Pertanika J. Sci. & Techno!' 1(1): 119-124 (1993)ISSN: 0128-7680

© Universiti Pertanian Malaysia Press

Evaluation of Infiltration in Furrow Irrigation ­Part 2 : Basic Infiltration Rate

T.S. Lee l and W.R. WalkerJDepartment of Field Engineering,

Faculty of Engineering,Universiti Pertanian Malaysia,

Serdang, 43400 UPM Selangor Selangor Darul Ehsan, Malaysia2Department of Inigation Engineering,

College of Engineering, Utah State University,Logan, Utah, USA 84322

Received 24 June 1992

ABSTRAKKomplikasi penentuan penyusupan didalam satu saluran furrow disebabkan ciridinamik pengaliran air dan juga bentuk geometri saluran disamping fakturfaktur lain. Penilaian penyusupan dalam sebuah furrow adalah penting demiuntuk menilaikan penggunaan air dalam sistem sistem pengairan. Kegunaanpersamaan Kostiakov dalam bentuk dipanjangkan dicadangkan untukmenentukan ciri ciri penyusupan dalam furrow. Akan tetapi, persamaan initertakluk kepada penilaian kadar penyusupan asas masa panjang, dimana ianyahanya ditentukan secara praktik melalui gerafhidro masuk keluar peristiwapengairan yang susah dan memakan masa. Satu kaedah analisis yang berdasarkanteori gelombang kinematik dan data data aliran susupan dicadangkan untukmenilaikan kadar penyusupan asas yang penting untuk penentuan betul ciriciri penyusupan aliran furrow.

ABSTRACTPart 1 of this title was the simulation of the recession flow in a furrow. This partuses the recession simulation further to establish the basic infiltration rate ina furrow and, therefore, the infiltration characteristics in a furrow. Determininginfiltration in a furrow is complicated by the dynamic flow nature of irrigationwater, as well as the geometric shape of the channel, among other factors. Theevaluation of this infiltration in furrows is important in order to evaluate thewater use in such irrigation systems. The use of the Kostiakov equation in itsextended form has been suggested for the determination of infiltration char­acteristics in a furrow. This equation, however, depends on the evaluation ofthe long-term basic infiltration rate, which can be determined practically by along-term tedious inflow/outflow hydrograph of the irrigation event. An ana­lytical method based on the kinematic wave theory and recession flow data isproposed here to evaluate the long-term basic infiltration rate pertinent to thecorrect evaluation of the infiltration flow characteristics in a furrow.

Keywords: Furrow, infiltration, recession flow

INTRODUCTION

The objective of this paper is to derive the analytical procedure todetermine the basic infiltration rate in a furrow using field recession data.

T.S. Lee & W.R. Walker

The difficulty in associating a descriptive and simple relationship for soilwater intake has been expressed and reiterated by many researchers. Manyequations have been proposed, each taking into account the variousconditions of the experiments. The difficulty in describing soil waterintake is further compounded by the variable nature of the infiltrationcharacteristics in both spatial and temporal dimensions.

Existing practical methods such as the single- and double-ringinfiltrometers, blocked ponding for furrows, etc. have not only resulted inan unsatisfactory simulation of actual furrow infiltration but they are alsotime-consuming and costly. Most of the existing methods of evaluatinginfiltration consider stationary ponded water, whereas in furrow irrigationthe infiltration characteristics are greatly influenced by the dynamic natureof flow, as well as the geometric shape of the furrow. With this considera­tion, Elliott and Walker (1982) investigated the extended form of theKostiakov equation and suggested that the value of f

o' the long-term basic

infiltration rate, can be determined independently of the time-dependentterms. The method is known as the inflow/outflow method. Anothermethod involves utilizing data from blocked furrow tests. However, thismethod gives results whose magnitudes fluctuate too much. The othermethod of estimating f

ois based on referring to published values for the

type of soil under consideration. The equation is the best solution forevaluating infiltration characteristics of the soil in furrows. In order todetrmine the soil constants of the equation, Christiansen et al. (1966)assumed a volume balance technique, which incorporates shape factors forthe surface and subsurface flow profiles. Ley (1978) used an optimalsearch technique to determine the value of f

oin which advance rate and

infiltrated volume were matched.Now, the best method (Walker and Skogerboe 1987) is to use the

extended Kostiakov equation and the two-point advance method coupledwith a volume balance analysis. With this approach the advance flowtrajectory was predicted through the use of the kinematic wave theoryapproach (Lee 1982). However, further use of this method can enable theexploitation of the recession flow data to be used to investigate the long­term basic infiltration rate as follows. This term is pertinent to theevaluation of the soil constants of the equation.

MATHEMATICAL DEVELOPMENT

Since the analytical solution of the recession flow in Part 1 of this paperis based on a value of constant basic infiltration rate f it offers anapproximation method to determine the optimal value of this parameter.Equations 21 and 25 in Part 1 were derived to determined the recessiontimes and the inlet flow depths during recession flow respectively (see Fig.

120 PertanikaJ. Sci. & Techno!. Vol. 1 No.1, 1993

Evaluation of Infiltration in Furrow Irrigation

2 in Part 1). These equations are repeated here respectively in Equations1 and 2 for convenience.

(1)

and

(2)

The characteristic recession time T' was defined as equal to R If ando 0

the characteristic recession's "advance" was defined as

QO.06T'X'= ----

RA(~)

Yo

(3)

where Q is in litres per second, T' in minutes and X' in metres.Since t *= t IT' and x* = xiX' where t and x are the time and location

r r r

of the trailing end of recession respectively, T' and X' can be solved forwith these four equations. Thus solving for a given field recorded (x, t)coordinate, we have

(4)

Rearranging and with further simplification,

cr -y_2_2

m+ 1-"

(5)

Pertanika 1. Sci. & Techno!. Vo!. 1 No.1, 1993 121

T.S. Lee & W.R. Walker

a -y2 2 I

m+l y 0' Y2_2_2-1

m+ 1-y 2

(6)

From field data (tr, x) and using equations for T', its value can be

evaluated and subsequently with T'=RJfo

' we can solve for fo

' An averagef

ocan be derived from a few sets of field data points.

RESULTS AND CONCLUSIONSFrom the actual field data (Elliott 1980) two sets of irrigation data arepresented as shown in Fig. 1 and 2 (Printz farm, Colorado) to illustrate therecession predicted f

ovalue compared with the measured f

ovalue. It is to

be noted that the values of the soil infiltration parameters k and a aredifferent for both cases of the recession predicted f and the measured f .o 0

This is due to the fact that these values are calculated from the two pointadvance volume balance approach (see part 1) once the field advance dataand the values of f

oare obtained. As can be seen from the prediction of

the advance (the advance simulation is shown here in passing, to illustratethe results of its simulation, on which its derivation principles are used forthis recession simulation) and recession trajectories, the simulation ismore exact when we use the fo values calculated by the analytical method.

240

200O'iz~

'"~ 160

~zo~ 120

~UJU~ 80

~;::

40

o Field Data

-- Time of cutoff

flodel---

k 0.014 m/mina

a -.059fo 0.00024 m/min

(measured}

Recess i on Curve

Advance Curve

Model--

Q 2.328 lpsSo 0.0025 10/10

n 0.02k 0.005 m/min a

a 0.35f o 0.0001 m/min

D'1 0.9196

D'2 1.4794

1, 1.6478

l2 0.5029

L 350 10

o~'----::--_L-_---L:------:.!---.L __.l.-_---::L _o 50 1DO 150 200 250 300 350

DISTANCE FROM RJRROW INLET (METRES)

Fig. 1. Predicted and observed furrow recession and advance using an approximated J. forirrigation event P 8-2-1, Colorado. [Field data source: Elliott 1980]

122 Pertanika J. Sci. & Techno!. Vol. 1 No.1, 1993

Evaluation of Infiltration in Furrow Irrigation

240

o Field Oata Model--

200

~6o~ 160

~z

~ 120

~

Q 2.328 lpsSo 0.0025 mlm

~ ~:~~5 m/mina

a 0.35f o 0.0001 m/min

0; 0.9196

iT2 1.4794

11 1.6478

12 0.502~

L 350 m

Recession Curve

-.!? -- -

Advance Curve

.~

~lodel--­

k 0.014 m/mina

a - .059f 0.00024 mImi no (measured)

"=-""""-- Time of cutoff

40

80OJU

~

°OJ=:::::'--:5'::-O---10'::-O---1'--SO----:-20.....0---:2:':'50:---3.LOO---3.::l:50-------­

DISTANCE FROM RJRROW lNLEf (ME1RES)

Fig. 2. Predicted and obselVed furrow advance and recession using an apfrroximated 1. fori17igation event P 3-2-5, ColO1·ado. (Field data source: Elliott 1980J

The recession time and distance data in a furrow irrigation event canbe used to evaluate the basic infiltration rate. Hence, the evaluation of thesoil infiltration parameters can be done without having to tediouslymeasure the inflow-outflow hydrographs during irrigation. With the evalu­ation of the basic infiltration rate, the two point advance and volumeapproach for the furrow can be used to determine its infiltration param­eters.

REFERENCESCHRISTlA 'SEN,J.E., A.A. BtSHOP, E.W. KIUERJR. and Y.S. FOK. 1966. Evaluation of intake rate

constants as related to advance of water in surface irrigation. Trans. A mer. Soc. CivilEngin. 9(5): 671-674.

ELLIOTT, R.L. 1980. Compilation of Furrow Irrigation Field Evaluation Data. Fort Collins,Colorado: Colorado State University.

ELLIOTT, R.L. and W.R.WALKER 1982. Field evaluation of furrow infiltration and advancefunctions. Trans. A mer. Soc. Agric. Engin. Paper No. 80-2075.

LEE T.S. 1982. Kinematic-wave simulation of furrow advance and recession. Master ofScience in Engineering Thesis, Utah State University, Logan, Utah.

LEyT.W. 1978. Sensitivity offurrow irrigation performance to field and operation variables.Master of Science Thesis, Colorado State University, Fort Collins, Colorado.

WALKER, W.R. and G'v. SKOGERBOE. 1987. Suiface Irrigation: Theory and Practice. NewJersey:Prentice Hall.

Pertanika J. Sci. & Techno!. Vo!. I No.1, 1993 123

fo

A

QWPB

Yt

tr

a, mS

0

n

a,kLR

0

Jcsh

o

T'X'A'A*

Q'Q*V\7P'WP*

T'(

X'X*

124

T.S. Lee & W.R. Walker

APPENDIX - LIST OF SYMBOLS

basic infiltration or intake ratecross-sectional area of flowdischargewetted perimeter of flowsurface width of flowdepth of flowadvance timeparameters from A = (JS"2parameters from WP = r

j{2

distance of flowrecession timeconstants of stage discharge relationshipslope 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 timecharacteristic distancecharacteristic area of flowdimensionless area of flowcharacteristic dischargedimensionless dischargecharacteristic wetted perimeterdimensionless wetted perimetercharacteristic timedimensionless timecharacteristic distancedimensionless distance of flow

PertanikaJ. Sci. & Techno!. Vol. 1 No. I, 1993