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

Hari Wibowo; Suripin; Robert Kodoatie; Isdiyana

doi:10.17577/IJERTV4IS060194

Volume 04, Issue 06 (June 2015)

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

DOI : 10.17577/IJERTV4IS060194

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Volume & Issue : Volume 04, Issue 06 (June 2015)
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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

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.

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

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
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

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
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

METHODS

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

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

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

DATA ANALYSIS

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
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

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.
Data from experiments Guy et al. (1966) 340 is also included
Data Bronwnie experimental results (1981).
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
RÂ² = 0.925 RÂ² = 0.849 y = 0.401×1.076 .742×1.247y = 1.104×0.921
= 0.893 RÂ² = 0.877 RÂ² = 0.681
RÂ² = 0.926
y = 0.436×0.883
		RÂ² = 0.859

1.600

1.40y0= 1

Q measurement

RÂ²

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
Investigator	MNE	RÂ²
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

CONCLUSIONS AND 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.
  1. REFERENCES

Arcement, G.J., and V.R. Schneider (1989). Guide for Selecting Mannings Roughness Coefficients for Natural Channels and Flood Plains. Water-Supply Paper 2339, U.S. Geological Survey.

Azamathulla, H. Md., Ahmad Z., and Aminuddin Ab. Ghani (2013). An Expert System for Predicting Mannings Roughness Coefficient in Open Channels by Using Gene expression Programming Neural Comput & Applic, 23:13431349.

Bahramifara, A, Shirkhanib,R., and Moham madic, M. (2013). An ANFIS-based Approach for Predicting the Manning Roughness Coefficient in Alluvial Channels at the Bank- full Stage ,IJE Transactions B: Applications Vol. 26, No. 2, pp.177-186.

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

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