USE OF MICRO TUBES AS AN ALTERNATIVE TO THE DESIGN OF DRIP IRRIGATION SYSTEM

Transcription

1 USE OF MICRO TUBES AS AN ALTERNATIVE TO THE DESIGN OF DRIP IRRIGATION SYSTEM Muhae Bhuiyan School o Civil, Environental an Cheical Engineering, RMIT University, Melbourne, VIC 3001, Australia, Eail: uhae.bhuiyan@rit.eu.au Air Keshtgar School o Civil, Environental an Cheical Engineering, RMIT University, Melbourne, VIC 3001, Australia, Eail: keshtgarair@gail.co Nira Jayasuriya School o Civil, Environental an Cheical Engineering, RMIT University, Melbourne, VIC 3001, Australia, Eail: jayasuriya@rit.eu.au Abstract Clogging an eission non-uniority have been the ajor obstacles in the evelopent o rip irrigation. To obtain best eission uniority (EU) the pressure regulators an pressure copensating eitters are in use since long back. As pressure copensating eitters ten to be ore coplex, we suggest the possibility o utilizing varying length sall bore polyethylene tubes (- ) along the laterals to provie sipler passages. The lengths o these sall bore icrotubes are varie accoring to the varying heas along a lateral that require to be copensate to eliver equal ischarges. As such, the copute set o varying length icrotubes that are eitting equal lows at the en-lateral can be replicate (i.e., by taking the sae set o lengths) to subsequent laterals o the aniol to unction the as larger eitters to have siilar characteristic hea-ischarge relationship. As because the sae set o icrotube lengths are replicate to other laterals at upstrea increasing heas, the variation o lows through those laterals are restricte by liiting their nuber to have EU 90 percent threshol. For case stuies with EU 90 percent threshol on lat-groun or a given set o icrotube (- ) an lateral (10-1 ) iaeters, the exponents in the heaischarge relationship varie narrowly: or larger ischarges an or saller ischarges. Variation o the corresponing icrotube lengths can be aroun 0-85% longer than the given iniu length ( in =1.5 ). When the require ischarges an iaeters o icrotube, lateral an aniol an soe other groun conitions are given, the length o the icrotubes, the heas, eission uniority an the best subunit iensions can be obtaine using the algorith evelope. Keywors: Eitters, Eission uniority, Laterals, Microtubes

2 1. Introuction The ain objective o rip irrigation syste is to provie soil oisture to each plant, which is suicient to eet its transpiration ean. The icrotube, also calle spaghetti tube can be use as pressure copensating eitters in rip irrigation syste. Utilizing these tubes as an alternative to current rippers will reuce the risk o clogging an blockage. Uneven istribution o lows ro the syste is always a proble ace by the rip irrigation esigners. In orer to overcoe all these probles the hyraulics o icrotube eitters in rip irrigation syste has been stuie by any researchers, soe o the notables are Bucks an Myers (1973), Wu an Gitlin (1973), Khatri et al. (1979), Bagarello et al. (1995), Bhatnagar an Srivastava (003), Aleia et al. (009), etc. Experiental results by Watters an Kellers (1978) conire that riction actor, o the Darcy- Weisbach equation to calculate the hea losses or sooth sall iaeter pipes ( to 1 ) can be calculate by using Blasuis orula. Experients carrie by von Bernuth an Wilson (1989) on larger iaeter pipes (1, 16 an 6 ) an or Reynols nuber less than 100,000 also showe that the Blasius equation is an accurate preictor o the Darcy-Weisbach riction actors. Khatri et al. (1979) worke with seven ierent iaeter icrotubes (0.8 to ) to easure inor hea losses in the syste. Coputations were one or the separation o inor losses to prouce coeicients or ierent low conitions. They conclue that using Blasuis equation has a reasonable accuracy or a range o tubes in turbulent low conition. Vereiren an Jobling (1980) use icrotube as eitter with very sall iaeters (0.5 to 1.1 ) which are susceptible to blockage. Bhuiyan et al. (1990) stuie on intereiate iaeter icrotubes ( to 3 ) which are easily available in the arket. In their work an algorith was evelope or one single lateral to siulate the set o icrotube lengths an ischarge (equal or every icrotube) or a given range o hea, icrotube an lateral iaeters an nuber o trees to be irrigate. The relation between pressure hea an ischarge has been stuie in Keller an Kareli (197a, b) to show that it ollows a power-law or custoary eitters. They also gave the principles or ischarge (or eission) uniority in the syste. So, the ai o this paper is to exten the previous researches on the analysis o rip irrigation syste to esign one typical subunit using icrotubes as eitters. A typical subunit woul coprise one aniol to branch into several laterals an then each lateral supplies to icrotubes at a regular interval to ischarge water at the roots o the plants. In the syste along with the icrotubes, the laterals woul also be consiere as larger eitters in the boy o the aniol. The analysis woul show that regarless o inlet hea, the ischarge istribution along a lateral woul be equal. However, aong the laterals in the aniol the ischarge woul ollow eission uniority (EU) greater than 90 percent.. Syste coponents Figure 1 shows a typical subunit consisting o aniol, laterals an icrotubes. Microtubes are eerging ro the sies o the laterals as eitters. The energy grae line o the syste is also shown

3 in the igure. The set o icrotubes with varying lengths have been shown below in one sie o the laterals. a) b) Figure 1: Scheatic layout o a typical rip irrigation subunit; a) subunit consist o aniol, laterals an icrotubes, an b) varying length icrotubes as eitters in one sie o a lateral, etails A an B show the installation ethos or aking coils (Keshtgar et al. 01) It will be eonstrate subsequently that to achieve equal ischarges qo q1 q... qn or up (positive) an lat (zero) slopes, the icrotube lengths woul be o 1... ( n in ). The icrotube length n at the en o the lateral is taken as the iniu length, eterine ro realistic istances between crops an laterals. But or a own slope (negative) the location o the iniu length, in ay be locate anywhere in the sequence o n points along the laterals. The increase in icrotube length is neee to issipate the ierence o energy (e.g., H H ) an give n 1 n

4 equal ischarges or all the icrotubes in the lateral. As shown in Figure 1(b) the increase length o icrotubes can be wrappe aroun a stick (etail A), or the lateral (etail B) to keep a constant istance between lateral an the plant. In this paper the ter coil is use with a iaeter o 3 c (using etail A), which can be altere by the esigner in other circustances. So with the given coniguration in the subunit, the laterals at ierent points in the aniol will eliver increasingly ore ischarges ue to increasing heas in their upstrea inlets, whereas the icrotubes in each o these laterals will eliver proportionately equal ischarges by iviing those increasing ischarges. Due to practical reason the scope o varying lateral lengths is liite to have equal low rates through each lateral. So a characteristic hea-ischarge power-law relationship or the above en-lateral will be evelope by regression analysis or the given set o ischarges an its corresponing heas necessary as explaine in the ollowing section. This relationship ay then be use to liit the wiely increasing variation o ischarges by axiising the nuber o laterals to be eerge ro the aniol o the subunit in orer to aintain the eission uniority o the laterals above soe given threshol value, say EU 90 percent. Here as the sae set o icrotube lengths an iaeters are use in all the ollowing laterals, these laterals also act as eitters with characteristic power-law relationship evelope in any lateral (say, at the en-lateral) in the boy o the aniol. 3. Basic hyraulics Darcy-Weisbach equation to calculate rictional hea losses in pipes can be written in MKS units as h v (1) g For lainar low the riction actor can be written as 6 () R e For turbulent low with Reynols nuber between 3000 an 100,000, Blasius equation which yiels goo approxiation or coputing riction actor, can be written as 0.3 (3) 0.5 R e where R e= Reynols nuber, h = rictional hea loss, an = length an iaeter o the pipes, g = acceleration ue to gravity, an v = velocity o low. Equations (1-3) can be cobine to obtain the equations or lainar (Equation ) an turbulent (Equation 5) lows, respectively: 1.3 q h () 0.86 q h (5).75

5 where h = riction hea loss (), q = ischarge (litre/hr), = iaeter o the pipe (), = length o the pipe (). Kineatic viscosity o water at 15 C is taken as = /s. Velocity an other inor losses o the syste can be written in general or as v h k (6) g where k = hea loss coeicient, which in three ierent inor loss coeicients are ierentiate as: (i) k e = 1., to calculate entrance hea loss assuing the entrance ro lateral as a re-entrant one, (ii) k v = 1, to calculate velocity hea, an (iii) k c = c 1.3, to calculate coil hea loss, where 1.3 has been extrapolate (or D / 1.0 an = 360, where D an are the coil an pipe iaeters an is the angle o ben subtene at the centre) ro Ito s (1960) iagra on loss coeicient or sooth bens, c is the nuber o coils that can be copute ro ierence o two icrotube lengths as c n 1 n D. Only whole nuber o coils is taken or the calculation o hea losses. Thus, Equation (6) can be rearrange to accooate the above three ierent inor losses as ollows: q h e (7) q h v (8) q h c (9) Energy grae line as shown in Figure is relate to hea losses in one sie o the lateral. Total hea at the inlet o the icrotube at point n can be calculate by suing all the hea losses as ollows: h e h h ( n) H (10) v n Q Q Q j Q 1 Figure : Energy grae line an hea losses in one sie o the lateral ( h e = entrance loss, h v = velocity loss, h c = coil hea loss, h (n) = icrotube riction hea loss at n, an h l (n) = lateral riction hea loss between n an n 1) (Keshtgar et al. 01)

6 By placing the icrotube with iniu length at the point n, the balance o 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 (11) v c e v where S an are slope o lateral an istance between icrotubes, respectively. Since the ischarges are sae in all the icrotubes, entrance an velocity hea losses are equal in all the icrotubes, so Equation (11) can be written as h ( n 1) h ( n 1) h ( n) h ( n) S (1) c l By substituting ull expressions or each o the hea balance ters there will be a total our equations or our cobinations o lainar an turbulent conitions in lateral an icrotubes as ollows: 1. Flow regies are lainar in both the icrotube an lateral l 1.3 n 1q cq 1.3 nq 1. 3nq S. Flow regies are lainar an turbulent in icrotube an lateral, respectively 1.3 n 1q cq 1.3 nq 0. 86nq l.75 l S 3. Flow regies are turbulent an lainar in icrotube an lateral, respectively 0.86 n 1q cq 0.86 nq 1. 3nq S Flow regies are turbulent in both the icrotube an lateral l (13) (1) (15) 0.86 n 1q cq 0.86 nq 0. 86nq l S Thereore, when the ischarge require in the trees, iaeters o icrotube an lateral, slope, istance between icrotubes, nuber o icrotubes an the iniu length o icrotube ( in n ) are known, the only unknown n 1 can be calculate ro the above equations. Proceeing in this way up to the inlet o the lateral, all the icrotube lengths will be known or elivering equal ischarges q. Ater suing all the hea losses along the lateral, the total hea at the entry o the lateral is equal to inlet hea H T. So in the lateral uner inlet hea H T, the total ischarge entering woul be Q l ( n 1) q. A coputer progra has been evelope using the above algorith. Figure 3 shows the lowchart o the progra to copute icrotube lengths, nuber o coils in each icrotube an the hea at the entry o the lateral H T. It also calculates the nuber o laterals that can be inclue in the aniol o a subunit to ulil the conition o eission uniority, EU 90 percent. The inlet heas or the (16)

7 successive laterals can be calculate using siilar riction an inor losses in the aniol reaches up to the entry point o the aniol. This entry hea o the aniol ( H sub) woul be the operating pressure o the subunit that nee to be provie or running the irrigation syste. Figure 3: Flowchart o the coputer progra evelope

8 . Hea-ischarge relationship Keller an Kareli (197) suggeste a power-or low equation or custoary eitters as x Q kh (17) where Q = the eitter ischarge (litre/hr), H = energy hea at the eitter (), k = the constant coeicient that characterizes each eitter, an x = the exponent that characterizes eitter low regie. By using the aoresai equation, the eitter s hea-ischarge relationship can be generalize to laterals or esigning the as eitters in the aniol line. To apply the concept, it is the sae set o icrotube lengths as calculate in the en-lateral are aapte to the rest o the laterals along the aniol. By taking a range o realistic ischarges neee or the trees, the consequent heas are copute using Equations (13-16) in Section 3. These heas an ischarges are plotte to obtain k an x or the chosen lateral with high R value or a easible accuracy to consier laterals as eitters. For the given aniol size ( ) an iniu operational hea require at the inlet o the en-lateral, the ischarge in the next lateral can be estiate by taking the corresponing inlet hea o the lateral in the characteristic relationship obtaine above. This inlet hea in the next lateral is HT h, where h = rictional hea loss in the aniol between two successive laterals which can be estiate by using either o Equation () or Equation (5). The coputation ay procee until EU 90 percent ulils an as a result the nuber o laterals that can be accooate in the aniol will be obtaine. 5. Eission uniority (EU) Ieally it is neee that the low rates through the syste shoul be unior even though the hea is not unior (Soloon an Keller 1978). In a well-esigne rip irrigation syste, the eission uniority or eitters shoul be greater than a speciic threshol level. An acceptable value o EU can be obtaine by liiting the variation o hea in the syste. Liiting the variation o hea can ecrease the variation o ischarge in eitter. Keller an Bliesner (1990) recoene that EU shoul be at least 85 percent or rippers on lat terrain. By using icrotubes as eitters it is assue that ischarge elivere ro aniol to the laterals will ollow the above characteristic heaischarge relationship, because the other paraeters such as icrotube lengths, pipe iaeters an coil nubers woul be kept sae as in the en-lateral. Thereore, EU or the subunit can be copute accoring to Keller an Kareli (197a, b) as Q EU 100 Q ll (18) la where Q ll = average o lowest ¼ o the lateral low rates an Q la = average o all the lateral low rates in the syste. For calculating EU o the syste a subroutine has been evelope as shown in Figure 3. This subroutine works with one aniol size an nees to know x an k paraeters o the

9 laterals as eitters. The output o the subroutine is the ischarges through the laterals, the inlet hea o the subunit H sub an the axiu nuber o laterals N l in the aniol or approaching the esire EU. 6. Results an iscussion The coputer coe that has been evelope can siulate any range o iaeter, ischarge an nuber o icrotube an lateral in one subunit. However, ro a practical point o view soe typical scenarios have been prepare or presenting nuerical results. While the chosen lateral iaeters are taken as 10, 1 an 1 ro a practical jugent, the icrotube iaeters are taken, 3 an to keep the ree ro clogging. These icrotubes are installe in one sie o the laterals. Using the above evelope algorith or any given ischarge ( q ) through the icrotubes, Table 1 shows the inlet hea require ( H T ), nuber o coils installe ( c ) an the longest length ( ax ) aongst all the estiate lengths o icrotubes in one lateral. It shows that the ax lengths ecrease with increase o ischarge. As also can be seen in Table 1 the lengths ax becoe alost constant to in or = an to soe other value or = an 3 at higher low rates. Table 1: Longest length icrotube ax (), nuber o coils c an inlet hea require H T () or a range o icrotube sizes an ischarges ( l = 10, in = 1.5, n = 11, = 1 an S = 0%, the shae cells are in the higher heas eee unsuitable in the current cases) q, litre/hr = = 3 = ax, H T, c ax, H T, c ax, H T, c Power-law regression results on x an k or the characteristic hea-ischarge relationships are shown in Table. The results are obtaine or two ranges o ischarges an its resulting heas, one or lower range an other one or higher range, where R are at least or a easible accuracy to consier laterals as large eitters. Graphical plots o these power-law relationships clearly illustrates

10 that while the laterals are peroring as eitters in its lower an higher ischarge ranges, the saller size icrotubes eliver less ischarges with relatively higher heas an larger size icrotubes eliver ore ischarges with relatively lower heas. The power-law results (Table ) woul be helpul or esigners to choose the appropriate values o x an k to run the progra or coputing EU o the syste an the optiu nuber o laterals ( N l ) in each subunit. This table can be evelope or ierent nuber o icrotubes an slopes ( S ) accoring to iel conitions. Table : Hea-ischarge relation in a typical lateral with in = 1.5, n = 11, = 1, S = 0% l 3 q, litre/hr H T, x k q, litre/hr H T, x k q, litre/hr H T, x k Table 3 shows the results o EU, hea at the inlet o the subunit ( H sub) an the optiu nuber o laterals ( N l ) or ierent icrotube an lateral sizes. In the table ischarges o 10, 7 an 3 litre/hr are use or, 3 an o icrotubes, respectively. Results show that by choosing larger size aniol, the nuber o laterals ( N l ) can be increase to achieve a corresponing threshol EU 90 percent. It also shows that the require subunit hea ecreases with the increase o aniol size. In act these subunit pressure heas ( H sub) are relate to the nuber o laterals ( N l ) obtaine an the EU achieve. As a general rule, it is also oun that by using saller size icrotubes, we can increase the nuber o laterals to have larger coan area uner each irrigation subunit. 7. Conclusions In this stuy an algorith has been evelope to esign a typical irrigation subunit using icrotubes an laterals as eitters. The esign starts ro en-lateral with the calculation o a set o varying icrotube lengths to low a given unior ischarge. It nees inoration about the icrotube

11 nuber an spacing, icrotube an lateral iaeters, an slope to workout various hea-ischarge relationships uner the calculate set o icrotube lengths in the en-lateral. This set o icrotube lengths is replicate in the subsequent laterals with the application o sae hea-ischarge relationships. Due to unequal heas at the inlets o the subsequent laterals, the resulting unequal ischarges through these laterals ay be allowe to vary up to a particular level peritte by the eission uniority (EU) speciie. This speciie EU will ictate the nuber o laterals to be installe uner a aniol in the subunit. Hence each lateral has been iagine as an inepenent larger eitter with characteristic hea-ischarge relationship as speciie uner en-lateral. Accoring to the ischarge an hea requireents (high or low ranges) the set o esign options ay be obtaine. The progra has the capability to hanle a wie range o pipe iaeter, length, plantation geoetry an slope in the groun. Table 3: Hea, EU an nuber o laterals in one subunit, in = 1.5, n = 11, = 1, an S = 0%, ( q, litre/hr) (10) 3 (7) l, (3) 0 3 N l EU % H sub, N l EU % H sub, Reerences Aleia C D G C, Botrel T A an Sith R J (009) Characterization o the icrotube eitters use in a novel icro-sprinkler. Irrigation Science 7(3): Bagarello V, Ferro V, Provenzano G an Puo D (1995) Experiental stuy on low-resistance law or sall-iaeter plastic pipes, J Irrig & Drain Eng, ASCE 11(5): Bhatnagar P R an Srivastava R C (003) Gravity-e rip irrigation syste or hilly terraces o the northwest Hialayas. Irrigation Science 1():

12 Bhuiyan M A, Mohsen M F N an ElMasri M Z (1990) Microtubes as an alternative to pressure copensating eitters in rip irrigation systes. Hyrosot, Coputational Mechanics Publications, Vol 3, No. Bhuiyan M A, Keshtgar A an Jayasuriya N (01) Design o rip irrigation syste using icrotubes or ull eission uniority, J. Irrigation & Drainage, ICID, uner review Bucks D A an Myers L E (1973) Trickle irrigation - application uniority ro siple eitter, Transaction o the ASAE, Vol. 16, No. 6, pp Ito H (1980) Pressure losses in sooth pipe bens, Trans. ASME (series D ), 8 (1). Keller J an Kareli D (197a) Trickle irrigation esign paraeters, Transactions o the Aerican Society o Agricultural Engineers, Vol.17, No., pp Keller J an Kareli D (197b) Trickle irrigation esign, Rain Bir Sprinkler Manuacturing Co., Glenora, Caliornia. Keller J an Bliesner R D (1990) Sprinkle an trickle irrigation, Van Nostran Reinhol, New York. Khatri K C, Wu I P, Gitlin H M an Phillips A (1979) Hyraulics o icrotube eitters, J Irrig & Drain Div, ASCE, 105(): Soloon K an Keller J (1978) Trickle irrigation uniority an eiciency, ASCE J Irrig & Drain Div, 10, von Bernuth R D an Wilson T (1989) Friction actors or sall iaeter plastic pipes, J Hyrau Eng, ASCE 115(): Vereiren I an Jobling G A (1980) Local irrigation, Irrigation an Drainage Paper No.36, Foo an Agriculture Organization, Unite Nations, Roe, Watters G Z an Keller J (1978) Trickle irrigation tubing hyraulics, (ASAE Technical paper No ) presente at the 1978 Suer Meeting o ASAE at Logan, Utah. Wu I P an Gitlin H M (1973) Hyraulics an uniority or rip irrigation. ASCE J Irrig & Drain Div, 99(IR).