Experiments on sediment transport in shallow flows in …hydrologie.org/hsj/340/hysj_34_04_0465.pdf · Experiments on sediment transport in shallow flows in high gradient channels

Hydrologjcal Sciences - Journal - des Sciences Hydrolog/ques, 34,4, 8/1989

Experiments on sediment transport in shallow flows in high gradient channels

NADIM M. AZIZ Department of Civil Engineering, Clemson University, Clemson, South Carolina, 29634-0911, USA

DAVID E. SCOTT The Piedmont Group, Greenville, South Carolina 29602, USA

Abstract The main objective of this paper is to present the results of an experimental study relating to the transport of sediment under certain conditions not typical of river sedimentation studies. The area of sediment transport lacks information on the transport down high gradient channels that are typical of streets, construction sites and agricultural land, in addition to mountain torrrents. The study of transport of non-cohesive sediment in high gradient channels includes determination of the transport capacity of shallow flows in high gradient channels with simulated bed roughness and various grain sizes. Regression analysis was performed to relate the dependent and independent variables in functional relationships and revealed good correlation.

Expériences sur le transport sédimentaire dans des canaux à faible débit et a dénivellation importante

Résumé L'objectif principal de cette étude est de présenter les résultats d'une recherche expérimentale sur le transport des sédiments sous certaines conditions non-caractéristiques d'études précédentes sur la sédimentation fluviale. L'étude sur le transport des sédiments manque d'information sur le transport le long des canaux à forte dénivellation tels que rues, sites de construction, terrains agricoles et torrents alpins. L'étude du transport des sédiments non-cohésifs dans les canaux à forte dénivellation comprend la mesure de la capacité de transport dans les canaux à faible débit avec des lits à rugosité simulée et à grosseur de grain variable. L'analyse inverse a été réalisée afin d'intégrer les variables déterminées et indéterminées dans un rapport fonctionnel, tout en révélant une parfaite corrélation.

NOTATION a,b constants D grain diameter g gravitational constant h flow depth Q water flow rate

Open for discussion until 1 February 1990 465

Nadim M. Aziz & David E. Scott 466

Qb sediment flow rate r correlation coefficient 5 channel slope 7 water density 7 sediment density

INTRODUCTION

Soil is usually disturbed for the purpose of construction and during agricultural activities such as tillage and irrigation. Such operations make soils vulnerable to erosion by air and water. There are several measures in current use for soil conservation and for erosion and sediment control. These are, however, preventative physical measures that are based on rates of erosion and transport. In order to evaluate better erosion and sediment transport rates for better control of soils, models that are physically based to suit such problems are needed.

During runoff from rainfall or from irrigation activities, the flow of water often carries considerable amounts of sediment. The amount of soil lost by water may be significant especially when the exposed soil lies on steep slopes. Under appropriate conditions of flow and sediment characteristics, the sediment is transported in a zone near the bed of the flow domain as a bed load.

The conservation of topsoil over crop land is a significant subject of research because of a potential threat to world productivity due to soil loss. The loss of fertile topsoil from farm land is mainly due to sheet and rill erosion, which account for 78% of all the soil eroded by water in the United States of America. Erosion of soil is inititiated due to raindrop impact or to shear stress from the flow of water. Whenever the soil surface is saturated and rainfall intensity exceeds the infiltration rate, runoff begins and the soil particles become available for transport by the flow. Both rainfall and runoff have their own detaching and transporting capacity; physically, these two processes are different and therefore must be studied separately.

In the case of runoff, which is the concern of this study, the transport capacity of the flow depends on the hydraulic conditions and sediment properties. Furrow flows, for example, are usually of shallow depths with flow depths of one or two centimetres. Such flows occur over a wide range of slopes. Furrows with slopes of 5% or more are found on steeply sloping fields that are not contour farmed. A 1% slope is common for bottom land fields, and a 0.2% furrow slope is common for land formed to facilitate drainage. Shallow flows over steep slopes usually fall in the supercritical flow range and transport significant amounts of sediment.

The motion of sediment in the bed zone takes place by rolling and sliding of grains. The solid grains are packed together and move along the inclined bed due to their own weight, the hydrodynamic forces of water, and the shear stresses in the sediment layer.

467 Sediment transport in shallow flows in high gradient channels

TRANSPORT IN SHALLOW FLOW

An important aspect of the present study is related to sediment transport in open channels of large slope and shallow water depth in which the flow is of a much smaller scale than that in rivers. As an example, in upland fields on steep furrows, water flow transports significant amounts of topsoil by sheet erosion.

Engineers engaged in river sedimentation or soil conservation are usually involved in predicting the transport rate of sediment due to stream flow or runoff. The scientific literature has an abundance of formulae for predicting sediment transport rate under different flow and sediment conditions. However, there is no universal formula that applies to the variety of possible situations. This fact is evidenced by the comparisons made by Vanoni (1975) on transport rate data in rivers by using some of the most famous sediment transport equations. The results of the comparison indicated that some formulae predicted transport rate of a completely different order of magnitude than the actual measurements. This observation does not imply that some of the formulae are incorrect; in fact these formulae are empirical or semi-empirical in nature and were obtained as the result of some physical tests.

In the light of this discrepancy, it seems plausible to divide the study of sediment transport into various classes with each class representing a unique set of physical situations. This can be applied easily to the classification of transport of sediment in rivers and to that in steep and shallow flows. This distinction can be clearly made due to the fact that river flows are usually slow compared with the flow of water on high gradient beds. Typical rivers also fall in the subcritical flow range, while the flow on steep slopes is normally classified as supercritical. In addition, the scale of flow depths in both processes is usually of a different magnitude. It has been noted (Meyer et al. 1983, for example) that the flow of water in steep crop-row furrows after a typical rainstorm has a flow depth of a few centimetres. Flow depth in rivers, however, can be in the order of tens of metres.

Because of the highly erosive nature of flows on steep slopes and the other reasons mentioned in the previous paragraphs, it seems that transport rate formulae that apply to such situations should not be extrapolated for predicting transport rate in rivers, and vice versa. Extensive reviews of sediment transport in rivers and streams are abundant in the scientific literature (Graf, 1971; Vanoni, 1975).

Analytical studies on sediment transport in shallow flows have been conducted in the past by modelling the flow of sediment as a non-Newtonian fluid. Prasad & Singh (1982), Aziz & Prasad (1985) and Aziz (1986) utilized shallow water wave theory in the development of models for the transport of sand-sized sediments in shallow flows. During the effort to verify these models it was observed that there is a lack of data on sediment transport in high gradient channels. The same was indicated by Aparicio & Berezowsky (1987) who developed a numerical model based on finite differences to mode! the flow over a sandy bed in the supercritical flow regime.

Most sediment transport data available in the literature are concerned


with river sedimentation. Few experiments, however, have been conducted to measure sediment transport on large slopes (Zuhdi, 1979; Meyer et al. 1983; Smart, 1984). All of these experiments have the following common procedures: the bed slope was set at predetermined values, sediment of a given size was fed at the upstream end by means of a hopper, and the total sediment transport rate was measured at equilibrium.

The experiments by Zuhdi (1979) and Meyer et al. (1983) were conducted for the purpose of predicting sediment transport in crop-row furrows. The tests were performed in a parabolic flume that resembles a typical furrow. They studied the transport rate under rain and no-rain situations. In order to simulate natural roughness in the flume, sand of the same size as that used in the test run was glued to the flume, and roughness was, therefore, over the entire wetted perimeter. The flow rates in these tests were set at constant values and the transport capacity of these flows was measured for preset bed slopes. The results were analysed in terms of dimensional analysis, and the ratio of sediment flow rate to water flow rate was compared to the slope showing a power relationship fit. Later measurements of flow conditions indicated that most of the Zuhdi (1979) experimental runs were made in the supercritical flow regime near a Froude number of two, and the observations made by Meyer et al. (1983) on the flow of the sediment in the channel used by Zuhdi (1979) indicate that the sand formed a general sheet of moving material.

In an effort to modify the Meyer-Peter-Muller (1948) equation, Smart (1984) conducted experiments on slopes of up to 25%. The laboratory setup was such that the sand bed was prevented from washing out completely by placing "bed-stops" at the downstream end. For a given slope and sand size, water inflow was increased until equilibrium was observed, thus measuring the transport rate of the uniform flow at the given slope. The result of these tests was the modification of the Meyer-Peter-Muller formula for steep slopes.

The ability of flows to transport sediment depends on both the flow and sediment properties, but the flow of water is the driving force in the erosion and transportation processes within a channel. The capacity of the flow to transport sediment in strongly affected by particle size and channel slope. Smaller size sediments tend to be more easily transported, and the transport capacity increases with increasing slopes. In this study, the transport capacity of the flow has been determined in the laboratory under different flow and sediment properties.

EXPERIMENTAL SETUP AND PROCEDURE

The study utilized a rectangular flume to measure the sediment transport capacity of flows in high gradient channels. The flume was 12 feet long with a cross-sectional area of 9 x 9 inches. The framework was made from steel sections, and the bed and the walls of the flume were made of plexiglass. In order to simulate flows over longer channels, water was added at the upper end of the channel at inflow rates of 0.0133, 0.0184, 0.0254, 0.0313 and


0.0382 ft3 s"x. Agricultural land in the plains usually has gentle slopes of less than 2%.

Such slopes may be needed to facilitate drainage in most cases. In farmland on the slope of hills, however, there is usually enough slope for drainage, but soil erosion and slope control become the major problem. Slopes of gradient more that 5% also occur on construction sites which face similar erosion problems. Controlling soil erosion in this case is also of significance. In this study channel gradients of 3, 4, 6, 8 and 10% were used to simulate high gradient channel situations.

The soil eroded and transported in channels is usually made up of individual particles and aggregates. The aggregates are of a much larger size and lower density than individual grains, and are usually deposited downstream. For the experiment at hand, stream bed sand was obtained from a local dealer, and sieved into four size groups. The range of the particle diameters was from medium to coarse sand with specific densities 2.55, 2.59, 2.9 and 3.1 for the mean grain diameters of 285, 508, 718 and 1015 microns (/an) respectively.

The flow system used consisted of a sump and a constant head reservoir. A flow meter was calibrated and used to control the flow rate at selected values. A point gauge which slides over guide rails was used for flow depth measurements. A sediment hopper was used to introduce sediment into the flow.

In order to simulate real flow roughness conditions, sand was glued to the bed of the channel. The sand used for the roughness was the same as the sand used for the experimental run. The bed was painted with a light coat of spray paint in order to give a contrast so that a distinction between the fixed bed and the transported sediment could be made and, therefore, deposition could be observed.

For each experimental run the flume was set at the desired slope, and the inflow of water was set at a predefined rate. When the flow was established over the entire channel, flow depth measurements were recorded. Sand was then introduced by the hopper until equilibrium was reached. At this equilibrium condition the sediment flow rate was constant, and the amount of sand transported by the flow represents the flow transport capacity. Any additional amount of sand introduced to the flow would be deposited and alter the channel roughness and, therefore, change flow conditions.

After equilibrium was established, depth measurements were recorded again. Samples of discharge (water and sand) were taken for each run, and the sample time was recorded. The captured sediment was placed in an oven to dry for 24 h, then weighed. The sediment discharge concentration corresponding to the equilibrium conditions was determined from these data. Tables 1-4 list the data obtained from the total of 96 experimental runs and in Figs 1-4 the data are plotted for each sand size. For channel slopes of 8 and 10 percent, and for high flow rates, the transport of the 285 j m particles in the flume was difficult to control. In these cases, large amounts of sand were carried by the flow, and it was impossible to determine the exact conditions of equilibrium with the experimental setup.


Table 1 Experimental data for the 285 urn sand

Slope Flow depth without sediment

Flow depth with sediment

Transport rate

(%) (f?-sh (ft) (ft) (lbs'1 ft')

10

0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0133 0.0184 0.0254

0.0125 0.0155 0.0205 0.0235 0.0260 0.0130 0.0160 0.0195 0.0215 0.0235 0.0115 0.0155 0.0175 0.0190 0.0225 0.0110 0.0135 0.0155 0.0090 0.0125 0.0135

0.0160 0.0185 0.0255 0.0270 0.0280 0.0130 0.0200 0.0215 0.0255 0.0275 0.0135 0.0175 0.0190 0.0230 0.0265 0.0125 0.0155 0.0190 0.0115 0.0135 0.0155

0.0171 0.0320 0.0660 0.0944 0.1341 0.0254 0.0578 0.0957 0.1433 0.1862 0.0466 0.1288 0.2085 0.2944 0.4363 0.0879 0.1721 0.2350 0.1412 0.2700 0.4179

0.1

j Q

o 0.01

0:001

D = 285 urn

o X

o X

c - 0 . 0 1 7 ? ft3s" iff i

0 -0.0245 f t W 1

+ -0.0333 f t W 1

*-0.0417 f lVJff1

O - 0.0503 ftW1

0 2 4 6 JO O i 0 p 6

Fig. 1 .Experimental data for 235 pm sand,

10


Table 2 Experimental data for the 508 ym sand

Slope

(%)

3

4

6

8

10

Q

(f?s-1)

0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382

Flow depth without sediment

(ft)

0.0145 0.0195 0.0225 0.0230 0.0265 0.0130 0.0155 0.0185 0.0215 0.0235 0.0105 0.0155 0.0180 0.0200 0.0210 0.0110 0.0145 0.0160 0.0185 0.0220 0.0120 0.0135 0.0145 0.0165 0.0210


(ft)

0.0170 0.0225 0.0255 0.0335 0.0345 0.0160 0.0190 0.0250 0.0235 0.0260 0.0140 0.0170 0.0190 0.0210 0.0280 0.0130 0.0160 0.0190 0.0210 0.0235 0.0130 0.0145 0.0175 0.0195 0.0220

Transport rate

(lbs'1 ft)

0.0126 0.0209 0.0337 0.0519 0.0716 0.0233 0.0414 0.0744 0.0992 0.1231 0.0423 0.0703 0.1116 0.1584 0.2534 0.0641 0.1437 0.2030 0.3036 0.2592 0.0738 0.1466 0.2251 0.2997 0.4450

0.1

o 0.01

0.001

D = 508 U-m

o

o X + a

X + 0

I

C - 0 * - 0 . x _ 0 o-o.

0.0 177 f t V V * .024 5 f t V ^ f 1

.0339 ftVrff1

.0417 ft,s ,ff; ,0509 f t W 1

0 2 4 6

% Slope

Fig. 2 Experimental data for 508 nm sand.

10

Nadim M. Aziz & David E. Scott All

Table 3 Experimental data for the 718 \tm sand

Slope

(%)

3

4

6

8

10

Q

(ft3*-1)

0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382


(ft)

0.0160 0.0195 0.0225 0.0265 0.0295 0.0155 0.0195 0.0215 0.0265 0.0285 0.0140 0.0190 0.0195 0.0220 0.0250 0.0135 0.0180 0.0185 0.0220 0.0220 0.0120 0.0150 0.0175 0.0195 0.0210


(ft)

0.0170 0.0210 0.0250 0.0305 0.0315 0.0170 0.0215 0.0245 0.0275 0.0325 0.0160 0.0220 0.0235 0.0255 0.0265 0.0155 0.0190 0.0205 0.0245 0.0255 0.0140 0.0170 0.0190 0.0230 0.0250

Transport rate

(Ibs^ft)

0.0133 0.0196 0.0345 0.0485 0.0643 0.0162 0.0274 0.0529 0.0784 0.1117 0.0387 0.0690 0.1048 0.1388 0.1961 0.0673 0.1161 0.1789 0.2656 0.3823 0.1182 0.1910 0.2560 0.3598 0.4889

0.1

a — .Q

a 0.01

0.001

D = 718 u.m

§

o x + D

A

o

o X

Û - 0 . 0 I 7 7 f t V V 1

c - 0 . 0 2 4 5 ft,s".1 ft"1

+ - 0 . 0 3 3 9 ft,s_ 1ff1

x-0.0417 fCs^ff1

O - 0.0509 f t W 1

4 6

% Slope

10

Fig. 3 Experimental data for 718 ym sand.


Table 4 Experimental data for the 1015 \im sand

Slope

(%)

Q

(ft3 s'1)


(ft)


(ft)

Transport rate

(Ibs^fi)

10

0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382 0.0133 0.0184 0.0254 0.0313 0.0382

0.1805 0.0225 0.0255 0.0320 0.0345 0.0185 0.0225 0.0265 0.0275 0.0320 0.0185 0.0205 0.0225 0.0260 0.0285 0.0145 0.0170 0.0195 0.0225 0.0245 0.0125 0.0170 0.0190 0.0200 0.0245

0.0200 0.0230 0.0300 0.0340 0.0380 0.0220 0.0235 0.0295 0.0320 0.0350 0.0210 0.0235 0.0260 0.0305 0.0345 0.0145 0.0200 0.0270 0.0260 0.0285 0.0170 0.0190 0.0255 0.0280 0.0290

0.0059 0.0124 0.0170 0.0341 0.0494 0.0137 0.0262 0.0458 0.0734 0.0837 0.0392 0.0648 0.1016 0.1509 0.1735 0.0700 0.1116 0.1496 0.2475 0.3311 0.0904 0.1323 0.2263 0.3778 0.5253

0.1

0.01

0.001 0

D = 1015 /xm

© X

+ a

a

9 + a

O x +

8

a -0.0177 ft3s_1ffi

a -0.0245 ftW1

+ -0.0339 ftVJff1

x-0.0417 ftVV1

O-0.0509 ft s^ff1

10 % Slope

Fig. 4 Experimental data for 1015 \mx sand.


OBSERVATIONS AND DATA ANALYSIS

Although bed forms in shallow flows have been observed in the past, there is little information on whether they are identical with those present in streams and rivers. In the present study, the behaviour of the bed in forming certain configurations was observed. Measurements of bed forms were not taken; however, the general observations as shown in Table 5 indicate that most of the sediment was transported as sheet flow.

Table 5 Observations on bed geometry

Q

(ft3 sl)

D

mm)

% Slope

3 4 10

0.0133

0.1984

0.0254

0.0313

0.382

508 718

1015

285 508 718

1015

285 508 718

1015

285 508 718

1015

285 508 718

1015

L L T

S T T T

S S S T

S S S S

S S S S

L L T T

S S S T

S S S S

S S S S

S S S S

S S S T

S S S T

S S S S

S s s s s s s s

s s s T

S S S S

S S S

s s s s s s s s s

s s s s s s s s s s s s s s s s s s s s

L = longitudinal bars; S = sheet flow; T = transverse bars.

The transport of sediment in this study is due to gravity flow on a constant channel slope. Under steady flow conditions over a constant slope, the mechanical power is equal to the time rate of conversion of potential energy into mechanical energy (Bagnold, 1973) and then into heat due to friction created by the sediment. Bagnold (1973) compared stream power to transport work rate in terms of quality. In other words, stream power represents the available power (power input) in the flow that will be used to transport the sediment in the bed. It is to be noted that stream power input is always greater than the power output.

Figures 1 to 4 of the collected data indicate that there is a certain relationship between sediment transport rate, flow rate and channel slope for a given grain size. These three variables can be compared in the form of transport rate vs. stream power. For each grain size, regression analysis was performed, and the data were fitted by a power equation of the form:


Qh = a(7QSy (1)

where Qb is the sediment mass flow rate, and (JQS) represents the stream power. Results of the regression analysis are listed in Table 6 which includes information about the constants of the regression equation and the correlation coefficients. The results indicate that the power relationship is a good fit for the experimental transport rate and stream power. Figure 5 represents all the data from the study along with the regression equation plot.

Table 6 Results of the regression analysis between the sediment transport rate and the stream power

Sand

size

(Urn)

285 508 718

1015 (All)

Number

data

21 25 25 25 96

of points

Regression

Qb = a a

2.515760 2.061156 2.661168 3.208987 2.580656

equations

OQS)b

b

1.709687 1.571606 1.728374 1.911755 1.730558

Correlation

coefficient

r2

0.91689 0.93537 0.95770 0.93460 0.92648

O.I r

O.OI =

0.001

Hill 1 1 1

1

= -

-

= :

i

+S"

/ \

! I l l

$ *

V** 'a 0

a

1 1 1

„v "0

a a

X

1

285 508 718 1015

1

/%

Mm Mm Mm Mm

1 1 1 1 1 M

0.010 0.100

stream power

Fig. 5 Regression analysis results of all experimental data for mass transport rate and stream power.

In an effort to relate the independent parameters (Q, S, D, y and y ) to the dependent parameters (Q^ and h), the following non-dimensional relation was obtained:


f^QJQ.S, h/D,7/(7s-7)] =0 (2)

where ix represents the functional relationship among the dimensionless terms. Combining the terms in such a way that they remain linearly independent, one can obtained the following relationship:

Q* 7

Q ( 7 , - 7)

hS_

D (3)

which upon fitting with the experimental data (Fig. 6) revealed that f2 is defined according to the following relationship

Q = a

7

Sh

D (4)

where a = 1.5 and b = 1.8 with an i2 = 0.91. It is to be noted that in gravity flows such as the one of interest here, one must include the gravitational acceleration, g, in the list of parameters that affect the system. By including g one obviously obtains a Froude number of the form:

p 2 Q

Fr = — gh-

Q r*-r

(5)

2.00

S.h D

Fig. 6 A plot of dimensionless data and regression curve.


which includes the measured terms, Q and h. These variables are already present in the terms of equation (3) and therefore, comparison of Fr with any of the other terms leads to using redundant parameters in the abscissa and ordinate of any plot.

SUMMARY AND CONCLUSIONS

An experimental study was conducted to measure the transport rate of flow in situations not typical of rivers and streams. The study involved the determination of sediment transport rates in high gradient channels, with shallow water flows.

Laboratory observations indicated that the sediment was mainly transported in a zone near the bed in which the sediment generally formed a sheet of flowing material. In some instances, sheet flow did not cover the entire bed depending on flow properties, sand size and channel slope.

Regression analysis performed on the data indicated that a power relationship between the volumetric sediment flow rate and the stream power gives a good correlation. The regression equations for the various grain sizes were slightly different. This may be partly attributed to the fact that the flow of grains took place in layers of different thicknesses. Dimensional analysis was also performed. Two non-dimensional terms, which include the dependent and independent parameters, were related by a power law relationship with good correlation.

The experimental study is directly applicable to the transport of sediment on roadside slopes and on hillsides where the slopes are high. The experiment itself lacks the ability to measure the thickness of the moving sediment layer and the dynamic concentration of sediment flow. These two parameters are essential for theoretical models and for their complete verification.

Acknowledgement The research on which this paper is based was partially funded by the USGS under grant number G-1043-04, through the South Carolina Water Resources Research Institute.

REFERENCES

Aparicio, J., & Berezowsky, M. (1987) A mathematical model for unsteady supercritical flow on a mobile sandy bed. Hydrol. Sci. J. 32 (3), 313-327.

Aziz, N. M. (1986) Sediment Transport on Steep Slopes. Tech. Report no. 121, SCWRRI. Aziz, N. M. & Prasad, S. N. (1985) Sediment transport in shallow flows. /. Hyclraul. Div. ASCE

111 (10), 1327-1343. Bagnold, R. A. (1973) The nature of saltation and of 'bed-load' transport in water. Proc. Roy.

Soc. London, Ser. A 332 473-504. Graf, W. H. (1971) Hydraulics of Sediment Transport, McGraw-Hill, New York. Meyer, L. D., Zuhdi, B. A., Coleman, N. L. & Prasad, S. N. (1983) Transport of sand-sized

sediment along crop-row furrows. Trans. Am. Soc. Agric. Eng. 26, (1), 106-111. Meyer-Peter, E. & Muller, R. (1948) Formulas for bed transport. In: Proc. 2nd IAHR Congress,

Stockholm. Prasad, S. N., & Singh, V. P. (1982) A hydrodynamic model of sediment transport in rill

flows. In: Recent Developments in the Explanation and Prediction of Erosion and Sediment


yield, IAHR Symp. no. 4, Univ. of Exeter, England. Smart, G. M. (1984) Sediment transport formula for steep channels. /. Hydraul. Eng. ASCE, 110

(3), 267-276. Vanoni, V. A. (1975) Ed. Sedimentation Engineering. ASCE Publication, New York. Zuhdi, B. A. (1979) Flume studies of sediment transport in shallow furrow flow with simulated

rainfall. M.S. Thesis, Dept. of Civil Engineering, The University of Mississippi.

Received 2 February 1988; accepted 20 January 1989

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