Roughness Coefficients for Selected Residue Materials

Transcription

1 University of Nersk - Linoln DigitlCommons@University of Nersk - Linoln Biologil Systems Engineering: Ppers nd Pulitions Biologil Systems Engineering Roughness Coeffiients for Seleted Residue Mterils John E. Gilley University of Nersk-Linoln, john.gilley@rs.usd.gov Eugene R. Kottwitz University of Nersk-Linoln Gry A. Wiemn University of Nersk-Linoln Follow this nd dditionl works t: Prt of the Biologil Engineering Commons Gilley, John E.; Kottwitz, Eugene R.; nd Wiemn, Gry A., "Roughness Coeffiients for Seleted Residue Mterils" (1991). Biologil Systems Engineering: Ppers nd Pulitions This Artile is rought to you for free nd open ess y the Biologil Systems Engineering t DigitlCommons@University of Nersk - Linoln. It hs een epted for inlusion in Biologil Systems Engineering: Ppers nd Pulitions y n uthorized dministrtor of DigitlCommons@University of Nersk - Linoln.

2 ROUGHNESS COEFFICIENTS FOR SELECTED RESIDUE MATERIALS By John E. Gilley, 1 Eugene R. Kottwitz, 2 nd Gry A. Wiemn 3 ABSTRACT: Anlysis of surfe runoff on uplnd res requires identifition of roughness oeffiients. A lortory study is onduted to mesure Dry-Weish nd Mnning roughness oeffiients for orn, otton, penut, pine needles, sorghum, soyens, sunflower, nd whet residue. Vrying rtes of flow re introdued into flume in whih seleted mounts of residue re seurely tthed. Roughness oeffiients re lulted from mesurements of dishrge rte nd flow veloity. The lortory dt re used to derive regression equtions for relting roughness oeffiients to Reynolds numer nd either perent residue over or residue rte. Seprte equtions re developed for Reynolds numer vlues from 500 to 20,000, nd from 20,000 to 110,000. Generlized equtions re presented for estimting roughness oeffiients for other residue mterils not used in this investigtion. Aurte predition of roughness oeffiients for residue mterils will improve our ility to understnd nd properly model uplnd flow hydrulis. INTRODUCTION Anlysis of surfe runoff on uplnd res requires identifition of hydruli roughness oeffiients. Roughness oeffiients re used in the lultion of flow veloity nd the routing of runoff hydrogrphs. The ility to understnd nd properly model uplnd flow hydrulis is lso essentil in the development of proess-sed erosion models. On griulturl res, resistne to flow my e used y fritionl drg over the soil surfe, stnding vegettive mteril, residue over nd roks lying on the surfe, rindrop impt, nd other ftors. Eh of these elements my ontriute to totl hydruli resistne. Conservtion tillge systems hve een developed tht rely hevily on surfe rop residues s primry mens of ontrolling runoff nd soil erosion. The effets of rindrop impt on flow resistne over smooth surfe were exmined y Shen nd Li (1973). A set of regression equtions were presented to desrie vritions in Dry-Weish frition ftors with rinfll intensity nd Reynolds numer. Gilley et l. (1990) mesured hydruli hrteristis of rills t 11 sites loted throughout the estern United Sttes. Regression equtions were developed tht relted Dry-Weish nd Mnning roughness oeffiients to Reynolds numer. A omprehensive desription of previous studies involving roughness oeffiients on griulturl nd nturl res ws provided y Engmn (1986). Hydruli roughness oeffiients were developed from runoff plot dt originlly olleted for erosion studies. Frition ftors were presented in tulr formt with desription of vrious surfes nd lnd uses. 'Agri. Engr., USDA-ARS, Univ. of Nersk, Linoln, NE Res. Engr., Dept. of Biologil Systems Engrg., Univ. of Nersk, Linoln, NE. 3 Res. Engr., Dept. of Biologil Systems Engrg., Univ. of Nersk, Linoln, NE. Note. Disussion open until Jnury 1, To extend the losing dte one month, written request must e filed with the ASCE Mnger of Journls. The mnusript for this pper ws sumitted for review nd possile pulition on August 9, This pper is prt of the Journl of Irrigtion nd Dringe Engineering, Vol. 117, No. 4, July/August, ASCE, ISSN /91/ /$ $.15 per pge. Pper No

3 Liong et l. (1989) developed simple method for ssigning Mnning roughness oeffiients to overlnd flow segments in kinemti wve models. The proposed method ws found to work well on gged sin. This proedure my e useful in estimting hydrogrphs for ungged wtersheds. Lortory mesurements of roughness oeffiients on surfes overed with snd or grvel were onduted y Woo nd Brter (1961), Emmett (1970), Phelps (1975), nd Svt (1980). Similr tests were performed under field onditions on nturl lndspes y Dunne nd Dietrih (1980), Roels (1984), nd Arhms et l. (1986). In most of these studies, roughness oeffiients deresed with inresing Reynolds numer. One roughness elements re sumerged, their ility to retrd overlnd flow is redued s the depth of overlnd flow eomes greter. A similr redution in roughness oeffiients with inresing Reynolds numer would e expeted for residue mterils. The quntity of rop mteril found on the soil surfe is usully gretest following hrvest. After hrvest, residue mteril is sujeted to deomposition. Tillge serves to inorporte the residue mteril into the soil nd thus redues surfe over. Proedures re ville for estimting the redution in surfe over used y tillge (Colvin et l. 1986). Crop residues found on the soil surfe re usully identified on perentover or residue-rte sis. Surfe over n e rpidly nd urtely mesured in the field. Crop growth models typilly provide estimtes of vegettive dry mtter prodution. Residue rte my lso e mesured y removing nd drying the vegettive mteril olleted from representtive re. The ojetive of this investigtion ws to develop regression equtions for estimting roughness oeffiients for seleted residue mterils. Reltionships re identified for prediting oth Dry-Weish nd Mnning roughness oeffiients. These equtions use Reynolds numer nd either perent over or residue rte s independent vriles. HYDRAULIC EQUATIONS The Dry-Weish nd Mnning equtions hve een widely used to desrie flow hrteristis. Both of these reltions ontin roughness oeffiient. Under uniform flow onditions, the Dry-Weish roughness oeffiient, /, is given s (Chow 1959) 8gRS f ^ (1) where g elertion due to grvity; S verge slope; V flow veloity; nd hydruli rdius, R, is defined s A R ~ p») where A ross-setionl flow re; nd P wetted perimeter. For retngulr flume with flow width y R + 2y 504

4 where y flow depth. For overlnd flow onditions where flow width is muh greter thn flow depth, hydruli rdius n e ssumed to e pproximtely equl to flow depth. The Mnning roughness oeffiient, n, is given s R 2/3 S 1/2 n V Mnning nd Dry-Weish roughness oeffiients n e relted using the following eqution 1/2 Reynolds numer is lso used to desrie flow hrteristis. Reynolds numer, R, is given s VR R (6) v where v kinemti visosity, whih n e determined diretly from wter temperture. The ontinuity eqution for flow is defined s Q VA (7) where Q flow rte. For retngulr flume, wter depth is given s Q y (8) V In this study, wter depth ws determined indiretly using (8), nd mesurements of Q, V, nd. EXPERIMENTAL PROCEDURES The types of residue used in this study inluded orn, otton, penut, pine needles, sorghum, soyens, sunflower, nd whet. Needles produed y ponderos pine were inluded to otin n estimte of roughness oeffiients on forested res. After the residue mterils hd een removed from the field, they were pled in n oven nd dried. For eh residue type, 10 seprte residue elements were seleted for mesurement of residue dimensions. Men residue dimeter nd length re shown in Tle 1. A mesured mss of residue mteril ws glued in rndom orienttion onto setion of reinfored fierglss sheeting. For eh residue type, five residue rtes were seleted. All of the residue mterils exept pine needles nd whet were pplied t rtes equivlent to 2, 4, 6, 8, nd 10 metri tons/ h. Rtes equivlent to 0.75, 2, 4, 6, nd 8 metri tons/h were used for pine needles, while whet strw ws pplied t rtes equivlent to 0.25, 0.50, 1, 2, nd 4 metri tons/h. Sine pine needle nd whet residue elements hd smller dimeters thn the other residue mterils, they furnished greter surfe over t given residue rte. The perentge of surfe over provided t given residue rte ws o- 505

5 TABLE 1. Dimeter, Length, Residue Rts, nd Surfe Cover of Vegettive Mterils Residue type (D Com Dimeter (m) Length (m) Residue rte (metri tons/h) Surfe over (%) ; ' tined using photogrphi grid proedure (Lflen et l. 1978). Residue overs on the fierglss sheets were photogrphed using 35-mm olor slide film. The slides were projeted onto sreen on whih grid hd een superimposed. The numer of grid intersetions over residue mteril ws determined visully from the projeted slides nd surfe over ws then lulted. For eh residue rte, six mesurements of surfe over were otined. The rnge in surfe over vlues for eh residue type is shown in Tle 1. The fierglss sheets with the tthed residue were pled in flume 0.91-m wide, 7.31-m long, nd m deep. The slope grdient of the flume ws mintined t 1.35%. Wter ws supplied to the flume using onstnt hed tnk. Two replited tests were run t 15 flow rtes rnging from 5.24 X 10~ 4 to 1.01 X 10-1 m 3 /s. Flow rte ws determined immeditely efore nd fter eh test to ensure stedy stte onditions. Wter temperture ws mesured following flow rte determintions. Reynolds numer vlues vried from pproximtely 500 to 110,000. It ws diffiult to mintin uniform flow onditions on the residue overed surfes for Reynolds numers less thn pproximtely 500. The flow pity of the flume would hve een exeeded for Reynolds numer vlues signifintly greter thn 110,000. One stedy stte runoff onditions hd eome estlished, line soures of fluoresent dye were injeted ross the flume t downslope distnes of 0.91 m nd 7.01 m. A fluorometer ws used to determine time of trvel of the dye onentrtion peks. Men flow veloity ws identified y dividing the distne etween the two line soures of dye (6.10 m) y the differene in trvel time etween the two dye onentrtion peks. Pek onentrtion ws used euse the dye onentrtion time urves were symmetri. For eh test sequene, three mesurements of flow veloity were mde. Roughness oeffiients for the fierglss sheets on whih the residue mterils were pled were lso identified. The experimentl proedures used to mesure roughness oeffiients for the fierglss sheets with nd without residue were identil. Roughness oeffiients indued y the re fierglss sheets t given Reynolds numer were sutrted from mesurements otined with tthed residue to determine hydruli resistne used y the residue mterils lone. 506

6 RESULTS AND ANALYSIS Surfe-over-residue-rte reltionships otined using regression nlysis re given herein. Equtions for estimting Dry-Weish nd Mnning roughness oeffiients for the residue mterils re lso provided. Finlly, proedures for prediting roughness oeffiients for residue mterils not inluded in this study re presented. Surfe Cover Residue Rte Conversion Both surfe over nd residue rte re used to hrterize the mount of vegettive mteril found on the soil surfe. It my sometimes e neessry to mke onversions etween surfe over nd residue rte for prtiulr vegettive mteril. Regression equtions for mking these onversions re shown in Tle 2. Surfe over nd residue rte vlues used to derive the regression equtions re presented in Tle 1. The rnge in surfe over nd residue rte vlues vried onsiderly etween residue mterils. The regression reltionships shown in Tle 2 should not e used for vlues of surfe over or residue rte outside of the rnge for whih they were derived. Dry-Weish Roughness Coeffiients Dry-Weish roughness oeffiients t vrying Reynolds numers for seleted rtes of whet residue re shown in Fig. 1. The trends presented in Fig. 1 re hrteristi not only of whet residue ut lso the other vegettive mterils used in this investigtion. It n e seen in Fig. 1 tht for given residue rte, the Dry-Weish frition ftor onsistently deresed s Reynolds numer inresed for Reynolds numers less thn pproximtely 20,000. Other investigtors hve otined similr results for sndovered surfes. The vrition in Dry-Weish roughness oeffiient with Reynolds numer ws muh less pronouned for Reynolds numers greter thn 20,000. Surfe over vlues of pproximtely 70%, 79%, nd 99% were provided y whet residue t rtes of 1, 2, nd 4 metri tons/h, respetively. These three whet residue rtes produed similr roughness oeffiients for Reynolds numers greter thn 20,000. TABLE 2. Regression Equtions for Surfe Cover versus Residue Rte Residue type (1) Regression oeffiient," Coeffiient of determintion, r "Regression oeffiient is used in eqution: surfe over 100 (1 e res,du,i ""), where surfe over is given s perentge nd residue rte is in metri tons per hetre. 507

7 CD 'g is CD O,0 CO o CD x: D) g 1 EC % CO U 4.00 Vh B B 2.00 l/h A A 1.00 Mi e e o.so wi l/h CO Q ,000 10,000 Reynolds Numer 100,000 FIG. 1. Dry-Weish Roughness Coeffiients s Funtion of Reynolds Numer for Seleted Rtes of Residue When developing regression reltionships for the dt presented in Fig. 1, seprte equtions were derived for Reynolds numers less thn nd greter thn 20,000. Regression equtions for Dry-Weish roughness oeffiient versus perent over nd Reynolds numer re presented in Tles 3 nd 4 for Reynolds numers less thn nd greter thn 20,000, respetively. For Reynolds numers less thn 20,000 (Tle 3), generlized eqution ws omputed using dt from ll of the residue types. Regression equtions for Dry-Weish roughness oeffiient versus TABLE 3. Regression Equtions for Dry-Weish Roughness Coeffiient versus Perent Cover nd Reynolds Numer for Reynolds Numer Less thn 20,000 Residue type (1) All residue types omined 6.30 x 10" x 1CT x 10" x 1(T x x 10' x 10 _1 Reg ession Coeffiients x 10~' x 10" x 10" x KT x 10" x KT x 10" x 10" x 10~' 3.88 x 10~' Coeffiient of determintion, r "Regression oeffiients,, nd <; used in eqution: / (perent over) /(Reynolds numer)'. 508

8 TABLE 4. Regression Equtions for Dry-Weish Roughness Coeffiient versus Perent Cover nd Reynolds Numer for Reynolds Numer Greter thn 20,000 Residue type 0) 1.23 x 10~ x 10" x 10" x 1CT x 10" x 10" x 1CT x 10" 4 Regression Coeffiients' x 10~' x 10~' 1.44 x 10" x 10" x 10 _ x 10" X 10" x 10~' 1.45 x 10"' Coeffiient of determintion, r "Regression oeffiients,, nd used in eqution:/ (Perent over) 6 /(Reynolds numer)'. residue rte nd Reynolds numer re reported in Tles 5 nd 6 for Reynolds numers less thn nd greter thn 20,000, respetively. Mesurements otined from the vrious residue mterils were omined (Tle 6) to develop generlized eqution for use with vlues of Reynolds numer greter thn 20,000. In the generlized eqution, the Dry-Weish roughness oeffiient n e seen to vry with residue rte in nerly liner fshion. Mnning Roughness Coeffiients Fig. 2 presents Mnning roughness oeffiients s funtion of Reynolds numer for seleted rtes of whet residue. As required y, the shpes of the urves shown in Figs. 1 nd 2 re very similr. The hrteristi redution in roughness oeffiient with inresing Reynolds numer for Reynolds numer vlues less thn 20,000 is evident in Fig. 2. TABLE 5. Regression Equtions for Dry-Weish Roughness Coeffiient versus Residue Rte nd Reynolds Numer for Reynolds Numer Less thn 20,000 Residue type (1) 4.60 x x 10 _l 1.01 x x x x x x Regression Coeffiients" x 10~' X 10"' x 10"' 9.91 x x 10"' 7.89 x 10~ x 10"' 7.10 x 10"' 5.60 x 10"' x 10"' 6.80 x 10"' Coeffiient of determintion, r "Regression oeffiients, >, nd used in eqution: / (residue rte)v(reynolds numer)' where residue rte is in metri tons per hetre. 509

9 TABLE 6. Regression Equtions for Dry-Wsish Roughness Coeffiient versus Residue Rte nd Reynolds Numer for Reynolds Numer Greter thn 20,000 Residue type (1) All residue types omined 1.80 x ,62 x 10"' x 10-' x 10~' 2.84 Regression Coeffiients" x 10' x 10' 'Regression oeffiients,, nd used in eqution: / : numer)" where residue rte is in metri tons per hetre X 10 ' 1.39 X 10"' 2.33 X 10"' 2.89 X 10"' 5.30 X 10" X X 10"' 3.35 x 10~ x 10~ x Coeffiient of determintion; r (residue rte)v(reynolds Seprte equtions for estimting Mnning roughness oeffiients were developed for Reynolds numers less thn nd greter thn 20,000. Tles 7 nd 8 present equtions used for prediting Mnning roughness oeffiients using perent over nd Reynolds numer s independent vriles. Using dt from ll of the residue types, generlized eqution ws derived for estimting roughness oeffiients for Reynolds numers less thn 20,000 (Tle 7). 0) o it <D O o 0) 0) 0) s: O) o e D) C ' to Mi G D 2.00 t/h A A 1.00t/h o s 0.50 t/h 0.25 t/h 1,000 10,000 Reynolds Numer 100,000 FIG. 2. Mnning Roughness Coeffiients s Funtion of Reynolds Numer for Seleted Rtes of Residue 510

10 TABLE 7. Regression Equtions for Mnning Roughness Coeffiient versus Perent Cover nd Reynolds Numer for Reynolds Numer Less thn 20,000 Residue type (1) All residue types omined 4.96 x x 10" x 10-' 5.39 x 10" x 10-' 4.51 x 10"' 4.13 x 10"' 2.07 x 10-' 1.89 x 10' Reg ession Coeffiients" 8.92 x 10-' 6.78 x 10~' 7.03 X 10-' X 10-' 9.13 x 10"' 4.39 X 10-' x 10-' 3.11 X 10" x x 10"' 1.92 X 10-' 1.98 x 10-' 3.58 X 10"' 8.93 x 10' 3.02 x 10"' 1.42 x 10"' Coeffiient of determintion, r' "Regression oeffiients,, nd used in eqution: n (perent over) 6 /(Reynolds numer) 0. As n e seen in Fig. 2, very little hnge in Mnning roughness oeffiients ourred for Reynolds numer vlues greter thn 20,000. For some of the residue mterils, smll inrese in hydruli resistne ourred with inresing Reynolds numer for Reynolds numers ove 20,000. This is further demonstrted y the negtive oeffiients shown for seleted residue mterils in Tle 8. The phenomenon of greter roughness oeffiient with inresing Reynolds numer for very rough surfes ws disussed y Morris (1963). Mnning roughness oeffiients n e estimted from vlues of residue rte for Reynolds numers less thn nd greter thn 20,000 using Tles 9 nd 10, respetively. Agin, s evidened y the negtive oeffiients in Tle 10, smll inreses in roughness oeffiients s Reynolds numer eme lrger were found for some residue mterils t Reynolds numers TABLE 8. Regression Equtions for Mnning Roughness Coeffiient versus Perent Cover nd Reynolds Numer for Reynolds Numer Greter thn 20,000 Residue type (1) Com 5.19 x 10" X 10" X X IO" X 10" x 'X 10" X 10" 4 Regression Coeffiients x 10"' 4.11 x 10"' x 10"' 9.61 x 10"' 8.58 x 10-' x x x 3.11 x 1.89 x 5.10 x 3.30 x x 10"' io-' 10"' 10" 3 io-' 10" 2 10"' 10' Coeffiient of determintion, r "Regression oeffiients,, nd used in eqution: n (perent over) k /(Reynolds numer)". 511

11 Wl TABLE 9. Regression Equtions for Mnning Roughness Coeffiient versus Residue Rte nd Reynolds Numer for Reynolds Numer Less thn 20,000 Residue type (D Com 5.18 x IO x 10~ x 10-' 2.00 x 10"' 2.60 x 10"' 7.25 x 10-' 1.24 x 10"' 1.13 Regression Coeffiients x 10' 6.26 x 10~' 6.83 x 10~' 5.02 x 10 M 4.22 x 10~' 5.97 x KT x 10-' 4.96 x 10-' 2.37 X 10~ X 10~ X 10-' 1.83 X 10"' 1.98 X 10"' 3.59 X 10-' 1.02 X 10"' 3.36 X 10-' Coeffiient of determintion, r 2 ; "Regression oeffiients,, nd used in eqution: n (residue rte)*/(reynolds numer) where residue rte is in metri tons per hetre. ove 20,000. For Reynolds numers greter thn 20,000, generlized eqution ws otined for estimting Mnning roughness oeffiients (Tle 10). Use of Regression Equtions If roughness oeffiients re required for other vegettive mterils, the residue type used in this study most similr to the mteril under onsidertion should e identified. Estimtes of resistne ftors n then e mde using the previously identified equtions. The generlized reltionships n lso e used to predit roughness oeffiients for other vegettive mterils. When using the generlized reltionships, the physil hrteristis of the mteril under onsidertion should e similr to those used in this investigtion (Tle 1). TABLE 10. Regression Equtions for Mnning Roughness Coeffiient versus Residue Rte nd Reynolds Numer for Reynolds Numer Greter thn 20,000 Residue type (D All residue types omined 1.21 x 10"' 1.61 X 10"" x 10" x IO' x 10-' 3.00 x IO' x x X KT 2 Reg ression Coeffiients x 10-' 6.61 x 10"' 4.87 x 10-' 5.72 x 10"' 6.81 x 10-' 5.92 x 10"' 7.37 x 10-' 4.57 x 10"' 5.73 X 10"' 1.74 x x x 6.27 x 1.90 x 4.55 x 1.17 x x 6.44 x io-' 10" 2 io- 3 10" 2 io-' 10" 2 io-' IO" 3 IO" 2 Coeffiient of determintion, r "Regression oeffiients,, nd used in eqution: n (residue rte)''/(reynolds numer)" where residue rte is in metri tons per hetre. 512

12 Residue mterils used in this study were glued in ple during the experimentl tests. Under nturl onditions, the residue mterils my move t higher flow rtes using sustntil hnges in flow resistne. At present, the sher stress required to initite movement of residue mterils is not well defined. SUMMARY AND CONCLUSIONS Anlysis of surfe runoff on uplnd res requires identifition of hydruli roughness oeffiients. Totl hydruli resistne t site my e omposite of roughness omponents used y severl ftors. In this investigtion, roughness oeffiients were identified for seleted residue mterils. Experimentl vriles used in this study inluded residue type, residue rte, nd flow rte. Seleted rtes of orn, otton, penut, pine needles, sorghum, soyens, sunflower, nd whet residue were glued in rndom orienttion on setions of reinfored fierglss sheeting. Mesurements of residue surfe over were mde, nd the fierglss sheets were pled in flume. Stedy uniform flow onditions were then estlished for wide rnge of dishrge rtes. Dry-Weish nd Mnning roughness oeffiients were lulted from mesurements of dishrge rte nd flow veloity. Regression reltionships were developed, whih relted the roughness oeffiients to Reynolds numer nd either perent residue over or residue rte. Both surfe over nd residue rte re frequently used to desrie the mount of vegettive mteril found on soil surfe. Generlized equtions for prediting roughness oeffiients for other types of residue mteril re lso presented. Severl ftors my ontriute to hydruli resistne on uplnd res. Informtion is needed on roughness oeffiients provided y eh of these ftors, their ontriution to totl hydruli roughness, nd the effet of flow rte on roughness oeffiients. This informtion will improve our ility to understnd nd urtely model uplnd flow hydrulis. ACKNOWLEDGMENT This pper is ontriution from USDA-ARS, in oopertion with the Agriulturl Reserh Division, University of Nersk, Linoln, nd is pulished s Journl Series No APPENDIX I. REFERENCES Arhms, A. D., Prsons, A. J., Luk, S. H. (1986). "Resistne to overlnd flow on desert hillslopes." J. Hydro., 88, Chow, V. T. (1959). Open hnnel hydrulis. MGrw Hill, New York, N.Y. Colvin, T. S., Berry, E. C, Erh, D. C, nd Lflen, J. M. (1986). "Tillge implement effets on orn nd soyen residue." Trns. Am. So. Agri. Engrs., Amerin Soiety of Agriulturl Engineers, 29(1), Dunne, T., nd Dietrih, W. E. (1980). "Experimentl study of Horton overlnd flow on tropil hillslopes. 2. Hydruli hrteristis nd hillslope hydrogrphs." Z. Geomphol. Suppl. Bnd., 35, Emmett, W. W. (1970). "The hydrulis of overlnd flow on hillslopes." U.S. Geologil Survey Prof. Pper 662-A, U.S. Govt. Printing Offie, Wshington, D.C. 513

13 Engmn, E. T. (1986). "Roughness oeffiients for routing surfe runoff." /. Irrig. Drin. Engrg., ASCE, 112(1), Gilley, J. E., Kottwitz, E. R., nd Simnton, J. R. (1990). "Hydruli hrteristis of rills." Trns. Am. So. Agri. Engrs., Amerin Soiety of Agriulturl Engineers, 33(6), Lflen, J. M, Bker, J. L., Hrtwig, R. O., Buhele, W. F., nd Johnson, H. P. (1978). "Soil nd wter loss from ontinuous row ropping." Trns. Am. So. Agri. Engrs., Amerin Soiety of Agriulturl Engineers, 21, Liong, S. Y., Selvlingm, S., nd Brdy, D. K. (1989). "Roughness vlues for overlnd flow in suthments." J. Irrig. Drin. Engrg., ASCE, 115, Morris, H. M. (1963). Applied hydrulis in engineering. Ronld Press, New York, N.Y. Phelps, H. O. (1975). "Shllow lminr flows over rough grnulr surfes." J. Hydr. Div., ASCE, 101, Roels, J. M. (1984). "Flow resistne in onentrted overlnd flow on rough slope surfes." Erth Surfe Proesses nd Lndforms, 9, Svt, J. (1980). "Resistne to flow in rough superritil sheet flow." Erth Surfe Proesses nd Lndforms, 5, Shen, W. S., nd Li, R. H. (1973). "Rinfll effet on sheet flow over smooth surfe." J. Hydr. Div., ASCE, 99, Woo, D. C, nd Brter, E. F. (1961). "Lminr flow in rough retngulr hnnels." J. Geophys. Res., 66(12), APPENDIX II. The following NOTATION symols re used in this pper: A f g n P Q R R S V y V ross-setionl flow re; flow width; Dry-Weish roughness oeffiient; elertion due to grvity; Mnning roughness oeffiient; wetted perimeter; flow rte; hydruli rdius; Reynolds numer; verge slope; flow veloity; flow depth; nd kinemti visosity. 514