Flume Width and 

Water Depth Effects in 

Sediment-Transport 

Experiments

GEOLOGICAL SURVEY PROFESSIONAL PAPER 562-H
Flume Width and 

Water Depth Effects in 

Sediment-Transport 

Experiments

By GARNETT P. WILLIAMS

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 562-H

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1970
UNITED STATES DEPARTMENT OF THE INTERIOR 

WALTER J. HIGKEL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 - Price 55 cents (paper cover)
CONTENTS

Abstract _ _______________________________

Introduction. _____________________________

Equipment and measurements_____________

Flume______________________________

Water supply and discharge measurementSediment infeed_ ______________________

Sediment-transport measurement- _______

Sediment.____________________________

Depth measurement_________________

Velocity._____________________________

Slope__ _____________________________

Bed-form characteristics._______________

Procedure__ _ ____________________________

Results.._________________________________

General- _____.!__--__-____-___________

Page 

HI

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2

2

2

2

2

2

2

4

4

4

4

5

Results Continued

Water discharge.___________

Mean velocity____________

Slope.______--_-__-_-__-__

Stream power._____________

Bed forms.__-_-_-_--_----_

Bed-form heights. ______

Bed-form wavelengths. __ 

Travel velocity.________

Resistance factors_______

Sidewall correction procedureTest one.._ ____________

Test two----....._-_.

Conclusions. ___________________

References. _ ___-_-.____._______

Page

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24

25

26

29

29

ILLUSTRATIONS

Page

FIGURE 1. Photographs of flume and associated equipment__.__._________________-______-_____--_--------_-_-_-__ H3

2-17. Graphs showing 

2. Size distribution of sand__________________...__._.____.________________________---_-_-____---- 4

3. Relation of unit water discharge to unit sediment-transport rate______________________-___-_----_-_ 7

4. Mean velocity-unit transport relations.__________________________--_-__----------------_--------- 9

5. Mean velocity-unit transport relations----.-----.------------------------------------------------ 10

6. Slope-transport relations.___________________________-_________---_-_------------_-------------- 11

7. Adjustment factors to correct slope for sidewall effect._____-_______________-_-____------_---------- 12

8. Unit stream power-unit sediment-transport relations showing flume-width effect. _________________ 14

9. Adjustment factors to correct stream power for sidewall effect..__________________-__--_-__.------_-- 16

10. Single curve giving adjustment in slope, stream power, or shear stress to correct for flume sidewall influence. 17

11. Unit transport rate adjustment factors to correct for flume sidewall eflfect____--___-_----------------- 18

12. Unit stream power-unit sediment-transport relations in an infinitely wide channel.-----.-------------- 19

13. Variation of total sediment-transport rate with different water depths, for constant stream power ____ 19

14. Dune-height adjustment factors to correct for flume-width effect._______________--_-___-_----------- 20

15. Flume-width effects on friction factor-transport relations.-__-__-___---_---------------------------- 23

16. Velocity-slope test of sidewall correction procedure_____-_-___------------------------------------- 27

17. Slope-transport rate test of sidewall correction procedure..__-_______-__---------------------------- 28

TABLES

TABLES 1, 2. Summary of experimental data:

1. English units---.-.-.--.

2. Metric units.-______-_..

Page

H33

35

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FLUME WIDTH AND WATER DEPTH EFFECTS IN SEDIMENT-TRANSPORT EXPERIMENTS

By GARNETT P. WILLIAMS

ABSTRACT

This paper reports 177 flume experiments made in channels of 

different widths and water depths, the purpose being to find how 

the flume width and flow depth influence experimental results. 

No attempt was made to derive a sediment-transport formula. 

Sediment transport rates, grain size (.nearly uniform-sized particles with a 1.35 mm median diameter), water depth, .and channel width were controlled; the dependent variables were water 

discharge, mean velocity, slope (energy gradient), and bed-form 

characteristics. The flume widths were 0.25, 0.5, 1.0, and 2.0 ft. 

For each of these widths a series of runs (from slow to fast 

transport rates) was made at depths of 0.1, 0.3, 0.5, and 0.7 ft, 

that is at depths of about 20 to 160 grain diameters.

The narrower flume widths affected some variables significantly, as explained below, but in a channel 2 ft wide flume 

sidewall effects very nearly or completely disappeared. Relations 

from the narrower channels, where wall effects were pronounced, 

could therefore be compared to the relations for wide channels 

in which wall effects were absent.

The channel width did not affect the unit water discharge-unit 

sediment-transport relations, at constant water depth. The relation between mean velocity and sediment-transport rate therefore was not affected by the flume width, because for a given 

width and depth the mean velocity varies directly with the discharge. Water depth influenced these relations in that # greater 

discharge, and, at low transport rates, a faster velocity was 

needed to move sediment at a given rate as depth increased.

The slope or energy gradient decreased as the channel became 

wider, for a given unit transport rate and water depth. This 

means that any factors involving slope, such as stream power and 

shear stress, showed the same trend. By measuring the change 

in these dependent variables with channel width it was possible 

to get an empirical adjustment equation to correct the slope, 

stream power, and shear stress for the flume sidewall effect. 

Multiplying the laboratory value of slope, unit stream power, or 

shear stress by the adjustment factor

where D is water depth and W is flume width, gives the slope 

power, or shear for a wide channel (no sidewall influence) for 

the same water depth and unit sediment-transport rate.

Adjustment factors also are given for correcting the unit 

sediment-transport rate for sidewall effects, taking transport

rate as a dependent variable and stream power as the flow quantity which governs transport rate.

For a given stream power or bed shear stress in wide channels 

(negligible wall effects) the sediment-transport rate increased 

fourfold to sixfold as the water depth was decreased from 0.7 

to 0.1 ft. The curves suggest that this depth effect may disappear 

at depths of about 1.0 to 1.5 ft.

The flume width influenced the bed-form characteristics in 

various ways. Bed forms in wide channels can have heights and 

travel rates quite different from those observed in narrow channels. Except for runs at the 0.1-ft depth, bed forms did not become three dimensional (curving from wall to wall) until the 

flume was widened to 1 ft (for fast transport rates) or 2 ft. 

Thus the disappearance of sidewall effects on the measured value 

of the energy gradient corresponded approximately with the appearance of three-dimensional bed forms.

Two different tests of the validity of the Johnson-Brooks sidewall correction procedure showed that for the present movablebed data the degree of agreement between predicted and 

measured flow depths varied with the hydraulic or transport conditions. Best agreement (predicted depths within about ±30 percent of measured depths) usually occurred with channels ^ 1 ft 

wide and for runs which did not have extremely rough beds. A 

review of the literature suggests that for many rigid-boundary 

flows this sidewall correction procedure is reasonably reliable.

INTRODUCTION

The movement of solid particles by flowing water 

affects pollution, the rate at which land is eroded, the 

filling of reservoirs, and many related problems. Sediment transport is difficult to study in nature because 

of the problem of accurately measuring the travel 

rates of sand and gravel during most flow conditions. 

Many investigators have therefore resorted to artificial 

watercourses (flumes) in the laboratory. Flume experiments use water and sediment in quantities small 

enough to control, and this valuable control of variables 

means a better understanding of the role of individual 

factors.

Each laboratory, understandably, has built equipment to suit its particular interests, capacity, and needs. 

The sediment-transport experiments reported in the literature therefore differ in type and size of apparatus

Hi
H2 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

used, experimental procedure, and in other respects. 

Consequently the data from any one investigation usually do not agree with the data of others. The present 

study explores the questions of how the results of sediment-transport experiments can be affected by flume 

width and water depth two features which usually 

have varied randomly from one study to the next. An 

equally important purpose of the investigation was to 

make some progress toward relating flume data to 

natural-river conditions by evaluating flume sidewall 

effects. This study makes no attempt to derive or test 

a sediment-transport formula.

The encouragement and advice of Ealph A. Bagnold 

have been an invaluable support throughout this entire 

investigation. I am grateful to William W. Emmett, 

Harold P. Guy, Everett V. Eichardson, Neil L. Coleman, Edward J. Gilroy, Emmett M. Laursen, Jacob 

Davidian, and William H. Kirby for helpful suggestions or generous assistance.

EQUIPMENT AND MEASUREMENTS 

FLUME

Williams (1967) described in detail the 52-ft-long 

nonrecirculating flume (fig. 1) used for the experiments. 

The flume could be tilted from horizontal to a maximum 

slope of about 0.035 ft per ft, and the maximum usable 

width was 3.9 ft. For most of the experiments both 

walls were of transparent plastic (Plexiglas), although 

for some tests at widths of 0.25 and 0.5 ft one wall 

consisted of smooth plywood. The smooth wood surface 

probably was not appreciably rougher than the plastic.

WATER SUPPLY AND DISCHARGE MEASUREMENT

Three pipelines (diameters 8, 6, and 4 inches) supplied water to the flume. Water destined for the 6- and 

4-inch lines went from the sump to a constant-head 

tank and then flowed through the pipelines to the flume. 

For the 8-inch line a second pump sent water directly 

from the sump to the stilling tank at the head of the 

flume. A valve in each pipeline regulated the flow rate.

Elbow meters precalibrated at the Georgia Institute 

of Technology measured the discharge in the 6- and 

4-inch lines. Another calibration of the meters in place 

(Washington, D.C.) near the end of the investigation 

showed that they were accurate to ±1.8 percent. The 

8-inch line had a factory-calibrated orifice plate. For 

four runs at the very lowest discharges (depth 0.1 ft 

in a 0.25 ft-wide channel), the discharge had to be 

measured volumetrically. Maximum available discharges were 3.5, 2.0, and 0.8 cfs (cubic feet per second) 

in the 8-, 6-, and 4-inch lines, respectively.

SEDIMENT INFEED

In the early stages of the investigation a submerged 

elevator just upstream from the flume test section fed 

sediment into the stream. This feed method was only 

partly satisfactory. Although the sand entered the test 

section at a constant rate, a minor amount of sediment 

leakage along the sides of the elevator prevented a 

computation of the exact sediment infeed rate. Secondly, faster sediment-transport rates could not be 

studied because the 4-ft-long by 2.5-ft-deep sand supply 

was used up before a run could be completed. Changing 

to a vibrating feeder (fig. 1) partway through the study 

eliminated these problems, 'and this "drop-in" feed 

method turned out to be much better than the elevator 

system. The slowest infeed rates required a second vibrating feeder, very small, and this is not shown in 

figure 1.

SEDIMENT-TRANSPORT MEASUREMENT

The water-sediment mixture leaving the flume fell 

into a sediment-collection box (figure 1). Water escaped 

through screens along the top of the box while all the 

sand settled to the bottom. Weighing the box and its 

contents periodically in place gave the sediment-transport rate (total sediment load) in submerged weight.

During the early stages of the study, the volume of 

the collection box (which sat on a platform scale) was 

9 cubic feet, but this box proved to be too small for 

transport rates greater than about 0.2 Ib per sec-ft. The 

44-cubic-foot collection box adopted partway through 

the investigation was much better. This larger box hung 

from a crossbeam, and the scale sat to one side of the 

box; one support of the crossbeam rested on the scale 

platform, and the recorded weight was adjusted by an 

appropriate factor to get the actual weight of the box 

and its contents.

SEDIMENT

The quartz sand used for the experiments was fairly 

uniform in size (2 percent <0.8 mm and 2 percent >2.0 

mm) with a median sieve diameter of 1.35 mm (fig. 2). 

Transported material trapped in the collection box had 

virtually the same size distribution as the material remaining on the flume bed. The average fall velocity for 

75 randomly selected grains was 14.5 centimeters per 

second at a water temperature of 31.5° C. Most of the 

grains were not particularly spherical, and their edges 

were of intermediate roundness.

DEPTH MEASUREMENT

Elevations of the water- and bed-surfaces were measured to the nearest 0.001 ft with a point-gage at regular 

intervals along the test section, beginning at station 3.0 

ft and ending at station 49.0 ft. The horizontal intervals
FLUME WIDTH AND WATER DEPTH EFFECTS H3

FIGURE 1. Flume and associated equipment. A, General view looking downstream with elevator feed system in use. B, 

Upstream view showing elevator feed system and preliminary channel. C, Measurement of sediment-transport rates with 

collection box resting on scale platform. D, General view looking downstream with "drop-in" feed system. E, Upstream 

view of "drop-in" feeder. F, Measurement of sediment-transport rates using the suspended collection box.
H4 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

were usually 4 ft, occasionally 2 ft. After the elevations 

were plotted on arithmetic coordinate graph paper, 

straight lines of best fit by eye were drawn through the 

points for each surface. With uniform flow the lines 

were parallel, and the elevation difference normal to the 

two lines gave the mean water depth.

VELOCITY

Mean velocity equals the discharge divided by the 

product of mean depth times channel width. Travel 

times of small chips of wood over a 40-ft distance gave 

the surface velocity. The accepted surface velocity was 

the average of three observations made with a stopwatch.

SLOPE

The slope of the water surface, equal to that of the 

sand bed, is the sum of the flume slope (measured by a 

surveyor's level) and the water-surface slope relative 

to the flume (obtained from the graphs of bed and water-surface profiles). After equilibrium (defined below)

100

rsj 

CO

<

o

80

60

40

LU

o 

cc

LU 

Q_

0

Visualaccumulation 

tube analysis

Sieve analysis

0.5 1 2

PARTICLE DIAMETER, 

IN MILLIMETERS

FIGURE 2. Size distribution of sand.

evolved, the inclination of any one profile usually deviated by no more than about 2 percent from the average 

of several such profiles. For some rui is at a depth of 0.7 

ft and for runs with very rough water and bed surfaces 

± 4: percent was the maximum deviation.

BED-FORM CHARACTERISTICS

The bed-form height recorded for each run represents 

an average value of 3 to 10 different bed features. Measurements were perpendicular to the bed slope and in 

the downstream half of the flume generally using the 

point gage along the center of the channel, but for some 

of the early runs just from a scale on the flume wall.

A count of the number of crests along the complete 

flume test section gave the average bed-form wavelength. 

The specific downstream location of each crest, at a 

given time, was also listed for some of the initial runs.

The travel velocities of the bed forms were obtained 

in the downstream half of the test section by timing the 

bed form as it traversed a known horizontal distance. 

For some of the early runs only one bed form was timed, 

but generally the travel velocity is an average of the 

travel rate of five or six bed forms.

PROCEDURE

In a typical sediment-transport experiment, the major variables are the water discharge, mean velocity, 

mean depth, channel width, energy gradient (slope, for 

uniform flow), rate of sediment transport, bed roughness, and sediment characteristics (size, size distribution, shape, and density). Other factors, such as water 

temperature, may have some influence under certain 

conditions.

For the present study the independent variables 

those variables determined before beginning a run 

were the sediment-transport rate, mean depth, channel 

width, and sediment characteristics. The dependent variables those factors whose values were unknown until 

after the experiment were water discharge (or mean 

velocity, at constant depth and width), slope, and bed 

roughness. In laboratory studies with movable (sand) 

beds it is practically impossible to set up an "ideal" experiment in which all variables are independent except 

one.

The reason for controlling sediment-transport rates 

was that this is by far the most convenient way to operate a nonrecirculating flume. (A study by Guy and 

others (1967) gave identical results for recirculating 

versus nonrecirculating flumes.) The purpose in keeping depth constant was to keep the wall drag and crosssectional flow dimensions as constant as possible from 

run to run. Depth effects can then be evaluated separately from flume-width effects.
FLUME WIDTH AND WATER DEPTH EFFECTS H5

There was no convenient way of regulating the water 

temperature. It varied little if at all during a single 

run but ranged from 8° to 28 °C during the investigation. The study by Colby and Scott (1965) suggests 

that such temperature changes should not significantly 

influence the transport rates of coarse sand and that 

temperature effects on transport rate are relatively 

minor compared to the effects of mean velocity and 

shear. However, no one has yet made a carefully controlled comprehensive study with different grain sizes 

to determine what influence water temperature has on 

sediment-transport rates.

An individual run began with the sand bed scraped 

to approximately a flat surface. The flume slope was set 

at the estimated probable equilibrium slope. The next 

step was to start the steady sediment infeed, thus fixing 

the unit sediment-transport rate for the run. At the 

same time the water discharge was turned on and adjusted to get the desired depth. The range of acceptance 

for water depth was about ±7 percent of the desired 

mean depth. I then took repeated water and bed surface 

profiles, and if necessary changed the discharge and (or) 

the flume tailgate-setting to get a uniform flow of the 

desired depth. The requirements for equilibrium were 

(a) constant slope with time and (b) no net gain or loss 

of sand in the flume with time. With the elevator feed 

system both of these requirements were judged by comparing successive sets of profiles and successive transport 

measurements, as with recirculating flumes. The drop-in 

feed method made possible an additional verification, 

namely sediment input rate=sediment output rate. The 

run and measurements of the basic variables began after 

equilibrium conditions with uniform flow developed.

Sediment-transport measuring periods were always 

long enough for many bed forms to migrate out of the 

flume. These relatively long collecting periods assured 

a reliable measurement of the sediment-transport rate.

The final values of depth and of slope relative to the 

flume in nearly all cases are an average of several sets 

of profiles.

Eeproducibility of runs was good.

A few runs using the drop-in feed method for situations studied earlier with the rising-platform system 

showed that the feed method did not significantly influence the experimental results.

The experiments for each channel width and mean 

depth consisted of a series of runs from slow to fast 

sediment-transport rates. This was done for four constant water depths, at a fixed width. The whole process 

was then repeated for a different channel width, using 

the same depths as before. Transport rates and water 

discharges were reckoned in terms of unit (foot) width 

for comparison purposes. I systematically widened the

373-261 O 70 2

channel and made more runs until reaching the limits 

of the equipment or until the chief dependent variables 

(unit discharge and slope) no longer changed significantly with increasing flume width for a given water 

depth and unit transport rate.

The depths and widths studied were:

Width (ft.) 

0.25 

0.5 

1.0 

2.0 

3.9

Depth (ft.)

0.1, 0.3, 0.5, and 0.7 

0.1, 0.3, 0.5, and 0.7 

0.1, 0.3, 0.5, and 0.7 

0.1, 0.3, 0.5, and 0.7 

0.7 (fiveruns).

No attempt was made to directly determine threshold 

flow conditions at which sediment transport would just 

begin.

RESULTS 

GENERAL

Tables 1 and 2 at the end of the paper give all the 

experimental data, arranged in order of increasing sediment-transport rates for each set of channel dimensions. 

All measurements except for water temperature were 

taken in English-system units, so table 2 is merely the 

basic data converted into metric units.

For every run the sediment moved only as bedload, 

according to visual observations. The results may have 

been different for grains transported in suspension, and 

experiments of the present type should be repeated with 

finer (and coarser) grains and probably with heterogeneous mixtures too.

At the fastest transport rates (flat-bed stage) the 

grains, according to visual estimation, moved within a 

zone no more than about 1 centimeter high (about 8 

grain diameters) regardless of water depth. The height 

of this layer of moving grains decreased as transport 

rate decreased.

The many data obtained in this study could be analyzed in various ways, but the discussion here will deal 

mainly with plots of the individual variables, in an attempt to isolate flume-width and water-depth effects.

Any influence of the channel width should be disclosed by plotting each of the dependent variables (water discharge, mean velocity, slope, and bed-form characteristics) as functions of the independent variable, 

sediment-transport rate, for a constant depth. The same 

plots for a constant width should reveal the effect of 

water depth. Such diagrams are intended only to relate 

a dependent variable to the independent variables, as 

is customary with experimental data. The purpose is 

not to recommend any one of the dependent variables 

by itself as an important indicator of sediment-transport rate.
H6 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

WATER DISCHARGE

GENERAL

A logarithmic plot, not shown here, of unit water 

discharge (discharge (Q] per foot width (TF)) as a 

function of unit sediment-transport rate (i) revealed 

an insensitive relation between these two variables in 

that the line of best fit was rather flat. In other words 

a large increase in sediment-transport rate required only 

a relatively small increase in discharge, particularly 

at low transport rates. The expected depth effect but 

no flume width effect appeared on the plot. The logarithmic diagram of figure 3 with the ordinate, unit 

discharge, expanded to about five times its usual length, 

permits a closer examination of these relations.

All the lines in figure 3 were fitted by least squares, 

with the equations rectified to the general form (Q/W] 

 C=a(i) b. O is -a constant for each depth, a is a coefficient, and & is an exponent. Values of the constant O 

for this least-squares analysis were 0.087, 0.35, 0.68, 

and 1.07 for depths of 0.1, 0.3, 0.5, and 0.7 ft, 

respectively.

WIDTH EFFECT

In figure 3 the lines for all four flume widths at any 

constant depth fall within a narrow band which becomes 

narrower as transport rate increases. For any depth 

(Z>) and unit transport rate the lines for the different 

flume widths generally show no channel-width effect or, 

as at low transport rates for Z>=0.3 ft, any difference 

due to width is negligible. Deviations from the average 

unit discharge, at any transport rate and depth, range 

from 0 to 6 percent. The only exceptions are the 0.25- 

ft-wide channel at depths of 0.1 and 0.7 ffc, where the 

maximum deviations are about 8 percent and 12 percent, 

respectively. The maximum percent discrepancy from 

an average unit discharge diminishes as transport rate 

increases. For the complete range of conditions covered in the experiments the average deviation is about 

±3 percent.

For all practical purposes, therefore, the flume width 

had no significant effect on the unit discharge-unit 

transport relations, at a constant water depth.

DEPTH EFFECTS

Water depth of course affects the unit discharge 

unit transport relations more discharge is needed to 

move sediment at a given rate as depth increases (fig. 

3).

The water depth is important in rivers and streams 

because of its relation to flooding, irrigation, and navigation. In most field situations discharge would be independent or imposed on a given reach, and depth reacts 

to changes in discharge and resistance to flow. An important question concerning depth in natural rivers is : 

How does depth vary with water discharge at a constant 

slope ?

Laboratory flumes differ from most natural streams in 

that the flume width is fixed. Thus in a river the mean 

velocity, depth, and width all absorb a change in discharge, whereas in a laboratory flume any change in 

discharge will appear only in velocity and depth. 

Hence, the rate at which depth changes with discharge 

for flumes may be greater than the rate for natural 

streams.

For the present data the rate at which depth changes 

with discharge, at constant slope, can be found analytically (multiple regression) or graphically. A plot of 

unit discharge versus slope at constant depth revealed 

a power relation between any two of these variables, up 

to the stage where the washing out of bed forms reduced the slope values (discussed on p. H13) . Having the 

general form of the equation, I ran a multiple regression analysis using (a) discharges from an average 

least-squares curve for each depth on a discharge-transport rate diagram and (b) slope values from the "widechannel" slope-transport rate curves (discussed on 

p.H8).

The analysis revealed that at constant slope the depth 

varied with (0/TF) 0 - 71.

Let us compare this exponent, obtained on the basis 

of many flume experiments, with the exponent predicted 

by the minimum variance theory of Langbein (see 

Scheidegger and Langbein, 1966). The minimum variance theory postulates that the major dependent variables absorb any increase in discharge as equally as possible under the existing constraints. If the major dependent variables are velocity, depth, friction factor 

(Darcy-Weisbach), and unit stream power (slope and 

width being constant for the present question), the 

minimum variance analysis predicts that at constant 

slope and width the water depth varies with Q °-64.

At constant width Q is proportional to the product of 

velocity and depth, and if velocity ( V) and depth have 

a power relation with discharge (Leopold and Maddock, 

1953) then the exponents of velocity and depth add up 

to 1.0. Thus if the exponent of depth is 0.71 then V ex

The relations shown in figure 3 converge as sedimenttransport rate increases. The diagram magnifies this convergence by about five times compared to a regular 

logarithmic graph, so the convergence is less important 

than appears from figure 3. Thus the rate at which 

water discharge increased with increase in transport 

rate varied considerably with the particular range of 

transport rates and to a slight extent with the water 

depth.
FLUME WIDTH AND WATER DEPTH EFFECTS H7

UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 

0.001 0.01 0.1 1.0 10.0

- 300.0

0.2 -

10.0 0.1'

0.0001 0.001 0.01 0.1 1.0 10.0 

UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH

FIGTTBE 3. Relation of unit water discharge to unit sediment-transport rate, at constant water depth

(ordinate scale magnified about fivefold).
H8 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

MEAN VELOCITY 

WIDTH EFFECT

For any constant flume width and water depth the 

mean velocity varies directly with the discharge. Thus 

a regular logarithmic plot (not included here) showed 

that mean velocity was not very sensitive to changes 

in sediment-transport rate, as was true with discharge.

Figure 4, with the mean-velocity scale magnified 

about five times, shows the velocity-transport relations 

for the various channel widths at constant water depth. 

For any one depth there is no distinction on the basis 

of flume width. The single line of best-fit for each depth 

was fitted by least squares. The range of scatter in velocity values is ±6 percent, for any transport rate 

and depth, except for Z? = 0.1 ft where the velocity for 

some runs is 12 percent greater than that indicated 

by the curve. As with the unit discharge-unit transport relations, then, the flume width had no significant 

influence on the velocity-transport relations, at a constant water depth.

DEPTH EFFECT

Figure 5 contains the four lines of best fit from figure 4, to see if water depth affects the velocity-transport relations. The strange result is that water depth 

had a pronounced influence at low transport rates but 

this influence gradually diminished as transport rate 

increased. At mean velocities greater than about 4 fps 

(feet per second) the depth effect disappeared for all 

practical purposes. At slower mean velocities, those 

common in flume studies, the curves diverge widely on 

the basis of water depth.

The depth effect shown here at low mean velocities 

agrees qualitatively with the remarks of Colby (1964). 

Colby analyzed the influence of depth on the mean velocity-sediment transport relation but confined his 

attention to medium and fine sands. His graphs cannot readily be compared to the present data because of 

the uncertainties in extrapolating his curves to the 

coarse sand range.

SLOPE

WIDTH EFFECT

Figure 6 shows the flume width effects on the slopetransport relations for each of the four constant water 

depths. Where the relations follow a power law, that 

is at intermediate transport rates, the lines for all widths 

and depths were fitted by least squares with the constraint that for a given depth the lines for all four 

widths are mutually parallel. The curved lines at the 

extremes of the transport range were fitted by eye.

The slope or energy gradient ($) is the loss of energy

(in foot-pounds per pound of fluid) to overcome friction per unit length of stream. As the channel becomes 

wider at a constant depth the sidewalls retard a lesser 

proportion of the cross-sectional flow area. This lesser 

retardation means a lesser rate of energy loss, that is, a 

flatter slope. The decrease in slope that occurred with 

increasing flume width (fig. 6) was greatest between 

the 0.25- and 0.5-ft-wide channels and gradually diminished in wider channels. According to the least-squares 

analyses, the slope values in the 2-ft-wide channel were 

0.0, 2.1, 2.9, and 7.7 percent less than those in the 1-ftwide channel for depths of 0.1, 0.3, 0.5 and 0.7 ft, respectively (at any constant transport rate within the 

least-squares range). This result suggests that further 

increases in flume width would bring even lesser changes 

(if any) in slope values.

To find the slope in an infinitely wide channel, for a 

given depth and unit sediment-transport rate, S was 

plotted as a function of W/D. More precisely, instead of 

W/D the abscissa was a parameter

X=

because in this manner X=l when W/D=infinity. 

Then a simple extrapolation of the curve from the four 

experimental points such that the curve levelled off at 

X= 1 gave the value of S in an infinitely wide channel, 

for the given depth and unit transport rate. This method 

indicated that slope values in a channel of infinite 

width were about 1, 4, and 5 percent less than the 

slopes in the 2-ft-wide channel for depths of 0.3, 0.5, 

and 0.7 ft, iespectively. (The five runs at W= 3.9 ft 

for D=0.7 ft were omitted in this analysis because of 

the very limited range of transport rates covered by 

these runs.) The dashed lines in figure 6 represent these 

extrapolated slope-transport relations for infinitely 

wide channels.

How much adjustment should be made to the slope 

value found in a narrow channel (laboratory flume) to 

find the slope that would pertain to the same depth and 

sediment-transport rate in a wide channel (for example, 

a natural river)? In the absence of any theory which 

corrects the equilibrium slope for the sidewall (flume 

width) effect the present data provide the necessary 

"adjustment factors." For example, at a depth of 0.5 

ft and unit transport rate of 0.01 Ib per sec-ft, the slope 

in the 0.5-ft-wide channel was 0.00326 whereas in a 

channel of infinite width the slope would be 0.00224. 

One must therefore adjust the narrow channel slope by 

a factor of S;S or 0.69. Figure 7, based on computations made in this manner, shows adjustment curves 

for each of the four depths. All lines on figure 7 were 

fitted by eye.
UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 

0.001 0.01 0.1 1.0 10.0

UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGH

0.001 0.01 0.1 

0.0001 0.001 0.01 0.1 1.0 10.0 

UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH

0.0001 0.001 0.01 0.1 

UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGH

FIGTOE 4._Mean velocity-unit transport relations, at constant water depth (mean-velocity scale magnified abo
H10 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

o

z 

o

z 

<

8.0 

7.0

6.0 

5.0

= 4.0

j j

r

!- 3.0

2.0

UNIT SEDIMENT-TRANSPORT, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 

______0.001_________O.QI__________0.1__________U)_________10.0 | I | I r=\ 300.0

DEPTH 0.3 FT

DEPTH 0.1 FT

200.0

o

z 

o

100.0

90.0

80.0

70.0

60.0

50.0

40.0

1.0

0.0001 0.001 0.01 0.1 1.0 10.0 

UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH

FIGURE 5. Mean velocity-unit transport relations showing depth effect (mean-velocity scale magnified about fivefold).

The lines on the slope-transport diagrams (fig. 6) 

seem to diverge at the lowest sediment-transport rates 

and then remain equidistant from one another at transport rates greater than about 0.005 Ib per sec-ft. The 

appropriate adjustment factor therefore depends in part 

on the sediment-transport rate. One set of curves (fig. 

IB) suffices for rates greater than about 0.005 Ib per 

sec-ft. For lesser rates a slightly different adjustment 

factor for each transport rate should be given, according to figure 6; however, because of the greater chance

of error in slope measurements at extremely flat slopes 

only one set of curves (fig. 7J.), representing average 

adjustment factors for any transport rate less than 

about 0.005 Ib/sec-ft, is given here. This introduces 

some possible error for the extreme conditions of deep 

depths (0.5, 0.7 ft) in very narrow channels (0.25, 0.5 

ft) at extremely low transport rates (<0.001 Ib per 

sec-ft). Aside from these rare conditions the wide-channel slopes obtained by the adjustment factors of figure 

7 are accurate to within about dr five percent for the
FLUME WIDTH AND WATER DEPTH EFFECTS

UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 

0.0001 0.001 0.01 0.1 1-0 10.0

Hll

o 

o

Width 1.0 ft 

Widths 2.0 and 3.9 ft

0.0001 0.001 0.01 0.1 1.0 10.0 

UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH

FIGURE 6. Slope-transport relations showing influence of flume width.
H12 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Width

Depth ratio

0.5 1.0 2.0 5.0 10.0 20.0

Width 

Depth

ratio

0.5 1.0 2.0 5.0 10.0 20.0

0.9

0.8

0.7

0.6

< 0.5

LLJ

0.4

0.3

I i i i i 11 i i i i i 11

DEPTH 0.1 FT

-B

DEPTH 0.3 FT 

DEPTHS 0.5,0.7 FT

DEPTH 0.1 FT 

DEPTH 0.3 FT

/ Cruff(1965), smooth 

/ steel boundaries

(0.092<D<0.74 ft)

/ Lane (1955),

nature of boundaries 

and actual depths 

not specified. 

A. K0.005 Ib per sec-ft

_______I I I I I I I I I 1 I I I I I I I L

DEPTH 0.5 FT 

DEPTH 0.7 FT

B. />0.005 Ib per sec-ft

i i

EXPLANATION

Depth (ft)

Width (ft)

0.1

0.3

0.5

0.7

0.25 0.5 1.0 2.0

FIGURE 7. Adjustment factors to be multiplied by the laboratory value to correct slope for sidewall effect.

present data. Greater accuracy would depend in part 

on greater precision in fixing the slope-transport relation for an infinitely wide channel.

Thus for a given water depth, one can change the 

slope obtained in a flume of one width to the different 

slope which would obtain at another width, at least for 

grain sizes and flow conditions comparable to those 

studied here (fig. 6). What is more important, one can 

adjust the slope obtained in a "narrow" channel (sidewall effect significant) to the "wide-channel" slope (no 

wall effect), for the same depth and unit sediment-transport rate. To use figure 7 for this purpose, take the narrow channel width and depth and multiply the indicated adjustment factor by the narrow-channel slope. 

This gives the slope which would occur in a wide channel for the same depth and unit transport rate.

The slope-transport curves of figure 6 can be interpreted as plots of shear stress versus transport rate. 

This is because depth was contant and wide-channel 

shear can be defined as yDS, where y= specific weight of 

water. The slope-adjustment factors of figure 7 

therefore also represent adjustments in yDS.

The sidewall influence for these movable- and roughbed studies probably is less than that which occurs 

when all three boundaries are smooth and rigid. Gruff 

(1965) computed shear stresses by using data from a 

smooth rectangular flume; Lane (1955) took another 

approach and got a different curve. For comparison 

purposes figure 1A includes the relations proposed by 

Gruff and Lane. This diagram suggests that when the 

bed and sidewalls are smooth and rigid greater width/ 

depth ratios are needed to eliminate wall effects than 

are needed for channels of smooth walls and movable 

sand beds.
FLUME WIDTH AND WATER DEPTH EFFECTS H13

DEPTH EFFECT

The slope-transport curves of figure 6 could be used 

to obtain a depth effect for a constant flume width, but 

the resulting relation would include the effect of a 

changing discharge. A more pertinent question about 

natural streams is: How does depth vary with slope at 

constant water discharge? The multiple regression 

analysis mentioned earlier disclosed that for the present 

data depth varied with /S^-28, at a constant discharge. 

The negative exponent means that for a given discharge 

the depth decreases if the slope steepens.

What value would the minimum variance theory 

assign to this exponent? If the major dependent variables are velocity, depth, friction factor, and unit 

stream power (discharge and channel width being constant), the minimum variance theory predicts that 

depth varies with /S^0- 27 , for a constant discharge and 

width.

The slope values at depths of 0.3 and 0.5 ft (fig. 6) 

show a curious change in trend at high transport rates 

(0.2 to 0.5 Ib per sec-ft). In this range of transport rates 

the slopes tend to become constant (or even decrease 

slightly) as transport rate increases. At higher transport rates the slopes resume increasing. Brooks (1958) 

reported a similar pattern for slope values; however, 

he used fine sands, for which the nonuniqueness of slope 

values covered a much wider range of transport rates. 

For the coarse sand used here the relatively short 

range of transport rates affected by the nonuniqueness 

reduces the importance of this phenomenon.

A nonuniqueness not uncommonly appears in natural 

streams having beds of medium and fine sand (Dawdy, 

1961). There, however, the effect shows up in the water 

depth rather than in the slope because a river slope 

usually stays virtually constant.

There probably are not enough runs at the pertinent 

sediment-transport rates to determine how, if at all, the 

channel width affected the nonuniqueness in slopes. 

There is a depth effect in that the phenomenon is absent 

at D=0.1 ft but shows up at D=0.3 ft.

One feature of the bed configuration should be mentioned at this time. The bed forms progressed from 

dunes to antidunes to flat bed as transport rate increased. (With finer sands the only flat-bed stage that 

has been reported for flume studies occurs between the 

dune and antidune ranges rather than after the antidunes.)

The flat-bed stage arrived gradually: as i increased, 

the flat bed occupied a greater upstream portion of 

the flume, with antidunes occupying a correspondingly 

shorter and shorter reach at the downstream end. The 

washed-out or flat-bed zone upstream had a shallower 

depth and flatter slope than the downstream antidune

373-2610 70 3

reach. (In some ways this is similar to the "sand wave" 

described by Vanoni and Brooks, 1957, p. 41.) For this 

particular range of transport rates, therefore, a uniform 

flow over the full flume test section was not possible. The 

slope profiles drawn for these runs were single "average" straight-line profiles representing the whole 

flume, and discharge was regulated on the basis of these 

average profiles. (In tables 1 and 2 such runs are 

labelled "antidune" runs, and only those runs where 

antidunes disappeared completely are called "flat bed" 

runs.)

The dip in slope values shown in figure 6 occurs precisely in the range of "nonuniform" flow, where both 

antidunes and flat bed existed simultaneously in the 

flume. Slopes resumed their "normal" rate of increase 

with transport rate only after the flat bed occupied the 

full flume length.

The major findings about flume width and depth 

effects on the energy gradient are as follows:

1. A lesser slope evolved as the channel become wider, 

for the same unit transport rate and depth. Such 

a trend might have been predicted, but the present 

study actually measures this change. The resulting 

adjustment factors give slope values in an infinitely 

wide channel, the proportion of the energy gradient 

due to sidewall effects in narrow channels, and a 

means of correlating slopes from flumes of different 

widths.

2. Flume width did not affect the rate of change of 

slope with change in unit sediment-transport rate 

as long as water depth remained constant.

3. For depths ranging from 0.1 to 0.7 ft the sidewall 

effects became virtually insignificant at a flume width 

of 2ft.

4. The large difference in roughness between bed and 

sidewalls seems to contribute to an elimination of 

wall effects at lesser width/depth ratios than in 

flumes of smooth rigid boundaries.

5. At constant unit discharge, depth varied with /S~°-28. 

The minimum variance theory predicts this same 

relation.

6. The nonuniqueness of slope values associated with. 

the washing out of bed forms seems to be less important with coarse sands than with medium and fine 

sands.

STREAM POWER 

GENERAL

Stream power (Bagnold, 1966) is the rate at which 

a stream loses energy per unit boundary area. The 

power per unit bed area, «, is equal to yQS/W. Figure 

8 shows the unit stream power-unit transport relations for the present data.
>QS 

UNIT STREAM POWER -r- , IN POUNDS PER SECOND PER FOOT

P o . ro y o p .- r° w

ro <-nOo O L_ wiOo o

UNIT STREAM POWER^, IN KILOGRAMS PER SECOND PER METER 

W
PLUME WIDTH AND WATER DEPTH EFFECTS HIS

The graphs reveal that the change in trend at high 

transport rates which appeared on the slope-transport 

diagrams (fig. 6) disappears on the power-transport 

plots. This is because a discharge slightly greater than 

expected accompanied the lesser slope values for the 

pertinent transport rates, in order to maintain the same 

constant water depth. The result is a unique relation 

between stream power and sediment transport for a constant water depth, regardless of bed configuration.

The unit stream power-unit transport relations for 

the three deeper depths (and approximately for 

Z?=0.1 ft) follow a power law over most of the range 

of transport rates covered. As with the dischargetransport and slope-transport relations, flume width 

did not affect the rate of increase in unit power with 

increase in transport rate, at constant water depth. The 

straight-line portions for the three greater depths in 

figure 8 and nearly all of the relation for D=0.1 ft, were 

fitted by least squares by using the constraint that the 

lines for all widths at a given depth are mutually 

parallel. The curved lines at the lowest transport rates 

on all four diagrams were fitted by eye.

Unit stream power varied with the 0.61 power of unit 

transport rate, at constant channel width, within the 

range of transport rates covered by the least-squares 

analysis (0.005 ^^ 1.0 Ib per sec-ft and 0.3 ^D^ 0.7 

ft). If we consider stream power as the independent 

variable then i ocw1- 64.

WIDTH EFFECT

The transportation of an imposed sediment load requires a certain basic stream power or work rate. In 

narrow channels the sidewalk take up a significant part 

of the total available power. Consequently, narrow channels need a greater stream power (c/) the basic work 

rate required to move the sediment load plus the power 

used up on the sidewalls.

For the present study the data permit a determination of these two powers for a given depth and width. 

Moreover, the unit power measured in a narrow channel 

can be corrected to yield the lesser power needed to 

move the same unit transport rate in a wide channel at 

the same depth. This can be done because the sidewall 

effect disappeared at the 2-ft width, according to the 

least-squares computations, except for Z?=0.7 ft. For 

Z?=0.7 ft the same extrapolation method as on the 

slope-transport relations was used. The dashed line in 

figure 8 represents this extrapolated relation for Z?=0.7 

ft in an infinitely wide channel.

Figure 9 gives the adjustment factors to correct unit 

stream power for the flume sidewall effect, at a constant depth and unit transport rate. These factors represent simply the wide-channel unit power < > divided

by the narrow-channel value «>'. For any given channel 

width and depth, multiply the narrow-channel unit 

power by the adjustment factor shown in figure 9 to 

find the unit power needed to transport the same unit 

sediment load in an infinitely wide channel, at the same 

water depth.

Figure 9 shows that the stream power adjustment 

factor depends primarily on the width/depth ratio, as 

expected, but that the adjustment also varies slightly 

with both water depth and sediment transport rate.

In fact, since unit discharge Q/W did not vary 

significantly with flume width (fig. 3) one might expect that the unit power yQS/W adjustment factors 

would be the same as the slope-adjustment factors of 

figure 7. A comparison of figures 7 and 9 shows that the 

two diagrams are indeed virtually the same. The chief 

exception is for a depth of 0.1 ft, where narrow channels need a greater adjustment for to than for slope. 

This is probably due to the slightly different unit discharge-unit transport relation that appeared for the 

0.25-ft-wide channel at this depth (fig. 3).

A minor difference between the power- and slopeadjustment factors is that with stream power the sidewall influence, according to figures 7 and 9, may be 

eliminated at slightly lesser W/D ratios. There seems 

to be no ready explanation for this.

For practical purposes it might be better to ignore 

the minor influence of sediment-transport rate and to 

concentrate on the general surilarity in the adjustment 

factors of slope, shear stress, and stream power (figs. 7 

and 9). Because all these curves have the same shape, a 

simple curve-fitting procedure will permit one curve to 

describe all the data. For the present data the plot 

which brings all the points reasonably close to a single 

curve is the adjustment factor as a function of 

(W/D)T/D. Figure 10, which has all the slope (or 

shear) and stream power adjustment factors (figs. 7 

and 9) for the complete range of transport rates studied, 

shows this plot. Figure 10, in other words, includes the 

same data as figures 7 and 9 but with (W/D)i/D 

rather than W/D on the abscissa. One advantage to 

this type of diagram is that no interpolation is needed 

to get the adjustment factors for widths and depths 

intermediate between those studied here (for example, 

a depth of 0.4 ft and (or) width of 0.75 ft).

The single greatest deviation of the curve from a 

measured adjustment factor is 26 percent, but in 73 

percent of the cases the discrepancy between the measured values and the curve is ^ 5 percent, the arithmetic 

average. Data for the deeper water depths in narrower 

channels tend to show the largest deviations, owing to 

the steepness of the curve for these widths and depths 

(%. 10).
H16 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 

Width

ratio

Depth 

0.5 1.0 2.0 5.0 10.0 20.0

DEPTH 0.1 FT

DEPTH 0.3 FT

5.0 10.0 20.0

DEPTH 0.1 FT

DEPTH 0.3 FT

DEPTH 0.5,0.7 FT

A. l<0.005 Ib per sec-ft

DEPTH 0.5 FT

DEPTH 0.7 FT 

B. />0.005 Ib per sec-ft

I I t I M I I L I I I I I I I I

EXPLANATION

Width (ft)

Depth (ft)

0.1

0.3

0.5

0.7

0.25 0.5 1.0 2.0

FIGURE 9. Adjustment factors to be multiplied by the laboratory value to correct stream power for sidewall effect

The equation of the general adjustment-factor curve 

of figure 10 is

X* Y=-

where Y is the adjustment factor for slope, stream 

power, or shear stress and X is (W/D)^/D. This equation 

reduces to

Y==

1+0.18 wv

The coefficient (0.18) has dimensions of length (feet), 

and the adjustment factor Y is dimensionless.

Using coefficients of 0.10 and 0.24 in place of 0.18 

produces two curves which include nearly all of the

plotted points. The coefficient of 0.18 was determined 

by least-squares from the data of the narrower channels, as the predicted adjustment factors for these data 

(steep portion of curve in fig. 10) are the most sensitive 

to changes in the coefficient. (For the wider channels 

small changes in the "coefficient have a negligible influence on the predicted adjustment factor.)

With the above formula the adjustment factor varies 

not only with the width/depth ratio but also with the 

actual magnitudes of width and depth for the same 

W/D ratio. (The separate adjustment curves, such as 

those in fig. 9, show this same feature.) For example, 

at a width/depth ratio of 3 the adjustment factor computed from the general equation progresses from 0.82 

at a depth of 0.1 ft to 0.94 for #=0.3 ft to 0.96 for
FLUME WIDTH AND WATER DEPTH EFFECTS H17

<

a:

o

Q_

o£ i 

t/}

Q_

O

0.0

(W/D)jD, IN (FEET)"2 

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 =1

ADJUSTMENT FACTOR=Y=

+ 0.18( W 2

EXPLANATION

Sample use of tick-marks 

Slope (or shear) adjustment factor: _ 

/<0.005lb per sec-ft^ 

/>0.005lb per sec-ff° 

Stream power adjustment factor: 

/<0.005Ib per sec-fU 

/>0.005lb per sec-ftp

FIGURE 10. Adjustment factors to be multiplied by the laboratory value of slope (energy gradient), unit stream power, or shear 

stress to correct for the flume sidewall effect.

Z> = 0.5 ft, the width in each case being three times the 

depth. Similarly, at a width/depth ratio of 5 the calculated adjustment factor is 0.93 for Z>=0.1 ft (TF=0.5 

ft), 0.98 for Z>=0.3 ft, and 0.99 for Z> = 0.5 ft. More adjustment is needed, in other words, as water depth decreases, for a given W/D ratio.

The above equation for finding the necessary adjustment in the "narrow-flume" value of slope, shear stress, 

or unit stream power is one of the main results of this 

study. The formula may or may not apply to other flow 

conditions and sediments.

The unit power may often be independent or constant, 

and one would like to know how to adjust the sedimenttransport rate (considered as a dependent variable) to 

correct for the sidewall influence. Figure 8 also provides the information needed for these adjustment factors. The adjustment to transport rate varies depending 

on the specific unit power, in addition to depth and

width/depth ratio. Figure 11 shows the necessary adjustment in unit sediment-transport rate for various 

values of unit stream power. (Fig. 11 therefore does not 

reflect the control of variables for the experiments it 

comes from the measured power transport relations 

but pretends that stream power was independent and 

transport rate was dependent.)

One of the most striking revelations of figure 11 is that 

the unit sediment-transport rate in a wide channel can 

easily be 2 to 5 times greater than in a narrow channel, 

for the same unit stream power and water depth. Also 

the sidewall effect is much more pronounced at low 

flow rates (low values of stream power).

DEPTH EFFECT

In addition to flume-width effects the present data 

reveal the influence of water depth on the power-transport relation. The discussion here deals with the more
HIS SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

« = 0.03 Ib per sec-ft 

x 0.06<«l1.0lb per sec-ft

3.0

2.0

1.0

2.0 5.0 10.0 

Width/Depth ratio » 

20.0

DEPTH 0.1 FT

DEPTH 0.3 FT

I \ I1111 

«= 0.2 Ib per sec-ft

DEPTH 0.7 FT

«= 0.1 

Ib per sec-ft

" = 0.05 Ib per sec-ft

0.155 «i3.0lb persec10.0

5.0

2.0

0.5 

DEPTH 0.5 FT

1.0 2.0 5.0 

Width/Depth ratio -

1.0 

10.0

o

a.

« = O.llb per sec-ft 

« = 0.08 Ib per sec-ft

I I I I I I I i^ 1 

\ « = 0.1 Ib per sec-ft

V% - «=0.06lb per 

sec-:-ft

5.0

2.0 ^

0.5 1.0 2.0 ~ ' ------ 1-0

Width/Depth ratio ^ Width/Depth ratio ^ 

FIGUBE 11. Unit transport rate adjustment factors to be multiplied by the laboratory value to correct for flume sidewall effect.

common field situations where stream power is usually 

the imposed or independent variable and depth and 

transport rate are dependent.

Figure 12 shows the power-transport curves for 

"wide" channels (wall effect negligible) for the four 

flow depths studied. For a given unit power the transport rate increased as depth decreased. This means that 

power for power a shallow stream transports sediment 

at a faster rate than a deeper stream, within the range 

of depths studied here. The transport rate increased 

four to six times as depth was decreased from 0.7 to 

0.1 ft (that is, from about 160 to 20 gram diameters), 

for a given stream power.

The depth effect in the power-transport relations 

diminished as the water became deeper. The curves of 

figure 13, prepared from figure 12, suggest that at some 

depth greater than 0.7 ft (probably around 1.0 to 1.5 

ft) the unit transport rate may no longer decrease with 

increase in depth, for a given stream power.

The transport rate at zero depth should be zero. For 

this reason it seems unlikely that the transport rate 

could go on increasing at depths much below 0.1 ft. The 

curves showing the depth effect at depths less than 0.1 

ft (about 20 grain diameters) therefore might be similar to the broken extensions shown in figure 13 (R. A. 

Bagnold, written commun., 1968).

Bagnold (1966, p. 19), in comparing shallow depths 

where saltating grains reach the water surface to large 

depths where the saltation height is a negligible portion of the flow depth, predicted strictly on theoretical 

grounds that the bedload transport rate at the shallow 

depth would be three times the rate at the greater depth, 

for a given stream power. Figures 12 and 13 suggest 

that a factor of about 4 to 6 applies to the present data, 

except for very low flow rates.

For unit stream powers from 0.1 to 1.0 Ib per sec-ft 

(that is, for most of the conditions covered in the experiments), the unit sediment transport rate changed 

at the same rate with depth, regardless of the stream 

power (fig. 13).

Further experimentation with grains larger and 

smaller than 1.35 mm would be useful in determining 

whether the depth effect as observed here is influenced 

by such features as (a) depth/grain-size ratio, as contrasted to depth alone, (b) bed-form heights relative 

to water depth, and (c) the ratio of bedload to suspended load.
FLUME WIDTH AND WATER DEPTH EFFECTS H19

o

2 10

UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 

0.001 0.01 0.1 1.0 10.0

o 

z 

o

1.0

0.1

T I

DEPTH 0.5 FT

I

DEPTH 0.3 FT_

I

10.0

o

z 

o

1.0

o 

o

0.1

fc 0.01

 r 0.0001 0.001 0.01 0.1 1.0 10 ,_

§ UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH § 

FIGUBE 12. Unit stream power-unit sediment-transport relations in an infinitely wide channel.

UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 

 

0.001 \ \0.01 r0.1 1.0

< > = 0.1 Ibs per sec-ft 

(= 0.067 kg per sec-m)

30.0

- 25.0

I

<*>= 1.0 Ibs per sec-ft 

(= 0.67 kg per sec-m)

T

1.0 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4

0.3 -w= o.05 Ibs per sec-ftS* 

Q« _(= 0.034 kg per sec-m)

0.11-

0

0.001 0.01 0.1 1.0

UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH

FIGUBE 13. Variation of total sediment-transport rate with different water depths, for constant stream power.

- 20.0 ~

- 15.0 -

- 10.0

- 5.0
H20 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

BED FORMS

The sizes, shapes, and travel rates of the sand features 

which form on a streambed influence the level to which 

the water will rise in a channel of fixed width and slope, 

the navigability of a watercourse, and the depth to 

which bridge piers must extend.

The types of bed configuration (Kennedy, 1966) 

which appeared with increasing sediment-transport 

rates were flat bed (at very low transport rates, for some 

runs only), dunes, antidunes (always moving downstream) , and flat bed (sheet flow).

This order of appearance differs from that found 

with medium and fine sands (Simons and others, 1965). 

With increasing transport rate medium and fine sands 

produce a bed of ripples, ripples on dunes, dunes, flat 

bed, antidunes, and chutes and pools. The chief differences between such sands and the present coarse material are that with the latter (a) the bed often remained 

flat at the very lowest transport rates (possibly because 

the run began with an artificially flattened bed), (b) 

no ripples formed, and (c) a flat-bed stage came after 

rather than before the antidune stage.

No dunes occurred at a depth of 0.1 ft. At widths of 

1 and 2 ft the runs at slow transport rates for Z> = 0.1 

ft produced bars which alternated or meandered from 

wall to wall (see Williams, 1967, p. B21).

In the 0.25- and 0.5-ft-wide channels, the bed forms 

at all depths were mostly two dimensional, except for 

the antidunes at J9 = 0.1 ft in the 0.5-ft-wide channel. 

At widths of 1 ft or more, the bed forms for the three 

deeper water depths were two dimensional during slow 

transport rates but gradually became three dimensional 

(curving from wall to wall) as transport rates increased. 

Thus the disappearance of sidewall effects on such factors as slope and stream power corresponded roughly 

with the onset of three dimensionality in the 'bed forms.

The following analyses are based on graphs (not 

included here) of the individual bed-form characteristics as function of the independent variable unit sediment-transport rate.

BED-FORM HEIGHTS

1. General. Neither flume width nor water depth affected the rate of growth of bed-form height with 

increasing unit transport rate. Dune heights, for 

example, increased with ^10 28. The specific height 

corresponding to any unit transport rate, however, 

usually changed significantly with flume width 

and depth.

2. Width effect. Least-squares lines of best fit for the 

dune height-unit transport relations (keeping the 

lines for the various flume widths parallel to one 

another for each depth) showed that dune heights

increased as the channel became wider, for a given 

unit transport rate and depth. For the 0.3 and 0.5 

ft depths this width effect disappeared in the two 

wider channels. For J9=0.7 ft the width effect appeared to be almost eliminated at TF=2.0 ft, but 

this conclusion is only tentative because dunes in 

the five runs in the 3.9-ft-wide channel seemed to 

be higher than those in the narrower channels.

Figure 14 gives the necessary adjustment factors to correct dune height for the channel width 

effect (0.3^Z>^0.5 ft). Notice that this effect can 

be substantial. Dunes in the 0.25-ft-wide channel 

were only about half as high as those in the 1- and 

2-ft-wide channels, for a given unit transport rate 

and water depth.

Flume width had no significant influence on antidune heights. This is strange in view of the 

channel width effect on dunes.

3. Depth effect. Dune heights increased considerably 

with increase in water depth, at constant flume 

width and unit sediment-transport rate. The leastsquares lines indicate that in the 2-ft-wide channel, where sidewall effects were negligible (or at 

least minor, such as for J9=0.7 ft), dune heights 

increased with Z>°-74, for any selected unit sedimenttransport rate.

Narrower channels gave slightly different exponents. In the 0.25-, 0.5- and 1.0-ft-wide channels dune heights grew about with the 1.0,1.0, and 

0.7 powers of water depth, respectively, at constant unit transport rate. Thus the exponent decreased slightly as the channel became wider.

Antidune heights at constant unit transport rate 

increased with water depth for depths at 0.1 to 

0.5 ft, especially in going from the 0.1- to the 

0.3-ft depth. Heights for Z>=0.7 ft, however, were 

not significantly different from those at Z>=0.5 

ft, for the same unit transport rate.

<

2.5

LL.

z 2.0

LU

g 1.5

< 1.0 i 

:E 

o

 DEPTH 0.5 FT . DEPTH 0.3 FT

EXPLANATION

.-10.25 

^ J| 0.5

*.£ i.o

i 2.0

Depth "o.T

A 

 

 

in ft ~6T

A 

 &

a- 

-0-

0.5 1.0

Width

Depth

2.0 

ratio -

5.0 10.0

FIGURE 14. Dune-height adjustment factors to -be multiplied 

by the laboratory value to correct for flume-width effect.
FLUME WIDTH AND WATER DEPTH EFFECTS H21

BED-FORM WAVELENGTHS

1. Width effects. The flume width did not influence 

the bed-form wavelength-unit transport relation 

for a given water depth. However, the channel 

width may have had an effect (data are inconclusive) in that the effect of water depth on the wavelengths seemed to vary with the flume width, as 

will be mentioned below.

2. Depth effects. For unit transport rates less than about 

0.01 Ib per sec-ft (about half the range covered) 

the water depth had no influence on the bed-form 

(dune) wavelengths. As transport rate increased, 

however, a depth effect became more and more 

pronounced, at least in the two narrower channels: 

bed-form wavelengths increased with increase in 

water depth. The plots suggested that this effect 

may not exist for channel widths ^1 ft, at depths 

of 0.3 to 0.7 ft. But there are not enough runs in 

this range to say with certainty. Even in the wider 

channels the wavelengths for Z>=0.1 ft (antidunes) were considerably shorter than those for 

greater depths, at any selected unit transport rate. 

Antidunes tended to form at lesser unit transport rates as water depth decreased, at least in the 

two narrower channels. In fact at Z>=0.1 ft antidunes always formed at slower transport rates, 

regardless of channel width. (By the same token 

the flat-bed stage which followed also came at 

slower unit transport rates.) For depths between 

0.3 and 0.7 ft the data for the 1- and 2-ft-wide 

channels are inconclusive on this issue.

TRAVEL VELOCITY

1. General Bed forms travelled faster with increasing 

sediment-transport rate. The rate of dune movement increased about with i ° 7S , with no significant 

difference due to depth or width. For antidunes the 

exponent was less, about 0.7 to 0.4, depending 

on the flume width.

2. Width effects. Least-squares lines for the travel velocity-sediment transport relations (keeping the 

lines for all four widths parallel to one another, 

for a given depth) revealed a definite width effect: dunes in the two narrower channels, where 

sidewall effects were significant, travelled faster 

than dunes in wider channels, for a given water 

depth and unit sediment-transport rate. For depths 

of 0.3 and 0.5 ft the order of magnitude of this increased travel velocity was about 1.5 times. Sidewall effects disappeared at the two wider channels 

for depths of 0.3 and 0.5 ft but were still present 

for Z>=0.7 ft, according to the least-squares lines. 

The travel velocities for Z> = 0.7 ft showed more

scatter than those at lesser depths, so the sidewall 

effect may or may not have been eliminated at D~ 

0.7 ft.

Plots of the calculated travel-velocity adjustment factors as a function of TF/Z>, for depths of 

0.3 and 0.5 ft, showed too much scatter to permit 

drawing reliable curves.

Analyzing antidune travel velocities by leastsquares was not feasible because of the small number of antidune runs for 'any one width and depth 

combination. But the scatter on the plots was generally small enough for representative lines to be 

fitted by eye, These lines suggest the following: (a) 

no width effect occurred at Z>=0.1 ft and (b) a 

width, effect occurred for the three deeper depths in 

that the rate at which antidune travel-velocities increase with i probably decreased as the- channel 

widened, for 0.25 ^TF^l.O ft.

3. Depth effects. For a given channel width and unit 

sediment-transport rate, dunes travelled faster 

as water depth decreased. The dune travel velocity 

increased about with D'1 - 5 for wide channels where 

sidewall effects were negligible (W= 1.0 ft and 2.0 

ft for the two shallower depths, and assumed to 

be W=2.0 and 3.9 ft for Z> = 0.7 ft). The exponent 

was less in narrower channels, however. For the 0.5- 

ft-wide channel dune travel velocity increased 

about with. D^ 2 , while for TF=0.25 ft the exponent was about 1.0.

Antidune travel rates showed no depth effect for 

0.3 ^Z>^0.7 ft. However, at Z>=0.1 ft the antidunes for a given transport rate movednearly twice 

as fast as those at the greater depths, at least in the 

two narrower channels.

The effects of flume width and water depth on bedform characteristics, at constant unit sediment-transport rate, are summarized as follows:

1. In the two narrower channels where sidewall effects 

were significant, dune heights were less but these 

dunes travelled faster, for a given depth, Antidunes heights and bed-form wavelengths remained 

virtually the same regardless of channel width. 

Data are inconclusive concerning flume width 

effects on the travel velocities of antidunes.

2. With increase in water depth at constant flume width 

the dunes grew higher and travelled at a slower 

rate. Antidune heights also increased with depth, 

with the possible exception of depths from 0.5 

to 0.7 ft. Travel rates of antidunes showed no 

marked depth effect for the three greater depths, 

but antidunes at Z> = 0.1 ft travelled faster than 

those at deeper depths. No depth influence on bedform wavelengths appeared for transport rates less
H22 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

-than about 0.01 Ib per sec-ft, but as-i increased 

beyond this value (involving some dune runs and 

all antidune runs) the wavelengths probably increased with water depth, at constant transport 

rate.

The width and depth effects mentioned above 

suggest that many bed-form characteristics measured in narrow flumes probably cannot be applied 

with assurance to wide channels.

Why did the dunes grow higher as the flume became wider, at constant unit transport rate and 

depth? The most likely reason is that the increase 

in width brings a different velocity distribution 

within the cross-sectional flow area. Rouse (1961, 

p. 276-277) shows that in narrow rectangular channels the velocity near the bed increases more 

rapidly with height and the maximum velocity occurs closer to the bed than in wide channels. These 

velocity characteristics would restrict bed-forms to 

lower heights in narrow channels. 

Higher dunes by themselves should cause a steeper 

slope, if the bed roughness alone governed the slope 

(transport rate and depth constant). But the general 

trend with increasing width was a lesser slope, in spite 

of the higher dunes. Hence the greater width predominated over the increase in bed roughness, in regard to the slope that evolved. A wider channel at the 

same depth meant a proportionally smaller retardation of the flow by the sidewalls, as discussed earlier.

RESISTANCE FACTORS

GENERAL

The resistance factor or friction factor as an indicator 

of boundary resistance is important in river and canal 

hydraulics because this resistance directly affects the 

size of the cross-sectional flow area and the rate at which 

a channel conveys water.

Table 1 includes two commonly-used resistance factors: Manning n (=1.49 R^^^/V) and Darcy-Weisbach / ( = 80RS/V2 ) , in which R is the hydraulic radius 

and g is the acceleration due to gravity. (The values of 

n and / in metric units are the same as those for English 

units.) Both of these resistance factors changed in the 

same way as functions of the independent variable i, so 

only one of them need be examined here.

WIDTH EFFECT

Figure 15 shows how the Darcy-Weisbach friction 

factors changed with flume width, for a constant depth 

and unit transport rate. The straight portions of the 

lines were fitted by least-squares with the constraint that 

the lines for the various widths be mutually parallel,

for any one depth. The curved lines at fast transport 

rates were fitted by eye.

At a constant depth the relations for all widths are 

similar in that the friction factor gradually increased as 

bed forms grew higher. This trend extended over about 

the first two-thirds of the range of transport rates 

studied. The highest friction factors (greatest bed resistance) occurred when antidunes covered the full 

flume test section. The friction factor began declining 

when antidunes started washing out at the upstream end 

of the test section, even though the remaining antidunes 

in the downstream zone were higher than in runs at 

lesser transport rates.

With further increase in transport rate, the decline 

in friction factor continued as antidunes occupied a 

lesser and lesser zone downstream, and in fact the decline continued during the subsequent flat-bed stage 

throughout the remainder of the range of transport 

rates investigated.

The friction factor began decreasing at transport 

rates slightly less than those rates at which the change 

in trend of slope values occurred (compare fig. 6 to fig. 

15). At still faster transport rates the friction factor 

declined regardless of how slope was changing. The 

friction factor at constant depth and width varies with 

/SyF2, and at fast transport rates V2 increased with i 

faster than S changed with *.

Since the channel width did not affect the mean velocity, for a given transport rate and depth, any changes 

in the friction factor due to flume width must be due 

to the changes in the hydraulic radius and the slope. 

Figure 15 shows that the Darcy-Weisbach friction factor increased as the channel became wider, for a constant 

depth and unit transport rate. Thus with increase in 

flume width the hydraulic radius increased more substantially than the slope decreased. The R and S values 

in tables 1 and 2 verify this.

Knowing the effect of flume width on the variables 

R, &, and F, it was possible to compute the friction factors for an infinitely wide channel. Mean velocity was 

the same for any flume width, at a given depth and 

transport rate> so the best-fit curves of figure 4 provided 

values of V. The hydraulic radius in an infinitely wide 

channel equals the mean depth D. Figure 6 was the most 

convenient source for the wide-channel slopes, although 

the slope-adjustment factors of figures 7 or 10 could be 

used as well. For each selected transport rate and depth 

the appropriate R, S, and V values provided the friction 

factor in an infinitely wide channel (dashed lines in 

fig. 15).

The empirical system used here to correct friction factors for the sidewall effect keeps the same depth for 

both the narrow flume and the infinitely wide channel.
FLUME WIDTH AND WATER DEPTH EFFECTS H23

UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS

(IMMERSED WEIGHT) PER SECOND PER METER WIDTH

0.001 0.01 0.1 1.0

Of.

O

J. 0.02 -

0.1 

0.05

0.02

0.01

0.1 

0.05

Q;02

a.oi

0.0001

dunes antidunes -flat bed

DEPTH 0.3 FT

flatbed antidunes flat bed

Infinitely wide 

-...channel

Oil FT

o.oor o.oi o.i

UNfT SEDIMENT-TRANSPORT KA.TB, IN POUNDS 

(tM-WEISID WEIGHT) PER SECOND PER FOOT

1.0

EXPLANATION

Depth (ft}

Width (ft)

0.1

0.3

0.5

0.25 0.5 1.0 2.0 3.9

FIGURE 15. Flume-width, effects on friction factor-transport relations.
H24 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Mean velocity also stays the same, but the two channels 

have different slopes. Some investigators regularly use 

a theoretical method to adjust friction factors for the 

sidewall effect. This system, known as the sidewall correction method (see Vanoni and Brooks, 1957), keeps 

both velocity and slope the same for the two channels 

and changes only the hydraulic radius. The section 

"Sidewall correction procedure" deals with the sidewall 

correction method in more detail.

DEPTH EFFECT

An increase in depth at any fixed width and transport 

rate brought an increase in R, a decrease in S (fig. 6), 

and an increase in V (fig. 5). The change of the quotient 

JKS/V2 with depth should therefore be calculable from 

a knowledge of how R, S, and V changed with depth, 

at a fixed transport rate and flume width. An easier 

method simply compares the curves for the various 

depths for any chosen width, as taken from figure 15.

Such a comparison shows that there is little if any 

significant difference between the friction factor-transport relations for the three greater depths. The curves 

for all three depths reach their peak and begin declining 

at about the same unit transport rate. The trends of S 

alone (fig. 6) indicate this might be expected for depths 

of 0.3 and 0.5 ft but would not be expected for Z>=0.7 

ft, because at the latter depth no dip or nonuniquiness in 

slope values appeared. More runs at Z>=0.7 ft would be 

needed to clarify this point.

At low transport rates the friction factors for Z>=0.1 

ft are about 1.5 times greater than those for the other 

three depths. Antidunes at Z>=0.1 ft began washing out 

at much lesser transport rates, however, so the curve 

begins to decline correspondingly earlier (about one log 

cycle of transport rates sooner). At transport rates of 

about 0.1 Ib per sec-ft or a little less, the friction factors 

for all depths are nearly the same, differing by a factor 

of about 1.2.

The labelling of the bed configuration in figure 15 

(with flat-bed zones determined from narrow-channel 

data) shows a feature mentioned in the bed-form discussion: antidunes and the subsequent flat-bed stage 

appeared at slower unit transport rates as depth 

decreased.

The scatter on the friction factor-transport diagrams 

prevents drawing conclusions more specific than those 

mentioned here.

SIDEWALL CORRECTION PROCEDURE

The results presented thus far show that flume width 

can have a considerable influence in sediment-transport 

experiments. Clearly, a reliable means of evaluating and 

eliminating sidewall effects would be a very useful tool

indeed. Whenever possible such tools should be supported by theory rather than being empirical rules based 

on limited observations. Several "theories" or formulae 

for sidewall correction have been proposed but are not 

very popular.

The few investigators in the United States who use 

a sidewall correction prefer a method which has evolved 

gradually over the past 55 years. Schoklitsdh (1914) 

outlined the foundation of this particular sidewall correction method. After about 20 years two more papers 

appeared, almost simultaneously: Horton (1933) in 

November of 1933 and Einstein (1934) in February of 

1934. Though starting from different viewpoints and 

prepared independently of one another, these two papers arrived at the same general formula. Oolebatch 

(1941), apparently unaware of the Schoklitsch and Einstein papers, proposed a variable correction factor to 

Horton's equation. These correction factors presumably 

apply to canals and ditches cut in earth and rock and 

have received very little attention. Also in 1941, Einstein gave an example showing 'how to apply his 1934 

treatment to flume studies of sediment transport (Einstein, 1942). Johnson (1942) took Einstein's equation 

and added the refinements of (a) showing how to compute the hydraulic radius of smooth sidewalls and (b) 

changing the basic friction fonnula from that of Manning to that of Darcy-Weisbach in order to include a 

viscosity factor. Brooks simplified the procedure, and 

it is explained in detail by Vanoni and Brooks (1957).

The method as proposed applies only to fully rough 

flow, where the bed resistance coefficient stays constant 

for varying flow conditions (Reynolds number) for a 

given bed roughness. The general approach is to imaginarily divide the cross-sectional flow area into three 

subsections, each representing a separate "channel" in 

which only one particular boundary (bed or sidewall) 

affects the flow. You assume that the mean velocity and 

energy gradient for each subchannel equal the mean 

velocity and energy gradient for the entire flume. The 

calculations involve any of the resistance formulae (for 

example, Darcy-Weisbach or Manning), with variables 

F, £, JR, and the resistance coefficient. The goal is the 

friction factor and hydraulic radius of just the bed; 

for this bed section you can then compute any other 

quantity involving the hydraulic radius or depth, such 

as the discharge. Any such factor supposedly is free of 

sidewall influence.

Many people do not use the sidewall correction procedure, partly from theoretical objections but primarily 

because of the scarcity of data showing whether or not 

the method gives accurate answers. Some advocates of 

the procedure claim as one verification of its validity 

the results of flume experiments with a fixed, rough
FLUME WIDTH AND WATER DEPTH EFFECTS H25

bottom and smoother sidewalls (for example, the tests 

of Johnson, 1944). Runs at various depths in such tests 

give different composite resistance coefficients but almost identical values of the predicted "wide-channel" 

friction factor.

The literature contains at least five instances where 

authors devoted specific attention to testing this sidewall correction method.

Colebatch (1941) made from one to three runs in each 

of three types of board-and-dirt model channels and 

concluded that the method (Horton's formula) gave 

errors up to ±15 percent of the composite resistance 

coefficient.

Hay wood (1940, 1942) analyzed data from two environments: (a) eight natural drainage ditches with 

boundaries that had a uniform roughness at low stage 

and a different but also uniform roughness along the 

banks (higher flow depths) and (b) a rectangular flume 

with smooth walls and sand-roughened bottom. Haywood remarked that the data check very closely the lines 

predicted by the sidewall correction formula, and he 

decided that the method (that is, the composite resistance equation of Einstein's 1934 paper) was "sufficiently accurate."

Yassin (1953) studied uniform but different fixed 

roughnesses on a flume bed and sidewalls. He first determined the resistance coefficients of various boundary 

surfaces individually, for a range of flow conditions. 

Then he installed channels of composite roughnesses 

(for example, bed rough and sidewalls smooth), using 

the surfaces whose coefficients he had measured in the 

initial tests. Yassin found that the sidewall correction 

equation, with the separately-measured boundary resistance-coefficients, gave theoretical values of the composite resistance coefficient which agreed with the 

measured coefficients to within about ±5 percent.

Taylor (1961) did flume experiments on flow over a 

fixed cobblestone bed. He found that by applying the 

sidewall correction procedure the resulting bed friction 

factor-relative bed roughness relation agreed quite well 

with the relation predicted by the Karman-Prandtl resistance equation for rough, two-dimensional channels. 

In spite of this good agreement, Taylor expressed serious misgivings about the theoretical considerations on 

which the sidewall correction method is based, and consequently he cautioned against applying the method to 

situations where it is not previously known to work.

The available evidence therefore favors use of the 

sidewall correction procedure, at least for fixed-boundary situations and for flow conditions common in 

laboratories.

The present movable-bed tests either eliminated sidewall effects or came close enough to doing so to permit 

a safe extrapolation to infinitely wide channels. These 

wide-channel relations can test the sidewall correction 

method for the sediment-transport experiments reported 

herein. For this purpose the present data were analyzed 

in two ways.

TEST ONE

The sidewall correction procedure specifies that the 

velocity and slope for a narrow channel will be the same 

as for an infinitely-wide channel but that a different 

depth (/?&) will evolve for the wide channel. The method 

predicts the value of /?&. Needed for the first test was a 

master graph showing the wide-channel velocity-slope 

relations for the four depths studied. For any combination of V and /S (for example from a narrow-channel 

experiment) one could then interpolate on the widechannel graph to get the applicable depth in a wide 

channel. This depth should equal /?& as given by the 

sidewall correction method.

Specifically, the steps in this test were:

1. Plot slope as a function of mean velocity for a constant depth, to show the influence of flume width.

2. Apply a least-squares fit to the points for each widthdepth combination. (The runs at D=0.1 ft showed 

no width effect, so only one line was fitted to all of 

these points.)

3. Determine by extrapolation the slope-velocity relation for an infinitely wide channel, for each water 

depth. The procedure here was firstly to select any 

velocity on the S-V diagram and plot slope values 

as a function of the corresponding W/D ratios. 

The resulting graphs verified a power law between 

these variables. Assuming that for a given depth 

the channel could eventually become so wide that 

further increases in width would no longer affect 

the slope, the applicable function was of the form

S=A

W/Z>J

where A and B are the coefficient and exponent to 

be determined. As W/D approaches infinity the 

right-hand side of this equation approaches A. 

Thus in an infinitely wide channel the value A 

represents the slope corresponding to the given 

velocity and depth.

The procedure for getting the wide-channel S-V 

relation for each depth was therefore to (a) choose 

a velocity, (b) read the values of 8 from the leastsquares S-V lines for the successive W/D values,
H26 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

and (c) perform a final least-squares analysis with

variables log S and log

1+ W/D,

Such an analysis produced the coefficient A (equal 

to the wide-channel slope) for the given, velocity 

and depth. The wide-channel S-V relation could 

then be drawn by using the same inclination obtained in step two for the narrow-channel relations. 

For each depth the procedure had to be done twice, 

as the power relation between slope and velocity 

changed inclination at higher velocities.

4. Make a single graph containing the four wide 

channel slope-velocity curves (one curve for each 

depth).

5. Draw lines for intermediate depths on this graph by 

interpolation.

6. For each individual run, take the slope and velocity 

values and consult the above graph to find the 

depth that would obtain in an infinitely wide 

channel for this same slope and velocity.

7. Compare each such depth (Dmelis ) to that predicted 

by the sidewall correction procedure (/?&).

Figure 16 shows the results of this test, with the discrepancy ratio Dme&s/Ri plotted as a function of sediment-transport rate. Euns at Z> = 0.1 ft could not be 

tested because the wide channel depths would be less 

than 0.1 ft, and there was no reliable way of finding 

£>meas for such depths.

The 142 runs involved in this test had discrepancy 

ratios ranging from 0.41 to 1.90; the median was 0.98, 

the arithmetical average 1.01, and the standard deviation 0.29. Thus about 67 percent of the discrepancy 

ratios fall between 0.72 and 1.30.

The agreement varies with the hydraulic and (or) 

sediment-transport conditions. At the lowest transport 

rates (flat slopes, low mean velocities) the discrepancy ratios range from about 1.0 to 1.9, with a slight 

tendency for the poorest agreement to be associated 

with the two narrowest channels. The ratios improve 

considerably at intermediate transport rates. Agreement becomes poorest at those rather fast transport 

rates at which bed forms (antidunes) reach their greatest heights. At this stage the most discrepant values 

again seem to be associated with the narrower channels. The predicted depths show immediate improvement as soon as the flat-bed stage arrives.

Over some of the range of conditions studied the 

agreement is good. This tends to support those investigators who believe in the sidewall correction method.

Some possible causes of the poorer agreement where it 

occurs, in no special order of probability, are:

(a) imprecise measurements (such as might occur for 

very flat slopes, especially at deeper depths 

where bed and water-surface irregularities are 

higher) ;

(b) effect of bed configuration (for example, well-developed antidunes) that is, large differences in 

relative roughness between bed and sidewalls;

(c) effect of sediment in motion;

(d) the method used to analyze the slope-velocity data;

(e) defects in the theory of the sidewall correction

procedure.

I tried a variation of this test by obtaining the widechannel velocity-slope relations in a different way, so as 

to avoid extrapolating the 8-V data. The procedure 

here for each depth was to choose values of unit transport rate and for a given transport rate take (a) the 

slope from the S-4 relation for infinitely wide channels 

(fig. 6) and (b) the corresponding velocity from the 

least-squares lines on the velocity-transport graphs (fig. 

4). Repeating for the other depths gave the wide-channel velocity-slope relations. Then for each run an interpolation on this master graph gave the wide-channel 

depth corresponding to each narrow-channel velocity 

and slope, as before. The results of this test showed no 

significant differences from the first velocity-slope test.

TEST TWO

The second major test of the sidewall correction procedure involved only the slope and sediment-transport 

rate. Mean velocity, as seen earlier, did not change with 

flume width for a constant depth. That is, for a given 

unit transport rate and depth the wide-channel V was 

the same as the narrow-channel V. The assumption in 

this test is that if the sidewall correction procedure 

changes the hydraulic conditions (depth and unit discharge) then no simultaneous change should be made in 

the unit sediment-transport rate. In other words, the 

same unit transport rate applies to both the narrow 

flume and the infinitely wide channel (Johnson, 1942).

The master chart for this test therefore was the widechannel slope-transport relations (from fig. 6). For 

each individual run the question asked was: what is 

the wide-channel depth corresponding to the narrowchannel slope and transport rate? This depth should 

equal /?&, the depth predicted by the sidewall correction 

procedure.

Figure 17 shows the results of this second major test 

of the sidewall correction method. The agreement 

between predicted and "observed" depths is better here 

than with the first test. Of the 133 runs which could be 

tested, the discrepancy ratios ranged from 0.47 to 1.95;
FLUME WIDTH AND WATER DEPTH EFFECTS H27

UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS 

(IMMERSED WEIGHT) PER SECOND PER METER WIDTH 

0.001 0.01 0.1 1.0

2.0 

1.0

0.5

«« 

2 -o

E <*

o

11 2.0 

o

 

< i n

IREPANCY R

o :Ln <

*S)

O

2.0

1.0

1 1 1 1 

EXPERIMENTAL DEPTH 0.7 FT

 A _ 

1 1 1 1

1 1 1 1

- ^ EXPERIMENTAL DEPTH 0.5 FT 

 A- A

« A4 A

: ** e^" ~ ** e ^ _ **S * :

 A ^ _ 

1 1 1 1

1 1 1 1

EXPERIMENTAL DEPTH 0.3 FT

"*V* -H-V*. ;/* ,JA «-tfti>- -t«-^ A

i i i i

.0001 0.001 0.01 0.1

UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS 

(IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH

1.0

EXPLANATION

Depth

Width (ft)

0.25 0.5 .0 2.0 3.9

0.3

0.5

0.7

FIGURE 16. Velocity-slope test of sidewall correction procedure (Vanoni and Brooks, 1957).
H28 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS

(IMMERSED WEIGHT) PER SECOND PER METER WIDTH

0.001 0.01 0.1 1.0

«/)

o

E 

O

1

c

H

O

> 

V. 

2 

< 

O

u

Q

V. 

I/

2

2.0 

1.0

0.5

-Q

O£

i 2.0

3

c 1 0

i i.v

= 0.5

_ 

_l

£

J

2

i 

2.0 

1.0

0.5

1 1 1 1 

EXPERIMENTAL DEPTH 0.7 FT

 $ 

-A x ^""^Ty:* ~& Q _ 

I A A 0 i

i- A A _: 

i i i i

i i i i

EXPERIMENTAL DEPTH 0.5 FT ~

- A A A A^ e e - 

 A A 

1 1 1 1

1 1 1 1

EXPERIMENTAL DEPTH 0.3 FT

E * *A A / i

1 1 1 1

0.0001 0.001 0.01 0.1

UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS 

(IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH

1.0

EXPLANATION

Depth (ft)

Width (ft)

0.3

0.5

0.7

0.25 0.5 2.0 3.9

FIGURE 17. Slope-transport rate test of sidewall correction procedure (Vanoni and Brooks, 1957).
FLUME WIDTH AND WATER DEPTH EFFECTS H29

the median was 1.09 and the arithmetical average 1.05. 

The standard deviation of 0.22 means that about 67 

percent of the discrepancy ratios fall between 0.82 and 

1.27.

To a lesser extent the same tendencies noticed with 

the first test show up here. The predicted depths are 

slightly small at low transport rates. Where bedforms 

attain their greatest heights the predicted depths are a 

little too large, and this trend disappears as soon as the 

flat-bed stage appears.

The two tests applied here to the sidewall correction 

method do not rigidly prove or disprove its validity. 

On balance, however, the degree of agreement as shown 

in figures 16 and 17 together with the studies of Haywood, Yassin, and Taylor support using the procedure. With sediment-transport studies the procedure 

may be more reliable with smooth rather than with 

very rough beds.

The wide-channel slopes, stream powers, and shear 

stresses for the present flume experiments can easily 

vary by a factor of 3 from the narrow-channel values 

(see figs. 6 and 8), at a given depth and unit transport 

rate. If these factors involving slope are considered 

constant (independent) then the depths and unit transport rates vary severalfold from narrow to wide channels. Hence if data from narrow flumes are to be related 

to wide streams some sort of sidewall correction must 

be applied. At the present time the only feasible ways 

to do this are to use either a sidewall correction procedure, for example the one described most recently by 

Vanoni and Brooks (1957) for adjusting the hydraulic 

radius, or empirical correction factors of the sort given 

in the present study.

CONCLUSIONS

1. Flume width had no measurable influence on the unit 

discharge-unit sediment-transport relations and 

the mean velocity-transport relations, at constant 

water depth.

2. The energy gradient (slope), unit stream power, and 

shear stress decreased as the flume became wider, 

for a constant depth and unit sediment-transport 

rate. For experimental depths from 0.1 to 0.7 ft, 

a 2-ft-wide flume was wide enough to eliminate 

sidewall effects on the slope, power, and shear 

stress. (Values of these variables in the 2-ft-wide 

channel were within 0 to 5 percent of the values 

estimated for an infinitely wide channel.)

3. Multiplying the laboratory value of slope, unit 

stream power, or shear stress by the adjustment 

factor

1

gives the slope, power, or shear for a wide channel 

(no sidewall effect), for the same water depth 

and unit sediment-transport rate.

4. Depths from 0.1 to 0.7 ft affected the unit stream 

power-unit sediment-transport relations in that 

for a given stream power the transport rate 

increased about fourfold to sixfold as depth 

decreased from 0.7 to 0.1 ft.

5. Bedforms in narrow channels (widths less than 1 ft) 

differed in various ways from those in wider 

channels, for the same unit transport rate and 

depth.

6. For a given depth and unit transport rate the DarcyWeisbach friction factor increased as the flume 

became wider, and this increase can be determined 

from a knowledge of the flume width effects on the 

individual variables R, $, and V.

7. Five studies by other investigators, together with 

the present data, support the use of the sidewall 

correction procedure (Vanoni and Brooks, 1957) 

for relating flume data to infinitely wide channels, 

at least for most of the common laboratory flow 

conditions. The procedure may not be reliable, 

however, for those particular sediment-transport 

rates associated with high antidunes. Further 

checks should be made of the sidewall correction 

procedure to determine the range of widths and 

depths and the boundary roughnesses to which the 

method applies.

REFERENCES

Bagnold, R. A., 1966, An approach to the sediment transport 

problem from general physics: U.S. Geol. Survey Prof. 

Paper 422-1, 37 p.

Brooks, N. H., 1958, Mechanics of streams with movable beds 

of fine sand: Am. Soc. Civil Engineers Trans., v. 123, p. 

526-594.

Colby, B. R., 1964, Discharge of sands and mean-velocity relationships in sand-bed streams: U.S. Geol. Survey Prof. 

Paper 462-A, 47 p.

Colby, B. R., and Scott, C. H., 1965, Effects of water temperature on the discharge of bed material: U. S. Geol. Survey 

Prof. Paper 462-G, 25 p.

Colebatch, G. T., 1941, Model tests on Liawenee Canal roughness 

coefficients: Journal of the Institution of Engineers Australia Trans., v. 13, no. 2, p. 27-32.

Gruff, R. W., 1965, Cross-channel transfer of linear momentum 

in smooth rectangular channels: U.S. Geol. Survey WaterSupply Paper 1592-B, 26 p.

Dawdy, D. W., 1961, Depth-discharge relations of alluvial 

streams discontinuous rating curves: U.S. Geol. Survey 

Water-Supply Paper 1498-C, 16 p.

Einstein, H. A., 1934, Der Hydraulische Oder Profil-Radius: 

Schweizerische Bauzeitung, v. 103, no. 8, p. 89-91.

 1942, Formulas for the transportation of bed load: Am. 

Soc. Civil Engineers Trans., v. 107, p. 561-577.
H30 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Guy, H. P., Rathbun, R. E., and Richardson, E. V., 1967, Recirculation and sand-feed type flume experiments: Am. Soc. 

Civil Engineers Proc., v. 93, no. HY5, p. 97-114.

Hay wood, O. G., Jr., 1940, Flume experiments on the transportation by water of sands and light weight materials: Ph.D 

thesis, Massachusetts Inst Technology, 122 p.

 1942, Discussion of "Formulas for the transportation of

bed load:" Am. Soc. Civil Engineers Trans., v. 107, p. 583-

590. 

Horton, R. E., 1933, Separate roughness coefficients for channel

bottom and sides: Engineering News-Record, Nov. 30, 1933,

p. 652-653. 

Johnson, J. W., 1942, The importance of considering sidewall

friction in bed-load investigations: Civil Engineering, v.

12, p. 329-331.

 1944, Rectangular artificial roughness in open channels: 

Am. Geophys. Union Trans., 25th Annual Meeting, part VI, 

p. 906-912.

Kennedy, J. F., Chairman, 1966, Nomenclature for bed forms 

in alluvial channels, Report of the task force on bed forms 

in alluvial channels: Am. Soc. Civil Engineers Proc., v. 92, 

no. HY3, p. 51-64.

Lane, E. W., 1955, Design of stable channels: Am. Soc. Civil 

Engineers Trans., v. 120, p. 1234-1279.

Leopold, L. B., and Maddock, T., Jr., 1953, The hydraulic geometry of stream channels and some physiographic implications: U.S. Geol. Survey Prof. Paper 252, 57 p.

Rouse, H., 1961, Fluid mechanics for hydraulic engineers: New 

York, Dover Pubs.., Inc., 422 p.

Scheidegger, A. E., and Langbein, W. B., 1966, Probability concepts in geomorphology: U.S. Geol. Survey Prof. Paper 

500-C, 14 p.

Schoklitsch, A., 1914, Uber Schleppkraft und Geschiebebewegung: Leipzig and Berlin, W. Englemann, 66 p.

Simons, D. B., Richardson, E. V., and Nordin, C. F., Jr., 1965, 

Sedimentary structures generated by flow in alluvial channels, in Soc. Econ. Paleontologists and Mineralogists, Primary sedimentary structures and their hydrodynamic interpretation a symposium: Soc. Econ. Paleontologists and 

Mineralogists Spec. Pub. 12, p. 34-52, 253-264.

Taylor, R. H., Jr., 1961, Exploratory studies of open-channel 

flow over boundaries of laterally varying roughnesis: Calif. 

Insit. Technology Div. of Engineering, Report no. KH-R-4, 

65 p.

Vanoni, V. A., and Brooks, N. H., 1957, Laboratory studies of the 

roughness and suspended load of alluvial streams: Calif. 

Inst. Technology Sedimentation Laboratory, Report E-68, 

121 p. (also published as U.S. Army Corps of Engineers, 

M.R.D. Sediment Series 11,121 p.).

Williams, G. P., 1967, Flume experiments on the transport of a 

coarse sand: U.S. Geol. Survey Prof. Paper 562-B, 31 p.

Yassin, A. M., 1953, Mean roughness coefficient in open channels 

with different roughnesses of bed and side walls: Mitt, aus 

der Versuchsanstalt fur Wasserbau und Erdbau, Eidg. Tech. 

Hoch. Zurich, no. 27, 90 p.
TABLES

FLUME WIDTH AND WATER DEPTH EFFECTS 

TABLE 1. Summary of experimental data, in English units

H33

Unit 

water disRun charge, Slope, S 

Q (ft per ft) 

W 

(cfs per ft)

Depth,

(ft)

Sediment transport »

veloc- Unit 

ity, V Measur- transpor 

(fps) ing period rate, i 

(sec) (Ib per 

sec per ft;

- Sediment 

infeed » 

t (Ib per 

sec)

I

Surface velocity 

(fps)

Bed forms 2

Wnt-rr

temper- Height 

ature (ft)

0 Unit

"tream

T ontrth pOWBr, ?m Travel u 

(lt) velocity (Ibper 

(fps) sec per ft)

Hydraulic 

radius, 

JZ (ft)

Friction factor

draulic 

radius 

of bed, 

Rt (ft)

DarcyWeisbach, Manning, 

n 

(ftV6)

Channel width =0.25 ft.

1 ....

2......

3.. 

4... ...

5 ._

6 

7 

8 

9 ...

10.. 

11. . 

12 

13..... 

14 

15-....

16..... 

17. .

18 

19..... 

20 

21..... 

22..... 

23.. 

24.....

25-....

26. . 

27.....

28 

29..... 

30..... 

31..... 

32.. 

33 ..

34. .

35 ..

36 

37.....

38 

39 

40 

41. . 

42..... 

43.. 

44 

45.....

46 

47.....

48 

0.148 

.164 

.196 

.200 

.232 

.256 

.352

.440 

.460 

.488 

.476 

.540 

.584 

.648

.780

.868 

.948 

1.048 

1.080 

1.120 

1.120 

1.280 

1.352 

1.800 

2.160

.820 

.860 

.916 

.964 

1.064 

1.208 

1.292 

1.520 

1.720 

1.712 

1.840 

2.280 

2.756 

3.068

1.248 

1.240 

1.392 

1.720 

2.220 

2.468

2.700

2.960 

3.288

0. 00529 

.00640 

.00840 

.0132 

.0166 

.0213 

.0262

.00272 

.00258 

. 00295 

. 00310 

.00371 

.00435 

.00595

. 00942

.0131 

.0133

.0177 

.0174 

.0208 

.0205 

.0197 

.0222 

.0288 

.0350

.00237 

.00271 

.00288 

. 00363 

.00485 

.00651 

.00763 

.0104 

.0123 

.0158 

.0212 

.0188 

.0238 

.0309

.00250 

. 00234 

. 00300 

. 00539 

.00793 

.0101

.0146

.0183 

.0225

0.101 

.104 

.107 

.095 

.097 

.093 

.099

.304 

.303 

.300 

.294 

.304 

.303 

.306

.300

.305 

.307 

.304 

.292 

.301 

.287 

.293 

.299 

.303 

.307

.507 

.501 

.502 

.500 

.501 

.502 

.498 

.505 

.502 

.514 

.495 

.491 

.492 

.470

.702 

.704 

.714 

.726 

.711 

.701

.692

.686 

.679

1.46 

1.58 

1.83 

2.10 

2.39 

2.75 

3.55

1.45 

1.52 

1.61 

1.62 

1.77 

1.93 

2.12

2.60

2.81 

3.09 

3.45 

3.70 

3.72 

3.90 

4.37 

4.52 

5.94 

7.04

1.62 

1.72 

1.82 

1.93 

2.12 

2.40 

2.60 

3.01 

3.42 

3.33 

3.72 

4.64 

5.56 

6.53

1.77 

1.76 

1.95 

2.37 

3.12 

3.52

3.90

4.31 

4.84

2,580 

1,800 

1,200 

1,500 

5,400 

6,540 

4,200

55, 140 

17, 400 

11,340 

7,320 

15,180 

4,860 

3,330

2,595

1,740 

6,780 

780 

3,540 

480 

2,970 

2,700 

3,900 

1,980 

900

70, 920 

14, 280 

8,340 

12, 780 

7.200 

3,120 

2,460 

2,040 

5,790 

360 

240 

4,020 

1,320 

2,040

11, 640 

4,500 

5,640 

6,000 

5,520 

5,340

3,720

2,940 

3,120

0. 00212 

.00472 

.0100 

.0252 

.0572 

.101 

.220

.000540 

. 000920 

. 00141 

.00218 

. 00476 

. 00617 

.0144

.0370

.0608 

.0688 

.149 

.164 

.208 

.273 

.401 

.412 

.997 

1.390

. 000380 

. 00105 

.00252 

.00484 

.0102 

.0198 

.0325 

.0676 

.0964 

.144 

.284 

.426 

.737 

1.20

. 000386 

. 000612 

.00382 

.0194 

.0572 

.0888

.216

.328 

.543

0. 000500 

.00116 

.00250 

. 00660 

.0144 

.0243 

.0556

.000111

.0167

.0406

.0646 

.0833 

.108 

.238

. 0000754

.0244

.100 

.191 

.300

. 000155 

.000186 

.000889 

.00486 

.0125 

.0238

.0511

.0791 

.131

1.72 

1.84 

2.15 

2.53 

2.78 

3.20 

3.85

1.74 

1.70 

1.83 

1.86 

2.00 

2.20 

2.52

3.12

3.38 

3.57 

3.71 

4.00 

3.85 

4.12 

4.50 

4.62 

5.92 

6.84

1.62 

1.93 

2.12 

2.20 

2.46 

2.85 

3.22 

3.63 

3.94 

3.79 

4.06 

5.08 

6.01 

6.81

1.91 

1.89 

2.11 

3.04 

3.66 

3.82

4.59

4.73 

5.39

70.0 Flatbed...

79.0 do 

70.5 A 0.033- 

72.0 A .041.. 

74.5 A .046 

76.0 A .052..

65.0 D .014 

73.0 D .014.. 

76.5 D .015.. 

76.5 D .017.. 

75.0 D .020.. 

71.5 D .027- 

69.5 D .030.. 

figo /D .041- 68-°tA3 .062.. 

68.5 A .103- 

67.5 A .093.. 

69.5 A .160.. 

51.0 A .147- 

69.5 A .ISO65. 5 A .160.. 

67.5 A .142.. 

69.5 A .217.. 

67.0 Flat bed. ..

67.5 .....do .

74.0 .... .do ...

75.0 D .030.. 

75.5 D .033.. 

69.5 D .050.. 

68.5 D .060.. 

70.0 D .062.. 

70.0 D .067.. 

68. 5 D .080.. 

65.0 A . ISO73. 0 A .220.. 

73.5 A .280.. 

63.0 A .226- 

63.5 A .216- 

59.0 Flatbed....

60.0 D .026....

64.0 D .024....

56.0 D .050.. 

59.0 D .108- 

65.0 D .100.. 

62.5 D .122..

63-°(A !220- 

61.5 A .22... 

62.0 A .27...

0.53 

.61 

.66 

.90

6.06 

5.55 

4.40 

2.69 

2.66 

2.14 

1.15 

1.15 

1.30 

1.34 

1.46 

1.45 

1.30 

1.50 

1.53 

1.62

6.68 

3.57 

3.74 

3.38 

2.26 

2.09 

3.20 

1.85 

2.00 

2.50 

2.08 

2.42

3.83 

3.33

2.97 

2.56 

1.33 

2.67 

2.58 

2.67

0.0256 

.0313 

.0384 

.0476

.00117 

.00155 

.00458 

. 00321 

.00480 

.00640 

.0167 

. 03121 

. 0111J 

.0185 

.0190 

.0278 

.0417 

.0435 

.0455 

.0654 

.0526

.00138 

.00403 

. 00275 

.00471 

.0142 

.0196 

.0286 

.0270 

.0323 

.0439 

.0700 

.0971

. 000476 

.000280 

.00204 

.00770 

.0305 

.0333 

. 0816) 

. 0440) 

.0546 

.0833

0. 0487 

.0655 

.102 

.164 

.240 

.340 

.576

.0746 

.0743 

.0892 

.0916 

.125 

.158 

.250

.459

.706 

.784 

1.152 

1.174 

1.452 

1.432 

1.568 

1.868 

3.230 

4.710

.121 

.145 

.165 

.218 

.322 

.490 

.614 

.985 

1.32 

1.69 

2.43 

2.67 

4.07 

5.91

.194 

.181 

.261 

.579 

1.10 

1.57

2.46

3.38

4.62

0.056 

.057 

.058 

.054 

.055 

.053 

.055

.089 

.089 

.088 

.087 

.089 

.089 

.089

.088

.088 

.089 

.089 

.088 

.088 

.087 

.089 

.088 

.089 

.089

.099 

.100 

.100 

.100 

.100 

.100 

.100 

.100 

.099 

.100 

.100 

.099 

.099 

.099

.106 

.106 

.106 

.106 

.106 

.106

.106

.106 

.106

0.069 

.073 

.075 

.071 

.073 

.069 

.068

.142 

.124 

.124 

.125 

.131 

.137 

.157

.164

.185 

.172 

.181 

.160 

.179 

.162 

.142 

.147 

.118 

.101

.145 

.157 

.147 

.179 

.211 

.228 

.230 

.244 

.224 

.293 

.301 

.191 

.167 

.157

.163 

.138 

.168 

.268 

.223 

.232

.296

.309 

.306

0.0358 

.0377 

.0374 

.0416 

.0411 

.0384 

.0294

.0296 

.0257 

.0258 

.0264 

.0270 

.0268 

.0304

.0317

.0376 

.0319 

.0340 

.0288 

.0340 

.0302 

.0236 

.0246 

.0187 

.0162

.0230 

.0237 

.0224 

.0250 

.0278 

.0291 

.0291 

.0296 

.0268 

.0368 

.0394 

.0223 

.0196 

.0185

.0218 

.0206 

.0215 

.0262 

.0222 

.0223

.0262

.0269 

.0262

0. 0108 

.0111 

.0112 

.0116 

.0116 

.0111 

. 00985

.0107 

.0099 

.0099 

.0101 

.0102 

.0101 

.0108

.0110

.0120 

.0110 

.0114 

.0105 

.0114 

.0108 

. 00950 

. 00972 

.00850 

.00790

.00960 

.00971 

.00946 

.0100 

.0105 

.0108 

.0108 

.0108 

.0103 

.0125 

.0125 

. 00940 

.00880 

. 00860

.00959 

.00920 

.00930 

.0103 

.00950 

. 00950

.0104

.0104 

.0103

Channel width =0.5 ft

49..... 

50.__- 

51 

52 .. 

53.....

54 

55 

56 

57 

58 

59 

60 

61.....

62 

63 

64..... 

65..... 

66 

67 

68 

69 

70 

71 

72 ,.

73 

74 

75 

76 

77-....

0.110 

.128 

.144 

.150 

.166 

.180 

.208 

.264 

.294 

.384 

.466

.430 

.476 

.536 

.600 

.654 

.756 

.800 

.964 

1.068 

1.180 

1.244 

1.500 

1.920

.744 

.792 

.820 

.880 

.924

0.00383 

.00481 

.00558 

.00617 

.00758 

.0117 

.0162 

.0202 

.0217 

.0303 

.0367

.00177 

. 00183 

.00251 

. 00374 

.00553 

.00795 

.00901 

.0120 

.0136 

.0149 

.0165 

.0179 

.0234

. 00123 

.00161 

. 00191 

.00227 

.00260

0.101 

.101 

.102 

.102 

.104 

.097 

.098 

.100 

.098 

.087 

.082

.293 

.306 

.308 

.300 

.288 

.294 

.294 

.307 

.307 

.312 

.300 

.286 

.300

.493 

.500 

.492 

.506 

.502

1.09 

1.27 

1.41 

1.47 

1.60 

1.86 

2.12 

2.64 

3.00 

4.41 

5.69

1.47 

1.55 

1.74 

2.00 

2.27 

2.57 

2.72 

3.14 

3.48 

3.78 

4.15 

5.25 

6.40

1.51

1.58 

1.66 

1.74 

1.84

19, 260 

7,740 

5,160 

8,700 

3,420 

1,920 

1,380 

840 

420 

2,070 

2,310

19, 020 

21, 600 

7,980 

6,960 

3,660 

1,590 

1,980 

1,080 

810 

515 

415 

1,860 

1,620

38,580 

19, 820 

8,340 

12, 780 

6,420

0. 000149 

. 00181 

.00232 

.00488 

.00876 

.0224 

. 0464 

.107 

.135 

.396 

.626

. 000500 

.00144 

. 00364 

.0122 

.0254 

.0428 

.0586 

.111 

.173 

.237 

.386 

.646 

1.37

.000290 

. 00156 

.00228 

.00418 

.00632 .

0. 000111

.196 

.319

.313

.687 

. 000153

1.57 

1.74 

1.85 

2.00 

2.20 

2.56 

2.95 

3.65 

3.86 

4.88 

5.67

1.76 

1.84 

1.97 

2.52 

2.76 

3.16 

3.09 

3.37 

3.60 

4.04 

4.73

6.98

1.66 

1.81 

1.94 

2.09 

2.13

68.5 Flatbed....

71.5 ..do .....

79.5 ..do .

71.5 ..do.... ... ...

80.0 A? .......

73.0 A 0.040.. 

74.5 A .055.. 

75.5 A .068-- 

75.5 Flatbed .

46.5 ... do. . 

46.5 --do. . .

69.5 D .020.. 

68.5 D .022.. 

67.5 D .025.. 

66.0 D .035.. 

65.5 D .045.. 

64.0 A .070.. 

63.5 A .10... 

65.0 A .13.. . 

64. 5 A .15.. . 

63.5 A .18-. . 

64.5 A .20... 

50.5 Flatbed....

53.5 ...do ....

72.0 D .021- 

79.5 D .046.. 

79.0 D .044.. 

80.0 D .065.. 

79.0 D .072-

0.40 .

.60 

.70 

.80

6.63 

3.44 

2.55 

1.85 

1.50 

1.10 

1.10 

1.25 

1.65 

1.50 

1.80

7.2 

3.48 

3.22 

3.40 

3.18

.0283 

.0406 

.0500

.0017 

.0024 

.0067 

.0147 

.0182 

.0154 

.0172 

.0312 

.0333 

.0456 

.0700

. 000550 

.00133 

. 00120 

.00267 

.00308

0. 0262 

.0384 

.0500 

.0578 

.0786 

.131 

.210 

.334 

.398 

.726 

1.07

.0474 

.0543 

.0835 

.140 

.226 

.375 

.449 

.720 

.906 

1.09 

1.28 

1.68 

2.80

.0571 

.0797 

.0980 

.125 

.150

0.072 

.071 

.072 

.072 

.073 

.071 

.070 

.071 

.070 

.065 

.062

.135 

.138 

.138 

.136 

.134 

.135 

.135 

.137 

.137 

.139 

.136 

.134 

.136

.166 

.167 

.166 

.167 

.167

0.087 

.086 

.087 

.087 

.090 

.087 

.087 

.086 

.084 

.071 

.063

.181 

.182 

.193 

.200 

.206 

.218 

.220 

.238 

.226 

.228 

.214 

.178 

.177

.224 

.268 

.278 

.300 

.305

0. 0596 

.0546 

.0520 

.0528 

.0556 

.0616 

.0649 

.0531 

.0435 

.0260 

.0181

.0286 

.0270 

.0294 

.0327 

.0371 

.0417 

.0422 

.0428 

.0397 

.0374 

.0335 

.0224 

.0200

.0230 

.0278 

.0296 

.0322 

.0330

.0147 

.0141 

.0137 

.0139 

.0142 

.0147 

.0152 

.0138 

.0125 

.00950 

.00790

.0106 

.0110 

.0114 

.0120 

.0128 

.0136 

.0137 

.0139 

.0133 

.0129 

.0122 

.0100 

.00940

.0104 

.0115 

.0119 

.0124 

.0125

See footnotes at end of table.
H34 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 

TABLE 1. Summary of experimental data, in English units Continued

Unit 

water

At*

Run charge, Slope, S 

Q (ft per ft) 

W 

(cfs per ft)

(ft)

Sediment transport *

veloc- Unit infeed 1 faceveity, V Measur- transport (Ib per locity 

(fps) ing period rate, i sec) (fps) 

(sec) (Ib per 

sec per ft)

Bed forms 2

temper- Height 

ature (ft) (°F)

Lftfth Travel 

w velocity 

(fps)

Unit

power, 

a 

(Ib per 

sec per ft)

Hydraulic 

radius, 

U(ft)

Hy- -

draulic 

radius 

of bed, 

tf i (ft)

Friction factor

DarcyWeisbacb, 

/

Manning, 

n (ft1/6)

Channel width =0.5 ft Continued

78....-

79.....

80 

81.....

82. .

83 

84 

85 

86 

87 

88. .

89 

90. 

91. .

92 

93 

94 

.976

1.140

1.360

1.580

1.676

1.720

1.856

2.50

3.40

1.150

1.240

1.320

1.450

1.742

2.12

2.58

3.30

.00300

.00458

.00639

.00931

.0111

.0141

.0141

.0144

.0230

.00115

.00127

.00145

. 00211

.00324

.00456

.00951

.0135

.500

.493

.505

.512

.492

.504

.480

.515

.443

.700

.702

.715

.711

.702

.722

.694

.693

1.95

2.31

2.69

3.08

3.40

3.41

3.86

4.84

7.67

1.64

1.77

1.85

2.04

2.48

2.94

3.72

4.76

6,240

3,000

2,040

840

3,120

490

5,580

1,980

960

55,800

14,400

12,900

18,000

14,640

6,900

3,420

2,250

.00706

.0224

.0540

.0964

.173

.196

.352

.519

1.95

.000350

.000816

.00121

.00532

.0181

.0434

.184

.526

.0834

.169

.253

1.00

.000184

.000248

.000695

.00229

.00916

.0212

.0875

.268

.. 2.28

.. 3.00

.. 3.37

. 3.79

4.20

.. 4.01

4.85

5.32

7.85

1.79

1.89

1.92

2.22

2.80

3.43

4.29

5.44

77.5 D .061..

76.5 D .082..

79.0 D .079..

79. 5 A? .136..

52.0 A .22...

79.5 A .25...

49.5 A .20...

52.5 A .25...

48.0 Flatbed...

61.0 D .027...

65.5 D .041..

73.5 D .060..

75.0 D .083..

75.0 D .087..

57.0 D .104..

54. 5 A .25...

53. 5 A .22...

2.52 .00367

2.17 .0227

2.18 .0276

1.90 .0300

1.94 .'0385

1.95 .0350

2.07 .0510

2.27 .0770

....... .000688

5. 9 . 000589

5.71 .000822

2.96 .00232

2.34 .00590

2.36 .0178

2.26 .0341

2. 44 . 0561

.183

.326

.541

.916

1.15

1.51

1.63

2.23

4.88

.0825

.0981

.119

.191

.352

.603

1.53

2.77

.167

.166

.167

.168

.166

.167

.164

.167

.161

.184

.185

.186

.186

.184

.185

.183

.183

.312

.324

.339

.362

.348

.381

.339

.304

.205

.242

.234

.260

.328

.341

.360

.425

.403

.0340

.0366

.0379

.0425

.0411

.0521

.0400

.0265

.0162

.0202

.0193

.0203

.0243

.0250

.0251

.0324

.0281

.0127

.0132

.0134

.0142

.0139

.0157

.0138

.0112

.00870

.01000

.0098

.0100

.0109

.0111

.0111

.0125

.0116

Channel width= 1.0 ft

95.. 

96. .

97 

98 

99.....

100 

101 

102 

103 

104 

105 

106- ..

107 

108 .

109 .

110 

111 

112 .

113....

114 .

115....

116 

117. 

118- -

119....

120 

121 

122....

123 .

124. 

125 .

126 .

127 .

128 

129. 

130....

131.-.

132. 

133. 

134... .

135. 

136....

137. 

138 

139....

140....

141 

142 

143. 

144....

145....

146 

147....

0.115

.127

.142

.158

.154

.166

.191

.220

.233

.292

.400

.405

.440

.440

.438

.452

.470

.498

.503

.512

.530

.551

.570

.650

.741

.760

.760

.794

.860

1.05

1.12

1.30

1.97

.768

.845

.795

.866

.905

.960

.958

1.05

1.10

1.32

1.64

1.87

2.49

1.17

1.24

1.32

1.42

1.64

2.26

2.79

0.00407

.00411

.00495

.00590

.00751

.0108

.0128

.0151

.0199

.0222

.0331

.00110

.0012

.00136

.00162

. 00182

. 00200

. 00210

. 00211

.00236

. 00272

.00318

. 00397

. 00509

. 00557

. 00594

. 00592

.00643

. 00721

. 00824

.0109

.0129

.0162

. 00106

. 00137

. 00133

. 00144

. 00172

. 00184

.00216

. 00251

.00314

.00416

.00842

.0118

.0113

.00081

.00079

.00131

.00178

.00272

.00454

.00955

0.093

.100

.100

.102

.101

.095

.101

.099

.094

.097

.094

.297

.314

.313

.294

.294

.300

.303

.304

.295

.294

.290

.288

.287

.297

.293

.296

.306

.307

.324

.321

.324

.323

.503

.509

.485

.505

.517

.512

.502

.517

.504

.510

.486

.480

.477

.696

.711

.703

.716

.707

.695

.645

1.24

1.27

1.41

1.55

1.53

1.75

1.89

2.22

2.48

3.01

4.26

1.36

1.40

1.41

1.49

1.54

1.57

1.64

1.65

1.74

1.80

1.90

1.98

2.26

2.49

2.59

2.57

2.59

2.80

3.24

3.49

4.01

6.10

1.53

1.66

1.64

1.72

1.75

1.87

1.91

2.03

2.18

2.59

3.37

3.90

5.22

1.68

1.74

1.88

1.98

2.32

3.25

4.33

226, 620

17, 940

10, 140

5,400

2,460

1,440

1,684

2,183

960

473

1,630

24, 180

26,040

23,820

23,400

12,240

14,040

6,360

2,400

5,040

3,620

2,340

2,160

1,980

2,130

1,140

1,200

1,353

960

720

510

900

270

172, 500

14, 040

9,180

10,020

8,460

18, 420

3,840

6,300

2,640

1,800

2,820

1,380

1,380

186,720

86, 520

106,800

28, 380

14,400

3,240

2,160

0. 000541

.00145

.00291

.00593

.00935

.0198

.0344

.0577

.112

.168

.500

.000250

. 000310.

. 000540.

.00107 .

.00171 .

.00256 .

.00361 .

.00375 -

.00585 .

.00925 .

.0109 .

. 0160 .

.0316 .

. 0383 .

.0434 .

.0475 .

.0480 .

.0688 .

.0972 .

.163 .

.313

1.09

.000434

.00203 .

.00207 .

.00288 -

.00479 .

.00610 .

.00716 .

.0113 .

.0197

.0333

.135

.322

.605

.000467

.00143

.00323

.00583

.0201

.0806

.307

0. 000519

.519

.328

1.06

.000437

.138

.325

.550

. 000465

.00135

.00322

.00563

.0200

.0813

.319

1.66

. 1.68

. 1.89

. 2.08

. 2.22

. 2.41

. 2.67

- 2.86

. 3.39

- 3.85

5.22

. 1.56

1.67

1.76

1.85

1.87

2.06

2.16

2.10

2.14

2.30

2.31

2.50

2.92

2.92

3.00

3.05

3.05

3.33

3.67

3.74

4.65

1.76

1.91

1.92

1.97

2.02

2.25

2.20

2.38

. 2.54

. 3.14

3.77

4.45

5.63

1.82

1.83

2.04

2.16

2.53

3.60

4.36

57.0 Flatbed....

65.5 ...do 

66.5 ...do........

70.0 do... 

54.5 A.........

53.5 A .021..

63.5 A .042..

60.0 A .083..

74.5 A .053..

76.5 A .073..

66.5 Flatbed 

70.5 do 

73.0 D .021 

67.5 Flatbed....

65.5 D .042..

61. 5 D .042-

65.0 D .053-

63. OD .063..

64.0 D .042-

63. OD .053-

64.0 D .053-

61.0 D .053-

61.0 D .063-

60.5 D .073-

54.0 D .167-

68. 5 A .150-

71. 5 A .150-

60. OD .125..

71.0 A .167..

74. 5 A .250-

77.0 A .250-

68. 5 A .21...

67.5 Flatbed....

66. OD .044-

70. OD .083-

79. OD .042-

73.0 D .104-

74.5 D .063..

74. OD .042-

64.0 D .063..

65.5 D .167-

69.5 D .167-

69.5 D .167-

66.0 A .18.-.

66.0 A .28...

66.5 A .27 

71.5 D .050..

61.0 D .064-

70.5 D .083..

69.0 D .082-

66.0 D .154..

66.0 A .134..

68.0 A .273..

0.50 .........

.50 .0200

.60 .0216

.70 .0300

1.00 .0683

0.60 .0683

...... .00070

8. 9 . 0017

5. 8 . 0027

4. 8 . 0015

4. 3 , 0035

3. 6 . 0050

3. 5 . 0027

2. 3 . 0075

2. 4 . 0117

2. 0 . 0158

1. 8 . 0267

1. 3 . 0250

1. 4 . 0200

1. 3 . 0250

1. 5 . 0384

1. 5 . 0083

1. 6 . 0400

1. 6 . 0350

1.73 .0500

10. 7 . 000421

5. 2 . 0012

3. 9 . 00070

3. 7 . 0017

2. 8 . 0018

2. 9 . 0022

2. 5 . 0020

2. 0 . 0072

2.2 .0063

1. 8 . 0217

1.88 .0307

2.19 .0417

2.56 .0546

7. 9 . 000312

5. 3 . 000754

3. 7 . 00163

2. 6 . 00218

4. 5 . 00376

1. 9 . 0263

2. 3 . 0403

0. 0292

.0325

.0438

.0581

.0724

.112

.152

.206

.289

.404

.826

.0277

.0332

.0372

.0443

.0513

.0585

.0655

.0661

.0755

.0899

.109

.141

.206

.258

.281

.280

.318

.386

.539

.760

1.05

1.99

.0507

.0723

.0661

.0780

.0972

.110

.129

.165

.215

.342

.861

1.37

1.75

.0591

.0611

.108

.158

.278

.640

1.66

0.078

.083

.083

.085

.084

.080

.084

.083

.079

.081

.079

.186

.193

.193

.185

.185

.188

.189

.189

.186

.185

.183

.183

.182

.186

.185

.186

.190

.190

.197

.196

.197

.197

.252

.252

.246

.251

.254

.253

.250

.254

.250

.252

.246

.245

.244

.291

.294

.292

.295

.293

.290

.282

0.091

.092

.092

.094

.094

.090

.095

.093

.089

.090

.086

.221

.238

.244

.232

.235

.243

.242

.244

.238

.241

.239

.245

.243

.248

.245

.248

.260

.259

.268

.272

.270

.240

.348

.364

.346

.358

.386

.377

.380

.397

.394

.398

.396

.398

.344

.382

.365

.450

.504

.518

.491

.490

0.0531

.0546

.0533

.0537

.0692

.0727

.0775

.0647

.0660

.0511

.0371

.0284

.0307

.0339

.0347

.0367

.0393

.0360

.0374

.0371

.0398

.0417

.0475

.0469

.0430

.0422

.0430

.0467

.0449

.0396

.0452

.0406

.0221

.0294

.0323

.0313

.0314

.0367

.0343

.0379

.0400

.0424

.0403

.0470

.0489

.0260

.0215

.0198

.0278

.0346

.0381

.0320

.0370

0. 0140

.0142

.0141

.0142

.0161

.0163

.0170

.0155

.0155

.0137

.0117

.0117

.0123

.0129

.0130

.0133

.0138

.0133

.0135

.0134

.0139

.0142

.0152

.0151

.0145

.0139

.0146

.0151

.0148

.0140

.0148

.0144

.0105

.0127

.0132

.0129

.0130

.0141

.0136

0143

0147

.0151

.0147

.0159

.0163

.0119

.0111

.0106

.0126

.0141

.0148

.0135

.0144

Channel width=2.0 ft

148 

149 

ISOIS! 

152 

153 

0.120

.146

.175

.180

.260

.320

0. 00489

.00569

.00816

.0117

.0172

.0234

0.098

.091

.091

.089

.093

.099

1.22

1.60

1.92

2.02

2.80

3.23

56,280

19,560

11,550

6,000

3,945

900

0. 00170

.00354

.0119

.0272

.0775

.188

0.00330

.00782

.0241

.0574

.164

.403

1.85

1.98

2.30

2.58

3.17

4.23

80.0 B 0.12...

78.0 B .03 

77 n (B .03... 77>0 U* .02 

80.0 A .06 

80.0 A .08...

79.0 Flatbed....

11.0 .........

5.3 0.00148

4. 1 . 0041) 

0.5 .022 (

0. 6 . 022

0.82 .039

0. 0366

.0518

.0891

.131

.278

.465

0.089

.083

.083

.082

.085

.090

0.094

.087

.087

.086

.089

.095

0. 0751

.0475

.0472

.0606

.0480

.0520

0. 0170

.0133

.0133

.0150

.0134

.0142

See footnotes at end of table.
FLUME WIDTH AND WATER DEPTH EFFECTS 

TABLE 1. Summary of experimental data, in English units Continued

H35

Unit 

water

Sediment transport 1

Bun charge, Slope, S 

Q (ft per ft)

W 

(cfs per ft)

D veloc- Unit infeed i 

(ft) ity, V Measur- transport (Ib per 

(fps) ing period rate, i sec) 

(sec) (Ib per 

sec per ft)

Sur- Water - 

Bed forms 2

faceve- templocity er- Height Lengtl 

(fps) ature (ft) (ft) 1 Travel 

velocity 

(fps)

Unit

TTTT_ stream -LJ.Jpower, draulic 

a radius, 

(Ib per R (ft) 

sec per ft)

TT,. Hydraulic 

radius 

of bed, 

-R& (ft)

Friction factor

DarcyWeisbach, Manning, 

(ftV«)

Channel width =2.0 ft Continued

154 

155. 

156 .

157

158 1

159 .

160 

161 

162....

163 

164....

165 .

166 

167. 

168 

169 

170....

171 

172 

.428

.450

.500

.590

.845

1.105

.780

.855

.880

1.110

1.29

1.605

1.710

1.120

1.285

1.370

1.405

1.800

2.290

. 00118

.00154

.00210

.00330

. 00714

.0113

.00106

.00097

.00137

.00281

.00445

.00643

. 00877

.00060

.00080

. 00147

. 00172

.00280

.00560

.287

.293

.286

.290

.289

.293

.478

.490

.496

.496

.483

.490

.452

.692

.681

.711

.700

.702

.66

1.49

1.54

1.75

2.04

2.92

3.77

1.63

1.75

1.77

2.24

2.67

3.28

3.78

1.62

1.89

1.93

2.01

2.56

3.47

23, 340

48,900

5,700

7,770

6,510

2,605

83,940

53,940

7,860

7,650

3,830

3,595

1,150

103,080

32,700

11, 940

4,440

1,205

585

. 000670

.00120

.00420

.0124

.0700

.192

. 000710

.00131

.00305

.0141

.0362

.100

.197

.000585

. 00150

.00410

. 00730

.0296

.116

.00139

. 00239

. 00859

.0250

.150

.437

.00150

.00248

.00599

.0288

.0713

.194

.413

.00120

. 00280

.00799

.0150

.0583

.275

1.94

1.97

2.22

2.70

3.33

4.40

1.89

1.92

2.05

2.62

2.96

3.77

4.55

1.76

1.95

2.04

2.22

2.80

3.96

75.0 D 0.

78.0 D .

029..

035..

83.0 D .049..

83.0 D .070 ...

83.0 A .11...

76.5 A .18...

74.5 D .040..

79. 5 D .,054..

80.0 D .072..

76.5 D .11...

79.0 D .13...

80.0 A .16...

79.0 A .20 

72.5 D .071..

80.0 D . 068..

77.5 D .09...

82.0 D .11 

82.0 D .13 

81.0 A? .16...

6.2

3.28

2.38

1.3

1.46

5.8

3.63

3.10

3.42

2.53

2.2

2.1

3.75

3.5

3.1

3.6

3.1

2.5

.00132

.00204

.00334

.00920

.0278

.0322

.000489

. 00105

.00160

.00408

.0200

.0228

.0400

.000494

.00104

. 000651

.00188

.00398

.0343

.0315

.0432

.0655

.121

.376

.781

.0516

.0517

.0751

.194

.358

.644

.936

.0419

.0641

.126

.151

.314

.800

.223

.226

.222

.225

.224

.226

.324

.329

.331

.331

.327

.329

.311

.408

.405

.415

.412

.412

.399

.247

.258

.254

.263

.264

.267

.396

.388

.416

.434

.431

.436

.403

.500

.492

.589

.590

.595

.574

.0305

.0378

.0392

.0459

.0482

.0462

.0332

.0268

.0373

.0477

.0526

.0506

.0492

.0240

.0233

.0421

.0451

.0454

.0478

.0127

.0141

.0143

.0155

.0159

.0155

.0141

.0126

.0149

.0169

.0177

.0174

.0169

.0124

.0122

.0165

.0170

.0170

.0174

Channel width=3.9ft

173 

174....

175 

176 

177 

1.29

1.28

1.36

1.43

1.47

0.00096

. 000912

. 00115

. 00191

. 00214

0.730

.705

.708

.694

.67

1.77

1.82

1.92

2.06

2.20

20,820

16, 530

12,480

15,600

4,290

0. 00156

. 00205

.00367

.00830

.0112

0. 00644

.00800

.0152

.0308

.0420

2.00

2.01

2.22

2.68

82.5 D .

77.0 D .

83.5 D .

81.5 D .

79.0 D .

07...

13...

13...

15...

18 

3.6 0.000566

4.3

4.2

2.5

3.0

. 000556

.000790

.00114

.00287

0. 0772

.0730

.0974

.170

.197

0.531

.519

.521

.512

.498

0.650

.622

.635

.640

.616

0. 0419

.0368

.0419

.0594

.0568

0. 0171

.0160

.0170

.0202

.0196

1 Immersed weight. 

Letter A in height column indicates bed forms were antidunes; B, bars; D, dunes.

Both dunes and antidunes occurred.

Both bars and antidunes existed, simultaneously.

TABLE 2. Summary of experimental data, in metric units 

[Precision of measurements indicated by table 1, not table 2]

Bun

Unit 

water 

discharge, 

Q 

W 

(liters per 

sec per m)

Sediment transport >

Depth, velocity, 

Slope, D V Measuring 

S (cm) (cm per period 

sec) (sec)

Unit 

transport 

rate, i 

(kg per 

sec per 

m)

Bed forms 2

Sediment Surface Water 

infeed » velocity, tempera- 

(kg per (cm per ture Height Length 

sec) sec) (°C) (cm) (cm)

Travel 

velocity, 

(cm per 

sec)

Unit 

stream 

power, Hydraulic Hydraulic 

<a radius, radius of 

(kg per R bed, R t 

sec per (cm) (cm) 

m)

Channel width 7.5 cm

I.........

2.........

3

4

5. ...... .

6. 

7. 

8 ......

9. .

10.......

11 

12 

13 .

14... .

15.. ......

16........

17.. 

18........

19........

20........

21........

22.. 

23........

24........

25........

26. ....

27 ..

28.. ...

29........

30........

13.8

15.2

18.2

18.6

21.6

23.8

32.8

40.8

42.8

45.4

44.2

50.2

54.2

60.2

72.4

80.6

QQ fl

97.4

100.4

104.0

104.0

119.0

125.6

167.2

200.6

76.2

79.8

85.0

89.6

98.8

0. 00529 

.00640 

.00840 

.0132 

.0166 

.0213 

.0262

.00272 

.00258 

.00295 

.00310 

.00371 

.00435 

.00595

.00942

.0131 

.0133 

.0177 

.0174 

.0208 

.0205 

.0197 

.0222 

.0288 

.0350

.00237 

.00271 

.00288 

.00363 

.00485

3.1 

3.2 

3.3 

3.0 

3.0 

2.8 

3.0

9.3 

9.2 

9.1 

9.0 

9.2 

9.2 

9.4

9.0

9.5 

9.5 

9.5 

9.0 

9.0 

9.0 

9.0 

9.0 

9.0 

9.5

15.5 

15.3 

15.3 

15.2 

15.2

44.5 

48.0 

56.0 

64.0 

73.0 

84.0 

108.0

44.0 

46.5 

49.0 

49.5 

54.0 

59.0 

64.5

79.0

85.5 

94.0 

105.0 

113.0 

113.5 

119.0 

133.0 

138.0 

181.0 

214.5

49.5 

52.5 

55.5 

59.0 

64.5

2,580 

1,800 

1,200 

1,500 

5,400 

6,540 

4,200

55,140 

17,400 

11,340 

7,320 

15, 180 

4,860 

3,330

2,595

1,740 

6,780 

780 

3,540 

480 

2,970 

2,700 

3,900 

1,980 

900

70, 920 

14, 280 

8,340 

12, 780 

7.200

0. 00315 

.00702 

.0149 

.0375 

.0851 

.150 

.327

.000803 

. 00137 

.00210 

. 00324 

.00708 

. 00918 

.0214

. 0551 

.0905 .

.102 

.222

.244 

.310 

.406 

.597 

.613 

1.484 

2.068

. 000565 

. 00156 .

. 00375 .

, 00720 .

. 0152 .

0. 000227 

. 000526 

. 00113 

.00299 

.00653 

.0110 

.0252

. 0000503

. 00758

.0184

.0293 

.0378 

.0490 

.108

.0000342

52.5 

56.0 

65.5 

77.0 

84.5 

97.5 

117.5

53.0 

52.0 

56.0 

56.5 

61.0 

67.0 

77.0

95.0

103.0 

109.0 

113.0 

122.0 

117.5 

125.5 

137.0 

141.0 

180.5 

208.5

49.5 

59.0 

64.5 

67.0 

75.0

21.2 Flatbed.....

26.2 ...do.... ..

24.2 ...do .

21.6 A 1.0 

22.2 A 1.2.... 

23.6 A 1.4.... 

24.6 A 1.6 

IB 9 T* f\ A.

22.8 D 0.4... . 

24.8 D 0.4... . 

24.8 D 0.6 . 

23.8 D 0.6 . 

22.0 D 0.8 

20.8 D 1.0. 

200 (D 1.2 20-° U8 1.8 . 

20.2 A 3.2 

19.6 A 2.8 

20.8 A 4.8 

10.6 A 4.4.... 

20.8 A 5.4. 

18.8 A 4.8. 

19.8 A 4.4. 

20.8 A 6.6.... 

19.6 Flatbed.....

19.8 ... do..... ..

23.2 ...do.... ..

24.0 D 1.0..-. 

24.2 D 1.0 

20.8 D 1.6. 

20.4 D 1.8 

16 

19 

20

27

185 

169 

134 

82 

81 

65 

35 

35 

40 

41 

45 

44 

40 

46 

47 

49

204 

109 

114 

103

0.78 

.95 

1.17 

1.45

.036 

.047 

.14 

* .098 

.15 

.20 

.51 

.95) 

.34j 

.56 

.58 

.85 

1.27 

1.33 

1.39 

1.99 

1.60

.042 

.12 

.084 

.14

0. 0725 

.0975 

.152 

.244 

.357 

.506 

.857

.111 

.111 

.133 

.136 

.186 

.235 

.372

.683

1.051 

1.167 

1.714 

1.747 

2.161 

2.131 

2.333 

2.780 

4.806 

7.008

.180 

.216 

.246 

.324 

.479

1.7 

1.7 

1.8 

1.6 

1.7 

1.6 

1.7

2.7 

2.7 

2.7 

2.7 

2.8 

2.8 

2.8

2.6

2.6 

2.8 

2.8 

2.6 

2.6 

2.6 

2.8 

2.6 

2.8 

2.8

3.0 

3.0 

3.0 

3.0 

3.0

2.1 

2.2 

2.3 

2.1 

2.2 

2.2 

2.0

4.3 

3.8 

3.8 

3.8 

4.0 

4.2 

4.8

5.0

5.6 

5.2 

5.6 

4.8 

5.4 

5.0 

4.4 

4.4 

3.6 

3.0 

4 

4. 

4.8 

4.5 

5.5 

6.4

See footnotes at end of table.
H36, SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 2. Summary of experimental data, in metric units Continued

Run

Unit 

water 

discharge, 

Q 

W 

(liters per 

sec per m)

Slediment transport 

Slope, Depth, velocity, 

S D V Measuring 

(cm) (cm per period 

sec) (sec)

Unit Sediment Surface Water 

transport infeed > velocity, temperarate, i (kg per (cm per ture 

(kg per sec) sec) (°C) 

sec per 

m)

Bed forms 2

Height Length Travel 

velocity, 

(cm) (cm) (cm per 

sec)

Unit 

stream Hydraulic Hydraulic 

power, radius, radius of 

a R bed, Rb 

(kg per (cm) (cm) 

sec per 

m)

Channel width 7.5 cm Continued

31 ..

32........

33.. 

34........

35........

36 .. 

37 

38 

39. . 

40 

41.. ..

42........

43-.. .

44... .

45........

46.. ..

47.. ...

48-. ...

49 

50. ...

51- .

52 

53. .

54 

55 

56 ...

57 

58........

59 

60 ..

61 ..

62 

63 

64.. ......

65 

66 ..

67 

68 

69 

70 

71 

72. ....

' .-.....

74 ....

'6 

77 

78 

79-.-....

80 

81 

82.. ...

83 .......

84 

85 

86 

87 

88 

89 . 

90... .

Q1

92.._.....

93 .....

94. .

112. 2

120. 0

141. 2

159. 8

159. 0

171. 0

211. 8

256. 0

285.0

116.0

115. 2

19Q /L

159.8

206.2

250.8

275.0

305.5

10.2

11.8

13.4

14.0

15.4

16.8

19.4

24.6

27.4

35.6

43.2

40.0

44.2

49.8

55.8

60.8

70.2

74.4

89.6

99.2

109.6

115. 6

139. 4

178. 4

fid 9

73.6

76.2

81.8

85.8

90.6

106.0

126. 4

146. 8

155. 8

159. 8

172. 4

OQO O

315. 8

106. 8

11 c O

1 DA Q

161. 8

197. 0

OOQ fi

306. 6

.00651 

.00763 

.0104 

.0123 

.0158 

.0212 

.0188 

.0238 

.0309 

.00250 

.00234 

.00300 

.00539 

.00793 

.0101

.0146

.0183 

.0225

0. 00383 

.00481 

.00558 

. 00617 

.00758 

.0117 

.0162 

.0202 

.0217 

.0303 

.0367

.00177 

.00183 

.00251 

.00374 

.00553 

.00795 

.00901 

.0120 

.0136 

.0149 

.0165 

.0179 

.0234

.00123 

.00161 

.00191 

.00227 

.00260 

.00300 

.00458 

.00639 

. 00931 

.0111 

.0141 

.0141 

.0144 

.0230

.00115 

. 00127 

.00145 

. 00211 

.00324 

.00456 

.00951 

.0135

15.4 

15.2 

15.4 

15.5 

15.5 

15.0 

16.0 

15.0 

14.5 

21.4 

21.4 

21.8 

22.2 

21.6 

21.4

21.0

21.0 

21.0

3.1 

3.1 

3.1 

3.1 

3.2 

3.0 

3.0 

3.0 

3.0 

2.6 

2.4

8.9 

9.3 

9.4 

9.2 

8.8 

9.0 

9.0 

9.5 

9.5 

9.5 

9.0 

8.8 

9.2

15.0 

15.2 

15.0 

15.4 

15.3 

15.2 

15.0 

15.4 

15.5 

15.0 

15.5 

14. ft 

15.5 

13.5

21.4 

21.4 

21.8 

21.6 

21.4 

22.0 

21.0 

21.0

73.0 

79.0 

91.5 

104.0 

101.5 

113.5 

141.5 

169.5 

199.0 

54.0 

53.5 

59.5 

72.0 

95.0 

107.5

119.0

131.5

147.5

33.0 

38.5 

43.0 

45.0 

49.0 

56.5 

64.5 

80.5 

91.5 

134.5 

173.5

45.0 

47.0 

53.0 

61.0 

69.0 

78.5 

83.0 

95.5 

106.0 

115.0 

126.5 

160.0 

195.0

46.0 

48.0 

50.5 

53.0 

56.0 

59.5 

70.5 

82.0 

94.0 

103.5 

104.0 

117.5 

147.5 

234.0

50.0 

54.0 

56.5 

62.0 

75.5 

89.5 

113.5 

145.0

3,120 

2,460 

2,040 

5,790 

360 

240 

4,020 

1,320 

2,040 

11,640 

4,500 

5,640 

6,000 

5,520 

5,340

3,720

2,940 

3,120

19,260 

7,740 

5,160 

8,700 

3,420 

1,920 

1,380 

840 

420 

2,070 

2,310

19,020 

21,600 

7,980 

6,960 

3,660 

1,590 

1,980 

1,080 

810 

515 

415 

1,860 

1,620

38,580 

19, 820 

8,340 

12, 780 

6,420 

6,240 

3,000 

2,040 

840 

3,120 

490 

5,580 

1,980 

960

55,800 

14,400 

12,900 

18,000 

14,640 

6,900 

3,420 

2,250

.0295 

.0484 

.101 

.143 

.214 

.423 

.634 

1.097 

1.786 

.000574 

.000911 

.00568 

.0289 

.0851 

.132

.321

.488 

.808

0. 000222 

.00269 

.00345 

.00726 

.0130 

.0333 

.0690 

.159 

.201 

.589 

.931

.000744 

.00214 

.00542 

.0182 

.0378 

.0637 

.0872 

.165 

.257 

.353 

.574 

.961 

2.039

.000432 

.00232 

.00339 

.00622 

.00940 

.0105 

.0333 

.0804 

.143 

.257 

.292 

.524 

.772 

2.902

.000521 

.00121 

.00180 

.00792 

.0269 

.0646 

.274 

.783

.0111

.0454 

.0866 

.136 

.0000703 

.0000843 

.000403 

.00220 

. 00567 

.0108

.0232

.0359 

.0594

Channel width

0. 0000503

.0889 

.145

.142

.312 

.0000694

.0378

.0767 

.115 

.454

.0000834 

.000112 

.000315 

.00104 

.00415 

.00962 

.0397 

.122

87.0 

98.0 

110.5 

120.0 

115.5 

123.5 

155.0 

183.0 

207.5 

58.0 

57.5 

64.5 

92.5 

111.5 

116.5

140.0

144.0 

164.5

15.0 cm

48.0 

53.0 

56.5 

61.0 

67.0 

78.0 

90.0 

111.5 

117.5 

148.5 

173.0

53.5 

56.0 

60.0 

77.0 

84.0 

96.5 

94.0 

102.5 

109.5 

123.0 

144.0

213.0

50.5 

55.0 

59.0 

63.5 

65.0 

69.5 

91.5 

102.5 

115.5 

128.0 

122.0 

148.0 

162.0 

239.5

54.5 

57.5 

58.5 

67.5 

85.5 

104. *> 

131.0 

166.0

21.2 

21.2 

20.2 

18.4 

22.8 

23.0 

17.4 

17.6 

15.2 

15.6 

17.8 

13.4 

15.0 

18.4 

17.0

17.2

16.4 

16.6

20.2 

22.0 

26.4 

22.0 

26.8 

22.8 

23.8 

24.2 

24.2 

8.0 

8.0

20.8 

20.4 

19.8 

19.0 

18.6 

17.8 

17.4 

18.2 

18.0 

17.6 

18.0 

10.4 

12.0

22.2 

26.4 

26.2 

26.8 

26.0 

25.4 

24.8 

26.0 

26.4 

11.0 

26.6 

9.8 

11.6 

8.8

16.0 

18.6 

23.0 

23.8 

24.0 

14.0 

12.6 

12.0

D 1.8 . 

D 2.O.... 

D 2.4.... 

A 5.4.... 

A 6.8.... 

A 8.6.... 

A 6.8.... 

A 6.6. 

TOlnf V,0H

D 0.8- 

D 0.8-- 

D 1.6 

D 3.2-- 

D 3.0-... 

D 3.8---. 

JD 3.8---. 

U 6.8 

A 6.8..- 

A 8.2-..

Flatbed ..

...do ...... .

...do ..

...do 

A? ...... .

A 1.2 

A 1.6 

A 2.0 

Flatbed--.

...do ... ....

...do ....

D 0.6. 

D 0.6.-.- 

D 0.8---. 

D 1.0-- 

D 1.4---. 

A 2.2.... 

A 3.0--. 

A 4.0... . 

A 4.6---- 

A 5.4.-- 

A 6.0.- 

Flatbed--. ...do .

D O.6.... 

D 1.4--.. 

D 1.4... _ D 2.0 .. 

D 2.2-- 

D 1.8 

D 2.4-..- 

D 2.4---- 

A? 4.2 

A 6.8-.. 

A 7.6.-.. 

A 6.O.... 

A 7.6-.-.

TF1 Q * VmH

D 0.8... 

D 1.2.... 

D 1.8. 

D 2.6..... 

D 2.6 

D 3.2 

A 7.6...- 

A 6.8. 

69 

64 

98 

56 

61 

76 

63 

74

117

101 

91

78 

41 

81 

79 

81

12 .

18 

21 

24

202 

105 

78 

56 

46 

34 

34 

38 

50 

46 

55

219 

106 

98 

104 

97 

77 

66 

66 

58 

59 

59 

63 

69

180 

174 

90 

71 

72 

69 

74

.43 

.60 

.87 

.82 

.98 

1.34 

2.13 

2.96

.015 

.0085 

.062 

.23 

.93 

1.01 

2.49) 

1.34) 

1.66 

2.54

.86 

1.24 

1.52

,052 

.073 

.20 

.45 

.55 

.47 

.52 

.95 

1.01 

1.39 

2.13

.017 

.041 

.037 

.081 

.094 

.11 

.69 

.84 

.91 

1.17 

1.07 

1.55 

2.35

.021 

.18 

.025 

.071 

.018 

.54 

1.04 

1.71

.729 

.914 

1.466 

1.964 

2.515 

3.616 

3.973 

6.056 

8.794 

.289 

.269 

.388 

.862 

1.637 

2.336

3.660

5.029 

6.875

0. 0390 

.0571 

.0744 

.0860 

.117 

.195 

.312 

.497 

.592 

1.080 

1.592

.0705 

.0808 

.124 

.208 

.336 

.558 

.668 

1.071 

1.348 

1.622 

1.905 

2.500 

4.166

.0850 

.119 

.146 

.186 

.223 

.272 

.485 

.805 

1.363 

1.711 

2.247 

2.425 

3.318 

7.261

.123 

.146

.177 

.284 

.524 

.897 

2.277 

4.122

3.0 

3.0 

3.0 

3.0 

3.0 

3.0 

3.0 

3.0 

3.0 

3.2 

3.2 

3.2 

3.2 

3.2 

3.2

3.0

3.0 

3.0

2.2 

2.2 

2.2 

2.2 

2.0 

2.0 

2.0 

2.0 

2.0 

2.0 

2.0

4.1 

4.2 

4.2 

4.2 

4.0 

4.2 

4.0 

4.0 

4.0 

4.0 

4.0 

4.0 

4.0

5.1 

5.1 

5.1 

5.1 

5.1 

5.1 

5.0 

5.0 

5.0 

5.0 

5.0 

5.0 

5.0 

5.0

5.6 

5.6 

5.6 

5.6 

5.6 

5.6 

5.5 

5.5

7.0 

7.0 

7.4 

7.0 

9.0 

9.0 

6.0 

5.0 

5.0 

5.0 

4.2 

5.1 

8.2 

6.8 

7.0

9.0

9.5 

9.5

2.7 

2.6 

2.7 

2.7 

2.5 

2.5 

2.5 

2.5 

2.5 

2.0 

2.0

5.5 

5.5 

5.9 

6.0 

6.2 

6.6 

6.5 

7.0 

7.0 

7.0 

6.5 

5.5 

5.5

6.8 

8.2 

8.5 

9.1 

9.3 

9.5 

9.8 

10.4 

11.0 

10.5 

11.5 

10.5 

9.5 

6.0

7.4 

7.2 

8.0 

10.0 

10.4 

11.0 

13.0 

12.5

Channel width 30.5 cm

95 .

96 ..

97 

98 

99 

100 

101 

102 ....

103... 

104.......

10.6

11.8

13.2

14.6

14.4

15.4

17.8

20.4

21.6

27.2

0.00407 

.00411 

.00495 

. 00590 

. 00751 

.0108 

.0128 

.0151 

.0199 

.0222

2.8 

3.0 

3.0 

3.2 

3.0 

3.0 

3.0 

3.0 

3.0 

3.0

38.0 

39.0 

43.0 

47.0 

46.5 

53.5 

57.5 

67.5 

75.5 

91.5

226,620 

17,940 

10,140 

5,400 

2,460 

1,440 

1,684 

2,183 

960 

473

0.000805 

.00216 

.00433 

.00882 

.0139 

.0295 

.0512 

.0859 

.167 

.250

0. 000235 50.5 

51.0 

57.5 

63.5 

67.5 

73.5 

81.5 

87.0 

103.5 

117.5

13.8

18.6 

19.2 

21.0 

12.6 

11.8 

17.6 

15.6 

23.6 

24.8

T?1at Vtari

... do - .

...do ......

 do... 

j^

A 0.6. 

A 1.2 .. 

A 2.6. 

A 1.6..- 

A 2.2-.--

15 .

15 

18 

21 

30

18

.61 

.66

.91 

2.08 

2.08

0.0434 

.0484 

.0652 

.0865 

.108 

.167 

.226 

.307 

.430 

.601

2.4 

2.5 

2.5 

2.6 

2.6 

2.4 

2.6 

2.6 

2.4 

2.4

2.8 

2.8 

2.8 

2.8 

2.8 

2.8 

2.8 

2.8 

2.8 

2.8

See footnotes at end of table.
FLUME WIDTH AND WATER DEPTH EFFECTS H37

TABLE 2. Summary of experimental data, in metric units Continued

Bun

Unit 

water 

discharge, 

Q 

w

(liters per 

sec per m)

Sediment transport '

Slope, Depth, velocity, 

S D V Measuring 

(cm) (cm per period 

sec) (sec)

Unit Sediment 

transport infeed ' 

rate, i (kg per 

(kg per sec) 

sec per 

m)

Bed forms 2

Surface Water 

velocity, tempera- Height Length 

(cm per ture 

sec) (° C) (cm) (cm)

Travel 

velocity, 

(cm per 

sec)

Unit 

stream Hydraulic Hydraulic 

power, radius, radius of 

<a R bed, 

(kg per (cm) Rt 

sec per (cm) 

m)

Channel width 30.5 cm Continued

105. .-.

106 .

107 

108 

109 

110 .

111- .

112.......

113 

114......

115--....

116-.. ...

117 

118 - 

119 ....

120 

121 

122......

123 ..

124- 

125.-. 

126 

127.. ..

128.. .

129 

ISOIS! ...

132. .

133 . 

134 

135 

136 . 

137 

138 

139 

140 

141 

142 

143. 

144 -.

145 .

idfi

147 

37.2

37.6

40.8

40.8

40.6

42.0

43.6

46.2

46.8

47.6

49.2

51.2

53.0

60.4

68.8

70.6

70.6

73.8

79.8

97.6

104.0

120. 8

183. 0

71 4

78.6

73.8

80.4

84.0

89.2

89.0

97.6

102.2

122.6

152. 4

173. 8

231. 4

108.6

115. 2

122. 6

132. 0

152 4

210. 0

259. 2

.0331

.00110 

.00121 

.00136 

.00162 

.00182 

.00200 

.00210 

.00211 

.00236 

.00272 

.00318 

.00397 

.00509 

.00557 

.00594 

.00592 

.00643 

.00721 

.00824 

.0109 

.0129 

.0162

.00106 

.00137 

.00133 

.00144 

.00172 

.00184 

.00216 

.00251 

.00314 

.00416 

.00842 

.0118 

.0113

.00081 

.0079 

.00131 

.00178 

.00272 

.00454 

.00955

3.0

9.1 

9.6 

9.6 

9.0 

9.0 

9.1 

9.2 

9.3 

9.0 

9.0 

8.8 

8.8 

8.8 

9.0 

9.0 

9.0 

9.5 

9.5 

10.0 

10.0 

10.0 

9.8

15.3 

15.5 

14.8 

15.4 

15.8 

15.6 

15.4 

15.8 

15.4 

15.5 

15.0 

14.5 

14.5

21.2 

21.7 

21.4 

21.8 

21.6 

21.0 

20.0

130.0

41.5 

42.5 

43.0 

45.5 

47.0 

48.0 

50.0 

50.5 

53.0 

55.0 

58.0 

60.5 

69.0 

76.0 

79.0 

78.5 

79.0 

85.5 

99.0 

106.5 

122.0 

186.0

46.5 

50.5 

50.0 

52.5 

53.5 

57.0 

58.0 

62.0 

66.5 

79.0 

102.5 

119.0 

159.0

51.0 

53.0 

57.5 

60.5 

71.0 

99.0 

132.0

1,530

24,180 

26,040 

23, 820 

23,400 

12,240 

14,040 

6,360 

2,400 

5,040 

3,620 

2,340 

2,160 

1,980 

2,130 

1,140 

1,200 

1,353 

960 

720 

510 

900 

270

172, 500 

14,040 

9,180 

10,020 

8,460 

18, 420 

3,840 

6,300 

2,640 

1,800 

2,820 

1,380 

1,380

186, 720 

86, 520 

106,800 

28, 380 

14,400 

3,240 

2,160

. 744 . 235 

.000372 ............

.000461 ..... .

.000804 ............

.00159 ............

.00254 ............

.00381 --------

.00537 ............

.00558

.00870 ---....

.0138 .-.. .

.0162 ... .... -

.0238 ..- -

.0470 - .--.-.

.0570 ----------

.0646 ----------

.0707 . ...

.0714 ............

.102 ............

.145 ..--....

.243 ............

. 466 . 149 

1. 622 . 481

. 000646 . 000198 

.00302 ............

00308

00429

f\A7io

nnontt

.0107 ... --

.0168 ... 

.0293 ... ....

(\AQfi

. 201 . 0626 

. 479 . 147 

.900 .249

. 000695 . 000211 

. 00213 . 000612 

. 00481 . 00146 

. 00868 . 00255 

. 0299 . 00907 

. 120 . 0369 

. 457 . 145

159.0

47.5 

51.0 

53.5 

56.5 

57.0 

63.0 

66.0 

64.0 

65.0 

70.0 

70.5 

76.0 

89.0 

89.0 

91.5 

93.0 

93.0 

101.5 

112.0 

114.0 

141.5

53.5 

58.0 

58.5 

60.0 

61.5 

68.5 

67.0 

72.5 

77.5 

95.5 

115.0 

135.5 

171.5

55.5 

56.0 

62.0 

66.0 

77.0 

109.5 

133.0

19.2 Flatbed. 

21.4 .... .do...... ..

22.8 D0.6-. 

19.8 Flatbed.-.-.

18.6 D 1.2 

16.6 D 1.2. ... 

18.4 D 1.6 

17.2 D 2.0 

17.8 D 1.2. 

17.2 D 1.6. 

17.8 D 1.6. 

16.2 D 2.6. 

16.2 D 2.0. 

15.8 D 2.2. 

12.4 D 5.0- 

20.4 A 4.6- 

22.0 A 4.6- 

15.6 D 3.8-.-- 

21.8 A 5.0-... 

23.6 A 7.6- 

25.0 A 7.6 

20.4 A 6.4 

19.8 Flatbed.. 

19.0 D 1.4. 

21.0 D 2.6 

26.0 D 1.2. 

22.8 D 3.2-... 

23.6 D 2.0- 

23.2 D 1.2.--. 

17.8 D 2.0. 

18.8 D 5.0 

20.8 D 5.0- ... 

20.8 D 5.0. 

18.8 A 5.4. 

18.8 A 8.6. . 

19.0 A 8.2 

22.0 D 1.6- 

16.0 D 2.0- 

21.6 D 2.6. 

20.6 D 2.4.-.. 

19.0 D 4.6.-- 

18.8 A 4.0- 

20.0 A 8.4 

271 

177 

146 

131 

110 

107 

70 

73 

61 

55 

40 

43 

40 

46 

46 

49 

49 

53

326 

158 

119 

113 

85 

88 

76 

61 

67 

55 

57 

67 

78

241 

162 

113 

79 

137 

58 

70

.021

.052 

.082 

.046 

.11 

.15 

.082 

.23 

.36 

.48 

.81 

.76 

.61 

.76 

1.17 

.25 

1.22 

1.07 

1.52

.013 

.037 

.021 

.052 

.055 

.067 

.061 

.22 

.19 

.66 

.94 

1.27 

1.66

.0095 

.023 

.050 

.066 

.11 

.80 

1.23

1.229

.0412 

.0494 

.0554 

.0659 

.0763 

.0870 

.0975 

.0984 

.112 

.134 

.162 

.210 

.307 

.384 

.418 

.417 

.473 

.574 

.802 

1.131 

1.562 

2.961

.0754 

.108 

.0984 

.116 

.145 

.164 

.192 

.246 

.320 

.509 

1.281 

2.039 

2.604

.0879 

.0909 

.161 

.235 

.414 

.952 

2.470

2.4

5.7 

5.9 

5.9 

5.6 

5.6 

5.7 

5.7 

5.7 

5.6 

5.6 

5.6 

5.6 

5.6 

5.6 

5.5 

5.5 

6.0 

6.0 

6.0 

6.0 

6.0 

6.0

7.7 

7.7 

7.5 

7.7 

7.7 

7.8 

7.6 

7.8 

7.6 

7.6 

7.5 

7.5 

7.5

8.9 

9.0 

9.0 

9.0 

9.0 

9.0 

8.5

2.6

6.7 

7.3

7.4 

7.1 

7.2 

7.4 

7.4 

7.4 

7.2 

7.4 

7.2 

7.4 

7.4 

7.6 

7.5 

7.5 

8.0 

8.0 

8.0 

8.5 

8.0 

7.4

10.6 

11.1 

10.5 

10.9 

11.8 

11.4 

11.6 

12.2 

12.0 

12.2 

12.0 

12.0 

10.5

11.6 

11.1 

13.8 

15.4 

15.8 

15.0 

15.0

Channel width 61.0 cm

148 

149 

150----..

151 

152.... 

153 . 

154. 

155 

156 

157 

158 

159. 

160 .

161. ......

162 

163 .

164 

165 

166 

167. 

168 

169 

170 

171 

172. 

11.2

13.6

16.2

16.8

24.2

29.8

39.8

41.8

46 4

54.8

78.6

102.6

72.4

79.4

81.8

103.2

119. 8

149. 2

1 CO Q

104.0

119 4

127. 2

130. 6

167. 2

212. 8

0.00489 

.00569

.00816

.0117 

.0172 

.0234

.00118 

.00154 

.00210 

.00330 

.00714 

.0113 

.00106 

.00097 

.00137 

.00281 

.00445 

.00643 

.00877

.00060 

.00080 

.00147 

.00172 

.00280 

.00560

3.0

2.8

2.8

2.7 

2.8 

3.0

8.7 

9.0 

8.8 

8.8 

9.0 

9.0 

14.6 

15.0 

15.2 

15.2 

14.8 

15.0 

14.0

21.1 

20.8 

21.6 

21.5 

21.5 

20.0

37.0 

49.0

58.5

61.5 

85.5 

98.5

45.5 

47.0 

53.5 

62.0 

89.0 

115.0 

49.5 

53.5 

54.0 

68.5 

81.5 

100.0 

115.0

49.5 

57.5 

59.0 

61.5 

78.0 

106.0

56, 280 

19,560

11, 550

6,000 

3,945 

900

23,340 

48,900 

5,700 

7,770 

6,510 

2,605 

83, 940 

53,940 

7,860 

7,650 

3.830 

3,595 

1,150

103, 080 

32,700 

11, 940 

4,440 

1,205 

585

0. 00253 0. 00150 

. 00527 . 00355

. 0177 . 0109

. 0405 . 0260 

. 115 . 0744 

.280 .183

. 000997 . 000631 

. 00179 . 00108 

. 00625 . 00390 

. 0185 . 0113 

. 104 . 0680 

. 286 . 198 

. 00106 . 000680 

. 00195 . 00112 

. 00454 . 00272 

. 0210 . 0131 

. 0539 . 0323 

. 149 . 0880 

. 293 . 187

. 00870 . 000544 

. 00223 . 00127 

. 00610 . 00362 

. 0109 . 00680 

. 0440 . 0264 

. 173 . 125

56.5 

60.5

70.0

78.5 

96.5 

129.0

59.0 

60.0 

67.5 

82.5 

101.5 

134.0 

57.5 

58.5 

62.5 

80.0 

90.0 

115.0 

138.5

53.5 

59.5 

62.0 

67.5 

85.5 

120.5

26.6 B 3.5 

25.6 B 0.5 

250 IB < 0.5 25-°U«0.5. 

26.8 A 2.0 

26.8 A 2.5 

24.0 D 1.0. 

25.6 D 1.0- 

28.2 D 1.5. 

9ft 9 T\ 9 fl

28.4 A 3.5- 

24.8 A 5.5 

23.6 D 1.0. 

26.4 D 1.5 . 

26.8 D 2.0. 

24.8 D 3.5. 

26.0 D 4.0 - 

26.8 A 5.0-... 

26.2 A 6.0 

22.4 D 2.0. 

26.6 D 2.0. 

25.2 D 2.5. 

27.8 D 3.5. 

27.8 D 4.0. ... 

27.2 A? 5.0 

335 .

162 

125 

15 

18 

25

189 

100 

73

40 

45 

177 

111 

94 

104 

77 

67 

64

114 

107 

94 

110 

94 

76

.045 

.121 

.B7J 

.67 

1.19

.040 

.062 

.10 

.28 

.85 

.98 

.015 

.032 

.049 

.12 

.61 

.69 

1.22

.015 

.032 

.020 

.057 

.12 

1.05

0. 0545 

.0771

.133

.195 

.414 

.692

.0469 

.0643 

.0975 

.180 

.559 

1.162 

.0768 

.0769 

.112 

.289 

.533 

.958 

1.393

.0623 

.0954 

.187 

.225 

.467 

1.190

2.7 

2.5

2.5

2.5 

2.6 

2.8

6.8 

6.8 

6.8 

6.8 

7.0 

7.0 

9.8 

10.0 

10.0 

10.0 

10.0 

10.0 

9.5

12.4 

12.4 

12.6 

12.5 

12.5 

12.0

2.9 

2.7

2.7

2.6

2.7 

2.9

7.5 

7.8 

7.8 

8.0 

8.0 

8.0 

12.0 

11.8 

12.6 

13.2 

13.2 

13.5 

12.5

15.2 

15.0 

18.0 

18.0 

18.0 

17.5

Channel width 119.0 cm

173 

174 

175 

176 

177 .

119. 8

119.0

126.4

132. 8

136. 6

0.00096 

.00091 

.00115 

. 00191 

.00214

22.5 

21.5 

21.5 

21.0 

20.5

54.0 

55.5 

58.5 

63.0 

67.0

20, 820 

16, 530 

12, 480 

15,600 

4.290

0. 00232 0. 00292 

. 00305 . 00363 

. 00546 . 00689 

. 0124 . 0140 

. 0167 . 0191

61.0 

61.5 

67.5

81.5

28.0 D 2.0.-. 

25.0 D 4.0- 

28.6 D 4.0- 

27.6 D 4.5- 

26.2 D 5.5- 

110 

131

128 

76 

91

0.017 

.017 

.024 

.035 

.087

0.115 

.109 

.145 

.253 

.293

16.0 

16.0 

16.0 

15.5 

15.0

20.0 

19.0 

19.5 

19.5 

19.0

1 Immersed weight.

2 Letter A in height column indicates bed forms were antidunes; B, bars; D, dunes.

3 Both dunes and antidunes occurred.

4 Both bars and antidunes existed, simultaneously.

US. GOVERNMENT PRINTING OFFICE: 1970 O 373-261