revised equations for manning’s coefﬁcient for...

Intl. J. River Basin Management Vol. 5, No. 4 (2007), pp. 329–346

© 2007 IAHR, INBO & IAHS

Revised equations for Manning’s coefficient for sand-bed riversAMINUDDIN AB. GHANI, Deputy Director, River Engineering and Urban Drainage Research Centre (REDAC),Universiti Sains Malaysia, Engineering Campus, Seri Ampangan, 14300 Nibong Tebal, Penang, Malaysia,E-mail: [email protected]

NOR AZAZI ZAKARIA, Director, REDAC, Universiti Sains Malaysia, Engineering Campus,Seri Ampangan, 14300 Nibong Tebal, Penang, Malaysia. E-mail: [email protected]

CHANG CHUN KIAT, Science Officer, REDAC, Universiti Sains Malaysia, Engineering Campus,Seri Ampangan, 14300 Nibong Tebal, Penang, Malaysia. E-mail: [email protected]

JUNAIDAH ARIFFIN, Deputy Dean, Faculty of Civil Engineering, Universiti Teknologi MARA, 40450 Shah Alam,Malaysia

ZORKEFLEE ABU HASAN, Senior Lecturer, REDAC, Universiti Sains Malaysia, Engineering Campus,Seri Ampangan, 14300 Nibong Tebal, Penang, Malaysia. E-mail: [email protected]

AHMAD BAKRI ABDUL GHAFFAR, Postgraduate Student, REDAC, Universiti Sains Malaysia,Engineering Campus, Seri Ampangan, 14300 Nibong Tebal, Penang, Malaysia. E-mail: [email protected]

ABSTRACTThe procedure for selecting values of Manning n is subjective and requires judgment and skill which are developed primarily through experience.Government agencies and private sectors in developed nations such as the USA are still doing research on predicting n values for rivers. Since flow andboundary roughness vary with river conditions, such research is therefore pertinent for rivers in Malaysia where floods are one of primary concerns.Research on Manning n value was started by River Engineering and Urban Drainage Research Centre (REDAC), Universiti Sains Malaysia (USM)since 2000 at the Kinta River catchment. Further data collections were later made at two other major rivers i.e. Langat River and Kulim River. Two newequations are proposed for determining Manning n for sand-bed rivers in Malaysia based on 163 data collected from these three rivers. On average,both equations have an error less than 10% in predicting flow discharge for all 163 data.

Keywords: Flood mitigation; sand-bed rivers; flow resistance; Manning n.

1 Introduction

Southeast Asia has long experienced a monsoon climate with dryand wet seasons. With mean annual rainfall precipitation locallyin excess of 5,000 mm, the very intense rainstorms in the steepmountains of Malaysia have caused frequent and devastatingfloods in the last five years especially in 2003 (Northern states ofKedah, Penang and Perlis) and 2006 (Southern states of Malacca,Johor and Pahang). Urbanization also exacerbates the problemand increases river discharge due to increase in impervious areasof the upper watershed.

The protection of the communities against floods has becomethe primary concern of the Malaysian government. One of themethods commonly used to mitigate the floods is by constructinglevees or bunds along the lowland areas surrounding river chan-nel. A recent example of the flood mitigation project involves theMuda River, Kedah (Julien et al. 2006) that highlights several

Received on October 9, 2006. Accepted on April 18, 2007.

329

important points in the design of flood remediation countermea-sures against intense and regular flooding during the monsoonsof South-East Asia. The study reach covers 41.2 km between theriver mouth and Ladang Victoria (Figure 1) which was the areathat was heavily flooded in 2003. The hydraulic analysis usingHEC-RAS model of the existing river system in the study areawas carried out to provide information on the variations of riverwater levels, discharges, and velocities during flood events. Dueto lack of field measurement data to determine suitable values ofManning n, different values were tried during the calibration ofthe HEC-RAS model. The best results were obtained with Man-ning n of 0.030 and 0.050 for the main channel and floodplainsrespectively (Figure 2). Water level records at three locations(Ladang Victoria, Bumbong Lima and River Mouth) during the2003 flood were used to check the predicted water level by theHEC-RAS model. The model results are considered sufficientlyaccurate for the determination of levee heights. This study by

330 Aminuddin Ab. Ghani et al.

Figure 1 Flood mitigation for Muda River, Kedah.

Figure 2 Hydraulic analysis using HEC-RAS for Muda River, Kedah.

Julien et al. (2006) highlights the need to accurately determinethe suitable values of Manning n for both the main channel andfloodplain.

Most hydraulic computations related to indirect estimates ofdischarge require an evaluation of the roughness characteris-tics. A number of empirical equations were developed and theseresearches have been continued by government agencies and pri-vate sectors in the developed nation such as USA (Dooge 1991,Yen 2002). Natural channel morphology depends on the interac-tion between fluid flow and the erodible channel boundary. Veloc-ity is strongly related to flow resistance, which is one of the mostimportant elements in the interaction between the fluid flow andthe channel boundary (Graf 1998, Yen 2002, Julien et al. 2002).

Engineers use a number of flow resistance techniques involv-ing grain roughness, form roughness and a combination of both.The most common practice is to express the total resistance interms of Manning n. As a consequence, Manning’s equationhas been widely used for predicting discharge in natural chan-nels (Chow 1959, Barnes 1976, Raudkivi 1993, Karim 1995,Julien 2002). This paper summarizes the recent results in thisfield based on field data collected at three rivers in Malaysia i.e.Kinta, Langat and Kulim rivers (Abdul Ghaffar 2003, Ariffin2004, Chang 2006).

2 Existing equations for evaluation Manning’scoefficient

Manning n is often assumed to be a constant that is independent ofeither flow discharge or depth. However, Chow (1959) indicatesthat the value of n is highly variable and depends on a number offactors: (1) surface roughness – fine sediment size such as sandwill result in a relatively low value of n and coarse sedimentssuch as gravels, in a high value of n; (2) vegetation – may also beregarded as a kind of surface roughness depending on the height,density, distribution and type of vegetation; (3) channel irregular-ity – comprises irregularities in wetted perimeter and variationsin cross section, size and shape along the channel length. A grad-ual and uniform change in cross section, size and shape will notappreciably affect the value of n; (4) channel alignment – smoothcurvature with large radius will give a relatively low value ofn; (5)silting and scouring – silting may change a very irregular chan-nel into a comparatively uniform one and decrease n, whereasscouring may do the reverse and increase n; (6) obstruction – thepresence of log jams, bridge piers, and the like tends to increasen; (7) size and shape of channel – an increase in hydraulic radiusmay either increase or decrease n depending on the conditionof the channel; and (8) stage and discharge – n value in most

Revised equations for Manning’s coefficient for sand-bed rivers 331

Table 1 Suggested Manning n for natural streams (Chow, 1959).

Type of channel and description Minimum Normal Maximum

Stream on plainClean, straight, full stage, no rifts or deep pools 0.025 0.030 0.033Same as above, but more stones and weeds 0.030 0.035 0.040Clean, winding, some pools and shoals 0.033 0.040 0.045Same as above, but more stones and weeds 0.035 0.045 0.050Clean, winding, some pools and shoals, weeds 0.045 0.050 0.060

and more stones

streams decreases with increase in stage and discharge. How-ever, the n value may be large at high stages if the banks arerough and grassy. Chow also gives suggested values of n in atable where three values (minimum, normal, maximum) of n aregiven for each kind of channel. Table 1 gives values of n fromChow (1959) relevant to the present study.

Several available equations to predict values of n for rivers canbe found in Simons and Senturk (1992), Yang (1996) and Langet al. (2004). These equations can be categorized as: (1) equationsthat are based on bed sediment size; (2) equations that are basedon the ratio of flow depth or hydraulic radius over sediment size;and (3) equations that includes water-surface slope besides bedsediment size and hydraulic radius or flow depth. In the presentstudy, seven equations were evaluated as follows:

Category 1: Equations based on bed sediment size

Strickler (1923): n = 1

21.1d

1/650 (1)

Meyer-Peter & Muller (1948): n = 1

26d

1/690 (2)

Lane & Carlson (1953): n = 1

21.14d

1/675 (3)

Category 2: Equations based on ratio of R or yo oversediment size

Limerinos (1970): n = 0.113R1/6

0.35 + 2.0 log10

(R

d50

) (4)

Bray (1979): n = 0.113y1/6o

1.09 + 2.2 log10

(yo

d50

) (5)

Category 3: Equations based on So

Brownlie (1983): n =[

1.893

(R

d50

)0.1374

× S0.1112

]

× 0.034 × (d50)0.167 (6)

Bruschin (1985): n = d1/650

12.38×(

R

d50× So

)1/7.3

(7)

Herein, d is the representative sediment size in meters (d50, d75

or d90), R the hydraulic radius in meters, yo the uniform flowdepth in meters and So the water-surface slope. Equations withcategory 1 were developed from data for large, wide rivers withlow slopes. Bed material is the primary source of resistance(Rahmeyer, 2006). Limerinos (1970)’s equation was developedusing 50 data from gravel-bed streams in California where d50

ranges from 6 to 253 mm. The river channels are relatively widestream of simple trapezoidal shape that will contain the entiredischarge without overflow (Lang et al. 2004). Bray (1979)’sequation was calibrated to data from 67 gravel-bed reaches inAlberta, Canada where d50 ranges from 18 to 147 mm and chan-nel width is between 14 to 546 m (Lang et al. 2004). Equationsby Brownlie (1983) and Bruschin (1985) were based mainly onflume and sandy river data (Raudkivi, 1993).

3 Study sites

The data collection programme for the present study was imple-mented at three major rivers (Figure 3) in Malaysia from 2000until 2006. Initially the study was carried out at Kinta Riverin 2000 (Abdul Ghaffar, 2003). The second study was done atLangat River from 2000 until 2002 (Ariffin, 2004). The thirdstudy was later completed at Kulim River in 2006 (Chang, 2006).A short description of the three rivers is given herein includ-ing the present landuse and catchment size. Detailed hydrauliccharacteristics of the study sites are given in Section 4.

Figure 3 Locations of rivers for the present study.


Kinta River

The Kinta River catchment (Figure 4) comprises the entire2540 km2 of the Sungai Kinta in the central-eastern section ofPerak State. The topography of the catchment consists of steepforest-covered mountains and hills in the north and east, pro-gressively giving way to the expansive Kinta Valley to the southof Ipoh, most which lies between the 10 m and 50 m contour.Land use of the Kinta Valley consists of agriculture (e.g. Rubber,

Figure 4 Kinta River catchment.

(a) Kampar River @ KM 34 (b) Raia River @ Kampung Tanjung (c) Raia River @ Batu Gajah

(d) Kinta River (e) Pari River @ Manjoi (f) Pari River @ Buntong

Figure 5 Study sites @ Kinta River catchment.

oil palm and fruit trees), urban development and unproductiveex-mining land including tailings and ponds.

The major tributary of Kinta River from the north-west isthe Pari River (245 km2) which joints at Ipoh. Tributaries fromthe steeper eastern catchment include the Raia River (250 km2),Kampar River (430 km2) which joint at Tg Tualang. The studysites consist of four rivers (Figure 5), namely Kinta River,Raia River, Pari River and Kampar River, which are situ-ated in Kinta River Catchment as depicted in Figure 4. Sixstudy sites for this study were chosen based on the followingcriteria:

(a) Natural reach: undeveloped upper or middle reach (less than30% catchment development) – Kampar River @ KM 34(Figure 5a).

(b) Natural reach: Developed middle reach (more than 30%development) – Raia River @ Kampung Tanjung (Figure 5b)and Batu Gajah (Figure 5c).

(c) Modified reach: Developed middle reach (more than 30%development) – Kinta River (Figure 5d), Pari River @ Manjoi(Figure 5e) and Buntong (Figure 5f).

Langat River

The two study sites studied are located in the Langat River basin(Figure 6) in Selangor. The tributaries Sungai Lui and SungaiSemenyih flow into the main river Sungai Langat. In both theupper and lower region along Sungai Lui and Sungai Semenyihthere are scatter of rubber plantations and isolated villages. TheSungai Langat around Kajang area is densely populated judgingfrom the vast amount of traffic volume. In contrast, the lowerregion of Sungai Langat has yet to be fully developed. There arerubber and oil palm plantations within the catchment. Some areason both sides of the river banks under study are inaccessible asthey are covered by thick bushes and shrubs.


Figure 6 Langat River catchment.

(a) Langat River @ Kajang (b) Langat River @ Dengkil

Figure 7 Study sites @ Langat River catchment.

Measurements were made from two gauging stations namelyKajang and Dengkil along Sungai Langat with catchment size of380 km2 and 1240 km2 respectively (Figure 7).

Kulim River

The study area is located at the southern part of the state of Kedahin the northwestern corner of Peninsular Malaysia (Figure 8). Itlies within the district of Kulim and upstream of Seberang Peraiin Penang. Kulim River catchment consists of 15 subcatchments,with the total catchment area of 130 km2. Kulim river tributariesinclude Tebuan River, Kilang Sago Monsoon Drain, Wang PinangRiver, Keladi River and Klang Lama River drain the urban conur-bation of Kulim extending from town to the north. Downstreamof Kulim town, the catchment comprises mainly of rubber and oilpalm estate located mainly at the confluences of Kulim River trib-utaries. The study reach covers about 14.39 km of Kulim River,from the upstream (CH 14390) to the state boundary betweenKedah and Penang (CH 1900) and further downstream at theAra Kuda gauging station (CH 0). At the headwaters, the Kulim

Figure 8 Kulim River catchment.

(a) Kulim River @ CH 14390 (b) Kulim River @3014

Figure 9 Study sites @ Kulim River catchment.

catchment is hilly and densely forested and Kulim River ariseson the western slopes of Gunung Bongsu Range and flowing in anorth-westerly direction, and joined Keladi River in the vicinityof Kulim town. The river slopes are steep and the channel ele-vation drops from 500 m to 20 m average mean sea level over adistance of 9 km. The central area of the catchment is undulatingwith elevations ranging from 100 m down to 18 m average meansea level. Two study sites are located at CH 14390 and CH 3014(Figure 9).

4 Field data collection

Field measurements were obtained along selected cross sectionsof the study sites by using the Hydrological Procedure (DID,1976, 1977) and recent manuals (Yuqian, 1989; USACE 1995,Edwards & Glysson, 1999; FISRWG, 2001; Lagasse et al., 2001;Richardson et al., 2001). The data collection includes flow dis-charge, suspended load and bed load (Ab. Ghani et al., 2003).A total of 163 data sets were obtained with 122 data for KintaRiver, 23 data for Langat River and 18 data for Kulim River.


Table 2 Range of field data for Kinta River catchment (Ab. Ghani et al. 2003).

Study site Kampar River Raia River @ Raia River @ Kinta River @ Pari River @ Pari River @@ KM 34 Kampung Batu Gajah Ipoh Manjoi Buntong

Tanjung

No. of sample 21 20 21 20 20 20Discharge, Q(m3/s) 7.98–17.94 3.60–8.46 4.44–17.44 3.80–9.65 9.72–47.90 9.66–17.04Water surface width, B (m) 20.2–21.1 22.2–25.6 17.3–20.8 24.6–28.0 20.3 19.3–19.5Flow depth, yo (m) 0.55–1.28 0.24–0.49 0.41–1.76 0.35–0.57 0.69–1.87 0.68–0.89Hydraulic radius, R (m) 0.52–1.14 0.23–0.47 0.39–1.51 0.31–0.55 0.65–1.77 0.63–0.81Water surface slope, So 0.0010 0.0036 0.0017 0.0011 0.0011 0.0012Mean sediment size, d50 (mm) 0.85–1.10 0.60–1.60 0.50–0.85 0.40–1.00 1.70–3.00 0.85–1.20Manning n 0.031–0.052 0.050–0.062 0.037–0.114 0.029–0.044 0.035–0.042 0.029–0.037B/yo 17–38 46–107 12–45 48–86 11–29 22–29yo/d50 539.8–1277.2 182.3–559.3 589.4–2708.0 346.3–1154.9 314.7–738.4 587.8–978.9R/d50 510.4–1140.4 178.3–544.7 564.2–2316.0 337.5–1118.0 294.6–640.5 547.8–901.9Bed load, Tb (kg/s) 0.40–1.25 0.20–1.82 0.25–1.37 0.02–1.21 0.40–0.80 0.35–0.79Suspended load, Ts (kg/s) 0.10–1.49 0.07–1.39 0.09–2.04 0.21–12.31 0.79–16.81 0.67–4.41Total load, Tj (kg/s) 0.57–2.47 0.65–2.11 0.47–2.69 0.23–12.82 1.25–17.62 1.03–4.89

Table 3 Range of field data for Langat River catchment (Ariffin,2004).

Study site Langat River @ Langat River @Kajang Dengkil

No. of sample 20 3Discharge, Q(m3/s) 3.75–39.56 33.49–87.79Water surface width, B (m) 15.0–20.0 30.0–33.0Flow depth, yo (m) 0.45–1.39 1.90–3.23Hydraulic radius, R (m) 0.42–1.22 1.70–2.66Water surface slope, So 0.0043–0.0051 0.0167Mean sediment size, d50 (mm) 0.37–2.13 0.52–0.95Manning n 0.049–0.081 0.273–0.345B/yo 14.4–33.5 9.30–17.4yo/d50 292.6–2055.7 3004.4–3626.6R/d50 273.6–1885.6 2585.2–3249.9Bed load, Tb (kg/s) 0.02–1.29 0.27–0.65Suspended load, Ts (kg/s) 0.66–77.51 18.69–118.31Total load, Tj (kg/s) 0.78–77.86 18.96–118.93

Table 2 to Table 4 show a summary with ranges for discharge(Q), water-surface width (B), flow depth (yo), hydraulic radius(R), water-surface slope (So), mean sediment size (d50), aspectratio (B/yo), flow resistance parameters (yo/d50 and R/d50), bedload (Tb), suspended load (Ts) and total bed material load (Tj).The mean sediment sizes for all sites show that the study reachesare sand-bed streams where d50 ranges from 0.40 to 2.0 mm. Theaspect ratios for the three rivers are between 11 and 107 indicatingthat they are moderate-size channels. The water-surface slopesof the study reaches were determined by taking measurementsof water levels over a distance of 200 m where the cross sectionis located (FISRWG, 2001). For all study sites the water-surfaceslopes were found to be mild with ranges between 0.001 and0.005. No over bank flow occurred during all measurements.

Low sediment transport rates, Tj occurred during the mea-surements with ranges between 0.01 to 17.62 kg/s while thedischarges varied between 0.73 and 47.90 m3/s for Kinta River

Table 4 Range of field data for Kulim River catchment (Chang, 2006).

Study site Kulim River @ Kulim River @CH 14390 CH 3014

No. of sample 6 12Discharge, Q(m3/s) 0.73–3.13 3.73–9.98Water surface width, B (m) 9.0–13.0 13.0–19.0Flow depth, yo (m) 0.20–0.54 0.36–0.58Hydraulic radius, R (m) 0.22–0.57 0.40–0.63Water surface slope, So 0.001 0.001Mean sediment size, d50 (mm) 1.00–1.95 1.10–2.00Manning n 0.033–0.053 0.024–0.037B/yo 23.4–44.8 26.0–52.5yo/d50 126.9–369.01 240.0–550.9R/d50 141.4–406.6 266.5–570.9Bed load, Tb (kg/s) 0.06–0.33 0.11–0.36Suspended load, Ts (kg/s) 0.02–0.23 0.03–1.21Total load, Tj (kg/s) 0.09–0.56 0.27–1.35

and Kulim River. Higher flow discharge occurred at Langat Riverup to 88 m3/s that resulted in higher sediment transport rates upto 119 kg/s.

5 Data analysis

Figures 10 to 12 illustrate the variation of Manning n with flowdepths and discharges for the three rivers in the present study.Five cross sections along Kinta River (Figure 10) show that n

increases with the increase in both flow depth and discharge.This could be attributed to grassy banks (Figure 5) and irregularcross sections. Table 2 shows that the range of n for Kinta Riveris between 0.03 and 0.060. For Langat River (Figure 11), bothstudy sites show that n decreases with the increase in both flowdepths and discharges as occurs in most streams (Chow, 1959).The range of n for Langat River as given in Table 3 is between0.05 and 0.35. As for the Kulim River (Figure 12), CH 14390


0.01

0.1

1 10 100

Q (m3/s)

Ma

nn

ing

n

0.01

0.1

11 0 100Q (m3/s)

Ma

nn

ing

n

0.01

0.1

1 10Q (m3/s)

Ma

nn

ing

n

0.01

0.1

0.1 1 10

yo (m)

Ma

nn

ing

n

0.01

0.1

0.1 1yo (m)

Ma

nn

ing

n

0.01

0.1

0.1 1yo (m)

Ma

nn

ing

n

(a) Kampar River @ KM 34

(b) Kinta River

(c)Raia River @ KampungTanjung

Figure 10 Manning n against Q and yo for Kinta River catchment.


0.01

0.1

1

1 10 100Q (m3/s)

Ma

nn

ing

n

0.01

0.1

1 10 100Q (m3/s)

Ma

nn

ing

n

0.01

0.1

1 10 100Q (m3/s)

Ma

nn

ing

n

0.01

0.1

1

0.1 1 10

yo (m)

Ma

nn

ing

n

0.01

0.1

0.1 1yo (m)

Ma

nn

ing

n

0.01

0.1

0.1 1 10

yo (m)

Ma

nn

ing

n

(d) Raia River @ Batu Gajah

(e) Pari River @ Manjoi

(f) Pari River @ Buntong

Figure 10 (Continued).


0.1

1

10 100Q (m3/s)

Ma

nn

ing

n

0.01

0.1

1 10 100Q (m3/s)

Ma

nn

ing

n

0.01

0.1

0.1 1 10yo (m)

Ma

nn

ing

n

0.1

1

1 10yo (m)

Ma

nn

ing

n

(a) Langat River @ Kajang

(b) Langat River @ Dengkil

Figure 11 Manning n against Q and yo for Langat River catchment.

0.01

0.1

0.1 1 10Q (m3/s)

Ma

nn

ing

n

0.01

0.1

1 10 100Q (m3/s)

Ma

nn

ing

n

0.01

0.1

0.1 1yo (m)

Ma

nn

ing

n

0.01

0.1

0.1 1yo (m)

Ma

nn

ing

n

(a) Kulim River @ CH 14390

(b) Kulim River @ CH 3014

Figure 12 Manning n against Q and yo for Kulim River catchment.


0.01

0.1

0.01 0.1n measured

nc

om

pu

ted

Strickler (1923) Meyer-Peter & Muller (1948)Lane & Carlson (1953) Limerinos (1970)Bray (1979) Bruschin (1985)Brownlie (1983)

0.01

0.1

0.01 0.1n measured

nc

om

pu

ted


0.01

0.1

0.01 0.1n measured

nco

mp

ute

d


0.01

0.1

0.01 0.1n measured

nco

mp

ute

d


0.01

0.1

0.01 0.1n measured

nc

om

pu

ted


0.01

0.1

0.01 0.1n measured

nco

mp

ute

d


(a) Kampar River @KM 34 (b) Kinta River

(c) Raia River @Kampung Tanjung (d) RaiaRiver @ Batu Gajah

(e) Pari River @ Manjoi (f) Pari River @ Buntong

Figure 13 Measured n against computed nbased on existing equations for Kinta River catchment.


0.01

0.1

1

0.01 0.1 1

nmeasured

nco

mp

ute

d


0.01

0.1

0.01 0.1

nmeasured

nco

mp

ute

d



Figure 14 Measured n against computed n based on existing equations for Langat River catchment.

0.01

0.1

0.01 0.1n measured

nco

mp

ute

d


0.01

0.1

0.01 0.1n measured

nco

mp

ute

d



Figure 15 Measured n against computed n based on existing equations for Kulim River catchment.

at the upstream shows that n increases with both flow depth anddischarge while at CH 3014 at the downstream, n decreases withboth flow depths and discharges. The range of n for Kulim River(Table 4) is between 0.024 and 0.053.

These values of n obtained at the three rivers suggest that thestreams are natural channels with somewhat irregular side slopesand grass on slopes as given in Table 1 (Chow, 1959).

6 Evaluation of existing equations

The evaluations of Equations 1 to 7 for the three rivers are shownin Figures 13 to 15. Examples of measured and computed n fromthe seven equations for representative data are given in Tables 5 to7. The ranges of n predicted by these seven equations are between0.010 and 0.040. Figures 13 to 15 show that all existing equationsunderestimate the measured n values for all three rivers. As aconsequence, these results in an unsatisfactory overprediction ofdischarge as depicted in Figures 16 to 18.

Equations 1 to 3 were developed for large rivers hence theresults show that they are not directly applicable for the moderate-size channels in the present study. Similarly, Equations 4 and 5were based on data from gravel-bed streams; the results obtainedalso show that these two equations do not apply well for sand-bed streams for the three rivers in the present study. Even thoughEquations 6 and 7 were based on sandy river data, they are also notapplicable perhaps due to the presence of grassy banks and chan-nel irregularities in the present cross sections as discussed earlier.

The pattern in error as shown in Figures 13 to 15 suggests animproved equation needs to be developed for these three riversin the present study in particular and other rivers having similarcharacteristics in general.

7 Development of new equations

Since the sand-bed streams in the present study are moderate-sizechannels with an aspect ratio between 11 and 107 and of mildslope (0.001–0.005), attempts were made to derive new equations


Tabl

e5

Eva

luat

ions

ofE

xist

ing

Man

ning

nE

quat

ions

for

Kin

taR

iver

Cat

chm

ent(

Abd

ulG

haff

ar20

03;C

hang

2006

).

Stud

yB

yo

d50

So

QM

easu

red

Stri

ckle

rM

eyer

-Pet

er&

Lan

e&

Car

lson

Lim

erin

osB

ray

Bru

schi

nB

row

nlie

site

s(m

)(m

)(m

m)

(m3/s)

n(1

923)

Mul

ler

(194

8)(1

953)

(197

0)(1

979)

(198

5)(1

983)

QQ

QQ

QQ

Q

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

Kam

par

Riv

er@

KM

34

21.1

1.28

1.00

0.00

1017

.941

0.05

20.

015

62.1

30.

014

64.8

70.

0258

.59

0.02

52.1

10.

0162

.68

0.03

35.8

00.

0237

.58

20.6

0.59

0.90

0.00

108.

142

0.03

20.

015

17.4

90.

014

18.1

80.

0216

.46

0.02

14.9

10.

0118

.14

0.02

10.9

70.

0211

.51

20.5

0.76

0.90

0.00

109.

805

0.04

00.

015

26.7

10.

014

27.6

70.

0224

.88

0.02

22.6

40.

0127

.43

0.02

16.1

90.

0217

.00

20.3

0.70

0.90

0.00

108.

856

0.03

80.

015

22.8

20.

014

24.2

30.

0221

.59

0.02

19.3

90.

0123

.52

0.02

13.9

90.

0214

.69

20.2

0.67

1.00

0.00

108.

710

0.03

60.

015

21.0

80.

014

22.0

90.

0219

.88

0.02

17.9

70.

0121

.84

0.02

13.1

80.

0213

.83

Rai

aR

iver

@K

ampu

ngTa

njun

g

25.6

0.29

21.

600.

0048

3.82

50.

059

0.01

613

.83

0.01

614

.45

0.02

12.9

80.

0211

.86

0.02

14.7

70.

038.

290.

029.

0725

.10.

336

0.60

0.00

485.

544

0.05

00.

014

20.1

20.

014

20.2

80.

0118

.47

0.02

17.1

90.

0120

.97

0.03

10.3

50.

0211

.31

25.5

0.46

71.

000.

0048

8.01

50.

061

0.01

532

.38

0.01

532

.62

0.02

29.7

20.

0227

.75

0.01

33.9

50.

0317

.09

0.03

18.6

925

.50.

462

1.00

0.00

488.

045

0.05

90.

015

31.8

00.

014

33.0

10.

0229

.99

0.02

27.2

60.

0133

.35

0.03

16.8

10.

0318

.38

22.2

0.48

51.

100.

0048

8.04

60.

056

0.01

529

.42

0.01

530

.04

0.02

27.4

40.

0225

.23

0.01

30.9

00.

0315

.67

0.03

17.1

3

Rai

aR

iver

@B

atu

Gaj

ah

18.5

0.41

0.70

0.00

174.

805

0.03

50.

014

12.0

00.

014

12.3

10.

0111

.30

0.02

10.2

40.

0112

.48

0.02

7.08

0.02

7.54

20.0

0.65

0.85

0.00

178.

398

0.04

60.

015

26.3

70.

014

26.8

00.

0224

.21

0.02

22.4

10.

0127

.19

0.03

15.0

60.

0216

.03

18.0

0.56

0.65

0.00

176.

461

0.04

20.

014

19.5

50.

014

19.8

20.

0118

.19

0.02

16.5

60.

0120

.06

0.02

10.9

70.

0211

.68

17.3

0.45

0.65

0.00

174.

894

0.03

70.

014

12.9

60.

014

13.2

40.

0112

.06

0.02

11.0

40.

0113

.42

0.02

7.49

0.02

7.98

18.1

0.67

0.60

0.00

177.

776

0.04

70.

014

26.5

80.

013

27.1

50.

0124

.95

0.02

22.3

60.

0126

.98

0.03

14.4

20.

0215

.35

Kin

taR

iver

@Ip

oh

28.0

0.57

0.55

0.00

118.

457

0.04

20.

014

26.3

50.

014

25.1

40.

0123

.84

0.02

22.1

90.

0126

.83

0.02

15.2

60.

0216

.06

28.0

0.35

0.80

0.00

114.

430

0.03

60.

014

11.0

90.

014

11.1

60.

0210

.18

0.02

9.51

0.01

11.6

50.

027.

210.

027.

5927

.50.

320.

600.

0011

3.79

80.

036

0.01

410

.01

0.01

410

.09

0.01

9.25

0.02

8.56

0.01

10.4

50.

026.

330.

026.

6624

.60.

510.

500.

0011

7.49

00.

034

0.01

319

.32

0.01

517

.71

0.01

17.7

30.

0216

.28

0.01

19.6

90.

0211

.22

0.02

11.8

125

.30.

440.

400.

0011

5.70

00.

037

0.01

316

.31

0.01

316

.04

0.01

14.9

70.

0213

.71

0.01

16.5

60.

029.

360.

029.

85

Pari

Riv

er@

Man

joi

20.3

1.61

3.00

0.00

1135

.911

0.03

70.

018

74.6

90.

016

82.5

70.

0272

.06

0.02

63.9

80.

0277

.97

0.03

48.0

80.

0350

.59

20.3

1.39

2.50

0.00

1128

.719

0.03

70.

017

61.1

30.

016

66.6

70.

0258

.24

0.02

52.3

30.

0263

.75

0.03

39.0

50.

0341

.09

20.3

0.91

1.70

0.00

1114

.157

0.03

80.

016

33.0

90.

015

35.3

60.

0231

.47

0.02

28.3

20.

0234

.55

0.03

21.1

30.

0222

.23

20.3

0.77

2.20

0.00

1112

.479

0.03

30.

017

24.2

40.

016

25.4

90.

0223

.28

0.02

20.8

40.

0225

.61

0.03

16.3

70.

0217

.23

20.3

0.69

2.20

0.00

119.

722

0.03

60.

017

20.4

20.

016

22.3

30.

0219

.62

0.02

17.5

60.

0221

.63

0.02

13.9

80.

0214

.72

Pari

Riv

er@

Bun

tong

19.5

0.89

1.20

0.00

1217

.040

0.03

10.

015

33.7

90.

015

33.8

00.

0230

.51

0.02

28.7

50.

0134

.89

0.03

20.4

00.

0221

.51

19.5

0.71

1.10

0.00

1211

.138

0.03

30.

015

24.1

60.

016

23.6

30.

0221

.57

0.02

20.6

00.

0125

.06

0.02

14.8

10.

0215

.62

19.5

0.83

0.85

0.00

1215

.561

0.03

00.

015

32.2

80.

015

32.2

30.

0229

.77

0.02

27.2

60.

0132

.95

0.03

18.7

30.

0219

.76

19.5

0.75

1.10

0.00

1210

.878

0.03

60.

015

25.9

20.

015

25.5

40.

0223

.14

0.02

22.0

80.

0126

.84

0.02

15.8

00.

0216

.67

19.3

0.74

1.10

0.00

1210

.563

0.03

60.

015

25.1

40.

015

25.1

90.

0222

.74

0.02

21.4

30.

0126

.04

0.02

15.3

50.

0216

.19


Tabl

e6

Eva

luat

ions

ofex

istin

gm

anni

ngn

equa

tions

for

Lan

gatr

iver

catc

hmen

t(A

bdul

Gha

ffar

2003

;Cha

ng20

06).

Stud

yB

yo

d50

So

QM

easu

red

Stri

ckle

rM

eyer

-Pet

er&

Lan

e&

Car

lson

Lim

erin

osB

ray

Bru

schi

nB

row

nlie

site

s(m

)(m

)(m

m)

(m3/s)

n(1

923)

Mul

ler

(194

8)(1

953)

(197

0)(1

979)

(198

5)(1

983)

QQ

QQ

QQ

Q

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

Lan

gat

Riv

er@

Kaj

ang

18.0

0.62

2.13

0.00

509.

055

0.06

10.

017

32.6

6–

––

–0.

0228

.09

0.02

34.6

40.

0318

.34

0.03

20.0

820

.01.

061.

570.

0050

24.7

760.

059

0.01

689

.77

––

––

0.02

76.5

50.

0292

.99

0.03

45.1

90.

0349

.46

20.0

1.39

1.46

0.00

5039

.562

0.05

70.

016

141.

2–

––

–0.

0211

9.48

0.02

144.

270.

0368

.04

0.03

74.4

515

.00.

450.

950.

0043

3.78

90.

066

0.01

516

.77

––

––

0.02

14.3

70.

0117

.58

0.03

8.99

0.03

9.81

17.0

0.85

0.61

0.00

5014

.195

0.06

10.

014

62.8

4–

––

–0.

0252

.51

0.01

63.1

30.

0328

.58

0.03

31.2

8

Lan

gat

Riv

er@

Den

gkil

302.

440.

810.

0167

54.0

780.

287

0.01

410

72–

––

–0.

0287

1.41

0.02

1035

.36

0.04

375.

90.

0442

4.11

303.

230.

950.

0167

87.7

920.

273

0.01

516

15–

––

–0.

0213

06.8

90.

0215

47.2

30.

0455

9.5

0.04

631.

1833

1.90

0.52

0.01

6733

.488

0.34

50.

013

857.

4–

––

–0.

0268

9.03

0.01

818.

510.

0429

1.2

0.04

328.

55

Not

e:d

75an

dd

90ar

eno

tava

ilabl

e.

Tabl

e7

Eva

luat

ions

ofex

istin

gm

anni

ngn

equa

tions

for

Kul

imR

iver

catc

hmen

t(C

hang

2006

).

Stud

yB

yo

d50

So

QM

easu

red

Stri

ckle

rM

eyer

-Pet

er&

Lan

e&

Car

lson

Lim

erin

osB

ray

Bru

schi

nB

row

nlie

site

s(m

)(m

)(m

m)

(m3/s)

n(1

923)

Mul

ler

(194

8)(1

953)

(197

0)(1

979)

(198

5)(1

983)

QQ

QQ

QQ

Q

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

n(m

3/s)

Kul

imR

iver

@C

H14

390

9.00

0.38

1.40

0.00

101.

821

0.03

80.

016

4.37

0.01

64.

460.

024.

020.

023.

760.

014.

640.

023.

020.

023.

179.

500.

371.

000.

0010

1.30

10.

052

0.01

54.

550.

015

4.67

0.02

4.23

0.02

3.90

0.01

4.80

0.02

3.02

0.02

3.17

9.10

0.22

1.50

0.00

100.

858

0.03

20.

016

1.74

0.01

51.

820.

021.

620.

021.

490.

011.

860.

021.

310.

021.

379.

100.

201.

600.

0010

0.72

60.

033

0.01

61.

500.

015

1.58

0.02

1.41

0.02

1.28

0.02

1.60

0.02

1.15

0.02

1.21

13.0

00.

541.

950.

0010

3.13

50.

053

0.01

79.

870.

016

10.6

00.

029.

300.

028.

490.

0210

.48

0.02

6.86

0.02

7.20

Kul

imR

iver

@C

H30

14

18.9

0.43

1.70

0.00

104.

773

0.03

70.

016

10.8

10.

016

10.8

00.

0210

.02

0.02

9.30

0.02

11.5

00.

027.

540.

027.

9216

.90.

471.

500.

0010

5.44

80.

034

0.01

611

.56

0.01

611

.74

0.02

10.7

30.

029.

930.

0212

.24

0.02

7.83

0.02

8.22

13.0

0.50

1.10

0.00

103.

890

0.03

60.

015

9.29

0.01

69.

100.

028.

140.

027.

950.

019.

740.

026.

040.

026.

3519

.00.

611.

100.

0010

9.98

20.

028

0.01

518

.44

0.01

518

.23

0.02

16.6

50.

0215

.75

0.01

19.2

40.

0211

.68

0.02

12.2

718

.50.

411.

180.

0010

5.81

90.

025

0.01

59.

420.

015

9.42

0.02

8.64

0.02

8.09

0.01

9.95

0.02

6.34

0.02

6.66


1

10

100

1000

1 10 100 1000Qmeasured

Qco

mp

ute

d


1

10

100

1 10 100Qmeasured

Qco

mp

ute

d


1

10

100

1 10 100Qmeasured

Qco

mp

ute

d


1

10

100

1000

1 10 100 1000Qmeasured

Qco

mp

ute

d


1

10

100

1 10 100Qmeasured

Qco

mp

ute

d


1

10

100

11 0 100Qmeasured

Qco

mp

ute

d


(a) Kampar River @KM 34 (b) Kinta River

(c) Raia River@ Kampung Tanjung (d) Raia River@ Batu Gajah

(e) Pari River @ Manjoi (f) Pari River @ Buntong

Figure 16 Measured Q against computed Q based on existing equations for Kinta River catchment.


10

100

1000

10000

10 100 1000 10000

Qmeasured

Qco

mp

ute

d


1

10

100

1 10 100Qmeasured

Qco

mp

ute

d



Figure 17 Measured Q against computed Q based on existing equations for Langat River catchment.

1

10

100

1 10 100Qmeasured

Qco

mp

ute

d


1

10

100

1 10 100Qmeasured

Qco

mp

ute

d



Figure 18 Measured Q against computed Q based on existing equations for Kulim River catchment.

for Manning n. Based on the parameters used in Equations 1 to 7,the best parameters to use are yo/d50, and R/d50 (Abdul Ghaffar,2003). Figures 19 and 20 plot Manning’s n against both yo/d50,and R/d50, respectively.

The following two equations (Chang, 2006) are recom-mended for determining Manning n for moderate-size andsand-bed streams in Malaysia with a regression coefficientR2 = 0.86:

n = 4 × 10−8

(yo

d50

)2

− 5 × 10−5

(yo

d50

)+ 0.0582 (8)

n = 5 × 10−8

(R

d50

)2

− 7 × 10−5

(R

d50

)+ 0.0622 (9)

Both equations confirm that Manning n are affected by thevariation in flow depth and mean sediment size as found byStrickler (1923), Meyer-Peter & Muller (1948), Limerinos(1970), Bray (1979), Bruschin (1985), and Julien (2002).

Table 8 gives a summary of accuracy for Equations 8 and9 based on the discrepancy (ratio of computed discharge overmeasured discharge) for all the 168 data. The results show that65% of all the data are within ±0.25 range of discrepancy ratiofor Equation 8 (Figure 21) while 72% of all the data are within±0.25 range of discrepancy ratio for Equation 9 (Figure 22). Theaverage discrepancy ratio of Equation 8 for all 168 river data is0.93 while for Equation 9 is 1.03. This means that, on average,both equations have an error between 3% and 7% suggestingthe viability of using these new equations for predicting flowdischarge for the rivers with similar characteristics as studied.


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 500 1000 1500 2000 2500 3000 3500 4000

y/d50

Ma

nn

ing

n

Pari River @ Manjoi Pari River @ Buntong Raia River @ Kg TanjungRaia River @ Batu Gajah Kinta River @ Ipoh Kampar River @ KM 34Langat River @ Kajang Langat River @ Dengkil Kulim River @ CH14390Kulim River @ CH 3014

0582.010−510450

−52

50

−8

d

y

d

yn = × × +oo

Figure 19 Manning n against yo/d50.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 500 1000 1500 2000 2500 3000 3500

R/d50

Ma

nn

ing

n


0622.010−710550

2

50 d

R

d

Rn = −5−8× × +

Figure 20 Manning n against R/d50.


Table 8 Summary of accuracy of equations 8 and 9.

Equation River Location Discrepancy Ratio

0.75–1.25 (%) Average

8

PariManjoi 95.00 0.87Buntong 70.00 0.77

RaiaKampung Tanjung 40.00 1.25Batu Gajah 80.95 0.88

Kinta Ipoh 75.00 0.81Kampar KM 34 80.95 0.84

LangatKajang 35.00 1.24Dengkil 100.00 0.90

Kulim CH 14390 66.67 0.91CH 3014 16.67 0.67Average for All Data 65.64 0.93

9

PariManjoi 90.00 0.93Buntong 100.00 0.88

RaiaKampung Tanjung 25.00 1.31Batu Gajah 95.24 1.03

Kinta Ipoh 95.00 0.91Kampar KM 34 100.00 0.97

LangatKajang 20.00 1.40Dengkil 66.67 1.11

KulimCH 14390 100.00 0.94CH 3014 33.33 0.71Average for All Data 71.78 1.03

Note: Discrepancy Ratio = QComputed/QMeasured.

0.1

1

10

100

1000

0.1 1 10 100 1000

Qmeasured (m3/s)

Qc

om

pu

ted

(m

3/s

)

Pari River @ Manjoi Pari River @ Buntong Raia River @ Kg Tanjung

Raia River @ Batu Gajah Kinta River @ Ipoh Kampar River @ KM 34

Langat River @ Kajang Langat River @ Dengkil Kulim River @ CH14390

Kulim River @ CH 3014

Discre

pancy R

atio = 1.25

Discre

pancy R

atio = 0.75

Figure 21 Comparison between measured and predicted Q byequation 8.

8 Conclusions

Applications of Manning n values from the existing equationsresult in the computed discharges overpredicted the measureddischarges. Attempts were then made to derive new equations forcomputing Manning n for application to the moderate-size andsand-bed streams in Malaysia based on 168 data collected from

0.1

1

10

100

1000

0.1 1 10 100 1000

Qmeasured (m3/s)

Qc

om

pu

ted

(m

3/s

)


Discre

pancy R

atio = 1.25

Discre

pancy R

atio = 0.75

Figure 22 Comparison between measured and predicted Q byequation 9.

Kinta, Langat and Kulim Rivers. The resulting Equations 8 and9 have an error less than 10% in predicting flow discharge for allthe measured data.

Acknowledgements

The research study is funded by Department of Irrigation andDrainage Malaysia (JPS (PP)/SG/2/2000). The authors gratefullyacknowledge Prof. Pierre Y. Julien (Colorado State University,USA), Prof. Willi H. Hager (ETH Zurich, Switzerland) and thereviewers for their comments on the manuscript.

Notation

B = width of water surface (m)d = sediment size (mm)di = Size of particle intermediate axis for which i% of sample

of bed material is finern = Manning’s roughness coefficientQ = Discharge (m3/s)Tb = Bed load (kg/s)Ts = Suspended load (kg/s)Tj = Total bed material load (kg/s)R = Hydraulic radius (m)R2 = Regression coefficientSo = Water-surface slopeyo = average flow depth (m)

References

1. Ab. Ghani, A., Zakaria, N.A., Abdullah, R., Chang,C.K., Sinnakaudan, S.K. and Mohd Sidek, L. (2003).


River Sediment Data Collection and Analysis Study,Contract Research No. JPS (PP)/SG/2/2000, Department ofIrrigation and Drainage, Malaysia, Kuala Lumpur.

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revised equations for manning’s coefﬁcient for...

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