Determination of Manning s Flow Resistance Coefficient for Rivers in Malaysia

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1 Determiatio of Maig s Flow Resistace Coefficiet for Rivers i Malaysia AHMAD BAKRI ABDUL GHAFFAR, Research Studet, School of Civil Egieerig, Uiversiti Sais Malaysia, Egieerig Campus, Seri Ampaga, 143 Nibog Tebal, Peag, Malaysia AMINUDDIN AB. GHANI, Deputy Director, River Egieerig ad Urba Draiage Research Cetre (REDAC), Uiversiti Sais Malaysia, Egieerig Campus, Seri Ampaga, 143 Nibog Tebal, Peag, Malaysia NOR AZAZI ZAKARIA, Director, REDAC, Uiversiti Sais Malaysia, Egieerig Campus, Seri Ampaga, 143 Nibog Tebal, Peag, Malaysia ZORKEFLEE ABU HASAN, Seior Egieer, River Egieerig Sectio, Departmet of Irrigatio ad Draiage, Malaysia, Jala Sulta Salahuddi, 626 Kuala Lumpur, Malasysia CHANG CHUN KIAT, Research Officer, REDAC, Uiversiti Sais Malaysia, Egieerig Campus, Seri Ampaga, 143 Nibog Tebal, Peag, Malaysia ABSTRACT The procedure for selectig values of Maig s coefficiet () is subjective ad requires judgmet ad skill which are developed primarily through experiece. Govermet agecies ad private sectors i the developed coutries such as USA are still doig researches o predictig values for rivers. Sice flow ad boudary roughess vary with river coditios, the same type of research is therefore pertiet for rivers i Malaysia. Research to determie the Maig's value has bee started by REDAC sice 2 at the Kita River Basi. I view of the importace of predictig accurately the value, this type of research should be cotiued further. 1 Itroductio River egieerig is rather a ew field of study which has bee practiced quite recetly i Malaysia. This field of study ivolves the use of computer models to study flow i ope chaels. Most hydraulic computatios related to idirect estimates of discharge require a evaluatio of the roughess characteristic of the chael. For over a cetury, a umber of empirical equatios have bee formulated but the researches i this field have bee cotiued by the Govermet Agecies ad private sectors i the developed atio such as USA. Natural chael morphology depeds o the iteractio betwee fluid flow ad the erodible materials i the chael boudary. Velocity is strogly related to flow resistace, which is oe of the most importat elemets i the iteractio betwee fluid flow ad the chael boudary. The egieers have used a umber of flow resistace equatios ivolvig grai roughess, form roughess ad a combiatio of both, but the Maig s equatio has bee widely used iteratioally for predictig roughess values i atural chaels. This paper summarizes the recet results based o 14

2 field data collectio at several rivers i Malaysia. 2 Determiatio of Maig s Roughess Coefficiet, These are several available equatios to predict values of (Abdul Ghaffar, 3): Strickler (1923): = d 1/ 6 / 21.1 (2.1) Meyer-Peter & Muller (1948): 1/ = d 6 9 / 26 (2.2) Limerios (197): = (.113R 1/ 6 ) / ( log 1 {R/d }) (2.3) Bray (1979): 1/ 6 =.113y / ( log 1 {y o /d }) (2.4) Bruschi (198): = (d 1/ 6 / 12.38) (R S o / d ) 1/ 7. 3 (2.) Julie (2): =.62 d 1/ 6 (2.6) =.46 d 1/ 6 7 (2.7) =.38 d 1/ 6 9 (2.8) Evaluatio of these equatios for six cross sectios at Kita River Basi shows that oe of the equatios gives satisfactory predictio of the flow discharge (Figure 1). Further evaluatio was made usig the suggested values by Chow (199). The results as show i Figure 2 show that a uique value of is applicable for each cross sectio. river i Malaysia. These dimesioless variables are y o /d, R/d, B/y o, Dgr, Cv ad T j, where: y o d = Mea flow depth = Mea sedimet size R = Hydraulic radius B = River width Dgr = Dimesioless sedimet size Cv = Volumetric sedimet cocetratio 3 Developmet of New Equatios Several relatioships were obtaied to idetify dimesioless variable which are importat i determiig values of for Table 1 summarizes the resultig equatios. It is recommeded that the followig two equatios to be used for determiatio of i rivers i Malaysia. = 2E-8 (y o /d ) 2 3E- (y o /d ) +.11 (2.9) = 3E-8 (R/d ) 2 4E- (R/d ) +.37 (2.1)

3 Strickler Meyer-Peter & Muller Limerios Bray Bruschi Julie d Julie d Strickler Limerios Bruschi Pari Butog Meyer-Peter & Muller Bray Julie d Julie d Raia Kampug Tajug Strickler Limerios Bruschi Julie 7 Meyer-Peter & Muller Bray Julie d Julie d9 strickler Meyer-Peter & Muller Limerios Bray Bruschi Julie d Julie d Raia Batu Gajah 3 1 Kampar KM Strickler Meyer-Peter & Muller Limerios Bray Bruschi Julie d Julie d9 Strickler Meyer-Peter & Muller Limerios Bray Bruschi Julie d Julie d9 Figure 1 Evaluatio of Maig s Equatios Usig Equatios

4 Pari Butog 1 =. =.3 =.3 =.4 =.4 =. =. = =. =.3 =.3 =.4 =.4 =. =. = Raia Kampug Tajug 1 =. =.3 =.3 =.4 =. =.3 =.3 =.4 =.4 =. =. =.6 =.4 =. =. = Raia Batu Gajah 1 Kampar KM =. =.3 =.3 =.4 =.4 =. =. = =. =.3 =.3 =.4 =.4 =. =. =.6 Figure 2 Evaluatio of Maig s Equatio ( =..6). 17

5 =2E-8(y /d ) 2-3E-(y /d ) =3E-8(R/d ) 2-4E-(R/d ) R/d y /d Pari Butog Raia Tajug Village Kampar km 34 Pari Butog Raia Batu Gajah Raia Kg. Tajug Figure 3 Developmet of Equatio to determie the value of based o y o /d Figure 6 Developmet of Equatio to the value of based o R/d =-.11L(B/y ) =9E-7Dgr 2 -.1Dgr B/y. Dgr Pari Butog Pari Butog Raia Kg. Tajug Raia Kg. Tajug Figure 4 Developmet of Equatio to determie the value of based o B/y o. Figure 7 Developmet of Equatio to determie the value of based o Dgr =.e Cv Cv Pari Butog Raia Kg. Tajug 4 Coclusio For the iitial research, oly simple methods have bee used to determie the value of. The computed discharges are much bigger compared to the measured discharges by usig the existig equatios. So the use of ew equatios is recommeded because they ca predict the discharges satisfactorily. The discrepacy ratios obtaied are almost equal to oe. Figure Developmet of Equatio to determie the value of based o Cv. 18

6 Table 1 Developmet of Maig s Roughess Coefficiet for Kita River Basi. Idepedet Variables R 2 Referece to Figure Depedet Variables Equatio No. 2E-8(y o /d ) 2 3E-(y o /d ) E-8(R/d ) 2 4E-(R/d ) L (B/y o ) e Cv E-7 Dgr 2.1Dgr Ackowledgemets The research study is fuded by Departmet of Irrigatio ad Draiage Malaysia (JPS (PP)/SG/2/). The first author wishes to express his sicere gratitude ad thaks to Assoc. Prof. Dr. Amiuddi Ab. Ghai ad Assoc. Prof. Dr. Nor Azazi Zakaria for their help ad guidace i the completio of this paper. Notatio The followig symbols are used i this paper: A x-sectioal area B width of chael C Chezy s coefficiet C v Sedimet Cocetratio i ppm by volume d s Diameter of sedimet d, d 7, d 9 = d i = Size of particle itermediate axis for which i% of sample of bed material is fier Dgr Dimesioless grai size Fr Froude Number F Darcy-Weisbach frictio factor g Acceleratio due to gravity Κ Relative Roughess Maig s roughess coefficiet P Wetted Perimeter Q Discharge R Hydraulic Radius R 2 Square of correlatio coefficiet Re Reyold Number S Eergy Gradiet S o Chael Slope Ss Relative Desity of sad T j Total Load of Bed Materials t Time V Average Velocity of flow y o Depth of water ν kiematic viscocity ρ desity of water τ Shear stress µ dyamic viscosity Refereces 1. Bares, Jr., H. H. (1976). Roughess Characteristics of Natural Chaels. echaels/idex.html. Uiversity of Teessee, Koxville. 2. Bray, D. I. (1979). Estimatig Average Velocity i Gravel-bed Rivers. Joural Hydraul. Div., America Society of Egieers, (HY9), pp Bruschi, J. (198). Discussio o Browlie (1983): Flow Depth i Sadbed Chaels. Joural Hydraulic Egieerig ASCE, Vol. 111: pp

7 4. Chow, V. T. (199). Ope Chael Hydraulics. Mc-Graw-Hill, Sigapore.. Griffiths, G. A. (1981). Flow Resistace i Coarse Gravel Bed Rivers. Joural Hydraul. Div. America Society of Egieers. 17(HY7), pp Julie, P. Y. (2). River Mechaics. Cambridge: Cambridge Uiversity Press UK. 7. Limerios, J. T. (197). Determiatio of the Maig Coefficiet for Measured Bed Roughess i Natural Chaels. Water Supply paper 1898-B, U.S.Geological Survey, Washigto D.C. 8. Meyer-Peter, E., ad Muller, R. (1948). Formulas for Bed-load Trasport. Proced. 3 rd Meetig of IAHR, Stockholm, Swede, pp Strickler, A. (1923). Beitrage zur frage der geschwidigkeitsformel ud der rauhigkeitszahle fuer stroeme kaaele ud geschlossee leituge. Mitteiluge des eidgeossische Amtes fuer Wasserwirtschaft 16. Ber, Switzerlad. (i Germa) (Traslated as Cotributios to the questio of a velocity formula ad roughess data for streams, chaels ad closed pipelies by Roesga, T. ad Browlie,W.R). 1. Ye, B. C. (2). Ope Chael Flow Resistace. Joural of Hydraulic Egieerig ASCE, Vol. 128, No. 1, pp