Recession flow in a large field can be significant from the point of view of water-use efficiency. This is particularly

important in the case where the furrow field is long, thus the receding flow can contribute to the irrigation of crops.

Indeed, recession flow is very significant in the surge method of furrow irrigation. In the continuous mode of

operation in very long furrows the amount of recession flow can be significant. Herein is presented the mathematical

modelling of the recession flow. The analytical procedure is based on the kinematic wave approach used for the

simulation of the advance-flow trajectory for furrows. This resulting recession simulation was found to be very useful

for the evaluation of the basic infiltration rate in a furrow

Lee, Teang Shui

Walker, W. R.

Universiti Putra Malaysia Institutional Repository

Pertanika 15(3), 265-269 (1992)Evaluation of Infiltration in Furrow IrrigationPart 1: Recession FlowT.S. LEEl and w.R. WALKER2IDepartment ofField Engineering, Faculty of EngineeringUniversiti Pertanian Malaysia, 43400 Serdang,Selangor Darnl Ehsan, Malaysia2Department of Irrigation Engineering, College of EngineeringUtah State University, Logan, Utah 84322Keywords: furrow, infiltration, recession flowABSTRAKAliran susutan didalam ladang besar adalah bererti dari segi pandangan kecekapan penggunaan air. Ianya amatpenting dalam kes di mana ladang furrow adalah panjang di mana aliran susutan ada kesan kepada pengairantumbuhan. Aliran susutan dalam pengairan furrow adalah sangat bererti dengan cara pengairan pusuan.Dengan mod operasi lanjutan di dalam furrow yang panjang, jumlah aliran susutan amat bererti. Dikemukakandi sini satu teknik pemodelan matematik aliran susutan. Tatacara analisis ini berasaskan pendekatan gelombangkinematik yang telah diguna dalam simulasi aliran lajakan untuk furrow. Simulasi susutan yang dihasilkandidapati berguna demi untuk menilaikan kadar asas penyusupan di dalam furrow.ABSTRACTRecession flow in a large field can be significant from the point of view of water-use efficiency. This is particularlyimportant in the case where the furrow field is long, thus the receding flow can contribute to the irrigation of crops.Indeed, recession flow is very significant in the surge method of furrow irrigation. In the continuous mode ofoperation in very long furrows the amount of recession flow can be significant. Herein is presented the mathematicalmodelling of the recession flow. The analytical procedure is based on the kinematic wave approach used for thesimulation of the advance-jlow trajectory for furrows. This resulting recession simulation was found to be very usefulfor the evaluation of the basic infiltration rate in a furrow.INTRODUCTIONRecession flow in surface irrigation is consideredas the stage of flow when irrigation water is shutoff and the depletion of surface storage follows.Recession in furrows is important in the evalua-tion of irrigation efficiencies, especially when thefields are long. The importance of recession ishighly significant in surge flow considerationssince a substantial part of advance along the fieldoccurs during recession. The surge flow tech-nique of irrigation requires water to be suppliedand cut off according to prescribed on/off timeratios in order to achieve complete irrigation ofthe whole length of fields. It is particularly usefulin light soils and long furrows (Lee 1982). Reces-sion flow is also important in determining theinfiltration characteristics of the furrow and this iswhat the paper and its following part attempt toshow.The objective of this paper is to develop thesimulation of the recession phase of furrow irriga-tion using principles used for the development ofthe advance phase simulation.MATHEMATICAL DEVELOPMENTThere have been studies simulating recession flowin open channel flows, e.g. the work by Cungeand Woolhiser (1975). However, the simulation isfor border irrigation and thus would have to bemodified for use with furrows.The method of characteristics is used for thedevelopment of the simulation. Fig. 1 and 2 showa family of characteristics emanating from thepoint at the time of cut-off of irrigation at theT.S. LEE & W.R. WALKERinlet end, where Cunge and Woolhiser (1975)described the curve as the locus of the pointswhere velocity and depth are zero. They men-tioned that the forward and backward character-istics will be tangential to the vertical lines. Thesimulation of the advance-flow trajectory was re-ported earlier (Lee 1982) (it is shown here onlyfor the purpose of illustrating the simulation ofanother important phase of irrigation) and theuse of the kinematic wave theory to simulate fieldconditions was reported (Walker and Lee 1982;Walker and Humphreys 1983). The simulation ofthe recession phase is presented here. It is basedon the same principles as for the advance simula-tion, only with the exception that furrow irriga-tion has been continued long enough for thebasic infiltration rate f to be reached.°For the case of furrow advance, where thetime-varying infiltration rate holds true, numeri-cal solutions can be obtained (Lee 1982). How-ever, analytical solutions for irrigation recessioncan be obtained when infiltration rate is a con-stant and this is true for long-term irrigation,where the infiltration rate can be assumed to beconstant and equals the basic infiltration rate.Thus, when the rate of infiltration is constantDISTANCE FROM FURROW INLET. X •Fig. 1: Method ofcharacteristics grid for kinematic-waveadvance and recession.(1)(2)recession flowQ = ayrn+loA oQ-+-+WPf =0ot OX 0assume flow characteristicsandFig. 2: Concept ofcharacteristics ofrecession flow andcharacteristics of the assumed advance flow(3)The rate of cross-sectional area change for aprismatic channel is given byLENGTH OF FURROWBA A By By-- -BOT-YOT- Mthroughout the furrow the rate of advance of theassumed advance phase would be the same as therate water recedes down the same furrow. Asmentioned before, this analytical solution can befound only if the rate of infiltration is constant.The following assumptions are made. Firstly, thechannel geometry remains constant throughoutthe length of the furrow and the irrigation event.Secondly, there are no multiple recessions occur-ring in the furrow. Thirdly, once irrigation wateris cut off, the depth of the flow at the inlet end isinstantaneously zero. The depth of the flow atthe inlet end of the imaginary advance phase isho' equivalent to the depth of the recession flowat the outlet end. The continuity and stagedischarge equations used in advance simulationand now employed for recession are65432....ciUJI-a:gis~~ j-l L_-+--iUJuz0;UJ::;;::266 PERTANlKA VOL. 15 NO.3, 1992EVALUATION OF INFILTRATION IN FURROW IRRIGATION: RECESSION FLOWwhere B is the surface width of flow and Hence,Equation 1 can be nondimensionalized as follows(The performance of an irrigation system is gov-erned by a large number of variables, singling outeach variable and examining behavioural trendsdue to its variation would encompass an enor-mous list of combinations. By nondimensionalizingthese governing equations the number of indi-vidual variables can be reduced and provide foran examination of the general behaviour of modelresponses to parameter variation),I * 'i) '*AoA +~ + WP'wp*f = 0T'ot * X'ox * 0(4)(5)'02-'C>Y* *moy' 'y2 (12)y -;-;-+(m+l)y -,+Y,y =0ut oxRearranging,oy' 'm+I-0 2oy' 'y2-02+1-;;-;-+(m+l)y -,+Y1Y =0 (13)ut oXThe tom1 differential of the dependent vari-able y, with respect to the two independent vari-ables x and t, can be written asdy oy dx oyCit = 'bXCit + OT (14)Comparing Equations 13 and 14, we haveRearranging,oA* + T'Q' oQ * + f .....:L.w P * = 0ot* A'X' ox * 0 A'WP'(6)(15)(16)Substituting relevant coefficients,* 0 *oA +V*.....9.....+ WP *f*=Oot* ox* 0where(7)EVALUATION PROCEDUREEquations 15 and 16 are the characteristic equa-tion solution for the simulation of recession andcan be solved analytically as follows. On integrat-ing Equation 15 we haveWe define f * and V* as unity since f T' is theinfiltrated depthOequivalent to the hydraulic depthof water to be infiltrated, and QT is the volumeof water equal to the volume of water body A'X'.Therefore,where M is the constant of integration and t; isrecession time. At the inlet end the boundaryconditions are t; = 0 and y* = ho*' thusfT' fT'f:=-}-=+WP'* Q'T'V = A'XoA* oQ *--+ -+WP =0ot* OxA Y* 0-, 0-, 0 *oA A B Y *"2-1 YV = --, = -B'-t- = Y ot *I: t 0-u T' T'(8)(9)(10)(11)f*02-Y2-1Y Y 1 dy' = - f dt •.0" -1h 2 2M = 0Y, «j 2- Y2)Thus, we have(17)(18)(19)(20)PERTANIKA VOL. 15 NO.3, 1992 267T.S. LEE & W.R. WALKERThe locus of y* = 0 results in 720• cr -y, h 2ot,= -~--~Y,(<J 2 -Y) (21)640o'--- Time of cuto"oRecession completed"/and upon integrating givesSubstituting Equation 12 for Equation 11 gives"Advance completed ~"Go0Field dataModela 1.1351pslSo 0.0044 mtmn 0.02k 0/0092 m/min •a 0.139fo0.00005 m/min •O· 1.5489O'~ 1.6703n 2.334612 0.6050L 625mwUz240Viw::;>=16080iii 560OJI-::>z~ 480owI-a:;;:en 400zo~toii' 320~dt(22)(23)m+l-cr2cr -12 2m+1 -y___2cr -y2 2X'=where N is the integration constant. For the initialconditions t,' = 0 and x' = 0 we have• m+ 1-'(OI<:::...-_...l-_--L__-'-_-'-_--''--_........._--'o 100 200 300 400 500 600 700DISTANCE FROM FURROW INLET (METRES)Fig. 3: Predicted and observed furrow advance and recessionforinigation event B 2-2-1, Colm·ado. [Field data source:Elliott 1980J(m+l)hoN = -..,.....--i----,,.-yl(m+l-y)(24)1550With Equation 21 and 24 substituted for Equa-tion 23 and rearrangimg givesThe analytical solution of the characteristicequations 22 and 25 for a given range of x* is aset of (x', t,') coordinates describing recessionflow. Once the dimensionless set has been deter-mined, the actual distances can be evaluated withthe use of the characteristics time T' and charac-teristic distance X'.oo"'"Recession completedE)Field dataModelQ 0.792So 0.0092 mlmn 0.03k 0/002 m/min •a 0.4023'. 0.00007 m/min0', 0.95680', 1.703711 2.353962 0.7780L 450mAdvance compleled --...."'-.. Time of cutoff1450iii~::>z~o~;;:(f)zQ 200~a:~wuzViw~ 100(25)Im+ l-y 2y/m+ l- Y2)X'h' = -"----.....;;.----o m + 1500"oo'"o~::..<e._....L__-I. -"--__---'-__--Jo 100 200 300 400DISTANCE FROM FURROW INLET (METRES)Fig. 4: Predicted and observed furrow advance and recessionfor inigation event M 1-4-5, Colorado. [Field data source:Elliott 1980JRESULTS AND CONCLUSIONSField test results were extensively compiled byElliottt (1980) and were used to evaluate therecession flow. Only two cases were shown here.For the Benson farm (Colorado) the soil is loamysand, while for the Matchett farm (Colorado) thesoil is loam to dayey loam. Fig. 3 and 4 show themodel simulation, indicating a good model pre-diction in evaluating the recession flow.268 PERTANlKA VOL. 15 NO.3, 1992EVALUATION OF INFILTRATION IN FURROW IRRlGATION: RECESSION FLOWAPPENDIXliST OF SYMBOLSThe following conclusions were made fromthis study. The two-point advance-volume balancemethod of evaluating infiltration in continuousfurrow irrigation is confirmed to give a goodindication of infiltration together with theKostiakov Lewis equation. The method and theequation were used to derive the infiltration pa-rameters (from field data collected) required inthe modelling. These two details can be found inmost texts written on irrigation. This follows fromthe use of the infiltration characteristics so de-rived in the kinematic wave analysis of advance(Lee 1982) in which the simulation was solvedusing finite differences with a computer program,and now the recession phase which was separatelyderived but based on the same principles. Thekinematic wave analysis for furrow advance cansimilarly be pursued for the analysis of furrowrecession with the accompanying assumptions men-tioned previously.REFERENCESCUNGE, J.A. and D.A. WOOLHISER. 1975. Irrigation Sys-tems; Unsteady Flow In Open Channels. Vol II. ed.K. Mahmood and V. Ye\jevich. Fort Collins,Colorado: Water Resources Publications.ELLIOT, R.L. 1980. Compilation Of Furrow IrrigationField Evaluation Data. Fort Collins, Colorado:Colorado State University.LEE, S. 1982. Kinematic-wave Simulation Of FurrowAdvance And Recession. Master of Science InEngineering, Utah State University, Logan.WALKER, W.R. and A.S. HUMPHREYS. 1983. Kinematic-wave Furrow Irrigation Model. ASCE J Irrig.Drain. Div. 109 (IR4): 377-392.WALKER, W.R. and T.S. LEE. 1981. Kinematic-waveApproximation of Surged Furrow Advance.American Society Of Agriculture Engineers Pa-per 81-2544 ASAE Winter Meeting, Chicago.(Received 29 June 1992)foAQWPBYt,a, mcshoA'A*Q'Q*WP'WP*T't*X'X*basic infiltration or intake ratecross-sectional area of flowdischargewetted perimeter of flowsurface width of flowdepth of flowadvance timeparameter from A = 0"11'2parameter from WP = 'Y1y2distance of flowrecession timeconstants of stage discharge relation-shipslope of furrowMannings numbersoil infiltration parameterslength of furrowhydraulic radius or depthnumber count of characteristicssubscript of parameters at nodessubscript at shock wave advanceinlet flow depth at recessioncharacteristic area of flowdimensionless area of flowcharacteristic dischargedimensionless dischargecharacteristic wetted perimeterdimensionless wetted perimetercharacteristic timedimensionless timecharacteristic distancedimensionless distance of flowPERTANIKA VOL. 15 NO.3, 1992 269

Evaluation of Infiltration in Furrow Irrigation

Part 1: Recession Flow

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Evaluation of Infiltration in Furrow Irrigation Part 1: Recession Flow

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