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

DOI : 10.17577/IJERTV4IS060194

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

Hari Wibowo

1Student of Doktoral Program on University of Diponegoro,

50241Semarang, Central Java,Indonesia

1Water Resources Engineering Department,

Suripin 2, Robert Kodoatie2, 2 Civil Engineering Department, University of Diponegoro 50241Semarang

University of Tanjungpura, 78115 Pontianak, West Borneo, Indonesia

Isdiyana3

3RiverBalai,

Water ResourcesResearchCenter, Balitbang the Ministry ofPublic Works

AbstractIn hydraulic engineering, Manning roughness coefficient is an important parameter in designing hydraulic structures and simulation models. This equation is applied to both uniform open channel flow, which is used to calculate the average flow velocity. The procedure for selecting the value of Manning n is subjective and requires assessment and skills developed primarily through experience. ManyempiricalformulaMenningthat was developedin order toobtainthe valuekoefsieinManning roughness. Fromseveral studiesincludingthe formulationCowan(1956), ArcementandSchneider(1984), Limerinos(1970),

KarimandKennedy(1990), Riekenmann(1994), Riekenmann(2005) andChiariandRiekenmann(2007) Obtainingroughnesscoefficient(n) obtainedfromManninginsome formulationsareobtainedempiricalmethod forthe lowestn=0015andnhighestn =0.0075. AndnValue thecondition ofthenaturalchannel datahighestand lowest,namelyn=0.0027- 0.0590. Whilethe study ofEntropyformula(2014), Bojorunas(1952) andWibowo(2015), for theManningroughnessvaluesusingthe highestlaboratory datan=0.0256and the lowestn=0.0171, to which it results stillsatisfy the requirementsforthe value ofnon-cohesive material.with the value of and R2 0,926 and MNE (Measurement Normaled Errors) = 82% on the method Limerinos (1970)

Keywords Open Channel, Roughness Manning coefficient, Empiricalformula

  1. INTRODUCTION

    Manning coefficient n is a coefficient that represents the roughness or friction applied to the flow in the channel (Bilgin & Altun, 2008). In hydraulic engineering, Manning roughness coefficient is an important parameter in designing hydraulic structures (Azamathulla et al., 2013; Samandar, 2011; Bilgin & Altun, 2008).

    Manning equation is an empirical equation is applied to the uniform open channel flow, which is used to calculate the average flow velocity and the speed function of the channel, the hydraulic radius and slope of the channel (Bahramifar et al., 2013).

    In Europe, also known as the Manning formula Gauckler-Manning formula, or formula Gauckler-Manning- Strickler. It was first presented by the French Engineer

    Philippe Gauckler in 1867, and then re-developed by the Irlandia engineer Robert Manning in 1890 (Bahramifar et al., 2013).

    The study of the roughness coefficient has been much research done previously, including Cowan (1956) which examines pengenai hydraulic calculations, the roughness coefficient andAgricutural Engineering. Arcement and Schneider (1984) make modifications to the formulation Cowan (1956) by incorporating the element of stream power. Limerinos (1970) investigating the Manning roughness coefficient of the basic measurements in a natural channel. Brownlie (1983) had developed roughness coefficient n in the flow depth relationship in the form of hydraulic conditions and characteristics of the bed materials in large amounts of data flume and field. Karim and Kennedy (1990) developed a form of relationship to the value of n in the form of dimensionless variables in the form of relative depth and friction factor.

    Rickenmann (1994) proposed the equation to calculate the total Manning roughness coefficient. Rickenmann (2005) proposed the loss calculation on the flow resistance associated with a form of drag as a function of the slope and depth of the relative flow. Bahramifar et al. (2013) who evaluated the Manning by using ANFIS method approach in alluvial channels. Greco et al. (2014) analyzed using entropy method in order to determine the value roughness coefficient Manning.

    The purpose of this paper is to obtain the value of the roughness coefficient (n) Manning on the field by comparing based on existing Manning formula.

  2. MATERIAL

    2.1 Formulation of Manning

    The value of this coefficient can be searched with the knowing flow parameters as that of the equation Equation (2.1).

    = 1,00 2/31/2 ……………………………………..(1)

    where U is average flow velocity (m / sec); n is Manning roughness coefficient; R is hydraulic radius (meters) and S is slope of the line.

    2.2 Cowan (1956).

    Cowan (1956) developed a method to estimate the value of the Manning roughness n, by using the geometry and hydraulic parameters. The value of the roughness coefficient

    (n) is calculated using Equation (2)

    2.4 Limerinos (1970)

    Limerinos (1970) have examined the determination of manning coefficient of bottom friction measurements in a natural channel, to establish the relationship between the value of the base on the Manning roughness coefficient, n, and the index on the basis of particle size and size distribution of the river, get the value of roughness as Equation (4).

    = (0 + 1 + 2 + 3 + 4)………………….(2)

    where is the value of the basic values of n for which a

    1/6

    0,0926

    1,16+2,0 log

    =

    84

    ………………………………….(4)

    0

    straight line, according to a uniform and smooth natural

    ingredients it contains, 1 value added to 0 to correct for the effect of surface irregularities, 2value for variations in the shape and size of the cross section of the channel, 3value for barriers, 4 value for condition

    where n is the total Manning roughness coefficient, R is the hydraulic radius of the channel, and 84 diameter riverbed material with a percentage of 84% passes.

    Table 2. Value Roughness Coefficient (n) is Calculated by Equation Cowan

    vegetationandflowand 5correction factorforchannelbends.

    Variabel Desription Channel Recommended Value

    Basic, 0

    Earth

    0,020

    Rock

    0,025

    Fine Gravel

    0,024

    Coarse Gravel

    0,028

    Irregularity, 1

    Smooth

    0,000

    Minor

    0,005

    Moderate

    0,010

    Severe

    0,020

    Cross section,2

    Gradual

    0,000

    Occasional

    0,005

    Alternating

    0,010-0,015

    Obstructions, 3

    Negligible

    0,000

    Minor

    0,010-0,015

    Appreciable

    0,020-0,030

    Severe

    0,040-0,060

    Vegetation, 4

    Low

    0,005-0,010

    Medium

    0,010-0,020

    High

    0,025-0,050

    Very High

    0,050-0,100

    Meandering,

    Minor

    1,00

    Appreciable

    1,15

    Severe

    1,30

    Table 1. Base value of Mannings n (modified from Aldridge and Garrettm, 1973)

    Bed Material Median Base n value

    size of bed material

    (in milimeters)

    Straight

    uniform Channel

    Smooth Channel

    Sand

    Channel

    Sand ……………………… 0,20

    0,012

    0,3

    0,017

    0,4

    0,020

    0,5

    0,022

    0,6

    0,023

    0,8

    0,025

    1,0

    0,026

    Stable Channel and Flood Plains

    Coarse sand ……………….

    1-2

    0,026-

    0,035

    Fine Gravel ………………

    0,24

    Gravel………………………..

    2-64

    0,028-

    0,035

    Source : Aldridge and Garrettm, 1973

    2.3 Arcement and Schneider (1984).

    Arcement and Schneider (1984) has modified the Equation (2.2) to be used in the calculation of flood plains.

    Source : Chow, 1959. 2.5Brownlie (1983)

    Brownlie (1983) has developed a relationship at a depth of flow in the form of hydraulic conditions and characteristics of the bed materials in large amounts of data flume and field. The relationship shown in equation (5) and (6).

    • On the condition of Lower Regime;

      Correction factor to form sinusiodal (m) to 1 (one) in this caseand correct the differences in size and shape of the

      = 1,6940

      0,1374

      0,1112 0,1605 0,03450

      0,167

      .(5)

      channel

      n2 which is assumed to be equal to 0 (zero).

      50

    • In conditions of Upper Regime

    Equation (1) in the equation (3).

    = ( + 1 + 3 + 4)……………………….(3)

    = 1,0123

    0,0662

    0,0395

    0,1282

    0,167

    50

    0,03450

    ..(6)

    which is the basic value of n the openland surface. Selection on the basis of the value of the floodplains are the same as in the channel. Arcement and Schneider (1984) proposed that the effect of resistance to flow (Simons & Richardson, 1966) in the floodplains

    which, R = hydraulic radius (ft); S = slope of the line (ft / ft); d50 = median particle size of the bed material (ft) and G = coefficient of gradation on the base material. Where

    =

    1 84

    2 50

    + 50

    16

      1. 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)

        = 0,037 50

        0,126 0,465 …………………..(7)

        0

        (d in meters) and = 1,20 + 8,92

        50 0

      2. Riekenmann (1994)

    Riekenmann (1994) proposed the equation to calculate the total Manning roughness coefficient, as shown in Equation (8).

    Figure1. as a function of 1 Bajorunas(1952)

    1

    = 0,560,44 0,11 ……………………………..(8)

    0,33 0,45

    90

    2.11 Formulation Manning Based on Linear

      1. Riekenmann (2005)

        Rickenmann (2005) proposed the loss calculation on flow resistance associated with the drag shape as a function of the slope and depth of flow relative, as in Equation (9).

        Separation Based on Bed Configuration (Wibowo-Manning).

        Wibowo (2015) also states the linear separation of the Manning roughness coefficient based on the flow resistance

        = 0,083

        0,35

        0,33

        90

        ………………………………….(9)

        in the field of bed moves, equal as Equation (12). n As in the

        following Equation (13) and (14).

        = 1/6

      2. Chiari dan Rickenmann (2007)

    Chiari and Rickenmann (2007) proposed Manning on

    and

    6,0+5,75 log

    ……………………………..(13)

    the surface roughness values for total roughness that produces

    1 2 2 2

    =

    Equation (10).

    =

    ln

    …………………(14)

    0,0756 0,11

    0,06 90 0,28 0,33

    ………………………………….(10)

    2 1 cos tan sin 3

    Where is theshear stressrelativedue tothe basic

    2.10. Moramarco dan Singh (2010), Mirauda et al (2011),Mirauda dan Greco (2014) dan Greco et al. (2014).

    Moramarco and Singh (2010), Mirauda et al (2011), Mirauda and Greco (2014) and Greco et al. (2014) who examined the Manning roughness coefficient in open channel parameters based on entropy, which has resulted in Equation (11)

    Rh 1/6/

    form(" = ), = /( ); is shape form (=1);k3 is the correction factor (0,20 to 0,90), length of bedform; d is grain diameter; tan is dynamic friction coefficient and is the angle of the bed channel.

    Table 3. Value Factor Correction on Alluvial Material (Corey, 1956) Number Shape material Shape Factor

    1 0,20 0,39

    2 0,40 0,59

    3 0,60 0,79

    = M .1 ln

    ……………………………………(11)

    4 0,80 0,99

    0 0,4621

    5 1,00

    2.11 Formulation Manning based on Linear Separation

    Borojunas (1952) also states the linear separation of the Manning roughness coefficient into two (2) parts: first, the basic channel resistance granules associated friction on the surface (skin friction) known as grain roughness (n '), the basic flow resistance in relation to the existence of bedform and roughness changes known with the form (n"). His formulation shown in Equation (12).

    = + ………………………………..(12).

    in which n' = resistance due to friction surface (skin friction)

    Table 4. Angle Angle pupose () on Non Cohesive Soil (Piere, 2010)

    Number

    Class name

    (deg)

    1

    Sand Very Coarse

    32

    2

    Sand Coarse

    31

    3

    Sand medium

    30

    4

    Sand Fine

    30

    5

    Sand Very Fine

    30

    or grain roughness; = 1/6

    29,3

    and n '' = resistance due to

    form drag or roughness shape. =

    1,6835

    0,007

    4,000

    0,40

    4,60

    21,739

    0,25

    14,78

    0,007

    5,000

    0,40

    6,60

    18,939

    0,31

    13,44

    0,007

    6,000

    0,40

    8,15

    18,405

    0,67

    7,33

    0,007

    7,000

    0,40

    9,90

    17,677

    0,69

    10,56

    0,007

    8,000

    0,40

    10,05

    19,900

    0,77

    11,00

    0,008

    3,000

    0,40

    5,05

    14,851

    0,36

    7,56

    0,008

    4,000

    0,40

    7,60

    13,158

    0,37

    9,74

  3. METHODS

      1. The Field research

        The method implemented by comparing the results of experiments in laboratoritum and pitch of each empirical formula.

        location

        Figure 2. The Location Field Research Pontianak

        1. Data Field

          The field data is taken based on the results of field research on the cross-section of the river in the city of Pontianak (Trenches Bansir) as listed in the Table (5).

          Table 5. Results FlowVelocity Measurementin the Field

          Symbol

          Unit

          P1

          P2

          P3

          P4

          B

          meter

          9,000

          8,400

          9,000

          8,500

          h0

          meter

          0,800

          0,900

          0,700

          0,700

          U

          m/s

          0,116

          0,098

          0,139

          0,121

          bo

          meter

          1,125

          1,050

          1,125

          1,063

          Qo

          m3/s

          0,039

          0,057

          0,046

          0,027

          Qtotal

          m3/s

          0,929

          0,857

          1,019

          0,757

          Total wide m2 9,763 8,638 7,465 6,593

          velocity

          m/s

          0,116

          0,098

          0,139

          0,121

          Hydraulic

          radius

          0,888

          0,834

          0,717

          0,665

          Slope

          0,0000209

          0,0000209

          0,0000209

          0,0000209

          Roughness

          0,044

          0,041

          0,027

          0,030

          Average value n 0,036

          source: field Results

          Slope

          Qoutflow

          width

          h

          Uoutflow

          liter/s

          m

          cm

          cm/s

          cm

          cm

          0,008

          5,000

          0,40

          7,35

          17,007

          0,50

          10,94

          0,008

          6,000

          0,40

          7,05

          21,277

          0,71

          9,00

          0,008

          7,000

          0,40

          8,40

          20,833

          0,73

          9,22

          0,008

          8,000

          0,40

          9,50

          21,053

          0,76

          10,17

          0,010

          3,000

          0,40

          4,55

          16,484

          0,37

          7,94

          0,010

          4,000

          0,40

          5,30

          18,868

          0,39

          9,06

          0,010

          5,000

          0,40

          6,78

          18,437

          0,45

          10,39

          0,010

          6,000

          0,40

          6,53

          22,971

          0,52

          9,71

          0,010

          7,000

          0,40

          7,40

          23,649

          0,56

          7,50

          0,010

          8,000

          0,40

          8,50

          23,529

          0,78

          10,17

          0,00667

          2,514

          0,10

          8,00

          31,430

          0,75

          12,5

          0,00667

          2,868

          0,10

          11,00

          26,071

          1,70

          10,0

          0,00667

          2,680

          0,10

          12,50

          21,438

          0,50

          9,0

          0,00667

          4,521

          0,10

          14,00

          32,296

          0,90

          10,0

          0,01333

          3,061

          0,10

          12,00

          25,508

          0,80

          8,0

          0,01333

          3,708

          0,10

          13,00

          28,525

          1,50

          7,5

          0,01333

          3,817

          0,10

          14,00

          27,266

          1,70

          10,0

          0,01333

          4,345

          0,10

          15,00

          28,966

          0,25

          8,0

          0,00667

          2,811

          0,10

          11,00

          25,555

          0,80

          6,5

          0,00667

          4,260

          0,10

          12,10

          35,205

          2,00

          24,0

          0,00667

          2,866

          0,10

          12,50

          22,929

          1,20

          9,5

          0,00667

          4,104

          0,10

          14,00

          29,316

          0,80

          9,5

          0,01333

          2,902

          0,10

          10,00

          29,015

          0,50

          8,0

          0,01333

          4,993

          0,10

          13,00

          38,405

          0,80

          10,0

          0,01333

          5,448

          0,10

          14,00

          38,913

          1,40

          6,5

          0,01333

          6,429

          0,10

          15,00

          42,857

          2,20

          9,0

          Continue

        2. Data Laboratory.

    Results ofsecondary dataandprimary datafromdirect measurementsinthe laboratorycan be seen inTable (6)

    Slope

    Qoutflow

    width

    h

    Uoutflow

    liter/s

    m

    cm

    cm/s

    cm

    cm

    0,006

    3,000

    0,40

    5,20

    14,423

    0,14

    7,53

    0,006

    4,000

    0,40

    6,50

    15,385

    0,29

    7,42

    0,006

    5,000

    0,40

    7,70

    16,234

    0,38

    9,68

    0,006

    6,000

    0,40

    9,20

    16,304

    0,42

    10,56

    0,006

    7,000

    0,40

    10,20

    17,157

    0,46

    8,44

    0,006

    8,000

    0,40

    11,15

    17,937

    0,49

    10,17

    0,007

    3,000

    0,40

    4,20

    17,857

    0,13

    12,22

    Table 6. Results FlowVelocity Measurementinthe Laboratory

    Source : Laboratory Results

    Figure3. The Location Laboratory Research in Solo

    The Composition ofExperiment

    The experimental tests were carried out in the Hydraulics Laboratory of Bandung Institute of Technology, on a free surface flume of 10,0 m length and with a cross section of 0,4 x 0,6 m2 (Fig.2), whose slope can vary from 10/1000 % up to 4/300 %. at a distance of 1 from the upstream timber bulkhead installed upstream so that the sand does not exit. An example of a sample of sand with a maxsimum grain diameter of 0,25 mm to 0,5 mm. Picture design can be found at Fig.3

  4. DATA ANALYSIS

      1. Calculation Results Manning Roughness on Empirical formula

        • Example Method Cowan (1956)

          The formula used n n0 n1 n2 n3 n4 m5 no =

          0.020 (channel-forming material is ground) n1 = 0.005 (degree of irregularity, in the channel of small (minor), slightly eroded or on cliffs eroded channel), n2 = 0.000 (cross-sectional variation in channel, channel varies and

      2. Application of Flow Coefficient of Roughness on Discharge

    The general formula used as According Soewarno (1995) discharge or magnitude of flow of the river / channel is flowing through the volume flow through the a river cross section / channel unit time. Usually expressed in units of cubic meters per second (m3 / s) or liters per second (l / sec). Flow is the movement of water in the river channel / channels. In essence discharge measurement is a measurement of the wet cross-sectional area, flow velocity and water levelEquation (15).

    Q =U.A………………………………………(15)

    where;

    Q = discharge (m3/s)

    A = cross-sectional area the wet (m2) U = average flow velocity (m/s)

    Which U as in Equation (16)

    = 1,00 2/31/2 ……………………(16)

    Roughness coefficientbecause oftheirsidewalls,

    expressed inbedformEquation(8).

    forms cross-section is considered phased (gradual) that changes the shape channel occur slowly). n3 = 0.000 (relative

    = 1/6 and

    =

    / …………………..(8)

    effect and the digolong barriers can be ignored). n4 = 0.000 (because there is only a small grass. m = 1.00 degrees of bend, take the small (minor). From these analysis results obtained value of n

    n n0 n1 n2 n3 n4 m = (0,020 + 0,005 + 0,000 +

    0,000 + 0,000) x 1,000 = 0,025.

    Furthermore, The calculation is then performed in the Table (7).

    Tabel 7.Summary Calculation Results From Table 5 &6

    • Equation of Average Bed and Sidewall Shear Stress

    Shear stress bed ( ) and sidewallsaverage can be formulatedtoimplementusingthe overall balance offorceinthe direction of flow(Guo &Pierre, 2005). As definedin Equation(17)

    2 + = = ..(17) wherethe amount ofshear stress bed( ) byformulatedbyJavid&Mohammadi(2013) as Equation(18a)

    and(18b)

    = exp 0,57 0,33 0,57 4,25 +

    Roughness Coefficient Data on Cross Section Width

    (n) B=8-9 m B =10 cm B= 40

    3,04 ln() …………………(18a)

    cm = 0,5 (1

    ) ……………………………..(18b)

    Wibowo – 0,0256 0,0246 0,0232

    Bojurunas (1952)

    0,0218

    0,0220

    0,0233

    0,0192

    Keulegan(1938) suggested that thebisectorsofthe internal

    Metode Entropi

    0,0590

    0,0171 0,0184 0,0213

    angles ofthe polygonalchannels can beusedas adividing lineto

    Cowan (1956)

    0.0250

    n from Manningtable = 0,033

    illustratethe extent ofthethe bed ofandside wallarea.

    Arcement& Schneider

    0.0325

    asEquation(19).

    (1984)

    = + ……………………………………….(19)

    The drainagearea ofthe bed( )

    Limerinos (1970)

    0,0147

    formulatedbyJavid&Mohammadi(2013) as Equation(20a)

    Brownlie (1983)

    0,0144

    0,0089

    0,00939

    0,00982

    anddrainagearea ofthe side wall( ) inEquation(20b)

    Karim & Kennedy (1990)

    0.00815

    5

    0.0278

    0.0247

    7

    0.0270

    = 2 = 1,75442 1 exp 0,57

    Riekenmann (1994)

    0.0027

    0.0017

    0.0023

    0.0021

    ……(20a)

    Riekenmann (2005)

    0.0051

    0.0126

    0.0170

    0.0206

    = ;

    = = 1,75442 1

    0

    0

    Riekenmann &Chiari (2007)

    0.0126 0.0493 0.0652 0.0618

    exp 0,57 ……..(20b) The flow rate calculation results are presented in graphical

    Source: calculation results form. Data used in the calculation of this flow rate

    1.800

    1. Data experimental Wang and White (1993) : This data set consists of 108 running and experiments have been conducted on the transition regime characterized by resistance coefficient decreases rapidly with increasing strength of the current.

    2. Data from experiments Guy et al. (1966) 340 is also included

    3. Data Bronwnie experimental results (1981).

    4. Research data Sisingih (2000).

    Discharge Relationship between Measurement and Empirical Formula

    Tabel 8.Summary Calculation Results from the All Data

    (n)

    1

    Limerinos (1970)

    0.011

    – 0.018

    2

    Brownlie (1983)

    0.012

    – 0.024

    3

    Borujnas (1952)

    0.012

    – 0.023

    4

    Karim dan Kennedy (1990)

    0.013

    – 0.038

    5

    Riekenmann (1994)

    0.008

    – 0.090

    6

    Riekenmann (2005)

    0.012

    – 0.031

    7

    Chiari dan Rickenmann 2007

    0.025

    – 0.043

    8

    Metode Entropi – Wibowo

    0.017

    – 0.026

    9

    Wibowo (2015)

    0.017

    – 0.027

    No Investigator Roughness Coefficientt

    y = 1.635x1y.22=5 1.336×1.070

    R² = 0.925 R² = 0.849 y = 0.401×1.076

    .742×1.247y = 1.104×0.921

    = 0.893 R² = 0.877 R² = 0.681

    R² = 0.926

    y = 0.436×0.883

    R² = 0.859

    1.600

    1.40y0= 1

    Q measurement

    R²

    1.200

    1.000

    0.800

    0.600

    0.400

    y = 0.939×1.199

    Limerino

    s bronwlie

    Karim

    Riekenm ann

    4.3. Discussion

    Based on this analysis, the coefficient calculation is done perhitung this prediction accuracy using the average normal faults (MNE), namely

    0.200

    entropi

    MNE 100 N

    X ci X mi

    0.000

    0.000 1.000 2.000 3.000

    N i1 X mi

    Q In the empirical formulai

    Fig 3RelationsDischargeMeasurementsandCalculationsFrom the All data

    Fig 4RelationsDischargeMeasurementsandCalculationsFrom the All data with

    Nash Method.

    Where the results of with the formula estimate manning, Xmi, and Xci= empirical calculation results.

    Table 8. Resume Calculation Result Error Correction

    Investigator

    Mean Normalized Errors

    Correlation Coefficient

    MNE

    R²

    Limerinos (1970)

    82.220

    0.926

    Brownlie (1983)

    58.613

    0,681

    Borujnas (1952)

    52.036

    0,849

    Karim dan Kennedy (1990)

    69.821

    0,893

    Riekenmann (1994)

    39.989

    0,877

    Riekenmann (2005)

    68.551

    0,846

    Chiari dan Rickenmann 2007

    61.168

    0,894

    Metode Entropi – Wibowo

    82.189

    0,925

    Wibowo (2015)

    69.058

    0,859

    Results of analysis of the Manning roughness coefficient calculation (n) obtained the highest and lowest values of n for each method, for empirical method obtained the lowest n = 0008 and n highest n = 0.0071, this shows that by using laboratory data obtained results are still within reach Manning roughness table for sand = 0,020. On the condition of with the natural channel data highest n= 0.0590 and lowest n = 0.0027 (In natural conditions n = 0,025- 0,033).

    In the study of the entropy formula, bojorunas and Wibowo, for the Manning roughness values using laboratory data the highest n = 0.012 and the lowest n = 0.027.

    For the third method in the Manning roughness coefficient results showed results that approached with the table Manning to a grain of sand (n = 0,020). While the field data showed that are less good results.

    Similarly to the empirical formula. This is because the analysis used in the form of uniform flow, while the flow field is not uniform.

    Formulation development Manning coefficient of linearseparationin relation to theflow ratecan be seenin Figure(5)Table 8 presents a comparison of MNE from all studies show varying results btween 39, 989 % – 82,220%. In the method of data Limerinos and Entropy Method shows the model fit a large proportion of the 82% which means the value is quite satisfactory, because it is still the case that small forecasting error of 18%

    From Table 9, It is also seen that, the correlation coefficient between the actual and the forecast has a direct relationship

  5. CONCLUSIONS AND RECOMMENDATIONS

      1. Conclusions

        In the discussion of the previous chapter, we conclude some results as follows:

        • Effect of resistance form can not be ignored "/ =

          -17,316 + 0,6807, meaning that large semangkit roughness value relative basis, the value of the Manning roughness coefficient (n) small semangkin thus obtained a large flow rate.

        • The value of the roughness coefficient (n) obtained from Manning in some formulations are obtained empirical method for the lowest n = 0,008 and highest n = 0.090. and the condition of with the natural channel data n highest and lowest namely 0.0590 and 0.0027.

        • obtained simulating the relationship between Q and

          Strong positive as indicated by the value of R2 ranging from 0.681 to 0.926. If used best linear fitting as shown in Figure

          Q flume Qsim = 0,436Qflume

          0,8834

          with R2

          = 0,859

          2, obtained the highest coefficient of determination Limerinos method that R2 approximately 0.926; or in other words that the accuracy of the linear regression model between

          observation is very strong with a forecast of 0.926.

          which shows the model results correlate very well.

          • By using the relationship obtained by the method Nash

          Qsim = 0,950Qflume +0,0012 with R2 = 0,9797

          Fig5 elationsDischargeMeasurementsandCalculations

          ,which shows a very good correlation results.

          • In a study of entropy formula, bojorunas and Wibowo, for the Manning roughness values using the highest laboratory data n = 0.0256 and the lowest n = 0.0171, which results still meet the requirements for the value of non-cohesive material.

          • Development of the Manning formula can be applied in the field by the presence of a correction value.

          • Resultsbetween the dischargeand thedischargemeasurementresultscorrelatedonlinearse parationis good,whichis shown by thecorrelation coefficient(R2) 0,859.

          • In the method of data Limerinos and Entropy Method shows the model fit a large proportion of the 82% which means the value is quite satisfactory, because it is still the case that small forecasting error of 18%

          • Linear separation method by taking into account the basic shape can be used in predicting the flow in natural river..

      2. Recommendations

    • To obtain optimal results in the research study manning coefficient should be used as much as possible the data.

    • The amount of data retrieved should be quite a lot, both with respect to the number of observation points and the number density of the vertical point of channel cross section.

    • Development research can be carried out with the a cross-channel conditions in other places.

    1. ACKNOWLEDGEMENT

      Experimental workcarried outin the CentralSolo River, Indonesia. The authorwould like toacknowledge the assistance ofSuripin, RobertKodoatie, Isdiyana, KirnoandFamilyin conductingexperiments. Special thanks toHanifAjeng , Uray Nurhayati andAmirafor their helpduringthe work.

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