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Comparing the Calculation Method of the Manning Roughness Coefficient in Open Channels

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Comparing the Calculation Method of the Manning Roughness Coefficient in Open Channels International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 06, June-2015 Comparing the Calculation Method of the Manning Roughness Coefficient in Open Channels Hari Wibowo 2 2 1Student of Doktoral Program on University of Suripin , Robert Kodoatie , 2 Diponegoro, Civil Engineering Department, University of Diponegoro 50241Semarang, Central Java,Indonesia 1 Water Resources Engineering Department, 50241Semarang University of Tanjungpura, 78115 Pontianak, West Borneo, Indonesia Isdiyana3 3RiverBalai, Water ResourcesResearchCenter , Balitbang the Ministry ofPublic Works Abstract—In hydraulic engineering, Manning roughness Philippe Gauckler in 1867, and then re-developed by the coefficient is an important parameter in designing hydraulic Irlandia engineer Robert Manning in 1890 (Bahramifar et al., structures and simulation models. This equation is applied to 2013). both uniform open channel flow, which is used to calculate the The study of the roughness coefficient has been much average flow velocity. The procedure for selecting the value of Manning n is subjective and requires assessment and skills research done previously, including Cowan (1956) which developed primarily through experience. examines pengenai hydraulic calculations, the roughness ManyempiricalformulaMenningthat was developedin order coefficient andAgricutural Engineering. Arcement and toobtainthe valuekoefsieinManning roughness. Fromseveral Schneider (1984) make modifications to the formulation studiesincludingthe formulationCowan(1956), Cowan (1956) by incorporating the element of stream power. ArcementandSchneider(1984), Limerinos(1970), Limerinos (1970) investigating the Manning roughness KarimandKennedy(1990), Riekenmann(1994), coefficient of the basic measurements in a natural channel. Riekenmann(2005) andChiariandRiekenmann(2007) Brownlie (1983) had developed roughness coefficient n in the Obtainingroughnesscoefficient(n) obtainedfromManninginsome flow depth relationship in the form of hydraulic conditions formulationsareobtainedempiricalmethod forthe lowestn=0015andnhighestn =0.0075. AndnValue thecondition and characteristics of the bed materials in large amounts of ofthenaturalchannel datahighestand lowest,namelyn=0.0027- data flume and field. Karim and Kennedy (1990) developed a 0.0590. Whilethe study ofEntropyformula(2014), form of relationship to the value of n in the form of Bojorunas(1952) andWibowo(2015), for dimensionless variables in the form of relative depth and theManningroughnessvaluesusingthe highestlaboratory friction factor. datan=0.0256and the lowestn=0.0171, to which it results Rickenmann (1994) proposed the equation to calculate the stillsatisfy the requirementsforthe value ofnon-cohesive total Manning roughness coefficient. Rickenmann (2005) 2 material.with the value of and R 0,926 and MNE (Measurement proposed the loss calculation on the flow resistance Normaled Errors) = 82% on the method Limerinos (1970) associated with a form of drag as a function of the slope and depth of the relative flow. Bahramifar et al. (2013) who Keywords— Open Channel, Roughness Manning coefficient, evaluated the Manning by using ANFIS method approach in Empiricalformula alluvial channels. Greco et al. (2014) analyzed using entropy I. INTRODUCTION method in order to determine the value roughness coefficient Manning. Manning coefficient n is a coefficient that represents the The purpose of this paper is to obtain the value of the roughness or friction applied to the flow in the channel roughness coefficient (n) Manning on the field by comparing (Bilgin & Altun, 2008). In hydraulic engineering, Manning based on existing Manning formula. roughness coefficient is an important parameter in designing hydraulic structures (Azamathulla et al., 2013; Samandar, 2011; Bilgin & Altun, 2008). II. MATERIAL Manning equation is an empirical equation is applied to the uniform open channel flow, which is used to calculate the 2.1 Formulation of Manning average flow velocity and the speed function of the channel, The value of this coefficient can be searched with the the hydraulic radius and slope of the channel (Bahramifar et knowing flow parameters as that of the equation Equation al., 2013). (2.1). In Europe, also known as the Manning formula 1,00 Gauckler-Manning formula, or formula Gauckler-Manning- 푛 = 푅2/3푆1/2 ............................................(1) Strickler. It was first presented by the French Engineer 푈 IJERTV4IS060194 www.ijert.org 1278 (This work is licensed under a Creative Commons Attribution 4.0 International License.) International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 06, June-2015 where U is average flow velocity (m / sec); n is 2.4 Limerinos (1970) Manning roughness coefficient; R is hydraulic radius (meters) and S is slope of the line. Limerinos (1970) have examined the determination of manning coefficient of bottom friction measurements in a 2.2 Cowan (1956). natural channel, to establish the relationship between the Cowan (1956) developed a method to estimate the value value of the base on the Manning roughness coefficient, n, of the Manning roughness n, by using the geometry and and the index on the basis of particle size and size hydraulic parameters. The value of the roughness coefficient distribution of the river, get the value of roughness as (n) is calculated using Equation (2) Equation (4). 푛 0,0926 푛 = (푛0 + 푛1 + 푛2 + 푛3 + 푛4)푚......................(2) = ........................................(4) 푅1/6 푅 1,16+2,0 log ′ 푑 84 where 푛0is the value of the basic values of n for which a straight line, according to a uniform and smooth natural where n is the total Manning roughness coefficient, R is the ′ hydraulic radius of the channel, and 푑 84 diameter riverbed ingredients it contains, 푛1 value added to 푛0 to correct for the effect of surface irregularities, 푛 value for variations in material with a percentage of 84% passes. 2 the shape and size of the cross section of the channel, 푛3value Table 2. Value Roughness Coefficient (n) is Calculated by for barriers, 푛4 value for condition Equation Cowan vegetationandflowand 푛5correction factorforchannelbends. Variabel Desription Channel Recommended Value Table 1. Base value of Manning‟s n (modified from Aldridge Basic, 푛0 Earth 0,020 and Garrettm, 1973) Rock 0,025 Fine Gravel 0,024 Bed Material Median Base n value size Coarse Gravel 0,028 of bed Irregularity, 푛1 Smooth 0,000 material Minor 0,005 (in Moderate 0,010 milimeters) Severe 0,020 Straight Smooth Cross section,푛2 Gradual 0,000 uniform Channel Occasional 0,005 Channel Alternating 0,010-0,015 Sand Obstructions, 푛3 Negligible 0,000 Channel Minor 0,010-0,015 Sand ........................... 0,20 0,012 - Appreciable 0,020-0,030 0,3 0,017 Severe 0,040-0,060 0,4 0,020 Vegetation, 푛4 Low 0,005-0,010 0,5 0,022 Medium 0,010-0,020 0,6 0,023 High 0,025-0,050 0,8 0,025 Very High 0,050-0,100 1,0 0,026 Meandering, 푚 Minor 1,00 Stable Channel and Flood Plains Appreciable 1,15 Coarse sand ................... 1-2 0,026- - Severe 1,30 0,035 Fine Gravel .................. - - 0,24 Source : Chow, 1959. Gravel............................. 2-64 0,028- - 2.5Brownlie (1983) 0,035 Source : Aldridge and Garrettm, 1973 Brownlie (1983) has developed a relationship at a depth of flow in the form of hydraulic conditions and characteristics 2.3 Arcement and Schneider (1984). of the bed materials in large amounts of data flume and field. Arcement and Schneider (1984) has modified the The relationship shown in equation (5) and (6). Equation (2.2) to be used in the calculation of flood plains. On the condition of Lower Regime; Correction factor to form sinusiodal (m) to 1 (one) in this 푅 0,1374 caseand correct the differences in size and shape of the 푛 = 1,6940 푆0,1112 퐺0,1605 0,034푑 0,167 ….(5) 푑 50 50 channel n2 which is assumed to be equal to 0 (zero). Equation (1) in the equation (3). In conditions of Upper Regime 0,0662 푛 = (푛푏 + 푛1 + 푛3 + 푛4)푚............................(3) 푅 0,0395 0,1282 0,167 푛 = 1,0123 푆 퐺 0,034푑50 ..(6) 푑50 which 푛 is the basic value of n the openland surface. 푏 which, R = hydraulic radius (ft); S = slope of the line (ft / ft); Selection on the basis of the value of the floodplains are the d = median particle size of the bed material (ft) and G = same as in the channel. Arcement and Schneider (1984) 50 coefficient of gradation on the base material. Where proposed that the effect of resistance to flow (Simons & Richardson, 1966) in the floodplains IJERTV4IS060194 www.ijert.org 1279 (This work is licensed under a Creative Commons Attribution 4.0 International License.) International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 06, June-2015 1 푑 푑 퐺 = 84 + 50 2 푑50 푑16 2.6 Karim and Kennedy (1990) Karim and Kennedy (1990) apply the above procedure on the data field and flume gives the relationship in the form of relationship to the value of n as Equation (7) 0,465 0,126 푓 푛 = 0,037 푑50 ….....…................…..(7) 푓0 푓 ∆ (d50 in meters) and = 1,20 + 8,92 푓0 푕 2.7 Riekenmann (1994) Riekenmann (1994) proposed the equation to calculate the total Manning roughness coefficient, as shown in Equation ′ 1 Figure1.푛 ′as a function of ′ Bajorunas(1952) (8). 휓 1 0,56푔0,44푄0,11 = 0,33 0,45 ……..................................……….(8) 2.11 Formulation Manning Based on Linear 푛푡표푡 푆 푑90 2.8 Riekenmann (2005) Separation Based on Bed Configuration (Wibowo-Manning). Rickenmann (2005) proposed the loss calculation on flow resistance associated with the drag shape as a function Wibowo (2015) also states the linear separation of the of the slope and depth of flow relative, as in Equation (9). Manning roughness coefficient based on the flow resistance in the field of bed moves, equal as Equation (12). n‟ As in the 푛′ 푕 0,33 = 0,083푆−0,35 …........................................(9) following.Equation (13) and (14). 푛푡표푡 푑90 1/6 ′ 푅 .....푛 = 푅′ ...................................(13) 2.9 Chiari dan Rickenmann (2007) 6,0+5,75 log 푔 푘푠 Chiari and Rickenmann (2007) proposed Manning on and the surface roughness values for total roughness that produces 2 1 푅′ 2 휏 ′′ ln 푛′ 푘 2 Equation (10).
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