03. the validity of rouse equation for predicting suspended sediment

7/28/2019 03. the Validity of Rouse Equation for Predicting Suspended Sediment

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International Conference on Sustainable Development for Water and Waste Water Treatment Yogyakarta, INDONESIA, December 14-15, 2009

The Validity of Rouse Equation for Predicting Suspended SedimentConcentration Profiles in Transversal Direction of

Uniform Open Channel Flow

B. A. Kironoto Prof., Civil and Environmental Engineering Department, Universitas Gadjah Mada, Indonesia

Email: [email protected]

B. Yulistiyanto Dr., Civil and Environmental Engineering Department, Universitas Gadjah Mada, Indonesia

Email: [email protected]

Abstract

Among several equations to predict suspended sediment concentration profiles found inliteratures, Rouse equation can be considered as the most popular one. Rouse equation isbased on logarithmic velocity distribution of 2-Dimensional flow, that relatively similar tothe flow characteristics at the center of channel. As reported in literatures, Rouse equationcan predict suspended sediment concentration profiles satisfactorily, based on laboratoriesor fields data, especially those measured at the center of channel. However, in the edgeregion, near the side wall of channel, the validity of Rouse equation to predict suspended

sediment concentration profiles need to be evaluated. In order to evaluate the validity of Rouse Equation, 125 profiles of suspended sediment concentration of laboratory data measured by using optical silt measuring instruments type (Foslim probe) in flume at 5different positions in transversal direction , and 50 profiles of suspended sediment concentration of field data measured in Mataram irrigation channel by using Opcon

probe at 5 different positions were analyzed. The results of the analyzed data showed that the Rouse equation can satisfactorily predict the profiles of suspended sediment concentration data, especially for the data measured at the center of channel, either for laboratory or field data. However, away from the center of channel, the equation deviates

from the measured data, and needs to be corrected. By applying a certain correction factor to Rouse Parameter as a function of position in transversal direction, ' = f (z/B), the

Rouse equation can be used to predict the profiles for the whole cross section, from thecenter to the edge of the channel. At the center of the channel, ' 1, and tend to increase,

' > 1, closer to the edge of channel. The existence of bed load transport and the differenceof channel wall roughness slightly influence the '-values, however their influences are not

significant compared to the scattered data.

Keywords: Rouse equation, suspended sediment concentration, transversal direction,laboratory and field data.


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The Validity of Rouse Equation For Predicting Suspended Sediment Concentration Profiles in Transversal Direction of Uniform Open Channel Flow

1. INTRODUCTION

In irrigation channel design, reservoir design, and river improvement, the information of suspendedsediment profiles is often required. The information of suspended sediment load transport can beobtained through measurement or sampling of suspended sediments in the field, or by predicting withthe equations found in literatures. In literatures, many equations can be used to determine thesuspended sediment concentration distribution, such as Rouses equation (1937), Lane and Kalinskesequation (1941), Einsteins (1955) equation, etc. (as reported in Graf, 1984).

Among the equations mentioned above, the Rouses equation might be considered as the most popular one, because of its reliability and widely used in literatures.

The equations of suspended sediment concentration distributions are generally developed in 2D-openchannel flow, which have similar characteristics to that at the center of channel. In certain conditions,the information about the profile of suspended sediment concentration at different positions in

transversal direction, from center to the edge of channel are often required, for example, for predictingthe amount of suspended sediment discharge in channel, for studying the spread of pollutant in river flows, etc.

Whether the Rouses equation can be used or not to predict the profiles of suspended sedimentconcentration in transversal direction, from center to the edge of the channel, still needs to beexamined, and will be investigated in this study. The Study was carried out based on the measurementdata of suspended sediment concentration, measured at different positions, from center to the edge(side wall) of channel, either for laboratory and for field data (in Mataram Irrigation channel,Yogyakarta, Indonesia).

2. THEORETICAL BACKGROUND

Rouses Equation (1937, in Graf, 1984) was derived from the 2-dimensional of logarithmic velocitydistribution of turbulent flow, with the assumption that the diffusion coefficient of suspendedsediments, s, can be approached with the momentum transfer coefficient, m, and can be written in ageneral form as :

s = m (1)

Based on the assumption given above, Rouse (1937, in Graf, 1984) got an equation of suspendedsediment concentration distribution as follows :

z

a a Da

y y D

C C

= (2)

with

*uw

Z s

= (3)


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International Conference on Sustainable Development for Water and Waste Water Treatment

where C is the suspended sediment concentration at a point of a distance y from the reference point;

C a, concentration of the reference point, at a distance of a from reference point; D is a flow depth; w s ,is settling velocity of suspended sediment particles, Z is a Rouses parameter; is Von-Karmanconstant , and = 1.

From the equation (3) above, it is known that for certain value of friction velocity, , the value of Z is proportional to the settling velocity, w s, and so, the smaller of the size of sediment particles (whichmeans that the velocity to be smaller), the value of Z become smaller; and vice versa. According toequation (2), for the smaller value of Z , the distribution of suspended sediment concentration, C ,

become more uniform, and for the greater value of Z , the distribution of suspended sedimentconcentration, C , become more non-uniform. Chien (1954, in Graf, 1984) found that the value of inequation (1) approaching to = 1, for fine sediment particles, and tend to be smaller, < 1, with theincreasing value of sediment particles.

Settling velocity of suspended sediment particle can be calculated according to equation (Bogardi,

1978):

2

181 s s

sd

g w= (4)

or by using the settling velocity graph vs. sediment particles diameter (Bogardi, 1978). In equation (4),d s is a representative diameter of suspended sediment particles; ws is settling velocity of suspendedsediment particle; s and are density of sediment and water.

3. DATA FOR ANALYSIS

Two types of data were analyzed in this study, i.e., laboratory and field measurements data, whichcomprise of 125 profiles of suspended sediment concentration of laboratory data measured in flume

by using Foslim probe at 5 different positions in transversal direction , and 50 profiles of suspended

sediment concentration of field data

measured in Mataram irrigation channel by using Opcon probeat 5 different positions.

From the 125 profiles of laboratory data, 50 profiles were conducted in uniform open channel flowwithout bed load transport, while the rest of 75 profiles were conducted in uniform flow with bed loadtransport. The data were measured in sediment-recirculating flume located at the hydraulic laboratoryof enggineering science research center of Gadjah Mada University. The dimension of the flume is 10m in long, 0.6 m in width and 1.0 m in height. Bed material used in the flume was fine sand material,with roughness value, k s = 0.072 cm. For each runs, 5 profiles of suspended sediment concentration(and velocity profiles) were measured at different positions in transversal direction, from center to theedge of channel, i.e., at z = 1/2 B, 1/4 B, 1/8 B, 1/16 B and 1/30 B, where B is the channel width.

In addition to laboratory data, 50 of suspended sediment concentration profiles of field data were alsoanalyzed in this study. The profiles were measured from 10 different cross sections (rectangular channel) in Mataram Irigation Channel, in Yogyakarta. Channel dimensions vary between 1.5 m to 4.5m, with roughness values, k s = 2.25 cm. For each flows at certain cross section, 5 profiles of suspended sediment were measured at different positions in transversal direction, from center to theedge of channel, i.e., at, z = 1/2 B, 3/8 B, 1/4 B, 1/8 B, and 1/16 B, where B is the width of channel.Detail measurement locations in transversal direction, both for laboratory and filed measurements aregiven in Figure 1.


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Suspended sediment concentration profiles of laboratory data were measured by using Foslim probe-set, while for field data in Mataram Irrigation Channels, Yogyakarta, the profiles were measured byusing Opcon probe-set.

Main parameters of the flow data analyzed in this study are given in Table 1 and Table 2.

Fig. 1: Location of measurement at different positions in transversal direction(a . Laboratory measurement; b. Field measurement)

D

B = 0.60

1/16B 1/4B1/30B 1/8B z/B = 1/2B

D

B = 1.5 4

1/8B 3/8B1/16B 1/4B z/B = 1/2B


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Table. 1:The main flow parameters (laboratory data; Kironoto, et al, 2004)

Run Q S o D B/D U u *ct qb

(lt/dt) (-) (cm) (-) (cm/dt) (cm/dt) (gr/lt) (gr/dt)

RQ1S1 15.02 0.0005 12.0 5.00 20.861 1.19 1.128 -RQ1S2 0.001 10.7 5.61 23.395 1.41 1.131 -RQ1S3 0.0015 10.4 5.77 24.071 1.43 1.133 -RQ1S4 0.002 10.0 6.00 25.033 1.46 1.132 -RQ1S5 0.0025 9.2 6.52 27.210 1.70 1.140 -

RQ2S1 18.14 0.0005 12.8 4.69 23.62 1.30 1.274 -RQ2S2 0.001 12.1 4.96 24.986 1.44 1.269 -RQ2S3 0.0015 11.2 5.36 26.994 1.57 1.265 -RQ2S4 0.002 10.7 5.61 28.255 1.66 1.268 -

RQ2S5 0.0025 9.5 6.32 31.824 1.65 1.271 -MQ3S1 23.33 0.0005 15.5 3.87 25.086 1.49 1.406 0.006MQ3S2 0.001 15.1 3.97 25.751 1.46 1.399 0.014MQ3S3 0.0015 14.6 4.11 26.632 1.55 1.404 0.021MQ3S4 0.002 14.1 4.26 27.577 1.55 1.451 0.031MQ3S5 0.0025 13.7 4.38 28.382 1.69 1.410 0.036

MQ4S1 26.45 0.0005 15.8 3.8 27.901 1.71 1.540 0.015MQ4S2 0.001 15.4 3.9 28.625 1.72 1.540 0.022MQ4S3 0.0015 15.2 3.95 29.002 1.81 1.546 0.026MQ4S4 0.002 14.7 4.08 29.989 1.78 1.666 0.036MQ4S5 0.0025 14.3 4.20 30.827 1.78 1.665 0.041

MQ5S1 29.57 0.0005 16.8 3.57 29.335 1.77 1.795 0.017MQ5S2 0.001 16.5 3.64 29.869 1.84 1.798 0.028MQ5S3 0.0015 16.0 3.75 30.802 1.98 1.777 0.029MQ5S4 0.002 15.7 3.82 31.391 2.04 1.787 0.044MQ5S5 0.0025 15.3 3.92 32.211 2.24 1.795 0.054


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Table. 2: The main flow parameters (field data; Kironoto and Ikhsan, 2005)

Remarks :Q = measured flow discharged;S o = channel bed slope;

D = flow depth; B/D = aspect ratio; B = flume / channel wide (= 60 cm; for laboratory channel; for filed channel, B-value variates );U =mean flow velocity;u*ct = friction velocity in the center of channel ( z/B = 0.5);

= mean cross-sectional suspended sediment concentration; qb = (bed load ); for field data, no bed load mesurement data.

4. RESULTS OF ANALYSIS AND DISCUSSIONS

Typical examples of suspended sediment concentration profiles measured at different locations intransversal direction, from center to the edge of channel, are given in Figure 1, respectively, for laboratory and field data. The plot data in the figure are typically represented by Run RQ1S2 andFMQ6S6. For laboratory data, the profiles of suspended sediment concentration from center to theedge of channel are typically represented by profiles RQ1S2A, RQ1S2B, RQ1S2C, RQ1S2D, andRQ1S2E. While for field data, the profiles of suspended sediment concentration are typicallyrepresented by profiles of FMQ6S6A, FMQ6S6B, FMQ6S6C, FMQ6S6D, and FMQ6S6E. As shownin Figure 1, the profiles of suspended sediment concentration changed from center to the edge of channel, where closer to the edge, the suspended sediment concentration profiles become smaller andto be more non-uniform. These trends occur both for laboratory and field data used in this study. Thecharacteristics difference between the two types of data are the amount of suspended sedimentconcentration, channel dimension, and the channel walls raoughness ( i.e. , glass, plastered concrete andstone masonry walls), as given in Table 1 and 2 above.

RUNQ S o B D B/D U u *ct

Type of channel walls(m3/dt) ( - ) (m) (m) ( - ) (m/dt) (m/dt) (gr/lt)

FMQ1S1 2.182 0.00067 3.50 1.05 3.33 1.187 0.081 5.66 stone masonry wall

FMQ2S2 1.369 0.00073 2.00 1.07 1.87 1.174 0.080 5.21 plastered concrete wall










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Fig. 2: Typical examples of suspended sediment profiles at different positions in transversal direction(a). laboratory data, ( b). fields data

In Figure 2 are given examples of typical suspended sediment profiles data measured at the center (profiles FMQ6S6A and RQ2S2A) and at the edges (profiles FMQ6S6E and RQ2S2E) of the channel,

both for laboratory and field data; in the same figure is also shown the Rouse equation for differentvalues of ' (see Equation 8 below), where ' is a corection coefficient of given in Rouse

parameter (Equation 3). As shown in Figure 2, Rouse equation shows a good agreement with the datameasured at the center of the channel (profile RQ2S2E and profile FMQ6S6E), where ' = 1.However, closer to the wall, in the edge region of the channel, the best fit of Rouse equation to thedata, obtained for ' > 1, i.e. , ' = 2.86 and ' = 1.7, respectively for profile RQ2S2E and profileFMQ6S6E). These results mean that Rouse equation can still be used to predict the suspendedsediment concentration in the edge region of the channel, however, the -value of Rouse parameter inEquation 3, should be corrected as a function of z/B, i.e. = ' = f ( z/B).


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Fig. 3: Comparation between measured data of suspended sediment concentration profiles and Rouseequation(a. field data ; b. laboratory data)

The distribution of suspended sediment concentration in Rouse equation is influenced by the values of Rouse parameter, Z , which is proportional to settling velocity, w s. The smaller size of particles, thevalue of w s and Z become smaller, which give the distributions of suspended sediment concentration,C/C a , become more uniform, and vice versa , the greater value of Z , the distributions of suspendedsediment concentration, C/C a, become more non-uniform.

Considering the measured data of suspended sediment concentration profiles in the edge region of channel which are more uniform compared with the distribution in the center of the channel, andconsidering the characteristic of Rouse equation (and Rouse parameter, Z ), one can conclude thatcloser to the edge (side wall) ragion of the channel, the value of Rouse parameter, Z , become smaller.

The smaller value of Z from the center to the edge of channel, especially due to the smaller value of settling velocity, w s. The settling velocity, w s, that is a function of the size of suspended sediment

particle, as well as the suspended sediment concentration, theoritically also variate from the center tothe edge of channel. Fugate and Friedrichs (2001) showed that the settling velocity of suspendedsediment particles increase with the increasing value of suspended sediment concentration. This


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means that the settling velocity of particle, w s, in the edge region of channel is smaller compared with

that in the center of the channel.The variation of setting velocity, w s, in the channel can be obtained through suspended sedimentssampling, from the center to the edge of channel. Although the variations of w s (and friction velocity,u*) theoretically can be determined, but to determine these values (especially in the fields) are not easyand are not practical. To solve these difficulties, Rouse parameter, Z , was determined from the

parameters, such as, , w s, and -values obtained in the center of the channel, but to provide a goodagreement between the measurement data (in the edge region of channel) with Rouse equation, acorrection factor that is a function of position in transversal direction should be applied. A correctionfactor was determined using the measured data, as explined in the following.

By using the flow parameters as well as the suspended sediment parameters obtained at the center of the channel ( z / B = 0.5), Rouse parameter, Z (Equation. 3), can be written as:

ct ct

ct s

ct u

w

Z * = (5)

For the others positions in transversal direction, i.e., z/B < 0.5, correction factors - which consider thevariation of w s and u* in transversal direction - should be applied to Rouse parameter, as :

ct B z B z ct s B z

B z uCt

wCte Z

*/2/

/1/ .

.=

(6)

or ct B z

ct s

B z u

w Z

*// '

=

(7)

where

B z B z

B z

B z Cte

Cte

/2/

/1

/'

1

=

or B z

B z B z

B z Cte

Cte

/1

//

/'

=

(8)

In Equation. 8 above, Z z/B, is Rouse parameter which is a function of z/B (positions in transversaldirection), w sct is settling velocity of suspended sediment particle obtained from suspended sedimentsampling taken at the center of the channel, and is friction velocity at the center of the channel,which can be calculated with the energy gradient method, = ., or from the measured data of velocity profiles (with the Clauser method, see Kironoto, 2007). B z /' is a correction factor of Rouse

parameter, expressed as a function of z/B. In Figure 3 above, it is shown examples of determining thevalue of B z /' for data RQ2S2 and FMQ6S6. With the least square method, the value of correctionfactor, B z /' , can be obtained by finding the best fit between the measurement data with Rouseequation. For position at the center of the channel, namely at the position of z/B = 0.5, it is obtained

B z /' 1. The complete results of B z /' analyzed in this study are given in Table 3, 4, and 5,respectively, for laboratory data without bed load, laboratory data with bed load bed, and field data.From the results of '-values (for the simplification of writing, B z /' is written as '), in Figure 4 and5, one can see that although the scattered of data is rather significant, but a clear trend appears for thedata plotted in the figures, i.e., closer to the edge of the channel, the value of ' tend to increase.


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Whether the exixtance of bed load transport influence the '-values or not, can be seen in Figure 4.The data of '-values plotted in Figure 4, are distinguished into two groups, i.e, data without and with bed load transport (laboratory data only). As given in the figure, the trend of the two groups of datashow slight different trend especially for z/B < 0.25; the values of for the data with bed loadtransport tend larger than those for data without bed load. However, this different trend is notsignificant, compared with the scattered data of the two groups of data. The influence of wallroughness is investigated in Figure 5, where the data of '-values are distinguished into two groups of data, i.e., data with plastered concrete wall and data with stone masonry wall. As shown in Figure 5,the regression curve of the two groups of data show also a slight different trend for z/B < 0.25, wherethe '-values of data with stone masonry wall tend higher than that for plastered concrete wall;hovewer the difference between the two groups of data is also not significant.

In Figure 6, it is plotted the values of ' vs. z/B, both for laboratory and field data. It can be seen fromthe figure that, although the two groups of data shows difference relation, however, both of the data

show similar trend, i.e. , closer to the edge region of the channel, the values of ' tend increase. For z/B = 0,5, the values of ' 1, while for data closer to the edge of channel ( z/B < 0,5), ' > 1. For thesame value of z/B, the value of ' for laboratory data tend higher compared with that for field data.

Table 3. Correction factor of Rouse parameter, ', for laboratory data (without bed load )

Run '-value at different positions of z/B

1/2B 1/4B 1/8B 1/16B 1/30BRQ1S1 1.20 1.90 1.78 2.23 2.82

RQ1S2 0.44 1.13 1.19 1.50 2.79

RQ1S3 1.45 2.33 1.28 1.82 3.40

RQ1S4 1.62 2.16 2.47 2.65 3.52

RQ1S5 1.05 1.56 1.01 2.11 2.09

RQ2S1 0.93 2.03 1.67 2.12 1.70RQ2S2 0.97 1.56 2.60 2.68 2.86

RQ2S3 1.75 1.91 1.55 1.82 2.09

RQ2S4 0.92 2.49 2.39 2.23 3.17

RQ2S5 1.50 2.81 2.94 2.13 2.21

Average 1.19 1.99 1.89 2.13 2.66


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Table 4. Correction factor of Rouse parameter, ', for laboratory data (with bed load )

Run '-value for different positions of z/B

1/2B 1/4B 1/8B 1/16B 1/30BMQ3S1 0.71 1.04 1.01 2.96 2.14

MQ3S2 2.10 2.72 2.69 3.78 3.88

MQ3S3 1.27 2.15 2.17 2.11 2.52

MQ3S4 0.51 0.72 1.61 1.43 2.21

MQ3S5 0.80 1.88 1.64 2.97 2.94

MQ4S1 1.00 2.22 1.60 2.36 1.41

MQ4S2 1.10 1.72 1.92 2.88 4.13

MQ4S3 0.81 0.92 2.06 2.27 2.88MQ4S4 0.70 2.51 2.33 2.12 3.70

MQ4S5 1.09 2.50 2.61 3.90 4.17

MQ5S1 1.32 2.58 3.09 2.15 3.13

MQ5S2 1.18 2.62 2.05 1.47 3.39

MQ5S3 1.05 2.35 3.12 3.81 2.41

MQ5S4 0.95 1.27 2.51 3.58 3.92MQ5S5 1.20 2.80 2.56 2.73 3.65

Average 1.05 2.00 2.20 2.70 3.10

Table 5. Correction factor of Rouse parameter, ', for field data (Mataram cahnnel)

Run '-value for different positions of z/B

1/2 B 3/8 B 1/4 B 1/8 B 1/16 BFMQ1S1 1.00 1.05 1.10 1.15 1.90

FMQ2S2 1.00 1.40 1.50 1.60 1.70

FMQ3S3 1.05 1.10 1.10 1.50 1.60

FMQ4S4 0.95 1.30 1.20 1.30 1.40

FMQ5S5 1.05 1.60 1.50 1.70 1.70FMQ6S6 1.05 1.30 1.50 1.60 1.70

FMQ7S7 0.90 1.30 1.20 1.40 1.50

FMQ8S8 1.10 1.40 1.50 1.60 1.80

FMQ9S9 0.85 1.20 1.25 1.30 1.35

FMQ10S10 1.20 1.40 1.60 2.20 2.10 Average 0.99 1.29 1.32 1.46 1.63


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Fig. 4: Plot data of vs. z / B (data with and without bed load)

Fig. 5: Plot data of ' vs. z / B (plastered concrete and stone masonry walls data).

By considering that ' = f ( z/B) for laboratory and field data do not show significant difference in therange of our data used in this study compared with the scattered data, the final correlation of ' as afunction z/B is obtained for all groups of data; the regression equation for all data used in this study isgiven in Figure 7, and the regression equation for all the data (laboratory and field data) can be givenas following :

' = -0.55 ln ( z/B) + 0.75 (9)

where according to Equation. 9, for z/B = 0.5, ' = 1.1 1.


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Fig. 6: Plot data of ' vs. z / B for comparation of laboratory and field data

Fig. 7: Plot data of ' vs. z / B for comparation of laboratory and field data (averaged data)

5. CONCLUSIONS

From the results of analysis to the data used in this study, some conclusions might be drawn as thefollowing.

1. By comparing the measured data used in this study with Rouse equation, it can be concluded thatRouse equation can predict the profiles of suspended sediment concentration satisfactorily only atthe center of channel, while closer to the channel edge region (side wall channel region), theRouse equation deviate from the measured data.


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2.

In order to use the Rouse equation in the whole channel cross section, i.e. , from center to the edgeof channel cross section, a correlation factor of ' = f ( z/B) as given in Equation.9, sholud beapplied to Rouse parameter as given in Equation. 3 (or Equation. 7).

3. Although the plot of ' = f ( z/B) rather scattered, however the trends of data analyzed in thisstudy clearly appear, i.e. , closer to the channel edge region, ' tend to increase; at the center of the channel, ' 1; while closer to the channel edge, ' > 1.

4. The influence of sediment bed load transport, and channel wall roughness to the values of ' = f ( z/B) is not significant compared with the scattered data.

5. The conclusions drawn here are valid only in the range of data used in this study. Further researches are necessary for the other range of the data.

6. ACKNOWLEDGMENTS

This paper was based on further analysis of the measured data obtained previously by Kironoto et al(2004) and by Kironoto and Ikhsan (2005). The author thank to Totoh Andoyono, Fransiska Yustiana,and Chairul Muharis, and also to Cahyono Ikhsan, which have helped in the research process of Kironoto et al (2004), and Kironoto and Ikhsan (2005).

7. REFERENCES

[1] Bogardi, J. (1978). Sediment Transport in Alluvial Streams . Akademiai Kiado, Budapest,Hungary.

[2] Fugate, D. C., and Friedrichs, C. T., 2001, Determining concentration and fall velocity of estuarine particle populations using ADV, OBS, and LISST, Elsevier Science Ltd.,www.sciencedirect.com

[3] Garde, R.J. and Raju, K.G.R., 1977, Mechanics of Sediment Transportations and Alluvial Stream Problems , 2 nd Edition, Wiley Eastern limited, New Delhi .

[4] Graf, W.H., 1984, Hydraulics of Sediment Transport , McGraw-Hill Book Company, NewYork.

[5] Kironoto, B.A., Andoyono, T., Yustiana, F, and Muharis, C., 2004, The Study of SuspendedSediment Sampling for Determining Suspended Sediment Load in Open Channel Flow, Hibah

Bersaing Research , XII/1-Th. 2004, Institute for Research, Gadjah Mada University, Yogyakarta(in Indonesia).

[6] Kironoto, B.A., and Ikhsan, C., 2005, The Study of Suspended Sediment Sampling for Determining Suspended Sediment Load in Open Channel Flow, Hibah Bersaing Research ,,XII/2-Th 2005, Institute for Research, Gadjah Mada University, Yogyakarta (in Indonesia).

[7] Kironoto, B. A., 2007. "The using of Clauser Method for predicting Friction Velocity, , inMataram Rectangular Channel.", Media Teknik, No.4, XXIX, Edition of November 2007,Yogyakarta (in Indonesia).

03. the validity of rouse equation for predicting suspended sediment

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