wie variation is ue to the use of equa ength icrotubes throughout the syste. In another siiar stuy the eevate tank was provie to suppy unifor ischarge to ifferent hiy terraces in northwest iaayas (Bhatnagar an Srivastava, 2003). They recoene a star configuration ayout of icrotubes (1 iaeter) as eitters to service four rows by one atera. Their resuts show that this configuration iprove the eission unifority to 94-98%. In effect it is foun that the nuber of pants serve by this configuration is very iite copare to coercia type of rip irrigation systes. (De Aeia et a., 2009) worke on an epirica approach to eterine a new icrosprinker syste where icrotube engths can be ajuste to eiver a noina ischarge for a given pressure. They foun a set of pressure-ischarge an pressure-ength regression reationships for 1.07 an 1.5 icrotubes to eveop this new type of eitter. owever, it is foun that various fow regies have been ignore for its hea oss cacuations. Khatri et a. (1979) worke with seven ifferent iaeter icrotubes (0.8 to 4 ) to easure hea osses in the rip irrigation syste. The resuts showe that Darcy-Weisbach equation can be use aong with Basius friction factor equation for those hyrauicay sooth icrotubes. Anaysis was one for the separation of inor osses an to prouce coefficients for ifferent fow conitions. owever, finay it concue that the icrotubes are sighty soother than the hyrauicay sooth pipes as specifie in the Mooy iagra. Experienta resuts by (Watters an Keer, 1978) confire that the friction factor, f of the Darcy-Weisbach equation for sooth intereiate iaeter pipes (4 to 12 ) can be estiate by using Basius forua. They provie soe graphica soutions base on set of sipe equations to represent a wie range fow rates encountere 10

23 in rip irrigation systes. Experients by von Bernuth an Wison (von Bernuth, 1990) on arger iaeter pipes (14, 16 an 26 ) an for Reynos nuber ess than 100,000 aso showe that the Basius equation is an accurate preictor of the Darcy-Weisbach friction factors. It was concue that Basius equation has reasonabe accuracy for estiating friction factor for a range of tubes in turbuent fow conition. 2.2 Design Consierations for Eitters aong the Lateras The concept of best eission unifority was one of the key factors for the seection of atera ength an the nuber of eitters aong it. In this regar, Christiansen (1942) carrie out the first work for a pressurize sprinker syste. The paper propose a coefficient of unifority ( U ) for the syste base on getting the easure on average of c the absoute eviations of each observation fro the ean observation. In equation forat it can be written as: where, q U c (2.1) q 1 q n n i 1 n 1 q i q, q n q i i 1, an n = nuber of observe ischarge vaues. For a typica rip syste, the eitter fow rates epen on eitter characteristics, aging an variabiity in anufacturing of eitters, friction hea osses in the pipe network, topography of an an the nuber of cogge eitters in the syste. Ieay, the appication of water throughout the rip irrigation syste shou be absoutey unifor (Sooon an Keer, 1978). To achieve this objective Meyers an Bucks (1972) an Wu an Gitin (1973) have eveope a esign proceure using ifferent size pipes. The theoretica perforance of utiizing 5 ifferent size eitters aong a atera ine shows 3.3% eviation fro esign ischarge whist for a singe eitter size this vaue is +21% to -7.4% (Myers an Bucks, 1972). owe an ier (1974) propose a esign proceure base on Christiansen coefficient of unifority with consierations of eitter characteristics, frictiona hea osses an eevation ifferences of the topography. Wu an Gitin (1977) propose a technique to ivie a atera ine into severa sections an use ifferent size pipes for each section. Their stuy shows that this sipe fashion oifies the energy graient curve of each section to a straight ine except the ast section. They 11

24 aso concue when a atera or anifo is ivie into sections the ean ischarge of each can be use to estiate the tota energy rop by friction. This approach can be use for both unifor an non-unifor sopes; however, a sopes have to be own sopes. Wu an Gitin (1974, 1975) eveope a iensioness energy graient ine approach for irect cacuation of energy rop for a range of eitter fow variation (ess than 20%) aong a singe atera ine an a subain unit. Wu (1992) eveope a coputerise esign technique using energy graient ine etho to cacuate the fow rates. A step-by-step (SBS) cacuation has been carrie out to copare the resuts an fin out the eviations between two approaches. Karei an Peri (1977) suggeste a esign proceure for a singe atera by cacuating the pressure hea at each noe backwar fro the ownstrea noe. Pero (1979) eveope a graphica esign proceure using coputer progra for the esign of icroirrigation pipe syste. In this esign, fow rate is assue to be constant using ajustabe icrotube as feeer. The resuts of the siuation trias shou be potte to fin an optiu size for each atera. In another stuy, Pero (1977) eveope a pocket cacuator iterative proceure by eans of a series of iensioness soutions to esign a constant size atera with utipe outets. The copeent of the Christiansen coefficient is use as a criterion. Thus the average of the absoute eviations fro the ean outfow is consiere as a esign criterion. Finay a esign chart is presente to fin the perissibe nuber of outets for the given ean eviation. athoot et a. (1993) eveope a coputer progra that cacuates the veocity hea change an the variation of Reynos nuber aong the atera pipe. Sipe noniensiona charts are prepare for soe nuerica exapes to inicate that variation of Reynos nuber aong the atera is iportant. In this stuy the eitter spacing is unifor an the outfow of iniviua eitters is evauate stepwise fro the first eitter. The unifority of the syste is the ain esign criteria to fin the best atera ength. Kang an Nishiyaa (1996a, b) appie the finite eeent etho an goen section search to fin the operating pressure hea of the atera that can prouce the require 12

25 average eitter ischarge. A coputer progra eveope to cacuate the best subain position an the operating pressure by input the known paraeters such as average eitter ischarge, require water eission unifority an other conitions. Through a ifferent work, Vaesquino (2008) presente an aternative etho to siuate hyrauic perforance of ateras for sprinker an tricke irrigation systes. The etho estiates the outfow of siiar type of ateras but with ifferent engths. In this stuy two hea osses have been taken into account, one is transversa originating through the risers as a consequence of friction an oca osses an another one is ongituina originating aong the atera because of the friction an oca osses. The resuts of oe have been copare to step-by-step cacuation (SBS) an energy graient ine version (EGL) an it is concue that the resuts are coser to SBS etho, whie the eviation fro EGL etho is greater ue to consiering transversa hea osses. 2.3 Pressure Distribution aong the Latera Accoring to Christiansen work (Christiansen, 1942) for sprinker systes, a curve of pressure versus position aong the atera ine sees to have the sae genera shape regaress the aount of fow rate, hea oss an ength of ine. The fow conition in atera ine is steay an spatiay varie with eitter outfows, thus the istribution of ischarge aong the ine is increasing upstrea. Due to the variation of ischarge in the ine, the energy graient ine wi not be a straight ine but a curve of the exponentia type. Wu an Gitin (1975) eveope iensioness pressure curves for three types of fow regies in ateras. These iensioness curves propt the esigner to cacuate the energy rop aong the atera ine. They foruate a genera equation to cacuate the tota energy rop base on tota ischarge or average ischarge in the atera ine. So the soution is ony an approxiation since the energy graient ine is eterine by assuing a eitter fows are constant (or with sa variation). To overcoe the probe an increase the accuracy of esign this irect Energy Graient Line (EGL) approach oifie into Revise Energy Graient Line (REGL) approach using revise tota ischarge cacuation. It is concue that a ean fow approxiation can be use to eterine the ajuste tota ischarge for cacuating tota friction rop at the en of atera ine an use for irect cacuation for eitter fows for the REGL approach. It is aso concue that the coparison of EGL an REGL with Step By Step (SBS) etho for each eitter fro 13

26 ownstrea to upstrea shows ony 1% ifference in eitter fow variation as ong as the esign is ae within 20% eitter fow variation. Keer an Karei (1974) confire that genera shape an characteristics of the eitter hea-oss curve are essentiay inepenent of the eitter exponent an aount of hea osses. A etaie anaysis of any ateras using a coputer oe confire that for wie range of eitter characteristic vaues an pressure osses, the average pressure of the atera occurs at 40% of the atera ine. They aso foun that approxiatey 77% of the tota atera hea oss occurs between this 40% ength of atera ine fro starting point, eaving 23% between 60% of atera ine up to en. owe an ier (1974) presente esign equations for the eterination of atera ength to eet specific unifority criteria. The eitter fow function is utiize to eterine the aowabe pressure oss to eet the unifority stanars. Eitter fow variation is a function of the unifority coefficient. Thus, by knowing the eitter fow function, eevation change an esign unifority, the aowabe pipe friction oss can be copute. Then taking the pipe size, pipe roughness coefficient, reuction coefficient for iviing fow, average eitter fow rate, aowabe pipe friction oss eterine previousy, an either the nuber of eitters per atera, the atera ength can be eterine. For this purpose equations an iensioness graphs eveope to assist the esign of ateras. Design input ata incues the eitter fow function which cou be obtaine fro anufacturers specification an reuction coefficient for iviing fow an eitter friction an inet pressure of atera. When the aforesai ata are known the iensioness graphs can be use to eterine atera ength as a function of the nuber of eitters per atera. Yiiri (Yiiri, 2007) presente an anaytica technique to sove hyrauic esign probes of various types of utipe outet pipe ines in ifferent fow regies an unifor ine sope cases. This etho cou be generaize an appie for tricke, sprinker an even gate pipes. To cacuate the pressure an ischarge the iprove energy graient ine is eterine base on the average friction rop with a sipe exponentia function to express the non-unifor outfow concept. To eterine friction hea osses, the Darcy-Weisbach forua is use an the kinetic hea change is consiere whereas inor hea osses are negecte. To iprove the accuracy of the technique, 14

27 eterination of pipe segents in ifferent fow regies have been taken into account. For the unifority purposes, it is propose that the axiu ifference in the outet operating pressure hea aong the pipeine is ess than a percentage of the average pressure hea. The resut of soe exapes sove by this etho are copare to nuerica resuts of SBS etho carrie out by(athoot et a., 1993), which shows fairy sa ifference. 2.4 Manifo Design The esign of the anifo is siiar to the atera esign. owever, the spacing between outets is greater an arger fow rates are invove. The nuber of ateras an spacing between the eterines the anifo ength. The seection of the nuber of ateras epens on the consierations ike: a) keeping within esire pressure ifferences, b) econoic trae-off between the iaeter an of the ateras an the anifo, c) the etho of irrigation anageent, an ) the egree of autoation of the syste. Most of ateras an anifos in rip irrigation have been esigne base on a singe pipe size. The energy graient ine has been erive an presente by an exponentia curve that is use as basis for esigning ateras an anifo ines (Myers an Bucks, 1972, Wu an Gitin, 1973). owever, uner certain fie conitions, the ength of ateras an anifos ay be reativey ong an have non-unifor sopes, so the use of ifferent iaeter pipes is inevitabe. Wu an Gitin (1977a) propose a graphica etho to esign atera or anifo ine with varying pipe sizes. They showe that by choosing ifferent pipe iaeters the energy graient ine wi be cose to the sope of the pipeine an therefore, the pressure variation wi be reuce (Wu an Gitin, 1977a). 2.5 Chapter Suary This iterature review shows that cogging an non-unifority are the two ain probes of rip irrigation systes, which ifferent researchers trie to sove since ong back. Using icrotubes as eitters is a soution that has been stuie by very few researchers. The ost recent stuies show that the appication of this iea in soe eveoping countries for sa pots is efficient an hany for farers. 15

28 The hyrauic anaysis in orer to obtain the ischarge in any kin of eitter is another concern in rip irrigation esign. Resoution of this probe is iportant to eterine the efficiency of the syste, which is cae Eission Unifority (EU). Different ethos are iscusse to cacuate the eitter ischarge throughout the syste an each one has its own avantages an isavantages. Stepwise etho is the ost accurate etho but teious an tie consuing for anua cacuation, however coputer aie ethos can be introuce to reuce the tie an iprove the accuracy. 16

29 Chapter 3 Theoretica Deveopent 3.1 Layout of a Typica Irrigation Subunit Microtubes can be appie as eitters for unuating an hiy ans. Its ength can be ajuste accoring to the pressure istribution aong the atera ine an so equa ischarge cou be eivere to pants. Since the fow conition in the atera ine is steay an spatiay varie with ecreasing ischarge in the ownstrea irection, the resutant energy grae ine wou foow an exponentia curve. Figure 3.1 shows a typica subunit where icrotubes are eerging fro the ateras to function as eitters. It can be seen that the icrotubes have eerge fro one sie of the ateras so as to faciitate the operations of the far achineries an to reuce the copexity of pipe ayout. As can be seen the iniu pressure hea require, at the en of the very ast atera (en-atera) epens on the frictiona an other inor hea osses to overcoe. The frictiona hea oss prouce is irecty proportiona to the ength of the icrotube, which in turn is the istance between the atera an the pant where water to be ischarge. The choice of this istance wou epen on the irrigator s practice an the physica faciities to be operate in the fie. Figure 3.1 Scheatic ayout of a rip irrigation subunit using icrotubes as eitters 17

30 Figure 3.2 shows the etais of a singe atera ine where icrotubes have varying engths to copensate the extra heas eveope aong the atera. It wi be eonstrate ater that to achieve equa ischarges q 1 q2... qn for up (positive) an fat (zero) sopes, the icrotube engths wou be ( n in ). The icrotube ength n at the en of the atera is taken as the iniu ength, eterine fro reaistic istances between pants an ateras. The increase in icrotube ength is neee to issipate ifference of extra hea (e.g., n 1 n ) an give equa ischarge for a the icrotubes in the atera. As shown in Figure 3.2 the increase ength of icrotubes can be wrappe aroun a stick (etai A), or the atera itsef (etai B), to keep a constant istance between atera an the pant. In this stuy the ter coi is use with a iaeter of 3 c (using etai A), which can be atere by the esigner in other circustances. It is to note that there wou have extra oss of energy ue to these coiing. Figure 3.2 Scheatic ayout of a singe atera aong with varying engths of icrotubes; etais A an B shows the instaation ethos for aking cois So with the given configuration, the varying ength icrotubes wou reease equa ischarges throughout the en-atera. To obtain these engths an the nuber of cois, the tota hea at each icrotube inet shou be cacuate. Subsequenty there wi be two ayout configurations, one wi have the sae set of icrotube engths in the foowing ateras of the subunit, which in turn wi require to iit 18

31 the nuber of ateras in the subunit to prouce a pre-efine eission unifority (EU), an the other one is to vary the icrotube engths throughout the subunit to eiver equa ischarges (EU = 100%). Let us nae these two configurations, one wi be cae Preefine EU ayout an the other one wi be cae Fu EU ayout. The conceptua setting of eission unifority (EU) of these two ayout configurations is iscusse in ore etais in the foowing sections. 3.2 Basic yrauic In this stuy Darcy-Weisbach equation is use to cacuate the frictiona osses in ifferent pipeines throughout the subunit. As ischarges aong the ines are spatiay varying, fow regies are going to change accoring to the veocity conitions in it. Reynos nuber ay be cacuate to know the fow regie an thereby to seect the appropriate equations for estiating friction factors of Darcy-Weisbach equation. Darcy-Weisbach equation to cacuate frictiona hea osses in pipes can be written in MKS units as 2 v h f f (3.1) 2g For ainar fow the friction factor f can be written as f 64 (3.2) R e For turbuent fow with Reynos nuber between 3000 an 100,000, Basius equation gives goo approxiation for coputing friction factor f, which can be written as where, 0.32 f (3.3) 0.25 Re R e = Reynos nuber, h f = frictiona hea oss, an = ength an iaeter of the pipes, g = acceeration ue to gravity, an v = veocity of fow. Equations ( ) can be cobine to obtain the equations for ainar (Eq 3.4) an turbuent (Eq 3.5) fows, respectivey: 1.32 q h f (3.4) q h f (3.5)

32 where, h f = frictiona hea oss (), q= ischarge (itre/hr), = iaeter of the pipe (), = ength of the pipe (). Kineatic viscosity of water at 15 C is taken as /s. Veocity an other inor osses of the syste can be written in genera for as 2 v h k (3.6) 2g where, k = hea oss coefficient, which in three ifferent inor oss coefficients are ifferentiate as: i) k e = 1.2, to cacuate entrance hea oss assuing the entrance fro atera as a re-entrant one, ii) k v = 1, to cacuate veocity hea, an iii) k c c 1.3, to cacuate coi hea oss, where 1.3 has been extrapoate (for D / 12.0 an = 360, where D an are the coi an icrotube iaeters an is the ange of ben subtene at the centre) fro Ito s iagra (Ito, 1960) on oss coefficient for sooth bens, c is the nuber of cois that can be copute fro ifference of two icrotube engths as D c 1. Ony whoe nuber of cois is taken for the cacuation of hea osses. n n Thus, Eq (3.6) can be rearrange to accooate for the above three ifferent inor osses as foows: 2 q h e (3.7) 4 2 q h v (3.8) 4 2 q h c (3.9) 4 Energy grae ine as shown in Figure 3.3 is reate to hea osses in one sie of the atera. Tota hea at the inet of the icrotube at point n can be cacuate by suing a the hea osses as foows: h e h h ( n) (3.10) v f n By pacing the icrotube with iniu ength at the point n, the baance of energy heas between two successive points, ( n 1) an n can be written as h e h h ( n 1) h ( n 1) h h h ( n) h ( n) S (3.11) v f c e v f f 20

33 where S an are sope of atera an istance between icrotubes, respectivey. Since the ischarges are sae in a the icrotubes, entrance an veocity hea osses are equa in a the icrotubes, so Eq (3.11) can be written as h f ( n 1) h ( n 1) h ( n) h ( n) S (3.12) c f f Figure 3.3 Energy grae ine an hea osses in one sie of the atera ( h e = entrance oss, h v = veocity oss, h c = coi hea oss, h f (n) = icrotube friction hea oss at n, an h f (n) = atera friction hea oss between n an n 1) By substituting fu expressions for each of the hea baance ters there wi be a tota four equations for four cobinations of ainar an turbuent conitions in atera an icrotubes as foows: 1. Fow regies are ainar in both the icrotube an atera n 1q cq 1.32 nq 1. 32nq S (3.13) 2. Fow regies are ainar an turbuent in icrotube an atera, respectivey n 1q cq 1.32 nq nq S 3. Fow regies are turbuent an ainar in icrotube an atera, respectivey (3.14) 21

34 n 1q cq nq 1. 32nq S Fow regies are turbuent in both the icrotube an atera n 1q cq nq nq S (3.15) (3.16) Therefore, the ony unknown n 1 can be cacuate irecty fro the above equations when the ischarge require in the trees, iaeters of icrotube an atera, sope, istance between icrotubes, nuber of icrotubes an the iniu ength of icrotube ( in n ) are a known paraeters. Proceeing in this way up to the inet of the enatera, a the icrotube engths wi be known to eiver equa ischarges q. After suing a the hea osses aong the atera, the tota hea at the entry of the atera is equa to inet hea T. So at the entry of the atera, the tota ischarge wou be Q nq. So it is apparent that the ischarges through the icrotubes are a equa in the en-atera of a subunit. In the case of Pre-efine EU, the ischarges through the subsequent ateras wi vary ( Q Q... Q 1 2, where is the nuber of ateras obtaine in the subunit) accoring to the tota heas at their inets. owever, ischarges through the icrotubes in the foowing iniviua ateras wi be equa (respective Q s wi be ivie by the nuber of icrotubes) because of the sae varying set of icrotube engths as of the enatera is in use. On the other han, in the case of Fu EU, ischarges wi be equa throughout the subunit because icrotube engths are varie accoring to the tota heas eveope in the respective inets. 3.3 Pressure-Discharge Reationship Accoring to (Keer an Karei, 1974) an (owe an ier, 1974) the power aw reationship between fow rate an pressure hea for eitters can be written as: x q k (3.17) where, q = ischarge through eitters (itre/hr), k = the ischarge coefficient that characterizes icrotube eitters, = pressure hea at the entry of the eitters (), an x = the ischarge exponent that characterizes the eitter fow regie. For fuy turbuent 22

35 fow x = 0.5, for partiay turbuent fow 0.5 < x < 0.7, for the unstabe fow regie 0.7 < x < 1.0 an for ainar fow x = 1.0. For fixe orifice an nozze type eitters, fow is aways fuy turbuent, so x = 0.5; for ong path eitters 0.5 x 1. 0; an for pressure copensating eitters, 0.0 x < 0.5 (Keer an Karei, 1974). In reaity, ischarges through eitters vary ue to any reasons ike pressure variation, anufacturers iperfection, creeping over tie, etc, as observe by any researchers (notaby Brats an Wu, 1979b; Sooon 1979; ezarjaribi et a., 2008, etc). As an iea esign it is essentia that the eitter fow variation be known, particuary since rip irrigation syste efficiency epens on appication unifority an a successfu syste epens on physica an hyrauic characteristics of the eitters (A-Aou, 1995). Manufacturing a set of eitters with the sae k vaue is ipossibe ue to their copexity an constraints (Sooon an Keer, 1978). Soe of these constraints are reate to ou aage an non-unifor ixing of raw aterias uring prouction process. Eastoeric aterias are use to achieve fushing action an pressure copensation in the anufacture of pressure copensating eitters. These pastic parts are ifficut to anufacture with consistent iensions. Aso, the resiient ateria ay creep over a perio of tie an grauay change the fow rate even though pressure is constant (Sooon, 1979). Carpa an Scicoone (Capra an Scicoone, 1998) inicate that the ajor sources of eitter fow rate variation are eitter esign an the ateria use to anufacture the rip tubing an it s precision. Noray, anufacturers provie a coefficient k for each type of their proucts, which refect the eitter s hyrauic characteristics. owever, ue to anufacturing variation an inconsistency, any two eitters of the sae type teste at the sae teperature an pressure can have ifferent fow rates. As the fow rate of eitters is sa, therefore any sa variation within this evice wi cause arge ischarge variation through the syste. As such, the anufacturing variation of ifferent types of eitters has been teste to ientify the anufacturers caie coefficients (Sooon, 1977 an 1979; Sooon an Keer, 1978; ezarjaribi et a. 2008).. By easuring the fow rates of a sape of eitters at a reference pressure hea an then iviing the stanar eviation of ischarges by ean ischarge, the anufacturer s 23

36 coefficient of variation (CV) can be obtaine. Typica vaues of this paraeter ay range fro 0.02 to 0.1 for non-copensating eitters an even ay go beyon 0.1 for soe pressure copensating eitters. In this stuy by appying icrotubes as eitters in ateras, the probes of poor hyrauic esign an non-unifor ischarges ue to anufacturers caie coefficients, can be overcoe. The coefficient k in this work is reate to esign factors ike spacing between icrotubes, iaeters of atera an icrotubes, sopes, etc. ence using the vaues accoring to the given configuration wi give an accurate pressure-ischarge reationship. By using icrotubes as eitters, the ischarges of a the eitters in the atera can be ae equa (EU=100%) or varying with Pre-efine EU (say, > 90%) by appying Eqs ( ), which in turn copose each atera as a arger eitter attache to the anifo. On this basis, Eq (3.17) can be re-written for the characteristics of each atera to reate ischarge to pressure hea of each atera inet as, x q K T (3.18) where q = fow rate through each icrotube (itre/hr), K = the ischarge coefficient that characterizes ateras, T = the pressure hea at the atera inet () an x = the ischarge exponent that characterizes the atera fow regie. 3.4 Eission Unifority (EU) In rip irrigation, ieay the appication of water throughout the syste shou be unifor. It is necessary that the fow rates through the syste shou be unifor even though the pressure is not unifor (Sooon an Keer, 1978). In a we-esigne rip irrigation syste, the eission unifority (EU) for eitters shou be above a specific thresho eve. The EU is a function of the expecte ischarge variation ue to pressure variation throughout the syste. Basicay, EU is the ratio of the iniu eitter ischarge to the average ischarge of a the eitters uner consieration, which can aso be expresse as a percentage (Keer an Karei, 1974). An acceptabe vaue of EU can be obtaine by iiting the variation of pressure in the syste. Liiting the pressure variation can ecrease the variation of ischarge in the eitters. (Keer an Biesner, 1990) recoene that EU shou be at east 85% for rippers on fat terrain. Therefore, each 24

37 atera can be iagine as a arger eitter. This iea was first suggeste by (Keer an Karei, 1974) an appie by (Sooon an Keer, 1978) for pressure istribution aong the anifo. In this research, two systes of esign have been envisage. In one syste, cae Preefine EU, the set of the icrotube engths cacuate fro en-atera are provie for a the subsequent ateras unchange to eiver varying ischarges. The ischarges of this syste are varying in such a way so that the EU reains above certain specifie thresho eve. On the other syste, cae Fu EU, icrotube engths are varie in such a way so that the ischarges throughout the subunit becoe unifor to ake EU equa to 100% Pre-efine EU Syste In the Pre-efine EU syste, the fow aong the anifo ine eivers a ischarge to each atera accoring to its inet tota hea. Discharges fro the anifo to the ateras foow the pressure-ischarge reationship an energy grae ine as shown in Figure 3.3. Since a paraeters such as icrotube engths, sope an pipe iaeters are constant in this esign the ischarges through the ateras vary accoring to pressure hea aong the anifo ine an can be estiate using Eq (3.18). Therefore, the EU for the whoe subunit can be copute accoring to (Keer an Karei, 1974) as where Q EU 100 (3.19) Qa Q = average of owest ¼ of the atera fow rates an Q a = average of a the atera fow rates in the syste. To cacuate EU of the syste a the ischarges of ateras (arger eitters) shou be known. In the case of using traitiona eitters, the ain probes reating to estiation of ischarges are ue to pressure variation aong the pipeine an anufacturer s non-unifority in the batches of eitters prouce. Severa stuies have been carrie out to estiate the ischarges of eitters with respect to pressure variation. Soe of these stuies appie step-by-step etho (Wu, 1992; athoot et a., 1993) an soe others appie irect etho to cacuate ischarges of the eitters (Vaesquino, 2008, Wu, 1992, Wu an Gitin, 1973, Yiiri, 2007). Usuay, the cacuation of ischarge is associate with soe approxiations to sipify the proceure an obtain a soution for the syste. The ost coon approxiation assues that a 25

38 outets ischarge neary equa fow rates an base on this the frictiona oss an energy graient ine cou be obtaine. The tota frictiona rop at a point an aong the ine can be cacuate by an appropriate equation. Eventuay, this etho (Wu, 1992) offers a sipe irect cacuation of eitter fows base on energy graient ine (EGL). owever, two types of errors are introuce by this sipe EGL approach; one is associate with the shape of EGL an the other one is the tota frictiona rop at the en of the ine. The other approxiation is the refineent of the previous etho, by appying ean ischarge of the eitters to eveop a new forua to cacuate tota ischarge of the atera. Since the error prouce by the EGL approach is cause ainy by the tota ischarge use to cacuate the tota frictiona rop at the en of the ine; rather we have to use actua ischarge which is the suation of a the eitter ischarges in the atera ine. Then this ischarge cou be appie for cacuating tota frictiona rop of that ine. The actua tota ischarge can be cacuate by the ean fow of the eitters utipie by the tota nuber of eitters in the atera ine. The ean fow of the eitters can be eterine fro the ean pressure equation erive by(anyoji an Wu, 1987) aong the atera ine. ence eveoping a forua cobine with operating pressure an fow rate of the atera is essentia. owever, this forua cannot be sove irecty; a tria an error etho is use to eterine the tota ischarge in a subunit. The obtaine tota ischarge is the revise tota ischarge an the energy graient ine that has been eveope base on this vaue is cae Revise Energy Graient Line etho (Wu, 1992). In step-by-step technique (SBS) if the en pressure is given, the pressure an fow istribution for a given atera can be foun without resorting to approxiations. Starting fro the en, the outfow fro an outet, as eterine by the pressure, is cacuate. This gives the fow in the pipe section between this outet an the next one, fro which the pressure oss in this section can be foun an thus the pressure at the next outet (Pero, 1977). owever, soe fie appications inicate that the anufacturer s inforation are not reiabe an significant ifferences cou occur particuary in high pressure systes (ezarjaribi et a., 2008). In this stuy as wi be iscusse subsequenty, the stepwise etho is appie to the ateras (as arge eitters) for ischarge cacuation. The physica an echanica 26

39 characteristics of such arge eitters are unvarying, an thus constant hyrauic perforance is expecte. It ust be note that when a set of icrotube engths,..., 1, 2 for certain esign factors are chosen as eitters it can resove echanica issues reate to anufacturing non-hoogeneity of eitters. To fin the hyrauic paraeters x an K in the pressure-ischarge reationship, regression etho has been use. The perforance of the arge eitter (atera) with severa reaistic ischarges was teste an finay the best correation between ischarge an corresponing pressure heas obtaine to use for esign of the subunit. n Fu EU Syste To esign a Fu EU syste with the highest eission unifority (EU = 100%), it is require to vary the ength of the icrotubes for each ateras. The icrotube engths in successive ateras shou be esigne accoring to inet pressure heas of the ateras. Figure 3.4 shows the scheatic ayout of a typica subunit where a the atera fows are equa Q Q1 Q2... Q 1 Q. Consiering the frictiona osses of the anifo ine, the atera inet heas can be as accoring to fow regie. T1 T 2... T ( 1) T using Eq (3.4) or Eq (3.5) Figure 3.4 Scheatic ayout of a typica subunit with Fu EU 27

40 3.5 Chapter Suary To work out the probe of using icrotubes as eitters, reate hyrauic cacuations are require to be eveope in a step-by-step anner. The basic foruas of friction an other inor osses of pipeine network (branch) have been appie to erive foruations of the ischarges an tota heas in the syste. Whist the icrotube ength is variabe other esign paraeters such as pipe sizes, an sope, nuber an spacing of trees are to be provie as constants. The concept of pressure-ischarge reationship has been iscusse an generaize to cacuate the ischarge of each atera ine aong the anifo. As such two systes of esign have been propose. One is cae Pre-efine EU syste, where the set of the variabe icrotube engths cacuate for en-atera is repicate for a the subsequent ateras to eiver ischarges. These ischarges wi increase grauay accoring to the inet heas of the upstrea ateras. owever, the inet heas of this syste wi be varie in such a way so that the EU reains above certain specifie thresho eve. In practice, it wou iit the axiu nuber of ateras in the anifo so that the EU criterion is satisfie. On the other han the secon one is cae Fu EU syste, where icrotube engths are varie in such a way so that the ischarges throughout the subunit becoe unifor to ake EU equa to 100%. 28

41 Chapter 4 Moe Deveopent 4.1 Microtube Eitter Design Since the cacuation of pressures an icrotube engths are copicate an teious, coputer progras have been eveope to siuate the syste for ifferent EU situations an given set of esign paraeters. The resuts of the step by step cacuations, of the equations as expaine in Chapter 3, are obtaine by coputer progras eveope in Visua Basic 8.0. The require ata for the esign of the subunit are: atera an icrotube iaeters an, icrotube ischarge requireent q, icrotube spacing, an the groun sope S aong the pipeine Design for Pre-efine EU The esign processes for Pre-efine EU syste consists of three stages: a) Latera esign - the progra requires a requisite ischarge to copute the engths of the icrotubes eerging fro the ateras. As iscusse before an accoring to hea baancing equations in (3.13) to (3.16), the ischarges for a the icrotubes in the enatera are equa. The unknown variabe of those equations is the icrotube ength at each outet to issipate extra frictiona heas. So the tota hea at the inet of the atera ( ) can be obtaine by step-by-step cacuations at ifferent points of the icrotubes up to the inet of the atera. The set of icrotube engths cacuate at the en-atera wi be fitte in the subsequent ateras. As the tota heas in the subsequent ateras are ifferent, this set of icrotube engths is going to prouce varying ischarges through each atera. owever this unique set of icrotube engths obtaine for a given suite of esign paraeters, wou eiver equa ischarges through these icrotubes of the atera consiere. T b) Pressure-ischarge reationship - an appropriate ischarge range wou be appie to the progra to fin the corresponing tota heas. The choice of this ischarge range epens on the practice by the irrigators an the pressure hea that can be hane by the syste. So a range of tota heas wou be estiate for the range of ischarges through the icrotubes of the en-atera. The copute atera heas an corresponing ischarges are potte an regression equations are obtaine for appication by the 29

42 subsequent ateras. Since a the icrotubes uner a atera eiver equa ischarges, the atera ine ischarge wou be sipe utipication of this ischarge with the nuber of icrotube outets in the atera consiere. Therefore, the pressure-ischarge reationship obtaine fro the en-atera cou be expresse for a the ateras in the subunit. c) Manifo esign - to esign the anifo ine the progra has been eveope to cacuate the frictiona an other osses base on stepwise cacuation fro the en-atera up to the inet of the anifo. Then ischarge of each atera is cacuate accoring to the pressure-ischarge reationship obtaine in en-atera. At each step, the Reynos nuber aong the anifo ine is cacuate an proper frictiona hea oss foruas are use to cacuate the inet heas of the ateras. The pressure hea of the anifo an the nuber of ateras to achieve the best eission unifority (say, EU > 90%) are the ain outcoe of the progra Design for Fu EU It is esire to have a proceure with EU = 100% for the entire subunit. Unike the above etho, the Fu EU syste is base on variabe icrotube ength for each atera to issipate extra frictiona heas eveope in the respective upstrea reaches of the anifo. This Fu EU syste wou foow the sae proceure as expaine in Preefine EU syste except the set of icrotube engths cacuate at the en-atera wi be use to cacuate the new set of icrotube engths for the subsequent ateras. 4.2 Deveopent of Moe Agorith Three separate progras have been eveope for aforeentione purposes as foow: I. Progra 1: Coputing the icrotube ength an inet tota hea of the en-atera II. Progra 2: Fin the best nuber of ateras to achieve the Pre-efine EU III. Progra 3: Fining the engths of the icrotubes for other ateras to achieve 100% EU in the entire syste Progra 1 In this progra, the set of icrotube engths of the en-atera are require to be cacuate aong with its tota inet hea at the entry of the atera. As such, the foowing paraeters 30

43 require to be ecie prior to coencing siuation; these paraeters can be varie accoring to esign circustances or fie conitions: 1. Microtube iaeter 2. Microtube iniu ength, n 3. Coi iaeter 4. Latera iaeter 5. Latera ength 6. Microtube spacing, etc. Through this progra, the Eqs ( ) have been appie for ifferent fow conitions in the en-atera. The fow regie fro ainar to turbuent aong the atera ine epens on the esign ischarge, spacing of icrotubes an iaeters. At this point, the conitiona coans have been use in the progra to copute the unknown icrotube engths. Figure 4.1 (fowchart) iustrates the coputationa agorith for this coe. The resuts of this progra are arrange in graphs an tabes to provie a range of ischarges versus pressure heas for ifferent iaeters of icrotube an atera an icrotube spacing. The regression curve to fin the best reationship between pressure hea an ischarge has been unertaken an wi be iscusse ater Progra 2 This progra takes the resuts fro the previous progra an then coputes the frictiona hea osses aong the anifo ine. Using the sae set of icrotube engths as in enatera an appy the in other ateras of the anifo, each atera aong the anifo can be iagine as arge eitters. The hyrauic characteristics for these arge eitters as expaine before (Eq 3.18) are epenent on two paraeters K an x which are obtaine fro Progra 1. The icrotube engths an inet pressure hea of the en-atera, anifo iaeter, eission unifority (EU) that the esigners inten to appy an the nuber of ateras for the initiation of progra to achieve a pre-efine EU are the ajor input ata for this progra. If the siuate EU fro this progra is ess than the pre-efine EU, nuber of ateras was reuce for the next tria of the progra. 31

44 START INPUT DATA,,, q, in,, S FIND TE REYNOLDS NUMBER OF MICROTUBE FLOW REGIM IS LAMINAR YES FIND T REYNOLDS NO OF LATERAL NO FIND TE REYNOLDS NO OF LATERAL FLOW REGIM IS LAMINAR NO YES FLOW REGIM IS LAMINAR COMPUTE 1, 2,... n, NUMBER OF COILS AND MICROTUBE PRESSURES USING Eq (3.13) YES COMPUTE 1, 2,... n, NUMBER OF COILS AND MICROTUBE PRESSURES USING Eq (3.15) COMPUTE 1, 2,... n, NUMBER OF COILS AND MICROTUBE PRESSURES USING Eq (3.14) COMPUTE 1, 2,... n, NUMBER OF COILS AND MICROTUBE PRESSURES USING Eq (3.16) NO COMPUTE TE LATERAL INLET EAD T WRTIE TE MICROTUBE LENGTS AND NUMBER OF COILS AND PRESSURE EADS Figure 4.1 Fow chart of Progra 1 to cacuate the icrotube engths, inet pressure hea an nuber of cois in the en-atera 32

45 This progra starts with the tota hea of the en-atera an as the frictiona hea oss fro the ieiate upstrea reach of the anifo to fin the inet pressure hea of the foowing atera. In each step Reynos nuber was checke insie the anifo reach to seect the correct frictiona oss equation. So the new ischarge in the foowing atera is copute using Eq (3.18) an the process continue up to the first atera of the anifo. The tota nuber of ateras that wou be sufficient for the given subunit can be obtaine by aing or reoving one or ore new ateras each tie an check whether it has reache the esire pre-efine EU. The output of this coe incues the inet pressure hea of the anifo, tota ischarge an the best nuber of ateras appicabe for the given subunit. Figure 4.2 iustrates the coputationa agorith of this progra Progra 3 The ain purpose of this coe is to eveop an esign a syste with 100% eission unifority. The icrotube engths,... n, 1, 2 1 n an the inet tota hea of the enatera fro Progra 1 are appie for initiation of this progra an then use to cacuate the engths of the icrotubes for the foowing ateras. In this progra each ateras are aso iagine as arge eitters with variabe icrotube engths. The new set of engths as the ajor part of this arge eitter can be copute by increasing the engths in trias of sa increents to reach the vaue of the inet pressure hea of the atera. These new sets of icrotube engths are unique for each atera. Subsequenty for the convenience of esign of the syste, reate graphs an tabes are eveope for irect cacuation of the icrotube engths which has been iscusse in the foowing chapter. Figure 4.3 shows the coputationa agorith of this progra. 33

46 START INPUT K AND x SET K AND x AND INITIAL NUMBER OF LATERALS N TO COMPUTE: MANIFOLD DISCARGE LARGE EMITTER (LATERALS) DISCARGE LATERAL PRESSURE EADS COMPUTE EU OF SYSTEM USING Eq (3.19) WRITE EU, NUMBER OF LATERALS AND PRESSURE OF SUBUNIT EU 90 N N 1 Figure 4.2 Fow chart of Progra 2 to ajust the nuber of ateras require for a preefine EU 34

47 START INPUT DATA,,, q, in,, S COMPUTE,... 1, 2 n AND USING EQS ( ) COMPUTE LATERAL,, ALONG TE MANIFOLD USING EQS (3.4) AND (3.5) COMPUTE USING END- LATERAL SET OF MICROTUBE LENGTS 1, 2,... n 1 1 WRITE,... 1, 2 n AND n n Figure 4.3 Fow chart of Progra 3 to copute the new set of icrotube engths for successive ateras to achieve fu eission unifority 35

48 4.3 Chapter Suary Three agoriths (progras) have been eveope to siuate rip irrigation systes using icrotube as eitters. The foruations eveope in Chapter 3 cae into account to fin the unknown variabes of the syste. A three progras consier ifferent fow regies in the pipeines fro icrotubes to anifo as the fow rate is spatiay varie. When pipe sizes an terrain sope are known, the icrotube engths an nuber of cois can be copute using Progra 1 for en-atera. Progra 2 can be use after pressure-ischarge forua for certain esign is obtaine by regression between ischarges an corresponing pressures fro en-atera. Progra 2 requires the resuts of Progra 1 to continue the esign of anifo using a ateras as arge eitters with un-change hyrauic characteristics. The ai of Progra 3 is to esign a syste with equa outfows in the entire network. The concept of variabe icrotube ength is appie in this progra for a the ateras so that each atera has ifferent set of icrotube engths to issipate varying extra heas. 36

49 Chapter 5 Resuts an Discussion 5.1 Microtube Design for the En Latera Since Progra 1 has the ain roe in the esign of the syste an the resuts are to be use for the two other progras, soe typica specifications of the syste are chosen fro a practica point of view for presenting the outcoe. Whie the range of seecte atera iaeters are taken as 10, 12, 14 an 16, the icrotube iaeters are taken as 2, 3 an 4 fro a practica consieration of arket avaiabiity an aso to keep the free fro cogging. These icrotubes are instae on one sie of the ateras to ischarge a given q to the roots of the pants. For fat terrain ( S 0% ) Tabe 5.1 shows the resuts reate to inet tota hea require ( T ), nuber of cois ae ( c ) an the ongest ength ( ax ), an i at i = 5 aongst a the estiate set of engths of icrotubes in that en-atera. As can be seen in Tabe 5.1 the icrotube engths ax reain aost sae as in in = 2 for the higher ischarges, whie tota heas require has ove to high eve. To show the tren of icrotube engths in ifferent terrains the progra has aso been run for two ore sopes, S = 0.25% an 0.50%. The resuts show that soe pressure heas for saer iaeter icrotubes are very high an ay be unreaistic for orinary agricutura fars. These resuts have been shown in Appenix A. 5.2 Microtube Design for a Pre-efine EU As iscusse before in Progra 2 the icrotube engths copute for en-atera (in Progra 1) wou be assue for a the foowing ateras of the subunit. Thus a ateras wou have the sae hyrauic characteristics an cou be iagine to work as arge eitters aong the ine of anifo. Evienty, fow rates of these eitters are not equa an can be estiate if the inet tota heas of each ateras are known aong with the hyrauic constants ( x an K ) of Eq (3.18) are known. These hyrauic constants have been obtaine for a the noinate cobinations of icrotube an atera iaeters. Figure 5.1(a-f) shows the power-aw regression curves generate accoring to Progra 1 resuts for pressures an ischarges obtaine for en-atera. Different ischarge ranges ( q ) are seecte in those graphs to obtain the 2 R vaues greater than It ceary 37

50 iustrates that whie the ateras are perfore as eitters in its higher ranges, the saer size icrotubes eiver ess ischarges with reativey higher heas, on the other han arger size icrotubes eiver ore ischarges with reativey ower heas. Tabe 5.1 Longest ength icrotube ax (), an i, i 5 (), nuber of cois c an inet pressure hea require T () for the given icrotubes an ischarges ( = 10, in = 1.25, n = 10, = 1 an S = 0 %; the shae ces are consiere as unreaistic range of tota heas for current scenario) q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (1.60) 11 (3) (1.36) 4 (1) (1.27) 1 (0) (1.58) 11 (3) (1.35) 3 (1) (1.27) 1 (0) (1.56) 10 (3) (1.34) 3 (0) (1.26) 1 (0) (1.54) 9 (3) (1.34) 3 (0) (1.26) 1 (0) (1.52) 9 (2) (1.33) 3 (0) (1.26) 1 (0) (1.51) 8 (2) (1.33) 3 (0) (1.26) 1 (0) (1.50) 8 (2) (1.32) 3 (0) (1.26) 0 (0) (1.48) 8 (2) (1.32) 2 (0) (1.26) 0 (0) (1.46) 7 (2) (1.31) 2 (0) (1.26) 0 (0) (1.45) 6 (2) (1.31) 2 (0) (1.26) 0 (0) (1.42) 4 (1) (1.30) 1 (0) (1.26) 0 (0) (1.41) 4 (1) (1.30) 1 (0) (1.26) 0 (0) (1.38) 4 (1) (1.29) 1 (0) (1.25) 0 (0) More graphs for other atera iaeters an sopes are given in Appenix B. The hyrauic constants x an K obtaine fro these graphs are suarize in Tabes 5.2(a-c). These coputations are base on ischarging water fro one sie of the atera. 38

51 a) =4, q=1-8 (itre/hr) b) =4, q=8-20 (itre/hr) c) =3, q=1-6 (itre/hr) 39

52 ) =3, q=6-20 (itre/hr) e) =2, q=1-6 (itre/hr) f) =2, q=6-20 (itre/hr) Figure 5.1 Pressure-ischarge reationships for ateras as arge eitters ( = 10, in = 1.25, n = 10, = 1 an S = 0 %) The fow rate fro iniviua eitters epens on operating pressure, water teperature, anufacturing variations an egree to which the eitters are pugge. It is usuay assue that over soe range of pressure ( ), the eitter fow rate (Q ) is proportiona to x. The vaue of x characterizes the fow regie of the eitter, which noray ranges 40

53 between zero an one (Sooon, 1985). In this stuy, the anufacturing variation an pugging, which were the ain obstaces for iproveent of eission unifority have been eiinate ue to the use of icrotubes. As ateras can now be iagine as arge eitters aong the anifo, it is evient that the operating tota heas wou be the ain effective variabe for ischarges aong the outets of the ateras. In the foowing tabes the input ata epoye in soe exapes eonstrate the appication of this approach. In a previous work by athoot et a. (1993) base on step by step etho, the average eitter ischarge, the corresponing average pressure hea, the exponent an nuber of eitters are given so the iniviua ischarge an pressure hea for each eitter can be cacuate. Siiar technique has been appie for this stuy using ateras as arge eitters with pressure-ischarge reationship as shown in Tabes 5.2(a-c). Tabe 5.2 Pressure-ischarge reationships for ifferent ateras with in = 1.25, n = 10, an = 1 ; a) for S = 0%, b) for S = 0.25%, an c) for S = 0.50% a) S = 0% q, itre/hr T ( ) x K q, itre/hr T () x K q, itre/hr T () x K q, itre/hr T () x K

54 b) S = 0.25% q, itre/hr T ( ) x K q, itre/hr T () x K q, itre/hr T ( ) x K q, itre/hr T ( ) x c) S = 0.50% K q, itre/hr T ( ) x K q, itre/hr T ( ) x K q, itre/hr T ( ) x K q, itre/hr T ( ) x K

55 Previous stuy by Sooon an Keer (1978) inicate that for fixe orifice an nozze type eitters, x 0. 5, for ong path eitters 0 x 1 an for pressure copensating eitters 0 x In this stuy the exponentia paraeter x vaues are foun between 0.6 an 1.0 as shown in Tabes 5.2(a-c). Consiering these resuts it can be reasone that these type of ateras function as arge eitters aong the path of anifo an can be categorize as ong path eitters. Resuts fro Tabes 5.2(a-c) wou be hepfu for esigners to seect the appropriate x an K vaues to run the progra for coputing EU of the syste an thus the optiu nuber of ateras ( N ) in each subunit. This type of tabe can be eveope for ifferent nuber of icrotubes ( n ) an sopes ( S ) accoring to fie conitions. Tabes 5.3(a-b) show the resuts of the progra for eission unifority, tota hea at the inet of the subunit ( sub ) an the optiu nuber of ateras ( N ) for ifferent icrotube an atera sizes with S = 0% an 0.5%, respectivey. In those tabes ischarges of 10, 7 an 3 itre/hr are shown for 4, 3 an 2 of icrotubes respectivey, to achieve EU 90% for the given anifo iaeter. Resuts inicate that epoying arger size anifo ( ), the nuber of ateras ( N ) can be increase to achieve a corresponing EU 90%. It aso shows that the require subunit tota hea ecreases in genera with increasing of anifo iaeter. Tabe 5.3 EU an nuber of ateras in one subunit with in = 1.25, n = 10, an = 1 ; a) for S = 0%, an b) for S = 0.50% a) for S = 0%, 20 ( q, itre/hr) 4 (10) 3 (7) 2 (3), N EU % sub ( ) N EU % sub ( )

56 b) for S = 0.50%, ( q, itre/hr) (10) (7) (3), N EU % sub ( ) N EU % sub () Microtube Design for Fu EU Energy Graient Line Anaysis In Progra 3, icrotubes an ateras are esigne to ischarge equa fow rates throughout the subunit. When the inet tota hea at the en-atera is known, a the frictiona hea osses of the respective anifo reaches can be ae together to give corresponing inet tota heas of the foowing ateras. Inee the en-atera can be iagine as a arge eitter with known hyrauic characteristics as expaine earier. Since it is obvious that a the atera fow rates are equa, the frictiona osses aong the anifo are base on the respective fow rates in the reach, which are sipe utipe of the corresponing nuber of ateras ownstrea. For convenience of esign the energy graient ines for ateras an anifo can be eveope to cacuate the tota heas an the resuting icrotube engths require irecty. The energy graient ine is a curve of exponentia type for any atera or anifo. Since fow rate ecreases in the ownstrea irection, it is obvious that frictiona osses in the upper reaches are uch higher than the ower reaches. The tota hea osses are copute fro tota ength of the pipe an its ischarge, an other inor osses. In this stuy other inor osses are ue to cois, entrance an exit veocity osses. 44

57 Wu an Gitin (1975) an Wu (1992) worke to utiize the energy graient ine approach for irect cacuation of the eitter ischarges. The approach evove a etho for irect cacuation of outfows base on an assuption that there wou have 10-20% fow variation aong the atera. Evienty, the fow in the atera is steay an spatiay varie with ecreasing ischarges in the ownstrea irection. For a given pipe, the energy rop can be expresse as where, k x kq x (5.1) an are constants for a given fow conition ( = 1 for ainar fow, =1.75 for turbuent fow in sooth pipes an =2 for turbuent fow; =1.852 if azen-wiias equation is appie), = the energy rop for a given ength x an = the ischarge at a section of ength x Q x easure fro the inet point. Assuing the rip irrigation syste is esigne for an eitter with itte or aost no variation in fow, the shape of the hea rop ratio curve can be erive atheaticay (Wu an Gitin, 1975) fro Eq (5.1) as: R i i 1 1 (1 ) (5.2) where, R i is a hea rop ratio aong a atera, = tota hea rop up to the i en of the atera, is the tota hea rop at a ength ratio i, i x / X is a ength ratio i for a given position x fro the atera inet to the tota atera ength X. Wu an Gitin (1975) efine Eq (5.2) for three iensioness curves base on = 1, 1.75 an 2 for ainar, turbuent (in sooth pipe) an fuy turbuent fows, respectivey. In their approach, they consiere frictiona osses ony, negecte inor osses fro the eitters an ateras. Later Wu (1992) eveope equations an coputer progra, where eitters with turbuent an non-turbuent fows were ae to cacuate the eitter fow rates irecty. These approaches are eveope base on the assuption that the variation of ischarges through the eitters is negigibe. Step-by-step etho was in use to estiate the frictiona osses of the ateras. The siuate curves that have been rawn in Figures 5.2(a-c) for hea rop ratios, i versus ength ratios, i (to be cae siuate energy graient ines) aong the ength of the ateras are showing soe egrees of eviation fro the energy graient curves using the right-han-sie of Eq (5.2). The right-han-sie of the Eq (5.2) is sai to 45

58 be appicabe to ainar, turbuent an fuy turbuent fows if the exponent vaues are taken as = 1, 1.75 an 2, respectivey. Evienty the eviations as shown in Figures 5.2(a-c) are ue to the existence of ixe fow regies an inor osses consiere in the siuations of the hea rop ratios. The right-han-sie of the Eq (5.2) is eveope ony for frictiona hea oss for a given fow regie. As such the hea rop ratio curves in Figures 5.2(a-c) wou atch to Eq (5.2) if the exponent vaues are change to = 0.32, 0.1 an 0.05 for icrotube iaeters = 4, 3 an 2 respectivey. a) for 4 b) for 3 46

59 c) for 2 Figure 5.2 Coparison between siuate ( graient ines i vs i ) an Eq (5.2) erive energy To copare the energy graient ines for ifferent icrotube sizes the siuation resuts have aso been potte in Figure 5.3(a-) for two ateras 12 an 16 an sopes S = 0% an 0.25%. As shown in these figures, energy graient ines for the fat terrain are very cose an ore or ess straight, whie in upsope terrain the variation of these iensioness curves is wie. It is perceptibe that the seection of the sectiona energy sope ( / x ) shou be such that the siuate energy graient ine is aways above the hea require aong the pipe ine. A steeper sope siuate energy graient ine (particuary at the upstrea-en) wi prouce saer size pipes, which wi have ess cost (Wu, 1975). It is sai that the optia shape of the siuate energy graient ine is a curve having sag above the straight i i ine aroun 0.15 at the ie of the pipeine profie ( i 0. 5). owever coparing the cost of the esign eterine by using a straight energy graient ine with the one using optia energy graient ine, the cost ifference is ony about 2.5% (Wu, 1975). So fro a given set of esign paraeters on ischarges ( q ), iaeters (, ), spacing ( ) an tota hea rops ( ), a choice base on straight energy graient ine as shown in Figure 5.3(a-) wou be sufficient to ecie a cobination of these paraeters ( q,,, an ) in ifferent fie situations ( S %). Visua inspection of these figures shows that 47

60 the esign cobination cose to the straight energy graient ine wou prouce an optiu syste. For fat terrain, it cou be aost any cobination since ost curves are cose to straight ine. For sope ans it shows that the icrotube size 3 with any ischarge between q = 3 an 8 itre/hr wou have better perforances. a) 12, S 0% b) 16, S 0% 48

61 c) 12, S 0.25% ) 16, S 0.25% Figure 5.3 Siuate energy graient ines for typica ateras; a) for = 12, S 0%, b) 16, S 0%, c) 12, S 0.25% an ) 16, S 0.25% (there are 10 trees pace at an interva of 1 space aong the ateras) 49

62 5.3.2 Microtube Length Coputation A technique has been eveope for cacuating the icrotube engths without the use of the progra. A soution associate with esign tabes an graphs has been eveope for esigners to copute the varie icrotube engths. Deveoping the energy graient ine an generaizing its concept to the cacuation of icrotube ength ifferences, have propte to efine a new paraeter, M i as icrotube ength ifference ratio M (5.3) i i where, i x X is a ength ratio for a given position x fro the atera inet to the tota atera ength X, = ) is icrotube ength ifference at i an i ( ax i ) is the tota ength ifference for a given atera. The siuation inicates ( ax in that the icrotube tota ength ifference varies accoring to the fow conitions in the icrotubes an ateras. The vaues shown in Figures 5.4(a-f) inicate that it reuces with saer iaeter icrotubes aong a given atera. It is shown that the vaues of are ecining with increasing ischarge capacity of the icrotubes an becoing aost constant for saer iaeter icrotube (say at with the increase of atera sizes. 2 ). The vaues aso reuce a) 12, S 0%, 50

63 b) 14, S 0%, c) 16, S 0%, 51

64 ) 12, S 0.25% e) 14, S 0.25%, 52

65 f) 16, S 0.25%, Figure 5.4 Microtube tota ength ifference for typica ateras; a) for 12, S 0%, b) for 14, c) for 16 S 0%, ) for 12, S 0.25%, e) for 14, S 0.25% an f) for 16, S 0.25% (there are 10 trees pace at an interva of 1 space aong the atera) Subsequenty it is foun that with a the possibe atera an icrotube iaeters an ischarges, the siuate icrotube ength ifference ratios ( M ) foow a genera exponentia tren (shown in Figure 5.5). This genera tren ony varies with respect to the an sope, S. Whie M i can be rea in Figure 5.5 at a position i, we nee to know in for a given atera in orer to know the whoe set of icrotube engths aong that atera. Anaysis unertaken shows that the iniu icrotube engths, can be expresse as a genera quaratic equation as in where, a j 2 b j c i in n for the ateras (5.4) j p P is the position ratio for ateras aong the anifo ine at p fro the anifo inet to the tota anifo ength P, an a, b an c Tabes 5.4(a-b) for two atera sizes are constants as given in 12 an 16, respectivey. As icrotube ength-ifference istribution is reate to hea rop istribution, it is possibe that Eq (5.2) can aso be written for ength ifference ratios M i in a siiar for but with a ifferent 53

66 exponentia vaue (Eq 5.5) in orer to cacuate icrotube engths for any ateras. The siuate ength ifferences curves (Figure 5.5) that are appicabe for any ischarges an iaeters of atera an icrotube are base on a the friction an inor hea oses consiere earier, fits we if 1.2 an 1.64 for sopes of S 0% an 0.25%, respectivey. where, 1 M i 1 (1 i) (5.5) M i as above entione can be copute by knowing an in of each atera. So by substituting Eq (5.5) into Eq (5.3) we can get icrotube engths at ifferent i in a given atera as (5.6) i 1 in (1 i) where i is the icrotube ength at the position i, is the tota ength ifference obtaine fro Figure 5.4(a-f), an in is the iniu icrotube ength, for a particuar atera position j in the anifo, obtaine fro Eq (5.4) an Tabes 5.4(a-b). These tabes can be eveope for a wie range of possibe esign paraeters so that the esign can be one without utiizing the coputer progras irecty. To cacuate the operating pressure hea of the subunit, hence the pressure hea of the en atera obtaine fro Figure 5.1 shou be ae with the frictiona hea osses aong the anifo reaches to give. sub Figure 5.5 Microtube ength ifference istribution for any ischarge, an icrotube an atera size (this graph is erive for 10 trees pace at an interva of 2 space aong the atera) 54

67 The resuts of the siuation aso inicate that the icrotube tota ength ifferences ax in for each of the ateras in the anifo is equa to constant; in fact, the icrotube variation is a constant vaue espite of its varie ength in successive ateras aong the anifo. Tabes 5.4(a-c) show the coefficient of j for two atera sopes siuate for 6 ifferent fow rates. Tabe 5.4 Coefficients of Eq (5.4) for iniu possibe engths of icrotube in; a) for =12 an b) for =16 (these tabes are erive for ateras at an interva of 1 space aong the anifo, where 10 trees are pace at an interva of 1 space aong each of the atera) a) =12 q (itre/hr) = 4 = 3 = 2 A b c a b c a b c S=0% S=0.25% S=0% S=0.25% S=0% S=0.25% S=0% S=0.25% S=0% S=0.25% S=0% S=0.25%

68 b) =14 q (itre/hr) = 4 = 3 = 2 A b c a b c a b c S=0% S=0.25% S=0% S=0.25% S=0% S=0.25% S=0% S=0.25% S=0% S=0.25% S=0% S=0.25% c) =16 q (itre/hr) = 4 = 3 = 2 A b c a b c a b c S=0% S=0.25% S=0% S=0.25% S=0% S=0.25% S=0% S=0.25% S=0% S=0.25% S=0% S=0.25%

69 5.4 Chapter Suary The resuts of severa cobinations of pipe sizes an terrain sopes have been siuate using the agoriths as expaine in Chapters 3 an 4. Pressure-ischarge reationships, using Progra 1 of the en-atera setup, were eveope for ater uses in Pre-efine EU (Progra 2) an Fu EU (Progra 3) cases of the foowing ateras. These reationships are the key characteristics to run the Progras 2 an 3 to coe up with typica esign tabes an graphs for the chosen scenarios. In the Pre-efine EU case, two anifo sizes are consiere to cacuate the nuber of ateras to be accooate in reaching 90% or above eission unifority (EU). The resut shows that using arger size icrotube wou require onger pipe ength an ower pressure hea whie saer size icrotube wou require shorter pipe ength an higher pressure hea. The esign aso shows that by appying saer size anifo, the nuber of ateras to for a subunit can be increase. For Fu EU case, the energy grae ine (EGL) approach has been appie to obtain the set of esign graphs an tabes to cacuate the varying icrotube engths for each atera in the entire subunit. 57

70 Chapter 6 Typica Design Exapes In rip irrigation one of the ain objectives is to provie each pant with easure suppy of soi oisture which is sufficient to eet its transpiration eans. Drip irrigation offers unique agronoica, agro-technica, an econoica avantages for the we-organize use of water (Keer an Karei, 1974). So far this research has trie to eveop systes to eiver a given ischarge to the pant roots. In this regar two systes of esign have been anayse: one is base on Pre-efine EU where water is suppie with variation not beow a iiting thresho; in the other one the syste is such that the water is suppie with 100 percent unifority to ca it Fu EU syste. To eonstrate the appicabiity of these systes outcoe, soe exapes are prepare on the basis of typica esign paraeters in the irrigation fies. The ateria, which foows, provies an outine an aequate etai for the esign. 6.1 Irrigation Design Paraeters In rip irrigation, ony part of the soi voue is wette. The oisture content at which the irrigation shou be starte epens on soi, crop an water-yie-econoic factors. (Keer an Karei, 1974). The irrigation interva can be eterine by ientifying the axiu water that can be store in the soi an the consuptive use of crops as foows (Keer an Biesner, 1990) FC PWP Pw D Z s f ( ) (6.1) where, D = axiu net epth of each irrigation appication over the whoe area (), f = fraction of avaiabe oisture epetion aowe, FC = fie capacity (% by weight), PWP = peranent witing point (% by weight), Z = soi epth to be consiere (), s = specific gravity of soi (iensioness) an P w = wette area as a percent of the tota irrigate area (%). Noray, f is taken as 0.3 for rought sensitive crops an up to 0.6 for non-sensitive crops. The percentage of wette area as copare to the whoe irrigate area epens on eitter ischarge an spacing an soi type (Keer an Karei, 1974). A tabe of 58

71 quantitative estiates of P w base on irrigation epths cose to 40 in ifferent soi textures, was prepare by Karei an Peri (Karei an Peri, 1977), for various eitter ischarges an its spacing. Whie Keer an Karei (1974) state that there is no right an proper iniu vaue for P w, the genera concusion is that the syste with higher P w provies ore insurance to syste faiures, easier to scheue an bringing ore of the soi syste into action for nutrient storage an suppy. With the current knowege of practice a reasonabe esign is to wet at east one-thir ( P 33% ) of the potentia root voue of the soi. On the other han, P w shou be beow 50% for wiey space crops to achieve the avantages of keeping reativey ry strips. w The irrigation interva epens on the rate at which water is consue by the pants an the epth of irrigation appie by each cyce. To obtain the irrigation interva base on water store in root zone the foowing reation can be foruate: F D (6.2) ET c where, F = irrigation interva (ays), an ET K ET ) c ( c o = potentia evapotranspiration (), ET o = reference crop evapotranspiration (), K c = crop coefficient, D = gross epth of water that can be store in the soi (). This equation ensures that the use of water uring one irrigation cyce just equas the epth of water store in the root zone of the soi. To obtain the gross epth D, Eq (6.1) nees to be increase by a iniu of 10% in orer to take care of eaching, unavoiabe eep percoation an evaporation fro bare sois. Tscheschke (Tscheschke, 1973) foun that the 10% excess water eiinates potentia sat buit-up probes in the wette areas. The cacuation of ETo is base on Penan-Montieth equation (Aen et a., 2011) for a given set of eteoroogica ata. The crop coefficient K c vaues can be obtaine fro any stanar iterature. The tie each eitter is operate uring irrigation operation can be written as: t ET F c Ea q (6.3) 59

72 where t = tie each eitter is operate uring irrigation appication (hr), E a = appication efficiency of rip irrigation, = spacing between eitters (icrotubes) aong the ateras (), (itre/hr). = spacing between ateras aong the anifo (), an q = eitter ischarge Estiation of syste s capacity requireents ( Q ) are usuay base on the axiu consuptive use rate expecte uring peak perios. If it is require to operate the syste neary fu-tie (20-24 hrs), we have to ivie the pot into severa operationa units ( N ) so that the seection of irrigation interva ( F ) an uration (t ) are just right. The require syste capacity is then foun by: s o Q s A ET F c (6.4) t N o where Q s = tota fow rate avaiabe to the syste (itre/hr), an A = tota area of the pot ( 2 ). The potentia nuber of operationa units, N o, into which the syste wi be ivie shou fufi the conition as foows: F N o 24 (6.5) t 6.2 Syste Design A typica pot of L L with a fat sope in the x -irection ( S 0 ) an an upwar sope x y x in the y -irection ( S 0.25% ) is taken fro Liyae, Mebourne for the foowing case y stuies. A cay-oa type of soi has been consiere in the pot. The anifo ines are ai aong the x -irection an the ateras are ai aong the y -irection. So the icrotubes are autoaticay aigne aong the fat x -irection. Two ifferent crops (toato an grape) have been consiere to be pante in this pot. The fixe input ata reate to pot, piping syste, an soi are given in Tabe 6.1. In this regar the nearby eteoroogica ata of Latrobe University Station, Mebourne is coecte to use in Penan-Montieth equation. For esign purpose it is neee to cacuate the peak consuptive onth E o (February) an the corresponing K c to obtain axiu 60

73 potentia evapotranspiration, ET c. The esign output on water requireent an syste ischarge accoring to peak consuption are suarize in tabuar forat. Tabe 6.1 Input ata reate to pot, irrigation piping syste an soi for case stuies Variabe Description Vaue L Length of the pot in x -irection 104 x L y Length of the pot in y -irection 101 S x Sope of the pot in anifo -irection 0.00 % S y Sope of the pot in atera-irection 0.25 % Distance between icrotubes 1 Distance between ateras 2 in Miniu ength of icrotubes 1.25 n Nuber of icrotubes in one atera 10 Diaeter of icrotube 2, 3 Diaeter of atera 12 Diaeter of anifo 20 s Specific gravity of cay-oa soi (ensen et a., 1980) page FC Fie capacity of soi 27 % PWP Peranent witing point of soi 13 % E a Irrigation efficiency 90 % Exapes on Pre-efine EU For Grape Cutivation In this exape grape is consiere to be grown in the pot for the given set of paraeters as state in Tabe 6.1. Root zone epth, wette area an fraction of avaiabe oisture epetion aowe are assue to cacuate irrigation interva (ays) an uration (hours) for a suitaby given icrotube ischarge, q. It is aso require that the potentia evapotranspiration rate an the gross epth of each irrigation appication nee to be 61

74 estiate fro the above state equations. A the assue an copute outputs are shown in Tabe 6.2. Tabe 6.3 shows the icrotube engths, nuber of cois require in the en-atera. This sae set has been repeate for a the ateras uner each anifo an then in the whoe subunit. During this cacuation, it was taken care that the EU shou have ore than 90%. The tota pressure hea of the subains ateras as we as EU of the syste. sub is cacuate accoring to the nuber of Tabe 6.2 Assue an output ata reate to irrigation to Grape Variabe Description Vaue Z Soi epth of the root zone 900 P w Wette area uner the whoe area 50 % f Fraction of avaiabe oisture epetion aowe 0.5 (Aen et. a. 2011) ET o Reference crop evapotranspiration (peak ean) 5.84 /ay K c Crop coefficient for grape (February) 0.7 ET c Potentia crop evapotranspiration (peak ean) 4.1 /ay D F t Net epth of irrigation water Irrigation intervas Irrigation tie ays 4 hrs q Eitter fow rate 2.5 itre/hr Tabe 6.3 Output ata for siuation of Case Stuy on Grape, Design () paraeter Outet nuber st anifo of the right subain 3, c x, K x K sub

75 N 25 (sub-ivision of the 1 st subunit (ie, 1 st anifo) shown in Figure 6.1) EU 94 % _ 2.55 R sub Tota ength of icrotubes in each atera = Microtube ength, There are 25 ateras in each anifo, = 491 There are 9 anifos, 491 = 4421 Tota ength of the right subain icrotubes = 4421 Latera ength, Manifo ength, Subain ength, Nuber of trees Each anifo has = 250; = 2250 Tota ength of the right subain ateras = (48 + 1) = 441 Tota ength of the right subain anifos = 441 Tota ength of the right subain = 89 Tota nuber of trees can be pante = = 2250 Q _ 2.5 itre/hr = 5625 itre/hr = 1.56 itre/sec R sub 1 st anifo of the eft subain It is syetrica to right subain ain 2.56 (provie that a anifos on right subain work concurrenty) 1 st anifo of the right subain 2, c x, K x K sub 8.92 N 42 EU 92 % There cou be 42 ateras in the right subain an 8 ateras in the eft subain Manifo ength () Right Sub-ain (41 x 2+1)x 9 sets = 747 Left Sub-ain (7 x 2+1)x 9 sets = 135 owever, this unsyetrica arrangeent can be ae syetrica by taking 25 ateras in each subain 63

76 2 2 = = = ateras Manifo 11 = 99 S u b a i n Microtube L a t e r a 25 ateras 2 Main ine Pup Figure 6.1 Scheatic ayout of the pot use for grape The resuts show that using saer icrotube size is reasonabe as the engths of the icrotubes are uch ess an ipeentation in far syste wou be easier. owever, the tota pressure require to run the syste in case of saer icrotube is consieraby higher. The iensions of an can be ajuste accoring to the nuber of ateras an anifo ength. If the esigner is free to choose the fie iensions, use of icrotube size 3 wou be ore convenient to keep the shape of the pot as square. As shown on Figure 6.1 an Tabe 6.3, using icrotube size 2 can change the syetrica shape of the pot if esigner tens to use the axiu perissibe nuber of ateras an two subains have to serve the whoe area. owever, if possibe to ajust the fie easureents an reove one subain, the esign wou be coser to an econoic scenario. 64

77 Since in reaity the fie iensions epen upon non-technica factors such as ownership an easeent iitations, soe optiization ethos are neee to be appie to fin the ost efficient soution for the syste keeping the easureents unchange. In these cases other irrigation factors such as tie of irrigation which affects on fow rate can be anipuate; other factors of esign shown in Tabe 6.2. For Toato Cutivation For the sae pot as state in Tabe 6.1, toato has been chosen to grow as per the assue vaues on root zone epth, wette area an fraction of avaiabe oisture epetion aowe as given in Tabe 6.4. Toato can be grown in cose spacing. Irrigation interva (ays) an uration (hours) for a given icrotube ischarge, q are cacuate as given in Tabe 6.4. Potentia evapotranspiration rate an the net epth of each irrigation appication are estiate fro the above state equations. In a siiar way to the cacuation for grape, Tabe 6.5 shows the piping syste, pressure an ischarge reate etais. During this cacuation it was aso taken care that the EU was ore than 90%. The tota pressure hea of each subain the nuber of ateras as we as EU of the syste. sub is cacuate accoring to Tabe 6.4 Assue an output ata reate to irrigation to Grape Variabe Description Vaue Z Soi epth of the root zone 800 P w Wette area uner the whoe area 50 % f Fraction of avaiabe oisture epetion aowe 0.5 ET o Reference crop evapotranspiration (peak ean) 5.84 /ay K c Crop coefficient for toato 1.15 ET c Potentia crop evapotranspiration (peak ean) 6.7 /ay D F t Net epth of irrigation water Irrigation intervas Irrigation tie ays 4 hrs q Eitter fow rate 2 itre/hr 65

78 Tabe 6.5 Output ata for siuation of Case Stuy on Toato, () Design paraeter Outet Nuber st anifo of the right subain, c x, K x K sub 1.4 N 25 (sub-ivision of the 1 st subunit (ie, 1 st anifo) shown in Figure 6.1) _ 1.5 (provie that a anifos on right subain work concurrenty) R sub EU 90 % 3 Microtube ength, Latera ength, Manifo ength, Subain ength, Nuber of trees Tota ength of icrotubes in each atera = There are 25 ateras in each anifo, = 497 There are 9 anifos, 497 = 4473 Tota ength of the right subain icrotubes = 4473 Each anifo has = 250; = 2250 Tota ength of the right subain ateras = (48 + 1) = 441 Tota ength of the right subain anifos = 441 Tota ength of the right subain = 89 Tota nuber of trees can be pante = = 2250 Q _ 2.0 itre/hr = 4500 itre/hr = 1.25 itre/sec R sub 1 st anifo of the eft subain It is syetrica to right subain ain st anifo of the subain c x, K x K

79 sub 5 N 50 EU 90 % Manifo ength () So there wi be ony one subain fro the ain ine, so the tota ength wi be (49 x 2+1)x 9 sets = 891 Figure 6.1 iustrates the scheatic ayout that cou be envisage for these exapes. The nuber of subains epens upon nuber of ateras in anifo. It is the ecision that shou be ae whether saer icrotube iaeter with onger anifo an fewer subains wou be appie or arger icrotube size with shorter ength of anifo an ore nuber of subains wou be appie. Even though the accurate anaysis of the syste is out of scope of this stuy, a genera unerstaning is given to reuce the ongoing cost of the syste ue to energy consuption in the ong ter operations Exapes on Fu EU To show the proceure of icrotube ength cacuation on Fu EU, two typica exapes have been consiere as foows: Exape 1 For a typica subunit in a fat terrain ( S 0%), there are 10 ateras ( 12) at an interva of 1 space. Each atera has 10 icrotubes ( 4) again at an interva of 1 space to ischarge q 1 itre/hr throughout the syste. The iniu icrotube ength in 0.5 has been set at the en-atera ( j = 1.0) as a esign paraeter so n as to cacuate the engths of the other icrotubes at i 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, an 0.9 for this en-atera. The tota ifference of icrotube ength 0.52 has been obtaine fro Figure 5.4(a). So, the icrotube engths can be cacuate using 1. 2 in Eq (5.6) as: 0.912, 0.818, 0.737, 0.667, 0.613, 0.569, 0.537, 0.515, an 0.503, respectivey. 67

80 The pressure hea require for this subunit wi be sub Exape 2 For a typica subunit in an upsope terrain ( S 0.25%), there are 10 ateras ( 12) at an interva of 1 space. Each atera has 10 icrotubes ( 2) again at an interva of 1 space to ischarge q 6 itre/hr throughout the syste. The iniu icrotube ength in at j = 0.7 atera has been foun using Eq 5.4 an Tabe 5.4(a), n so as to cacuate the engths of the other icrotubes at i 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, an 0.9 for this atera. The tota ifference of icrotube ength 0.23 has been obtaine fro Figure 5.4(). So, the icrotube engths can be cacuate using in Eq (5.6) as: 0.677, 0.631, 0.593, 0.563, 0.540, 0.523, 0.513, 0.506, an 0.504, respectivey. The pressure hea require for this subunit wi be sub 6.3 Chapter Suary The basic paraeters for esigning a rip irrigation syste have been expaine consiering the previous stuies an conventiona reations. Two pots with 0.25% sope an cay type of soi have been assue to set up those rip irrigation systes. The pant an soi ata incorporate with typica hyroogica statistics to cacuate the water requireents for toato an aize. The progra ran for two case scenarios with = 2 an 3 an the resuts on icrotube engths, nuber of cois an the tota hea require are obtaine. The nuber of ateras has been eterine to set a syste with 90% eission unifority. The resuts of the consiere case stuies showe that by appying saer size icrotubes, the iensions of the pot cou be increase; however the higher hea wou be require. 68

81 For fu eission unifority syste, the anua esign proceure is eonstrate with two ifferent exapes. The esign tabes an graphs are in use aong with the equations to show the sipicity of the esign proceure. 69

82 Chapter 7 Concusions an Recoenations 7.1 Concusions To reuce the probe of cogging an bockage of eitters ue to seient an sovabe aterias in rip irrigation, icrotubes with iaeters 2-4 have been propose to act as eitters. To carry out a we-organize esign with the axiu eission unifority (EU) within the syste, two soution agoriths, one is on Pre-efine EU an another one on Fu EU, have been eveope epoying icrotubes as eitters aong the ateras. Microtubes with ifferent engths were esigne to eiver equa voues of water accoring to pressure hea istribution aong the atera. The esign starts fro en-atera with the cacuation of a set of icrotube engths to fow a given ischarge. A progra has been eveope to cacuate these icrotube engths an corresponing tota heas. It nees inforation about the icrotube nuber an spacing, icrotube an atera iaeters, an sope to fow a given ischarge. For these esign inforation, pressureischarge power reationships are generate for subsequent appication. The ength of the icrotube is a variabe to ajust the pressure an eiver steay an unifor fow rates through the reaches of ateras, anifos, subunits an ain ines Design using Pre-efine Eission Unifority (EU) In the Pre-efine EU, another sipe coputer coe was eveope to estiate the nuber of ateras that can be instae in the anifo to fufi the EU requireent set by the esigner. It nees inforation about the atera spacing an iaeter, anifo iaeter an an sope to cacuate tota hea eveoping in ifferent reaches of the anifo. This coe takes input on icrotube engths an pressure-ischarge reationships fro the first progra of the en-atera. The set of icrotube engths are repicate in a the foowing ateras. ence, ateras work as arge eitters to eiver resutant ischarges for the varying pressure heas in the anifo reaches. Therefore, the nuber of ateras obtaine fro this coe can be fitte in a anifo to perfor in the best EU easure set by the esigner. 70

83 The Pre-efine EU anaysis shows that using saer iaeter icrotube increases the nuber of atera that can be ipeente in the anifo. owever the constraint of appying the saest icrotube size ( = 2) is to increase tota hea requisite of the syste an thus the operationa cost. On the other han, the arger icrotube size ( = 4) nees onger icrotube engths when ower ischarges are to be eivere. Consiering a these prospects an constraints, the ie size icrotube ( = 3) cou be a baance to fufi the present requireent of irrigation Design using Fu Eission Unifority (EU) In the other esign using Fu EU agorith, the icrotube engths are varie by soe increent in each successive atera copare to en-atera icrotubes. The variation of these icrotube engths are estiate accoring to the pressure heas to be issipate in each atera. Energy graient ine approach as is appie to atera an anifo ines to show the variation of tota hea, is anaogise with the variation of icrotube engths to present a new technique for esign. ence, by eveoping esign tabes, graphs an regression equations, the technique iustrates a sipe esign proceure for this approach. The chaenge of copensating the variabe pressure heas in the network has been ae by obtaining the proportionate ifference of icrotube engths require (siuate) in a baance to the extra tota hea there copare to the position at icrotube in of the enatera. The siuation resut shows that the exponentia energy graient curve can be atche with the icrotube ength ifference istribution curve appicabe for wie ranges of ischarge an icrotube an atera sizes. The Eq (5.6) aong with a graph on tota ifference of icrotube engths (Figures 5.4(a-f)) an the iniu icrotube ength require (Tabes 5.4(a-c)) for a given atera size, can ake the esign for unifor istribution of water in the subunit, uch easier. 7.2 Recoenations for Future Works A nove iea to appy icrotubes as eitters in rip irrigation systes is introuce in this research. The stuy trie to prouce esign tabes, graphs an regression equations to eveop sipe approaches for esigning rip systes. Despite of those efforts there are 71

84 sti soe gaps to be fie out by further works an researches. The foowing steps cou be ientifie as for future works for potentia eveopent: 1. The esign tabes of this stuy for the first progra (en-atera) are base on certain iniu ength an coi iaeter. Further work can be carrie out to anayse the effects of changing coi iaeter an iniu engths to soe other practica iaeters an engths on pressure hea an icrotube an anifo engths. 2. Econoica anaysis can be carrie out with this work to fin the optiu cobination of pipe iaeter an ength with ifferent terrain sopes. In the use of optiization oe, constraints can be ientifie as syste hea osses, pipe sizes, an easureents, etc. 3. A fu-fege esign anua can be prepare using a the possibe cobinations of the esign paraeters that have been ientifie in this research. 72

85 REFERENCES AL-AMOUD, A. I Significance of Energy Losses Due to Eitter Connections in Tricke Irrigation Lines. Journa of Agricutura Engineering Research, 60, 1-5. ALLEN, R. G., PEREIRA, L. S., DIRK, R. & SMIT, M Crop evapotranspiration: Guieines for coputing crop water requireents. FAO Irrigation an Drainage Paper No. 56, ANYOJI,. & WU, I. P STATISTICAL APPROAC FOR DRIP LATERAL DESIGN. Transactions of the Aerican Society of Agricutura Engineers, 30, BENAMI, A. & OFEN, A Irrigation Engineering. Sprinker, Tricke an Surface Irrigation. Principes, Design an Agricutura Practices. Irrigation Engineering: Sprinker, Tricke, Surface Irrigation. Principes, Design an Agricutura Practices. BATNAGAR, P. R. & SRIVASTAVA, R. C Gravity-fe rip irrigation syste for hiy terraces of the northwest iaayas. Irrigation Science, 21, BUIYAN, M. A., MOSEN, M.F.N. AND ELMASRI, M.Z Microtubes as an aternative to pressure copensating eitters in rip irrigation systes. yrosoft,coputationa Mechanics Pubications, 3. BRALTS, V. F. & WU, I. P Eitter fow variation an unifority for rip irrigation. St. Joseph Mich.: ASAE. BUCKS, D. A., NAKAYAMA, F. S. & GILBERT, R. G Tricke irrigation water quaity an preventive aintenance. Agricutura Water Manageent, 2, CAPRA, A. & SCICOLONE, B Water quaity an istribution unifority in rip/tricke irrigation systes. Journa of Agricutura Engineering Research, 70, CRISTIANSEN, J. E Irrigation by sprinking. Caifornia Agricutura Experienta Station Buetin 670. DE ALMEIDA, C. D. G. C., BOTREL, T. A. & SMIT, R. J Characterization of the icrotube eitters use in a nove icro-sprinker. Irrigation Science, 27, ELLA, V. B., REYES, M. R. & YODER, R Effect of hyrauic hea an sope of water istribution unifority of a ow-cost rip irrigation syste. Appie Engineering in Agricuture, 25, GILBERT, R. G., NAKAYAMA, F. S., BUCKS, D. A., FRENC, O. F. & ADAMSON, K. C Tricke irrigation: Eitter cogging an other fow probes. Agricutura Water Manageent, 3, ATOOT,. M., AL-AMOUD, A. I. & MOAMMAD, F. S Anaysis an esign of tricke-irrigation ateras. Journa of Irrigation an Drainage Engineering, 119, ENSEN, V. E., ISRAELSON, O. W. & STRINGAM, G. E Irrigation Principas an Practices. EZARJARIBI, A., DEGANI, A. A., MEFTA EIGT, M. & KIANI, A yrauic perforances of various tricke irrigation eitters. Journa of Agronoy, 7, OWELL, T. A. & ILER, E. A DESIGNING TRICKLE IRRIGATION LATERALS FOR UNIFORMITY. J. IRRIG. AND DRAIN. DIV. - PROC. A.S.C.E., 100. ITO, Pressure osses in sooth pipe bens Transaction of the ASME, Series D, 82. KARMELI, D. & PERI, G DESIGN PROCEDURE FOR A SPRINKLER LATERAL. 1, KELLER, J. & BLIESNER, R. D Sprinke an Tricke Irrigation. New York, N.Y.: Van Nostran Reinho. KELLER, J. & KARMELI, D TRICKLE IRRIGATION DESIGN PARAMETERS. Transactions of the Aerican Society of Agricutura Engineers, 17,

86 KATRI, K. C., WU, I. P., GITLIN,. M. & PILLIPS, A. L YDRAULICS OF MICROTUBE EMITTERS. ASCE J Irrig Drain Div, 105, MYERS, L. E. & BUCKS, D. A UNIFORM IRRIGATION WIT LOW-PRESSURE TRICKLE SYSTEMS. ASCE J Irrig Drain Div, 98, ÖZEKICI, B. & SNEED, R. E Manufacturing variation for various tricki irrigation onine eitters. Appie Engineering in Agricuture, 11, PEROLD, R. P DESIGN OF IRRIGATION PIPE LATERALS WIT MULTIPLE OUTLETS. ASCE J Irrig Drain Div, 103, POLAK P, S.R The potentia conterbution of ow cost irrigation syste to the iproveent of irrigation prouctivity in Inia. Inia -water resources anageent sector review: report on irrigation sector. Wor Bank, Washington, D.C. In cooperation with Inia SING, A. K., RAMAN, A., SARMA, S. P., UPADYAYA, A. & SIKKA, A. K Sa hoers' irrigation - Probes an options. Water Resources Manageent, 23, SOLOMON, K MANUFACTURING VARIATION OF TRICKLE EMITTERS. Transactions of the Aerican Society of Agricutura Engineers, 22, , SOLOMON, K. & KELLER, J TRICKLE IRRIGATION UNIFORMITY AND EFFICIENCY. ASCE J Irrig Drain Div, 104, SOLOMON, K GLOBAL UNIFORMITY OF TRICKLE IRRIGATION SYSTEMS. Transactions of the Aerican Society of Agricutura Engineers, 28, TSCESCKE, P. D Tricke irrigation sainity patterns as infuence by irrigation eves an appication rates.. M.S. Thesis, Utah State University, Logan, Utah 115p. VALLESQUINO, P An approach for siuating the hyrauic perforance of irrigation ateras. Irrigation Science, 26, VERMEIREN, I. & JOBLING, J. A Locaize Irrigation, 36, 202. VON BERNUT, R. D Sipe an accurate friction oss equation for pastic pipe. Journa of Irrigation an Drainage Engineering, 116, WATTERS, G. Z. & KELLER, J TRICKLE IRRIGATION TUBING YDRAULICS. Paper - Aerican Society of Agricutura Engineers. WU, I. P Energy graient ine approach for irect hyrauic cacuation in rip irrigation esign. Irrigation Science, 13, WU, I. P. & GITLIN,. M yrauics an unifority for rip irrigation. J. IRRIG. DRAIN DIV., PROC. ASCE, 99. WU, I. P. & GITLIN,. M. 1977a. Design of rip irrigation ines with varying pipe sizes. J. IRRIG. DRAIN. DIV.: PROC. ASCE., 103, IR4, Dec.1977, WU, I. P. & GITLIN,. M. 1977b. Design of rip irrigation subain. ASCE PROC., 103, YILDIRIM, G Anaytica reationships for esigning utipe outets pipeines. Journa of Irrigation an Drainage Engineering, 133,

87 Appenices 75

88 Appenix A Output Tabes fro Progra 1 76

89 Appenix A. Longest ength icrotube ax (), nuber of cois c an inet pressure hea require T () for the given icrotubes an ischarges ( = 12, 14, 16, in = 1.25, n = 10, = 1 an S = 0, 0.25 an 0.5 %; the shae ces are consiere as unreaistic range of tota heas an coi nubers) Tabe A.1 S = 0% a) = 12 q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (1.42) (1.30) (1.26) (1.41) (1.30) (1.26) (1.40) (1.29) (1.25) (1.39) (1.29) (1.25) (1.38) (1.29) (1.25) (1.37) (1.29) (1.25) (1.37) (1.28) (1.25) (1.37) (1.28) (1.25) (1.36) (1.28) (1.25) (1.35) (1.28) (1.25) (1.34) (1.27) (1.25) (1.33) ( (1.25) (1.32) (1.27) (1.25) 0 77

90 b) = 14 q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (1.34) (1.27) (1.25) (1.33) (1.27) (1.25) (1.33) (1.27) (1.25) (1.32) (1.27) (1.25) (1.32) (1.27) (1.25) (1.31) (1.27) (1.25) (1.31) (1.27) (1.25) (1.31) (1.26) (1.25) (1.30) (1.26) (1.25) (1.30) (1.26) (1.25) (1.29) (1.26) (1.25) (1.29) (1.26) (1.25) (1.28) (1.26) (1.25) 0 78

91 c) = 16 q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (1.30) (1.30) (1.29) (1.29) (1.29) (1.29) (1.28) (1.28) (1.28) (1.28) (1.27) (1.27) (1.27) (1.26) (1.26) (1.26) (1.26) (1.26) (1.26) (1.26) (1.26) (1.26) (1.25) (1.25) (1.25) (1.25)

92 Tabe A.2 S = 0.25% a) = 10 q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (4.19) (2.18) (1.43) (3.99) (2.11) (1.42) (3.82) (2.06) (1.41) (3.67) (2.01) (1.40) (3.54) (1.97) (1.39) (3.42) (1.93) (1.38) (3.31) (1.90) (1.37) (3.21) (1.87) (1.37) (3.04) (1.81) (1.36) (2.90) (1.77) (1.35) (2.72) (1.71) (1.34) (2.58) (1.67) (1.33) (2.27) (1.57) (1.25) 0 80

93 b) = 12 q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (4.00) (2.12) (1.42) (3.82) (2.06) (1.41) (3.66) (2.01) (1.40) (3.52) (1.96) (1.39) (3.39) (1.92) (1.38) (3.28) (1.89) (1.37) (3.18) (1.86) (1.37) (3.09) (1.83) (1.36) (2.93) (1.78) (1.35) (2.79) (1.73) (1.34) (2.63) (1.68) (1.33) (2.49) (1.64) (1.32) (2.42) (1.62) (1.25) 0 81

94 c) = 14 q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (3.92) (2.09) (1.41) (3.74) (2.04) (1.40) (3.59) (1.99) (1.39) (3.45) (1.94) (1.38) (3.33) (1.90) (1.38) (3.22) (1.87) (1.37) (3.12) (1.84) (1.36) (3.03) (1.81) (1.36) (2.88) (1.76) (1.35) (2.75) (1.72) (1.34) (2.59) (1.67) (1.33) (2.46) (1.63) (1.32) (2.38) (1.61) (1.25) 0 82

95 ) = 16 q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (3.88) (2.08) (1.41) (3.71) (2.02) (1.40) (3.56) (1.98) (1.39) (3.42) (1.93) (1.38) (3.30) (1.90) (1.37) (3.19) (1.86) (1.37) (3.10) (1.83) (1.36) (3.01) (1.80) (1.36) (2.85) (1.75) (1.35) (2.73) (1.71) (1.34) (2.57) (1.66) (1.33) (2.44) (1.62) (1.32) (2.37) (1.6) (1.25) 0 83

96 Tabe A.3 S = 0.5% a) = 10 q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (6.77) (2.99) (1.59) (6.40) (2.88) (1.57) (6.08) (2.78) (1.55) (5.80) (2.69) (1.53) (5.55) (2.61) (1.51) (5.32) (2.54) (1.50) (5.12) (2.47) (1.49) (4.94) (2.41) (1.48) (4.62) (2.31) (1.46) (4.35) (2.23) (1.44) (4.01) (2.12) (1.42) (3.75) (2.04) (1.40) (3.16) ( (1.26) 0 84

97 b) = 12 q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (6.59) (2.94) (1.58) (6.23) (2.82) (1.56) (5.92) (2.72) (1.54) (5.65) (2.64) (1.52) (5.40) (2.56) (1.50) (5.19) (2.56) (1.49) (4.99) (2.49) (1.48) (4.81) (2.43) (1.47) (4.50) (2.37) (1.45) (4.24) (2.28) (1.43) (3.92) (2.19) (1.41) (3.66) (2.09) (1.40) (3.52) (1.96) (1.25) 0 85

98 c) = 14 q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (6.51) (2.91) (1.57) (6.16) (2.80) (1.55) (5.85) (2.70) (1.53) (5.58) (2.62) (1.52) (5.34) (2.54) (1.50) ) (2.47) (1.49) (4.93) (2.41) (1.48) (4.76) (2.36) (1.46) (4.45) (2.26) (1.45) (4.2) (2.18) (1.43) (3.88) (2.08) (1.41) (3.63) (2.00) (1.39) (3.48) (1.95) (1.25) 0 86

99 ) = 16 q itre/hr T, = 4, & ax ( 5 ), c T, = 3, & ax ( 5 ), c T, = 2, & ax ( 5 ), c (6.47) (2.90) (1.57) (6.12) (2.79) (1.55) (5.82) (2.69) (1.53) (5.55) (2.61) (1.51) (5.31) (2.53) (1.50) (5.10) (2.46) (1.49) (4.91) (2.40) (1.47) (4.73) (2.35) (1.46) (4.43) (2.25) (1.44) (4.18) (2.17) (1.43) (3.86) (2.07) (1.41) (3.61) (1.99) (1.39) (3.47) (1.95) (1.25) 0 87

100 Appenix B Output Graphs fro Progra 1 88

101 Appenix B. Pressure-ischarge reationships for ateras as arge eitters ( in = 1.25, n =10 an = 1 ) Figure B.1 S = 0% an =12 a) = 4, q=1-8 (itre /hr) b) =4, q=8-20 (itre/hr) c) =3, q=1-6 (itre/hr) 89

102 ) =3, q=6-20 (itre/hr) e) =2, q=1-6 (itre/hr) f) =2, q=6-20 (itre/hr) 90

103 Figure B.2 S = 0% an =14 a) =4, q=1-8 (itre/hr) b) =4, q=8-20 (itre/hr) 91

104 c) =3, q=1-6 (itre/hr) ) =3, q=6-20 (itre/hr) e) =2, q=1-6 (itre/hr) 92

105 f) =2, q=6-20 (itre/hr) Figure B.3 S = 0% an =16 a) =4, q=1-8 (itre/hr) b) =4, q=8-20 (itre/hr) 93

106 c) =3, q=1-6 (itre/hr) ) =3, q=6-20 (itre/hr) e) =2, q=1-6 (itre/hr) 94

107 f) =2, q=6-20 (itre/hr) Figure B.4 S = 0.25% an =10 a) =4, q=1-8 (itre/hr) 95

108 b) =4, q=8-20 (itre/hr) c) =3, q=1-6 (itre/hr) ) =3, q=6-20 (itre/hr) e) =2, q=1-6 (itre/hr) 96

109 f) =2, q=6-20 (itre/hr) Figure B.5 S = 0.25% an =12 a) =4, q=1-8 (itre/hr) 97

110 b) =4, q=8-20 (itre/hr) c) =3, q=1-6 (itre/hr) ) =3, q=6-20 (itre/hr) 98

111 e) =2, q=1-6 (itre/hr) f) =2, q=6-20 (itre/hr) Figure B.6 S = 0.25% an =14 99

112 a) =4, q=1-8 (itre/hr) b) =4, q=8-20 (itre/hr) c) =3, q=1-6 (itre/hr) 100

113 ) =3, q=6-20 (itre/hr) e) =2, q=1-6 (itre/hr) f) =2, q=6-20 (itre/hr) 101

114 Figure B.7 S = 0.25% an =16 a) =4, q=1-8 (itre/hr) b) =4, q=8-20 (itre/hr) c) =3, q=1-6 (itre/hr) 102

115 ) =3, q=6-20 (itre/hr) e) =2, q=1-6 (itre/hr) f) =2, q=6-20 (itre/hr) 103

116 Figure B.8 S = 0.5% an =10 a) =4, q=1-8 (itre/hr) b) =4, q=8-20 (itre/hr) c) =3, q=1-6 (itre/hr) 104

117 ) =3, q=6-20 (itre/hr) e) =2, q=1-6 (itre/hr) f) =2, q=6-20 (itre/hr) 105

118 Figure B.9 S = 0.5% an =12 a) =4, q=1-8 (itre/hr) b) =4, q=8-20 (itre/hr) c) =3, q=1-6 (itre/hr) 106

119 ) =3, q=6-20 (itre/hr) e) =2, q=1-6 (itre/hr) f) =2, q=6-20 (itre/hr) 107

120 Figure B.10 S = 0.5% an =14 a) =4, q=1-8 (itre/hr) b) =4, q=8-20 (itre/hr) c) =3, q=1-6 (itre/hr) 108

121 ) =3, q=6-20 (itre/hr) e) =2, q=1-6 (itre/hr) f) =2, q=6-20 (itre/hr) 109

122 Figure B.11 S = 0.5% an =16 a) =4, q=1-8 (itre/hr) b) =4, q=8-20 (itre/hr) c) =3, q=1-6 (itre/hr) 110

123 ) =3, q=6-20 (itre/hr) e) =2, q=1-6 (itre/hr) f) =2, q=6-20 (itre/hr) 111