Transport and Dispersion of 

Fluorescent Tracer Particles 

for the Flat-Bed Condition, 

Rio Grande Conveyance 

Channel, Near Bernardo, 

New Mexico

GEOLOGICAL SURVEY PROFESSIONAL PAPER 562-1
Transport and Dispersion of 

Fluorescent Tracer Particles 

for the Flat-Bed Condition, 

Rio Grande Conveyance 

Channel, Near Bernardo, 

New Mexico

By R. E. RATHBUN, V. C. KENNEDY, and J. K. CULBERTSON 

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 562-1

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1971
UNITED STATES DEPARTMENT OF THE INTERIOR

GEOLOGICAL SURVEY 

William T. Pecora, Director

Library of Congress catalog-card No. 76-609684

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

Office, Washington, D.C. 20402 - Price 65 cents (paper cover)
CONTENTS

Abstract...................................................................

Introduction..............................................................

Design of the experiment.............................................

Selection of site...................................................

Type of injection..................................................

Quantity of fluorescent material..............................

The "dustpan" sampler.........................................

Sampling arrangement..........................................

Experimental procedure............................................

Preparation of the fluorescent materials...................

Injection of the fluorescent materials......................

Hydraulic and sediment-concentration measurements

Sampling procedure............................................

Analysis of the samples........................................

Page 

II

1

2

2

3

3

3

4

4

4

6

10

11

12

Presentation and discussion of results................................... 113

Lateral-dispersion characteristics of the tracer materials...... 17

Application of fluorescent tracers to the measurement of the

sediment-transport rate............................................. 28

"Dustpan" samples at cross section D ........................ 28

Depth-integrated samples at the weir ........................ 30

Velocities of the centroids of the tracer masses ................ 34

Longitudinal-dispersion characteristics of the tracer materials .................................................................... 45

Evaluation of the fluorescent tracer technique.......................... 47

Summary........................................................................ 49

Literature cited................................................................ 49

Appendix A discussion of the washing effect........................ 52

Appendix B determination of the weighting factors................ 53

Appendix C calculation of the sediment-transport rates from the

depth-integrated samples at the weir................................... 54

ILLUSTRATIONS

FIGURES 1-4. Photographs of: Page

1. Rio Grande conveyance channel and the weir used for total sediment concentration sampling............................... 12

2. Weir and baffles in the Rio Grande conveyance channel................................................................................. 2

3. Study reach viewed in an upstream direction from the weir............................................................................. 3

4. "Dustpan" sampler.................................................................................................................................. 4

5. Detailed sketch of the "dustpan" sampler.............................................................................................................. 5

6. Plan-view sketch of the study reach...................................................................................................................... 6

7-9. Photomicrographs of:

7. Two sieve classes of bed material from the Rio Grande conveyance channel................................................................. 7

8. Three sieve classes of fluorescent materials, run 1................................................................................................... 8

9. Four sieve classes of fluorescent materials, run 2.................................................................................................... 9

10. Photograph showing injection of the fluorescent materials, run 1................................................................................. 10

11. Discharge hydrograph........................................................................................................................................ 11

12. Cross-section measurements............................................................................................................................... 12

13. Photograph showing three boatcrews "dustpan" sampling at cross section D................................................................. 12

14. Photograph of equipment used for determining the number of fluorescent particles........................................................ 12

15-42. Graphs showing:

15. Variation with time of the concentration of the 0.177- to 0.250-mm sieve class of green quartz........................... 14

16. Variation with time of the concentration of the 0.350- to 0.500-mm sieve class of yellow quartz.......................... 15

17. Variation with time of the concentration of the 0.707- to 1.00-mm sieve class of red quartz............................... 16

18. Variation with time of the relative concentrations of the quartz and monazite at lateral positions of z= 18, 24.30, and

36 feet......................................................................................................................................... 18

19. Variation with time of the relative concentrations of the quartz and monazite at lateral positions of z= 42, 48, and

54 feet........................................................................................................................................ 20

20. Variation of the area under the curve of concentration versus time with lateral position, 2, for different sieve classes

of quartz tracer, run 1..................................................................................................................... 22

21. Variation of the area under the curve of concentration versus time with lateral position, 2, for different sieve classes

of quartz tracer, run 2..................................................................................................................... 23

22. Variation of the area under the curve of concentration versus time with lateral position, 2, for different sieve classes

of garnet tracer, run 2..................................................................................................................... 24

23. Variation of the area under the curve of concentration versus time with lateral position, 2, for different sieve classes

of monazite tracer, run 2................................................................................................................. 25

24. Variation with fall diameter of the mean lateral postions of the tracer distributions, run 1................................ 27

25. Variation with fall diameter of the mean lateral positions of the tracer distributions, run 2............................... 27

26. Variation with fall diameter of the variances of the lateral distributions of the tracer masses, run 1.................... 28

III
IV CONTENTS

FIGURES 15-42: Graphs showing: Pa^e

27. Variation with fall diameter of the variances of the lateral distributions of the tracer masses, run 2.................... 128

28. Variation with time of the relative mean fluorescent tracer concentrations of the weir samples, run 1................. 32

29. Variation with time of the relative mean fluorescent tracer concentrations of the weir samples, run 2 ................. 33

30. Variation with time of the relative mean concentration of yellow quartz, run 1................................................ 35

31. Variation with time of the relative mean concentration of green quartz, run 1................................................. 36

32. Variation with time of the relative mean concentration of red quartz, run 1.................................................... 37

33. Variation with time of the relative mean concentration of quartz tracer, run 2 ................................................ 38

34. Variation with time of the relative mean concentration of garnet tracer, run 2................................................ 40

35. Variation with time of the relative mean concentration of monazite tracer, run 2............................................ 42

36. Variation with fall diameter of the velocities of the centroids of the tracer masses, run 1................................. 43

37. Variation with fall diameter of the velocities of the centroids of the tracer masses, run 2................................. 44

38. Variation with fall diameter of the variances of the mean concentration versus time curves, run 1..................... 46

39. Variation, with fall diameter of the variances of the mean concentration versus time curves, run 2..................... 46

40. Variation with lateral position of the sediment-transport weighting factors, runs 1 and 2................................... 54

41. Sieve-size distributions of two depth-integrated samples obtained at the weir................................................. 55

42. Visual-accumulation-tube size distributions.............................................................................................. 55

TABLES

Pa»e

TABLE 1. Summary of the median fall diameters of the various sieve classes of fluorescent tracers from runs 1 and 2 and the bed material

	from the Rio Grande conveyance channel............................................................................................................ 15

2. Summary of the amounts of fluorescent material injected for each sieve class, runs 1 and 2................................................ 10

3. Summary of the hydraulic data for the study reach...................................................................................................... 10

4. Total-sediment-concentration measurements at the weir, run 1, December 13, 1966........................................................... 10

5. Total-sediment-concentration measurements at the weir, run 2, December 14, 1966........................................................... 11

6. Numbers of fluorescent particles per gram of fluorescent material for the sieve classes of fluorescent tracer materials used in

	runs 1 and 2................................................................................................................................................... 13

7. Summary of the z and cri values for the lateral distributions at cross section Z), run 1........................................................ 26

8. Summary of the z and oi values for the lateral distributions at cross section Z), run 2........................................................ 26

9. Summary of the z, crl, and erf (corrected) values for the dye-dispersion test...................................................................... 26

10. Summary of the calculation of the sediment-transport rate, "dustpan" samples at cross section Z), run 1............................... 29

11. Summary of the calculation of the sediment-transport rate, "dustpan" samples at cross section D, run 2............................... 29

12. Summary of the calculation of the sediment-transport rate, depth-integrated samples at the weir, run 1................................. 31

13. Summary of the calculation of the sediment-transport rate, depth-integrated samples at the weir, run 2................................. 31

14. Summary of the t. At, t0 .oi, and V data, run 1............................................................................................................. 43

15. Summary of the t, At, t(U)i, and V data, run 2............................................................................................................. 43

16. Summary of the oi values of the mean concentration at cross section D as a function of time data, run 1.............................. 45

17. Summary of the 07 values of the mean concentration at cross section Z) as a function of time data, run 2.............................. 45

18. Comparison of the median diameters and the gradations, of the size distributions of selected "dustpan," core, and depth- 

	integrated samples.......................................................................................................................................... 52

19. Comparison of the rfie, d5o, dM, and a values for selected "dustpan" samples at cross section Z), run 2................................. 53
CONTENTS 

SYMBOLS

A(z) Area under the experimental concentration as a function of 

time curve at lateral position z, in gram-hours per gram.

A r (z) Relative area, equal to A (z) divided by the total area under 

the A (z) as a function of z curve.

A' Area under the concentration as a function of time curve 

for the depth-integrated samples at the weir, in particlehours per gram.

Al Area under the concentration as a function of time curve for 

size class i of the depth-integrated samples at the weir, in 

particle-hours per gram.

B Width of the channel, in feet.

C(t) Concentration of fluorescent tracer in a size split of a "dustpan" sample, expressed as grams of fluorescent tracer per 

gram of total material in the size split.

Cr(t) Relative concentration of fluorescent tracer, equal to the 

concentration divided by the area under the concentration 

as a function of time curve.

C(t) Mean concentration of fluorescent tracer across the channel 

width, in grams per gram.

Cr (t) Relative mean concentration of fluorescent tracer, equal to 

the mean concentration divided by the area under the mean 

concentration as a function of time curve.

C(z) Concentration of fluorescent tracer at lateral position z, 

in grams per gram. (May also refer to the concentration of 

fluorescent dye at lateral position z in the dye-dispersion 

test, milligrams per liter.)

C*(z) Concentration of sediment at lateral position z, determined 

from a depth-integrated sample at z, milligrams per liter.

C' (t) Concentration of fluorescent tracer in a depth-integrated 

sample, expressed as number of fluorescent particles of a 

specific color per gram of total sediment in the sample, in 

particles per gram.

C'r(t) Relative mean concentration of fluorescent tracer in a depthintegrated sample, equal to the concentration divided by the 

area under the concentration as a function of time curve.

C'(t) Mean concentration of fluorescent tracer in a depth-integrated sample, determined from a composite of depth-integrated samples taken across the weir at equally spaced 

intervals, in particles per gram.

dia Partic'e diameter for which 16 percent by weight are smaller, 

in millimeters.

rfso Median particle diameter, in millimeters.

c?K4 Particle diameter for which 84 percent by weight are smaller, 

in millimeters.

KX, Ks Dispersion coefficients in the x, z directions, in square feet 

per second.

N Total number of fluorescent particles of all sizes of a specific 

color injected at the beginning of the experiment.

N,

n(t)

Pi

Q

q(z)

Q*

Q.;

Ai 

V

w

W(t) 

w(z)

Az

cr 

err

Total number of fluorescent particles of size class iof a specific

color injected at the beginning of the experiment.

Total number of fluorescent particles of a specific color in a

depth-integrated sample at time t.

Percent of the total weight of a depth-integrated sample that

is in sieve class i, in percent.

Total water discharge, in cubic feet per second.

Water discharge per unit of width at lateral position z, in

cubic feet per second per foot.

Total sediment-transport rate, in tons per day.

Total sediment-transport rate for size class i, in tons per day.

Sediment-transport rate per unit of width at lateral position

z, in tons per day per foot.

Mean sediment-transport rate per unit of width, in tons per

day per foot.

Fraction of the total water discharge in the width increment

Az centered at lateral position z.

Time, in hours.

Time required for the centroid of the tracer mass to reach 

the measurement section, in hours.

Time required for the mean concentration at the measurement section to decrease to 1.0 percent of the maximum mean 

concentration, in hours.

Time correction for the finite time interval required for 

injection of the fluorescent materials, in hours. 

Velocity of the centroid of the tracer mass, in feet per second. 

Weight of fluorescent material injected at the beginning of 

the experiment, in pounds.

Total weight of sediment in a depth-integrated sample at 

time t, in grams.

Weighting factor relating the unit sediment-transport rate 

at lateral position z with the mean unit sediment-transport 

rate for the cross section.

Lateral distance, measured from the right bank of the channel, 

in feet.

Increment of width, in feet.

Mean lateral position of the tracer mass at the measurement 

section, measured from the right bank, in feet. 

Specific weight of the water-sediment mixture, in pounds per 

cubic foot.

A measure of the gradation, equals i((/8-t/</50 + </.We?i6) 

Variance of the mean concentration as a function of time 

curves, in hours2 .

Variance of the lateral distributions of the tracer materials 

at the measurement section, in feet2 .
VI CONTENTS

ENGLISH-METRIC CONVERSIONS

Principal item English unit Factor Metric unit

(0.3048.......................... meter

Length.................................................. feet..................................... .J30.48........................... centimeter

(304.8........................... millimeter

Area..................................................... square feet........................... ^29.0........................... square centimeters

(.09290.......................... square meters

Weight.................................................. pounds................................. J453.6........................... grams

(.4536........................... kilograms

Velocity................................................. feet per second...................... J0.3048.......................... meters per second

(30.48........................... centimeters per second

Water discharge...................................... cubic feet per second............. J0.02832........................ cubic meters per second

/2.832XlO4..................... cubic centimeters per second

Sediment-transport rate............................ tons per day........................... 0.9072.......................... metric tons per day

Specific weight........................................ pounds per cubic feet.............. 0.01602........................ grams per cubic centimeter
SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TRANSPORT AND DISPERSION OF FLUORESCENT TRACER 

PARTICLES FOR THE FLAT-BED CONDITION, RIO GRANDE 

CONVEYANCE CHANNEL, NEAR BERNARDO, NEW MEXICO

By R. E. RATHBUN, V. C. KENNEDY, and J. K. CULBERTSON

ABSTRACT

A fluorescent tracer technique was applied to a study of the rates of 

transport and dispersion of sediment particles of various diameters 

and specific gravities for the high-velocity flat-bed condition of alluvialchannel flow. Two runs were conducted in the Rio Grande conveyance 

channel near Bernardo, N. Mex., on December 13 and 14, 1966. An 

instantaneous point source of fluorescent material was used in each 

run. Samples of the bed material moving on or near the bed surface 

were obtained throughout the passage of the tracer masses with the 

"dustpan" sampler especially designed for this study.

The mean lateral positions of the distributions of tracer materials 

tended to follow the thalweg of the channel and shifted toward the right 

bank in moving from the injection point to the measurement section. The 

amount of shift increased with increasing particle fall diameter.

The lateral dispersion of the tracer masses as represented by crj, the 

variance of the lateral distribution of fluorescent material at the measurement section, decreased with increasing fall diameter.

The sediment-transport rates calculated from the fluorescent tracer 

experiments were about 57 and 14 percent larger than the sedimenttransport rates measured at the weir in runs 1 and 2, respectively. The 

agreement in run 2 was good because positive and negative errors for 

the different sieve classes were compensating.

The variation of the centroid velocities of the quartz tracer masses 

with fall diameter was approximately U-shaped; the minimum velocity 

occurred for tracer particles having fall diameters comparable to or 

slightly larger than the median fall diameter of the bed material in transport. The maximum centroid velocities observed were for the 0.125- to 

0.177-millimeter sieve class of quartz tracer, and these were approximately 26 and 16 percent of the mean water velocity in runs 1 and 2, 

respectively.

The centroid velocities of the garnet and monazite tracer masses were 

about an order of magnitude less than the centroid velocities for quartz 

tracer particles of comparable fall diameter.

The longitudinal dispersion of quartz tracer particles as represented 

by of, the variance of the curves of mean concentration as a function 

of time at the measurement section, varied with fall diameter approximately inversely to the manner in which the centroid velocities varied 

with fall diameter. The of values for the garnet and monazite tracer 

particles showed relatively little variation with fall diameter but were 

about an order of magnitude larger than the of values for quartz particles 

of comparable fall diameter.

The fluorescent tracer technique is a simple and sensitive experimental method for the study of the transport and dispersion of groups

of particles in a natural or laboratory alluvial channel. However, considerable improvement in technique is still needed.

INTRODUCTION

Problems associated with rates of transport of sediment 

by natural and artificial waterways are many, both in 

number and in type. Among the problems are those involving river management, design and operation of canals 

and reservoirs, and degradation around bridge piers and 

below dams.

A problem closely related to the rate of sediment 

transport is the rate of dispersion of the sediment. Development of nuclear energy industries and the increasing use of agricultural chemicals have resulted in the 

undesirable presence of radioisotopes, pesticides, and 

herbicides in the environment. Furthermore, there is 

considerable evidence that these substances are adsorbed by sediment particles. Thus, in the event that 

toxic material is discharged or accidentally spilled into 

a stream, the sediment may remove most of it from solution. Thereafter, the rate of transport and of lateral and 

longitudinal dispersion of the sediment will control the 

movement and the concentration level of the toxic 

substance.

An understanding of the laws governing transport of 

sediments of differing size and specific gravity is also 

important in geomorphology, in stratigraphic studies, 

and in the search for concentrations of valuable heavy 

minerals.

Fluorescent tracers have been used extensively in the 

study of sediment transport and dispersion, but these 

investigations have been limited almost exclusively to 

research on beach erosion. Exceptions are the laboratory work of De Vries (1966) and Lean and Crickmore 

(1966) and the field study of Crickmore (1967). The

II
12 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

application of the fluorescent tracer technique to a study 

of the transport of sand-size particles in a gravel-bed 

stream by Kennedy (1968) and Kennedy and Kouba 

(1970) served as the foundation for the present research 

and suggested the possibility of a large-scale field study 

of the transport and dispersion of sand-size particles in a 

sand-channel stream.

This report describes a field study of the transport and 

dispersion of sediment particles of various sizes and 

specific gravities coated with fluorescent dye. Two experiments were conducted in the Rio Grande conveyance 

channel near Bernardo, N. Mex., on December 13 and 

14, 1966. A high-velocity flat-bed condition existed for both 

experiments. In the preliminary experiment, run 1, 

three size ranges of quartz, each coated with a different 

color of fluorescent dye, were used. In the second experiment, run 2, four materials of different specific gravity 

were each coated with a different color of fluorescent 

dye. These materials were quartz, garnet, monazite, and 

lead, and each material contained a range of particle 

sizes.

. This study was the joint effort of Water Resources 

Division personnel from Denver, Colo., Albuquerque, 

N. Mex., and Fort Collins, Colo. V. C. Kennedy originated 

and coordinated the project with the assistance of F. C. 

Ames. The Albuquerque Field Research Unit (J. K. 

Culbertson and C. H. Scott) provided extensive logistic 

support for the fieldwork. Fort Collins personnel conducted preliminary laboratory experiments with the 

"dustpan" sampler, and C. F. Nordin, Jr., and W. W. 

Sayre helped in the supervision of the experiments and 

contributed many ideas and suggestions during the 

analysis of the data and the preparation of the report.

Personnel from the New Mexico District who assisted 

with the fieldwork included J. P. Borland, B. M. Delaney, 

J. D. Dewey, Trancito Diaz, N.D. Hafneld, V. W. Norman, 

David Ortiz, and J. W. Shomaker. Graduate students 

from Colorado State University who assisted with the 

fieldwork included J. P. Bennett, W. E. Gaskill, and 

J. N. Loyacano. Graduate students assisting with the 

analysis of the samples included N. S. Grigg, Ziad 

Mughrabi, C. H. Neuhauser, and C. A. Ramirez.

Norman Prime of Menlo Park, Calif., prepared the 

photomicrographs of the fluorescent materials.

DESIGN OF THE EXPERIMENT

The experiment was designed to permit a study of the 

longitudinal- and lateral-dispersion characteristics of 

particles of various diameters and specific gravities in the 

sand-size range and also to permit an evaluation of the 

fluorescent tracer technique as a means of measuring 

the total sediment-transport rate of the bed material.

SELECTION OF SITE

The site chosen for the study was the Rio Grande 

conveyance channel near Bernardo, N. Mex. The channel 

contained a weir at which total sediment concentrations 

could be sampled. Figure 1 is a photograph of the channel 

and the weir. A series of baffles on the weir upstream of

FIGURE 1. Rio Grande conveyance channel and the weir used for total 

sediment concentration sampling.

the crest created sufficient turbulence to suspend all of 

the sediment in transport as it passed over the weir. The 

sediment suspended by the action of the baffles was 

sampled with the standard US DH-48 depth-integrating 

hand sampler (Guy and Norman, 1970). Figure 2 is a 

photograph of the baffles and the weir. Details of the

FIGURE 2. Weir and baffles in the Rio Grande conveyance channel.
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 13

design, construction, and operation of the weir have been 

presented by Harris and Richardson (1964) and Gonzalez, 

Scott, and Culbertson (1969).

The 800-foot straight reach immediately upstream of 

the weir was selected as the study reach so that the total 

sediment-transport rates computed at the weir could be 

used to check the sediment-transport rates computed 

from the fluorescent tracer experiments. Figure 3 is a 

photograph of the study reach as viewed in an upstream 

direction from the weir.

FIGURE 3. Study reach, viewed in an upstream direction from the

TYPE OF INJECTION

Possible types of injection procedures are the instantaneous line source, the continuous line source, the 

instantaneous point source, and the continuous point 

source. The mechanical requirements for a line source are 

more demanding than for a point source, and information 

on the lateral-dispersion characteristics of the channel 

cannot be obtained. The continuous source has the advantage that only a few samples are necessary after 

equilibrium has been attained at the measurement section. However, the continuous source must be maintained 

until equilibrium is obtained, and continuous feeding is 

demanding of both manpower and fluorescent materials. 

On the basis of these considerations, the instantaneous 

point-source method of injection was chosen for the 

study.

QUANTITY OF FLUORESCENT MATERIAL

One of the requirements of any tracer procedure is 

that the quantity of material introduced be small enough 

so that the natural sediment-transport process is not 

disturbed. At the same time, sufficient tracer material

must be injected so that statistically significant numbers 

of particles are obtained in the samples. The quantity 

of fluorescent material required was estimated in the 

following way.

It was assumed that the injected tracer material was 

instantaneously and uniformly mixed throughout the 

length of the study reach. This assumption was obviously 

conservative and resulted in estimated peak fluorescent 

tracer concentrations that were smaller than the actual 

experimental values. Concentration of fluorescent material in a sample as used in this report is defined as the 

ratio of the weight of tracer material in a specific size 

range of the sample to the total weight of all sediment in 

that size range of the sample. For the flat-bed condition, 

most of the material in transport is concentrated in a 

thin layer near the bed surface. Opinions differ as to the 

thickness of this moving layer. However, for the purpose 

of illustration, assume that the moving layer is 0.1 foot 

thick and that the water-sediment mixture in the moving 

layer is 50 percent sediment by volume. The study reach 

was 800 feet long from the injection point to the weir, 

and the mean channel width was about 70 feet. Thus, 

the total dry weight of sand participating in the transport 

process and present in the study reach at any instant is 

estimated as 800 X 70 X 0.50 X 2.65 X 62.4 = 463,000 

pounds. For the flat-bed condition in the Rio Grande conveyance channel, approximately 50 percent of the material 

in transport is in the size range from 0.125 to 0.250 mm 

(millimeter). Therefore, about 231,000 pounds of sediment 

in active storage in the 0.125- to 0.250-mm size range is 

present in the study reach at any instant. Fluorescent 

tracer concentrations of the order of 10~3 to 10~4 are 

adequate for purposes of analysis; and if the mean fluorescent tracer concentration in the reach is of this order, 

then the quantity of tracer material in the 0.125- to 

0.250-mm size range should be between about 23 and 231 

pounds.

THE "DUSTPAN" S4MPLER

The application of the fluorescent tracer technique to 

the study of the transport and dispersion rates of sediments for the high-velocity flat-bed condition required a 

different type of sampler from those usually used in sediment-transport studies. Because the concentrations of 

fluorescent tracer could not be determined in situ, it 

was necessary to obtain samples from the channel for 

laboratory analysis. These samples had to contain all 

sizes of the bed material in transport, and the sample 

time was necessarily as short as possible so that several 

samples could be obtained as the tracers moved through 

the measurement section. Thus, the sampling position 

best suited to meet these requirements was on or just 

above the bed surface.

405-770 OL - 71 - 2
14 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Sampling the moving bed material for a fluorescent 

tracer experiment, however, has one major advantage 

over sampling the bed-material discharge with any of the 

bedload samplers described by Hubbell (1964). This 

advantage is that the efficiency of the sampler is unimportant in fluorescent tracer experiments, provided that 

the fluorescent tracer particles of any specific size behave 

identically with nontagged particles of the same size. 

Efficiency was defined by Hubbell (1964) as "the ratio of 

the weight of bedload collected during any single sampling 

time to the weight of bedload that would have passed 

through the sampler width in the same time had the 

sampler not been there." The significant factor in the 

"dustpan" sample is the ratio of the number of fluorescent 

particles of a given size to the number of nonfluorescent 

particles of the same size.

A rear view of the "dustpan" sampler designed for this 

study and used in the experiments is shown in figure 4.

FIGURE 4. "Dustpan" sampler; rear view.

The flow expansion in both the horizontal and vertical 

directions resulted in a decrease in flow velocity and 

deposition of sediment in the sampler. The sampler was 

constructed from galvanized sheet metal, and a 6-foot 

length of 3/4-inch pipe was used as the handle. The fin 

on the top of the sampler served to stabilize the sampler in

high-velocity flows. A small wooden baffle was positioned 

across the inside of the sampler on the bottom about 6 

inches from the inlet. Dimensions of the sampler and the 

position of the baffle are shown in figure 5.

SAMPLING ARRANGEMENT

A plan-view sketch of the study reach is shown in 

figure 6. The injection point was 800 feet upstream of the 

weir. The injection point was not positioned nearer the 

highway bridge because of possible effects from the 

slight bend just upstream of the bridge. Measurement 

sections A,B,C, and D were 100, 300, 500, and 700 feet, 

respectively, downstream from the injection point. The 

position of the thalweg, or line of maximum depth, for 

the study reach is shown also in figure 6.

Because information concerning the rates of movement 

of sediment particles for the high-velocity flat-bed condition was nonexistent, sampling was concentrated initially 

at cross section D so as to insure that the fluorescent 

particles did not pass completely through the study reach 

before they could be sampled. Subsequent adjustments to 

the sampling arrangement were dependent on the qualitative examination of the samples from cross section D.

EXPERIMENTAL PROCEDURE

PREPARATION OF THE FLUORESCENT MATERIALS

The fluorescent materials used in the preliminary 

experiment, run 1, were some of the materials prepared 

by Kennedy and Kouba, and the preparation procedure 

used for this material has been described previously 

(Kennedy and Kouba, 1970). This material was prepared 

from a natural river sand that contained minerals other 

than quartz; hence, it should correctly be called quartzose 

sand. However, for brevity, it will be referred to as quartz 

in this report. The amounts available were 281 pounds of 

green quartz (approximately 0.15 to 0.30 mm), 252 pounds 

of yellow quartz (approximately 0.30 to 0.52 mm), and 

295 pounds of red quartz (approximately 0.52 to 1.29 mm).

The fluorescent materials for run 2 were prepared by 

a procedure similar to that of Kennedy and Kouba (1970). 

The fluorescent dyes used were the A series of Day-Glo 

pigments (Switzer Brothers, Inc., Cleveland, Ohio). 1 The 

rocket red (A-13), arc yellow (A-16), signal green (A-18), 

and horizon blue (A 19) dyes were chosen for use because 

they were the most easily distinguishable from each other 

by the human eye. A vinyl plastic VAGH, blend 1508 

(Union Carbide Corp., South Charleston, W. Va.) was 

also used with the dye to produce an abrasion-resistant 

coating.

1 Use of company names is for identification purposes only and does not imply official endorsement of any product.
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 15

T

CM

1

FIGURE 5. Detailed sketch of the "dustpan" sampler.

Commercial grade acetone was used as the solvent. 

A quantity of acetone was saturated with the vinyl plastic 

by adding the vinyl powder slowly to the acetone with 

constant stirring. The vinyl-acetone solution was then 

saturated with the appropriate dye. About 100 pounds 

of the material to be coated was placed in a small motordriven cement mixer. As the material tumbled, a small 

quantity of the solution was mixed into the material and 

the acetone allowed to evaporate. When the coating was

completely dry, more ot the dye solution was added. This 

process was continued until fluorescence of the material 

under an ultraviolet light indicated that an adequate 

coating had been obtained.

If no loosely cemented aggregates of particles existed in 

the dry material, the material was placed in canvas bags. 

If aggregates of particles existed, the material was passed 

between rubber rollers to break the aggregates into single 

particles.

TABLE 1. Summary of the median fall diameters of the various sieve classes of fluorescent tracers from runs 1 and 2 and the bed material from

the Rio Grande conveyance channel

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7)

Spec

Sieve class (mm)

0.125-0.177 

0.177-0.250 

0.250-0.350 

0.350-0.500 

0.500-0.707 

0.707-1.00

>1.00

0.156 

.201 

.270 

446

.630 ..

Median fall diameter (mm)

Run 1

Green quartz Yellow quartz Red quartz Quartz

0.150 ............................................ 0.152

.189 ............................................. .204

.231 0.271 ..................... .289

.............. .358 ..................... .420

.............. .452 0.539 .541

.613 .694 .

........................................... .839 ................

......................... 2.65

Run 2

Garnet

0.232 

.300 

.405 

.578 

.690 ..

4.08

Monazite

0.235 ..

.305 

.484 

.721

4.79

Lead

0.715 

1.12 

1.36

11.3
16 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

i- 0

- 100

-200

- 300

-400

-500

- 600

- 700

L 800

Measurement 

site

Measurement 

site

Measurement 

site

 D Measurement 

site

Weir

FIGURE 6. Plan-view sketch of the study reach.

One disadvantage of the fluorescent coatings prepared 

by this procedure was that the coatings were nonwetting.

Therefore, when the fluorescent materials were placed in 

water, the particles had a tendency to cluster together 

in groups. This clustering was avoided by adding detergent to the fluorescent material before injection.

The fluorescent materials prepared in this manner for 

run 2 consisted of 199 pounds of Ottawa flint quartz and 

194 pounds of Ottawa crystal quartz (Ottawa Silica Co., 

Ottawa, 111.), 232 pounds of garnet, 288 pounds of monazite, 

and 83 pounds of lead shot. The specific gravities of the 

coated materials were 2.65, 4.08, 4.79, and 11.3 for the 

quartz, garnet, monazite, and lead, respectively.

Median fall diameters were determined for each 

V2 sieve class of the fluorescent materials used in runs 

1 and 2, as well as for samples of the bed material from 

the Rio Grande conveyance channel. Fall diameters were 

determined either by dropping single particles in a column 

of quiescent distilled water or by the visual-accumulation 

tube method (U.S. Inter-Agency Committee on Water 

Resources, 1957a). The visual-accumulation tube was 

used to analyze the materials smaller than 0.350 mm, and 

the single-particle method was used for materials larger 

than 0.350 mm. Fall velocities obtained from the singleparticle method were converted to median fall diameters 

by means of table 2 of U.S. Inter-Agency Committee on 

Water Resources (1957b). The median fall diameters are 

summarized in table 1.

Photomicrographs of the material from two sieve classes 

of bed material from the Rio Grande conveyance channel, 

one sieve class of each of the three colors of fluorescent 

quartz used in run 1, and one sieve class of each of the 

four minerals used as tracers in run 2 are presented in 

figures 7,8, and 9, respectively.

The photomicrographs show that the tracer materials used in run 1 were angular. Hence, the particles 

would tend to have a shape factor less than the 0.7 

usually attributed to naturally worn quartz particles. 

This shape effect explains why the fall diameters for some 

sieve classes of tracer materials from run 1 were smaller 

than the lower limit of the sieve class. (See U.S. InterAgency Committee on Water Resources, 1957b, fig. 7.) 

The effect of shape on the difference between sieve diameter and fall diameter increases with fall diameter.

The fall diameters for the garnet, monazite, and lead 

tracer particles used in run 2 are larger than the sieve 

diameters because of the specific gravity effect.

INJECTION OF THE FLUORESCENT MATERIALS

The instantaneous point-source method of injection was 

used for both runs 1 and 2. Initially, the intent was to use 

a 4-inch inside diameter steel tube as an injection tube. 

However, the tube clogged when the material was poured 

rapidly into it; so in both runs 1 and 2 the fluorescent 

material was poured from the back of the boat as rapidly
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 17

FIGURE 7. Two sieve classes of bed material from the Rio Grande 

conveyance channel. A, 0.177-0.250 mm. B, 0.250-0.350 mm.
18 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 8. Three sieve classes of fluorescent materials, run 1. A, 

Green quartz, 0.177-0.250 mm. B, Yellow quartz, 0.350-0.500 mm. 

C, Red quartz, 0.707-1.00 mm.

as possible. Figure 10 is a photograph of the injection 

process for run 1. The injection point for run 1 was the 

centerline of the channel 800 feet upstream from the weir. 

The green fluorescent material was injected first, then 

the yellow fluorescent material, and then the red fluorescent material. The green, yellow, and red fluorescent 

materials required 2 minutes and 45 seconds, 2 minutes, 

and 2 minutes, respectively, for injection.

A tendency for the large particles to migrate toward the 

right bank (facing downstream) was observed in run 1, 

and therefore the injection point for run 2 was moved 7 

feet to the left of the centerline. As in run 1, the fluorescent material was dumped from the back of the boat 

as rapidly as possible. The crystal quartz was injected 

first, followed by the flint quartz, garnet, monazite, and 

lead; the materials required 1 minute, 1 minute, 1 minute 

and 10 seconds, 1 minute, and 35 seconds, respectively, 

for injection. The amounts of fluorescent material injected 

for each sieve class for runs 1 and 2 are summarized in 

table 2. The quantities shown for quartz in run 2 include 

both the crystal quartz and the flint quartz.

The totals given in table 2 are slightly less than the 

total amounts of fluorescent materials prepared because 

of the presence of small quantities of material in the ends 

of the size distributions. The only significant difference is
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 19

B D

FIGURE 9. Four sieve classes of fluorescent materials, run 2. A, Ottawa quartz. 0.250-0.350 mm. B, Garnet, 0.250-0.350 mm. C, Monazite,

0.250-0.350 mm. D, Lead, 0.177-0.250 mm.
no SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 10. Injection of the fluorescent materials, run 1.

for the monazite where there was considerable material 

in the 0.088- to 0.125-mm sieve class. However, particles 

smaller than 0.125 mm were not > considered in the analysis 

of the samples because of the difficulty of distinguishing 

between actual fluorescent particles and chips or flakes 

of dye from large particles.

TABLE 2. Summary of the amounts of fluorescent material injected 

for each sieve class, runs I and 2, in pounds

Quantity injected

Sieve class Run 1 Run 2

Green Yellow Red Quartz Garnet Monazite Lead 

quartz quartz quartz

0.125-0.177 39.6 .............................. 4.4 8.1 83.7 ............

0.250-0.350 111.8 69.3 ............... 53.0 94.7 30.9 46.8

0.350-0.500 130.5 ............... 126.0 77.0 56.5 33.2

0.500-0.707 49.2 65.3 177.1 9.5 30.4 ............

> 1.00 93.6 .........................................................

HYDRAULIC AND SEDIMENT-CONCENTRATION 

MEASUREMENTS

Prior to and during both experimental runs, measurements of the hydraulic parameters water discharge, 

water-surface slope, and cross-section measurements 

were obtained. Depth-integrated samples of suspended 

sediment were obtained at the weir at 5-foot intervals for 

lateral positions from 5 feet to 70 feet from the right bank 

throughout both runs. About 5 minutes and 8 minutes 

in runs 1 and 2, respectively, were required to obtain one 

complete set of samples across the weir. The 5-minute 

schedule was maintained for about 1 hour in run 1, and 

the 8-minute schedule for about 2 hours in run 2. Thereafter, the time interval between samples was increased 

gradually in both runs. 

The results of the hvdraulic measurements are summarized in table 3, and the total- sediment-concentration 

measurements at the weir are summarized in tables 4 and 

5 for runs 1 and 2, respectively. For run 1, the mean 

total-sediment-transport rate between the hours of 1313 

and 1504, December 13, when most of the fluorescent 

tracer material passed through the study reach, was 

5,490 tons per day of material larger than 0.062 mm. 

For run 2, the mean total- sediment- transport rate between 

the hours of 1006 and 1151, December 14, when most of 

the quartz tracer material passed through the study 

reach, was 4,220 tons per day of material larger than 

0.062 mm. 

The water discharge was not as constant as desired but 

decreased at an approximately uniform rate throughout 

both runs. Figure 11 is a discharge hydrograph based on 

the record from the gaging station just upstream of the

TABLE 3. Summary of the hydraulic data for the study reach

[cfs, cubic feet per second: fps, feet per second ; ft/ft, feet per foot]

Date Water-surface Water 

(Dec. Time Discharge Mean Mean Mean slope X 104 temperature 

1966) (cfs) width depth velocity (ft/ft) (° C) 

(ft) (ft) (fps)

13 0845 920 72.9 2.76 4.66 7.1 2.0

TABLE 4. Total-sediment-concentration measurements at the weir, 

run 1, December 13, 1966

[mg/1, milligrams per liter)

T. Water discharge Concentration Concentration 

lime (cfs) > 0.062 mm (mg/1) < 0.062 mm (mg/1)

1313 905 2,280 2,920 

1320 2,060 2,900 

1326 2,290 2,930 

1331 2,350 2,920 

1337 2,310 2,910

1341 2,280 2,880 

1346 2,470 2,800 

1350

1354 2,280 2,860 

1358 2,150 2,880

1404 900 2,260 2,860 

1408 2,590 2,660 

1422 2,390 2,820 

1434 2,120 2,810 

1444 2,180 2,780

1453 2,330 2,780 

1504 900 1,860 2,080 

1524 1,940 2,730 

1542 1,960 2,590 

1604 890 2,150 2,670

1624 2,500 2,640 

1713 1,900 2,580 

1737 2,440 2,590 

1806 845 2,000 2,490 

1838 1,920 2,470

1906 2,260 2,500 

1930 2,010 2,420 

2005 2,410 2,430
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION III

TABLE 5. Total-sediment-concentration measurements at the weir, 

run 2, December 14, 1966

Time Water discharge 

(cfs)

1006 740

1015

1023

1030

1038

1046

1054

1100

1109

1117

1125

1134

1142

1151 735

1218

1414

1435

1503

1534

1604

1634

1703

1738

1904

2013

2108

2205

2305

Concentration 

> 0.062 mm (mg/1)

2,120

2,180

2,000

2,080

2,170

2,260

2,150

2,160

2,040

2,180

2,130

1,960

2,150

2,000

1,950

1,690

1,860

2,460

2,300

2,090

2,010

1,830

2,040

1,820

2,150

2,030

2,060

2,160

Concentration 

< 0.062 ram (m<£/l)

2,270

2,200

2,210

2,220

2,210

2,230

2,230

2,210

2,210

2,200

2,200

2,180

2,180

2,180

2,160

1,940

2,070

2,040

2,020

2,020

2,010

1,980

1,960

1,950

1,960

1,950

1,930

1,890

w 1800

1000

< 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

I

U DECEMBER 1966

5

FIGURE 11. Discharge hydrograph, from the gaging station just upstream from the weir, for the period December 1 16, 1966.

weir for the period December 1 to December 16. Run 1 

was completed in the period between 1310 and 1800 hours 

on December 13, and run 2 was completed in the period 

between 1000 and 2400 hours on December 14.

The cross-section measurements obtained on December 

14 at 0815 hours are shown in figure 12. These measurements show that the thalweg is near the right bank at 

cross section A and near the left bank at cross section D.

A dispersion test for a water-soluble fluorescent dye 

was completed just prior to the start of run 1 to permit a 

determination of the limits of lateral dispersion for

particles of essentially zero diameter. A Rhodamine WT 

dye solution was injected continuously from a constanthead tank at the same injection point that was used for 

the fluorescent sediment tracers in run 1. Sampling was 

begun after sufficient time had elapsed to insure a steadystate concentration distribution at each of the cross sections. A complete set of samples across the width of the 

channel was obtained at cross sections A, B, and C, and 

two sets spaced about 7 minutes apart were obtained at 

cross section D. A nylon cord to which 24-ml (milliliter) 

screwcap vials were attached at 2-foot intervals was 

stretched across the channel. The cross-section samples 

were obtained simultaneously by dipping the vials into 

the channel. After the bottles filled, the cord was raised 

and the vials were removed from the line, capped, and 

labeled. The dye concentration of each sample was determined with a G..K. Turner fluorometer.

SAMPLING PROCEDURE

Sampling was begun by three 3-man boatcrews at 

cross section D just prior to the start of the injection of 

the fluorescent materials so that background samples 

could be obtained. These samples were used to check 

the bed material in the reach for naturally fluorescent 

materials which might be mistaken for the fluorescent 

tracer materials.

Two men in each crew sampled while the third marked 

sample bags and assisted in emptying the samplers. 

With the exception of positions near the banks, sampling 

for approximately 30 seconds was sufficient to obtain 

500- to 800-gram samples. Small canvas bags were used 

for sample storage. Figure 13 is a photograph of the three 

boatcrews in the process of sampling at cross section D.

In run 1, samples were collected at lateral positions 17,

23. 37, 43, 55, and 63 feet from the right bank. Unfortunately, no samples were obtained at position 30 until late 

in the experiment. Inspection of the samples indicated 

that the large red particles were moving toward the right 

bank; therefore, the crews were shifted toward the right 

bank, and samples were obtained at lateral positions 3, 7, 

and 12 feet from the right bank as well as at the other 

positions. The inspection of the samples also indicated 

that the tracer materials were moving through the study 

reach very rapidly; therefore, all three crews remained at 

cross section D for the entire experiment. After 5 hours, 

sampling was discontinued because inspection of the 

samples indicated that essentially all the fluorescent 

material had passed through the study reach.

In run 2, samples were collected at lateral positions 18,

24. 30, 36, 42, 48, 54, and 60 feet from the right bank at 

cross section D. Samples were collected as rapidly as possible for about 3 hours; then at the rate of three to four 

samples at each position per hour for another 4 hours;

405-770 OL - 71 - 3
112 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Right 

bank

Or

DISTANCE FROM RIGHT BANK, IN FEET 

FIGURE 12. Cross-section measurements obtained at 0815 hours. December 14. 1966.

then two samples at each position per hour for the next 3 

hours; and, finally, hourly samples at each position for 4

FIGURE 13. Three boatcrews "dustpan" sampling at cross section D.

more hours. Major sampling was discontinued about 14 

hours after injection of the fluorescent materials.

In addition to the "dustpan" samples, a number of 6- 

inch core samples were obtained at various positions in 

the study reach about 22 hours after injection of the 

fluorescent materials.

ANALYSIS OF THE SAMPLES

Analysis of the samples consisted of sieving the samples into the various size classes, counting the number of 

fluorescent particles of each color in each sieve class, and 

converting the number of fluorescent particles to concentrations. The concentration of a fluorescent tracer is the 

ratio of the weight of tracer material in a given size range 

of the sample to the total weight of all material in that 

size range of the sample.

All the samples were dried at room temperature. A V2 

series of 8-inch stainless steel sieves was used for the 

sieving, and samples were sieved on a Ro-Tap shaker for 

10 minutes. After completing the sieving of each sample, 

the sieves were inspected under an ultraviolet light to 

insure that no fluorescent particles remained which might 

contaminate the next sample.

The number of fluorescent particles of each color in 

^ach size class was determined by counting with the 

equipment shown in figure 14. The equipment consisted 

of an ultraviolet light source, a vibratory sand feeder, a

FIGURE 14. Equipment used for determining the number of fluorescent 

particles in the samples.
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 113

variac for controlling the voltage to the sand feeder, and a 

hand tabulator for keeping a running count of the number 

of fluorescent particles of each color. The procedure 

consisted of placing a split of a size fraction in the sand 

feeder, adjusting the voltage on the variac to give the 

desired feed rate, and counting the fluorescent particles 

of each color as they fell from the end of the sand feeder 

into the glass dish. Sizes smaller than the 0.125 mm were 

not counted because of the difficulty of differentiating 

between actual fluorescent particles and chips or flakes 

of dye from the large fluorescent particles.

A statistical analysis of the counting process (C. F. 

Nordin, Jr., written commun., 1968) has shown for tracer 

concentrations less than about 0.1 that the probability 

that the measured tracer concentration is between 0.9 

and 1.1 of the true tracer concentration is 95 percent if 

about 400 tracer particles are counted. Thus, it was 

necessary only to count until 400 fluorescent particles 

were obtained and then weigh that part of the particular 

size split associated with the 400 fluorescent particles. 

If the size split contained large numbers of particles of 

several colors, then the counting process was continued 

until 400 fluorescent particles of the lesser of the predominant colors in the size split were obtained. The entire 

size split was counted if the sample contained less than 

400 fluorescent particles of any color.

The numbers of fluorescent particles of each color in 

each size split were converted to concentrations with 

the numbers of fluorescent particles per gram of fluorescent material. These numbers were determined for the 

different sieve classes of each fluorescent material. A 

specific number of fluorescent particles (usually 1,000) 

of a specific sieve class was counted and weighed. This 

counting and weighing process was continued until a 

subsequent measurement did not change the overall 

mean by more than 2.0 percent. The numbers of fluorescent particles per gram of fluorescent material for the 

fluorescent materials used in runs 1 and 2 are given in 

table 6.

TABLE 6. Numbers of fluorescent particles per gram of fluorescent 

material for the sieve classes of fluorescent tracer materials used in 

runs 1 and 2

Particles per gram

Sieve class Run 1 Run 2

0.250-0.350

0.500-0.707

>1.00

Green Yellow 

quartz quartz

128,000 ..................

23,600 15,500 ...

............... 3,220

Red 

quartz

1,990

810

293 .

Quartz

101,000

15,800

2,540

Garnet

74,100

33,200

12,600

5380

2.760 ..

Monazite

87,000 .

7,520

Lead

4,910

PRESENTATION AND DISCUSSION OF 

RESULTS

The basic experimental data obtained in this study consisted of C(t), the fluorescent tracer concentration as a 

function of time from the "dustpan" samples obtained at 

the various lateral positions at cross section D; C' (t), the 

fluorescent tracer concentration as a function of time from 

the depth-integrated samples obtained at the weir; and 

the hydraulic and sediment-concentration measurements 

for the study reach at the time of the experiments.

A large number of graphs of fluorescent tracer concentration as a function of time for the different sieve classes 

and specific gravities were obtained for the two runs (54 

for run 1 and 105 for run 2). The C(t) data were obtained 

for all sieve classes of the quartz in run 1 and of the 

quartz, garnet, and monazite in run 2. None of the lead 

tracer particles in run 2 were found. The data for the 

0.500- to 0.707-mm sieve class of monazite in run 2 were 

discarded because of the possibility of contamination from 

the large red quartz particles from run 1 that apparently 

were temporarily trapped along the right bank. Background samples collected prior to the start of run 2 contained no fluorescent particles; however, samples obtained at lateral positions 18 and 24 feet about 4 hours 

after the start of run 2 contained some of the large red 

quartz particles from run 1.

A small number of the graphs representative of all of 

the data of fluorescent tracer concentration as a function 

of time were selected to be included as examples. For run 

1, one set of graphs of concentration as a function of 

time at lateral positions, z, of 7, 17, 23, 37, 43, and 55 feet 

from the right bank for one sieve class of each of the 

three colors was selected. These sieve classes were the 

0.177-0.250 mm for the green quartz, the 0.350-0.500 mm 

for the yellow quartz, and the 0.707-1.00 mm for the red 

quartz. The graphs are presented in figures 15, 16, and 

17 for the green, yellow, and red quartz, respectively.

For run 2, graphs of the concentration as a function of 

time at lateral positions, z, of 18, 24, 30, 36,42, 48, and 54 

feet for the 0.250- to 0.350-mm sieve class of quartz and 

the 0.177- to 0.250-mm sieve class of monazite were selected. These graphs are presented in figures 18 and 19. 

The concentrations plotted in figures 18 and 19 are relative concentrations; that is, each concentration value has 

been divided by the total area under the curve of concentration as a function of time. The relative concentrations 

are given by

C(t) /'
114 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

= 37 ft

z=43 ft

z=55 ft

1400 1500 1600 1700 1800 1900 2000 1300 1400 

TIME, IN HOURS

1500 1600 1700 1800 1900 2000

FIGURE 15. Variation with time of the concentration of the 0.177- to 0.250-mm sieve class of green quartz at lateral positions of 7, 17,

23, 37, 43, and 55 feet; cross section D, run 1.
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 115

300 n2500

z=37ft

z = 43ft

z=55ft

1300 1400 1500 1600 1700 1800 1900 2000 1300 1400

TIME, IN HOURS

1500 1600 1700 1800 1900 2000

FIGURE 16. Variation with time of the concentration of the 0.350- to 0.500-mm sieve class of yellow quartz at lateral positions of 7, 17,

23, 37, 43, and 55 feet; cross section D, run 1.
116 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

40,000

30,000

20,000

10,000

- 80,000

70,000

60,000

50,000

UJ

< 40,000

30,000 -

ill 20,000 -

10,000 -

0

1300

= 7 ft

= 17 ft

95,000

75,000

50,000

25,000

3000

2000

1000

2000

1500

1000

500

0

150

100

50

A

 4 L_»

i i

= 23ft

z = 37 ft

z=43ft

z=55 ft

1400 1500 1600 1700 1800 1900 2000 1300 1400 1500 1600 1700 1800 1900 2000

TIME, IN HOURS

FIGURE 17. Variation with time of the concentration of the 0.707- to 1.00-mm sieve class of red quartz at lateral positions of 7, 17, 23, 37,

43, and 55 feet; cross section Z), run 1.
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 117

The quantity C(t) is the fluorescent tracer concentration of a specific sieve class at a specific lateral position 

at time t. The quantity Cr (t) is the normalized, or relative, concentration obtained by dividing C(t) by the total 

area under the concentration versus time curve. The normalization procedure indicated by equation 1 corrects for 

the differences in the quantities of the quartz and monazite injected and facilitates presenting the results for the 

two minerals on the same graphs. These particular sieve 

classes were chosen for presentation because they have 

approximately the same median fall diameters (0.289 mm 

for the quartz and 0.305 mm for the monazite; see table 1).

Most of the results of this study depend upon the concentrations of fluorescent tracer material in the "dustpan" 

samples. Concentration of fluorescent material in a sieve 

class of a sample is defined as the grams of fluorescent 

tracer per gram of total material in that sieve class. If the 

tracer particles of a specific sieve diameter behave 

exactly as the nontagged particles of the same diameter, 

then the efficiency of the "dustpan" sampler is not 

important. This should be true for the quartz tracer particles if no significant shape differences exist between the 

tracer particles and the bed-material particles because 

the bed material is predominately quartz.

The efficiency of the "dustpan" sampler is of concern, 

however, when minerals with a specific gravity different 

from that of quartz are used as tracers, as in run 2. Concentrations for the garnet and monazite were expressed 

as the grams of garnet or monazite in the sieve class 

per gram of total material in that sieve class. The total 

material, however, was essentially all quartz; and because 

of the specific gravity difference between the minerals, 

the quartz associated with the garnet or monazite in a 

sieve class would have a smaller median fall diameter 

than the median fall diameter of the garnet or monazite. 

Therefore, if there were any washing of the sample during 

the sampling period or when the sampler was raised to 

the water surface, and if the effect of the washing were 

related to fall diameter, then the concentrations of the 

garnet and monazite would be affected.

An analysis of the size distributions of various "dustpan," core, and depth-integrated samples obtained during the two runs suggested that washing of the fines from 

the "dustpan" samples may have occurred. On the other 

hand, the analysis suggested that, if washing did occur, 

the effect was essentially uniform with respect to time 

and position at cross section D. If the washing effect is 

uniform with respect to time and position at cross section 

Z), then the results should not be affected significantly because the data analysis involves ratios of concentration 

integrals. Details of the analysis of the washing effect are 

presented in appendix A.

The experimental data from the two runs were used to 

determine (a) the lateral-dispersion characteristics of the

tracer materials between the injection point and cross 

section D; (b) the feasibility of applying the fluorescent 

tracer technique to sediment-transport-rate determinations; (c) the velocities of the centroids of the tracer materials between the injection point and cross section Z); 

and (d) the longitudinal-dispersion characteristics of the 

tracer materials between the injection point and cross 

section D. Each of these items is discussed in detail in 

the following sections.

LATERAL-DISPERSION CHARACTERISTICS OF THE 

TRACER MATERIALS

The lateral-dispersion coefficient, Kg, can be calculated from the rate of change of the variance of the lateral 

distribution of the tracer material with distance downstream (Sayre and Chang, 1968). In the fluorescent tracer 

experiments, however, meaningful data were obtained 

only at cross section D because of the rapid rate at which 

the tracer material moved through the study reach. Therefore, a true lateral dispersion coefficient could not be 

calculated. However, the variance, erf, of the area under 

the curves of fluorescent tracer concentration as a function of time versus lateral position at cross section D can 

be used as a measure of lateral dispersion between the 

injection point and cross section D. For a valid comparison, this procedure assumes that the initial period required for the establishment of the linear variation of the 

variance with distance is the same for all size classes and 

specific gravities of tracer materials.

The lateral distributions of the fluorescent tracer materials at cross section D were represented by plots of the 

areas under the curves of concentration versus time as a 

function of lateral position, z, in the cross section that

is,A(z) versus 2, where A(z)= I C(t)dt. The^(z) data

Jo

were normalized by dividing by the area under the^(z)

f B

versus z curves, or I A(z)dz where B is the channel 

Jo

width. Normalization facilitated the comparison of the 

lateral distributions for the different sieve classes and 

specific gravities of tracer materials. The graphs of the 

normalized, or relative, area, /4 r (z), as a function of z for 

the various sieve classes of fluorescent materials used in 

run 1 are presented in figure 20; and the graphs of Ar (z) 

versus z for the different sieve classes of quartz, garnet, 

and monazite tracers used in run 2 are presented in figures 

21, 22, and 23, respectively. Figures 20 through 23 show, 

in effect, the relative amounts of each fluorescent tracer 

that passed through each sampling position at cross 

section D during the runs, if it is assumed that the sediment-transport rate was constant during the run.
118 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

EXPLANATION 

 Quartz

1200 1400 1600 1800 

TIME, IN HOURS

2000 2200 2400

FIGURE 18.-Variation with time of the relative concentrations of the 0.250- to 0.350-mm sieve class of quartz and
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 119

1.50,

1.25 -

1.00

0.75

0.50

0.25

EXPLANATION

z- 30 ft

Quartz 

Monazite

1.50

z- 36 ft

EXPLANATION 

 Quartz

1600 1800 

TIME, IN HOURS

2200 2400

the 0.177- to 0.250-mm sieve class of monazite at lateral positions of z= 18, 24, 30, and 36 feet; cross section D, run 2.

405-770 OL - 71 - 4
120 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

2.50

2.00

1.50

1.00

 - 0.50

z=42ft

EXPLANATION

 Quartz

 Monazite

d 2.00

1.50

1.00

0.50 |

z=48ft

EXPLANATION

 Quartz

 Monazite

I \

'\\

1000 1200 1400 1600 1800 

TIME, IN HOURS

2000 2200 2400

FIGURE 19. Variation with time of the relative concentrations of the 0.250- to 0.350-mm sieve class of quartz and the 

0.177- to 0.250-mm sieve class of monazite at lateral positions of z = 42, 48, and 54 feet; cross section D, run 2.
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 121

4.00

3.00

2.00

1.00

z=54ft

EXPLANATION 

 Quartz

1200 1400 1600 1800 

TIME, IN HOURS

2000 2200 2400

The variance of the lateral distribution at cross section 

D, cr|, is given by

(B

*

.9 JO

(z]dz

f

(z)dz

(2)

where z is the lateral position measured from the right 

bank of the channel, B is the channel width, A (z) is the 

area under the curve of concentration versus time at 

lateral position z and is given by

A(z} = ^ C(t)dt 

Jo (3)

and z is the mean lateral position of the distribution, 

defined as

"B

zA(z)dz

z = (B

Jo

(z}dz

(4)

The integrals in equations 2 and 4 were determined by 

measuring with a planimeter the areas under the appropriate curves. The A (z) values at the ends of the distribution were assumed to be zero at lateral positions 

displaced toward the banks from the outside sampling 

positions a distance equal to one-half of the interval over 

which the outside sampling position was assumed to 

apply. The distributions presented in figures 20 through 

23 suggest that this assumption is valid, except perhaps 

for the red quartz particles in run 1. Because of the 

tendency for the large particles to move toward the right 

bank, the areas for the red quartz at z = l feet were large. 

However, an insufficient number of samples was obtained 

at positions between z=l feet and the right bank, and 

thus it was necessary to assume that these areas decreased linearly from the values at z=7 feet to zero at 

z = 2 feet.

The mean lateral position values, z, and the variances, 

(Tg, of the lateral distributions at cross section D are summarized in tables 7 and 8 for runs 1 and 2, respectively. 

The mean lateral position values are plotted as a function 

of the median fall diameters of the sieve classes in figures 24 and 25 for runs 1 and 2, respectively. The variances, erf, are plotted as a function of the median fall 

diameters of the sieve classes in figures 26 and 27 for 

runs 1 and 2, respectively. The numbers next to each 

point indicate the sieve-class numbers given in tables 7 

and 8.
122 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

0.08

0.06 -

0.04 -

0.02 -

0.08

EXPLANATION

Red quartz 

(mm)

 0.500-0.707 

A 0.707-1.00 

>1.00

EXPLANATION

Yellow quartz 

(mm)

 0.250-0.350 

A 0.350-0.500

 0.500-0.707

EXPLANATION

Green quartz 

(mm)

/ ,_ -> 0.125-0.177 

//\ A 0.177-0.250 

0.250-0.350

///\\ / ' 

10 20 30 40 50 

DISTANCE FROM RIGHT BANK (z), IN FEET

FIGURE 20. Variation of the area under the curve of concentration 

versus time with lateral position, z, at cross section D for the different 

sieve classes of the three colors of quartz tracer, run 1.
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 123

0.100

0.075 -

20 30 40 50 

DISTANCE FROM RIGHT BANK (z), IN FEET

FIGURE 21. Variation of the area under the curve of concentration versus time with lateral position, z, at cross section D for the different

sieve classes of quartz tracer, run 2.
124 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

0.150

0.125 -

0.100 -

0.075 -

0.050 -

- 0.025 -

0.100

0.075 -

0.050 -

0.025 *

10 20 30 40 50 

DISTANCE FROM RIGHT BANK (z), IN FEET

60 70

FIGURE 22. Variation of the area under the curve of concentration versus time with lateral position, z, at cross 

section D for the different sieve classes of garnet tracer, run 2.
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 125

0.125

0.100

0.075

0.050

 - 0.025

EXPLANATION

Monazite

(mm) 

 0.250-0.350

A 0.350-0.500

0.075

0.050 -

0.025 -

10 20 30 40 

DISTANCE FROM RIGHT BANK (z), IN FEET

50 60 70

FIGURE 23. Variation of the area under the curve of concentration versus time with lateral position, z, at cross section D for the different sieve

classes of monazite tracer, run 2.
126 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

The vertical dashed lines in figures 24 to 27 represent 

the size limits of the sieve classes used in the analysis of 

the samples. In several instances, the median fall diameters for some sieve classes of tracer material are smaller 

than the lower size limit of the sieve class. As discussed 

previously, shape effects probably contributed to this 

anomaly. The photomicrographs of the fluorescent materials used in run 1 (see fig. 8) indicate that this material 

was angular and thus had a shape factor less than the 0.7 

usually attributed to naturally worn quartz particles. The 

median fall diameters for the different sieve classes of 

garnet and monazite are in general displaced to the next 

larger sieve class because of the effect of specific gravity.

TABLE 7. Summary of the z and <j\ values for the lateral distributions 

at cross section D, run 1

Color of 

quartz

Sieve class 

(mm)

z

(ft)

Green

Yellow

Red

(1) 0.125-0.177

(2) 0.177-0.250

(3) 0.250-0.350

(3) 0.250-0.350

(4) 0.350-0.500

(5) 0.500-0.707

(5) 0.500-0.707

(6) 0.707-1.00

(7) > 1.00

33.7

34.4

33.2

26.7

22.7

18.7

19.0

17.9

16.5

69.8

63.1

62.7

82.3

61.0

34.2

33.2

50.5

71.4

TABLE 8. Summary of the z and <J\ values for the lateral distributions 

at cross section D, run 2

Mineral

Quartz

Si

(1)

(2)

(3)

(4)

(5)

(6)

ieve class 

(mm)

0.125-0.177

0.177-0.250

0.250-0.350

0.350-0.500

0.500-0.707

0.707-1.00

z

(ft)

45.1

44.2

40.3

37.9

37.0

37.8

<?i

(ft2 )

78.6

38.7

36.6

26.9

17.9

14.4

Garnet

Monazite

(1)

(2)

(3)

(4)

(5)

0.125-0.177 

0.177-0.250 

0.250-0.350 

0.350-0.500 

0.500-0.707

(1) 0.125-0.177

(2) 0.177-0.250

(3) 0.250-0.350

(4) 0.350-0.500

40.1

36.7

33.0

31.7

31.4

39.9

35.9

33.4

31.9

32.9

26.2

14.5

12.5

14.4

44.6

30.7

25.0

25.3

The mean lateral positions and the variances for the 

dye-dispersion test were calculated from summation 

approximations of equations 4 and 2, respectively. These 

approximations are

z 

2=B (5)

and

z2C(z)Az

C(z)Az

(6)

The approximations were assumed valid for the dyedispersion test because samples were obtained every 2 

feet across the channel width.

The results of the dye-dispersion test are summarized 

in table 9. The variances at the different cross sections 

were corrected for the effect of width by the method of 

Fischer (1967), and the corrected variances are given in 

table 9. A plot of the variance as a function of longitudinal 

distance from the source suggested that the second measurement, Z)(2), at cross section D was the more correct 

of the two. The Z)(2) values of z and oi for the dye-dispersion test are shown near the ordinates of figures 24 

and 26, respectively.

TABLE 9. Summary of the z, cr|, and crj (corrected) values for the 

dye-dispersion test

Cross 

section

A

B

C

D(l)

D(2)

Width (ft)

73.5

70

69

79

79

z

(ft)

26.8

22.6

30.7

35.2

34.2

o-l

(ft 2 )

7.88

19.5

32.8

103

68.5

<rl (corrected) 

(ft 2 )

7.74

21.2

36.5

87.7

58.4

The mean lateral positions for the quartz tracer particles ranged from 34.4 feet from the right bank for the 

0.177- to 0.250-mm sieve class of green quartz to 16.5 

feet for the > 1.00-mm sieve class of red quartz in run 1 

and from 45.1 feet from the right bank for the 0.125- to 

0.177-mm sieve class to 37.0 feet for the 0.500- to 

0.707-mm sieve class of quartz tracer in run 2. The tendency for the large tracer particles to move toward the 

right bank is evident from the results presented in figures 

24 and 25. The difference in the magnitude of the effect 

for runs 1 and 2 may be attributed to the fact that the injection point for run 2 was moved 7 feet to the left of the 

channel centerline after the behavior of the tracer particles in run 1 was observed. There was little difference in 

the z values of the garnet and monazite for particles of 

comparable fall diameter. However, the garnet and monazite z values were displaced 2 to 6 feet toward the right 

bank from the z values for quartz particles of comparable 

fall diameter.

A possible explanation for the movement of the large 

particles toward the right bank may be based on a 

consideration of the cross-section measurements obtained 

prior to the start of run 2. (See figs. 12 and 6.) The thalweg, 

or line of maximum depth, shifted from approximately
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 127

70

60

50

40

30

20

10

Lef

-

«-Dy<

-

"

EX

t bank z

*-(!)-*

i (1)

t 79ft

-(a~

2^

PLAN' ATI oh

Quartz

 Green

A Yellow

 Red

i

(3)

N

j

,

 (4)- 

4) 

k

\(5) ^A

i

« (5) * 

(*^«L

i

<-Size-* 

limit 

of 

ndicatec sieve" 

class

* (6) »

-

(7)

 Hi

i

0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 

MEDIAN FALL DIAMETER, IN MILLIMETERS

FIGURE 24. Variation with fall diameter of the mean lateral 

positions of the tracer distributions at cross section D, 

run 1. Numbers in parentheses are sieve class numbers; 

see tables 7 and 8.

the centerline at the injection point to the right bank at 

cross section A and then back to the left bank at cross 

section Z); the maximum depth was greatest at cross section A. The results of the fluorescent tracer experiments 

suggest that the large tracer particles, particularly in run 

1, tended to follow the thalweg from the injection point 

to the right bank and then to move down the reach along 

the bank.

Figures 26 and 27 show a distinct difference in the 

variation of erf with fall diameter for the large quartz 

tracer particles in runs 1 and 2, and there are at least 

two factors that contribute to this difference. These 

factors are the movement of the red quartz particles 

toward the right bank and the indication that some of 

these particles were trapped temporarily along the right 

bank. The lateral distributions for the three sieve classes 

of red quartz, and in particular the > 1.00-mm sieve class, 

are skewed toward the right bank (fig. 20). Temporary 

entrapment of some of the red quartz was indicated by 

the appearance of red quartz particles in samples obtained 

during the middle part of run 2 for positions near the right 

bank at cross section Z), even though background samples 

obtained at cross section D prior to the start of run 2 

indicated that all of the fluorescent material used in 

run 1 had passed through the study reach. Both of these

factors, the temporary entrapment and the displacemei

toward the right bank region where water velocities wei

less than the mean water velocity, would tend to increaj

erf over the values that might be expected if the re 

quartz particles had moved down the center of tl

chann

70

^ 60

z.

CD

H 

I 

O

E 50

O 

cc

tnuj 40

z.

3

0 30

1- 

cn 

o

0.

<

25 20

 z.

Ld

5 10

0 

0

el without interference.

Left

-

-

_

-

E

_

bank at 7

^(1)^

(1)

 ^

KPLAN

i 

9ft

« (2) -»

(2) 

^Y

ATION

 Quartz

A Garnet

 Monazite

1

* (3) *

\(3) ^^^

 S (2)

^^^

i

* Size -» 

limit of 

indicated 

sieve

class

* (4) *

M>

~j-~.. _ (3 

(3)~~"~

i

 (5) »

(5) «

- *

)

---- < 

-- A----3

(4) (5

i

« (6) »

-

)

4) 

f 

)

-

_

1 0.2 0.3 0.4 0.5 0.6 0.8 1.

MEDIAN FALL DIAMETER, IN MILLIMETERS

FIGURE 25. Variation with fall diameter of the mean lateral positions of 

the tracer distributions at cross section D, run 2. Numbers in parentheses are sieve class numbers; see tables 7 and 8.

The erf values for the three sieve classes of green quartz 

in run 1 were approximately the same as the cri value for 

the dye cloud in the dye-dispersion test. The cri value 

for the 0.250- to 0.350-mm sieve class of yellow quartz 

exceeded the cri value for the dye; however, the difference 

was small.

The cri values for garnet in general were less than the 

cri values for quartz particles of comparable fall diameter. 

The cri values for monazite, however, fall in line with 

the quartz values, with the exception of the value for the 

0.350- to 0.500-mm sieve class of monazite. Thus, the 

lateral dispersion of the heavy minerals as represented 

by the variance of the lateral distribution at cross section 

D generally decreases with increasing particle diameter, 

as it does for the quartz, with the exception, however,
128 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

100 

90 

80 

70 

60-

50

40

- 30

20

10

-Dye

(1)

^- 

limit 

of

indicated 

sieve 

class

*-(!)-

EXPLANATION

Quartz 

> Green

k Yellow 

I Red

0.1 0.2 0.3 0.4 0.5 0.6 0.8 

MEDIAN FALL DIAMETER, IN MILLIMETERS

1.0

FIGURE 26. Variation with fall diameter of the variances of the lateral 

distributions of the tracer masses at cross section /?, run 1. Number 

in parentheses are sieve class numbers; see tables 7 and 8.

100

90

80

70

60

50

40

~ 30

UJ

o

z

< 20

cc

 Size J

limit of

indicated

sieve

class

0.2 0.3 0.4 0.5 0.6 0.8 

MEDIAN FALL DIAMETER, IN MILLIMETERS

1.0

FIGURE 27. Variation with fall diameter of the variances of the lateral 

distributions of the tracer masses at cross section D, run 2. Numbers 

in parentheses are sieve class numbers; see tables 7 and 8.

that there is a slight increase in the variance for the large 

sizes of garnet and monazite.

The results of the two fluorescent tracer experiments 

suggest that at least two factors may be important in

causing lateral mixing of sediment particles. These are 

the turbulence in the flow and the thalweg. In run 1, the 

injection point apparently was on the thalweg and the 

large particles tended to follow the thalweg to the right 

bank whereas the small particles were mixed in the lateral 

direction to about the same extent as the dye cloud. Thus, 

in run 1 the lateral mixing of the small particles was 

caused primarily by the turbulence in the flow, and the 

lateral mixing of the coarse particles was caused primarily 

by the thalweg. Particles with a fall diameter of about 

0.5 mm were affected least by the two factors. (See fig. 26.) 

In run 2, the shift of the injection point apparently was 

sufficient to remove the fluorescent tracers from most of 

the influence of the thalweg and lateral mixing as indicated by crl decreased with increasing fall diameter. The 

large and heavy particles mixed the least because they 

spent a greater proportion of the time resting on or rolling 

along the bed surface than did the small particles.

APPLICATION OF FLUORESCENT TRACERS TO THE MEASUREMENT OF THE SEDIMENT-TRANSPORT RATE

The use of fluorescent tracers for the determination of 

the sediment-transport rate assumes that the tracer particles and the natural sediment particles behave identically. Also, the quantity of tracer material injected must 

be small in comparison with the natural sediment-transport rate. Sediment-transport rate as used in this report 

refers to the rate of movement of the channel bed material 

and includes the suspended bed-material load and the 

bedload but does not include the fine material or "wash 

load."

"DUSTPAN" SAMPLES AT CROSS SECTION D

The time-integration method was used to calculate the 

sediment-transport rate from the fluorescent tracer concentrations of the "dustpan" samples obtained at cross 

section D. The time-integration equation is based on the 

conservation of the tracer material as expressed by

W= I q»(t, z)C(t,z) dtdz, 

lo Jo

(7)

where W is the weight of tracer material injected, qs is the 

sediment-transport rate per unit of channel width, C is 

the fluorescent tracer concentration, and B is the channel 

width. The quantities qs and C are functions of lateral position, z, and time, t. If qs, the sediment-transport rate, is 

steady, it is independent of time, and equation 7 becomes

= qs (z) \X!C(t 

Jo

dtdz. (8)

Because samples were obtained at various positions 

across the channel at cross section D throughout the pas-
where qs (z) is the unit sediment-transport rate at z, qs is 

the mean unit sediment-transport rate for the cross section, and w(z) is the weighting factor at z. Substitution of 

equation 9 into equation 8 yields, after rearrangement,

W

fJo

w(z)A(z) dz

(10)

where A (z) is denned by equation 3. In general, the overall size distribution of the bed material in transport will 

not match exactly the size distribution of the tracer material. Therefore, equation 10 must be applied to each 

size class and the results summed to obtain the total 

sediment-transport rate. The weighting factors were 

determined from a set of depth-integrated samples obtained at the weir. Details of the procedure are given in 

appendix B.

The mean unit sediment-transport rates, qs, for the 

various sieve classes of quartz tracer were calculated 

from equation 10. The denominators of equation 10 were 

determined by plotting the product w(z)A(z) as a function of z and measuring the areas under the curves with a 

planimeter. These qs values were converted to the total 

sediment-transport rates, Qs, by multiplying by the 

channel width at cross section D. The Qs values for the 

various sieve classes calculated from the fluorescent 

tracer concentrations of the "dustpan" samples at cross 

section D are summarized in tables 10 and 11 for runs 1 

and 2, respectively. The measured Qs values determined 

from the depth-integrated samples obtained at the weir 

are presented also in tables 10 and 11. The calculations of the sediment-transport rates were limited to 

sieve sizes larger than 0.125 mm. For sizes smaller than 

0.125 mm, it was difficult to distinguish between chips of 

dye from large particles and actual fluorescent particles.

TABLE 10. Summary of the calculation of the sediment-transport rate, 

"dustpan" samples at cross section D, run 1

Color of 

quartz

Sieve class 

(mm)

Q, (calculated) 

(tons per day)

Qs (measured) 

(tons per day)

Q, (calculated) 

Qs (measured)

Green

Yellow

0.125-0.177 

0.177-0.250 

0.250-0.350

0.250-0.350 

0.350-0.500 

0.500-0.707

0.500-0.707 

0.707-1.00 

>1.00

2,109

2,336

1,670

1,277

323

55

39

16

14

1,515

1,191

922

922

357

33

33

0

0

1.39

1.96

1.81

1.38

.88

1.67

1.18

Total (maximum), 

(minimum)..

6,523

6,114

4,018

4,018

1.62

1.52

129

TABLE 11. Summary of the calculation of the sediment-transport rate, 

"dustpan" samples at cross section D, run 2

TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION

sage of the tracer mass, the variation of the quantity 

f*

C(t) dt with z was determined. However, it is necessary also to know how qs varies with z. It was assumed that

qs (z)=qsw(z), (9)

Quartz sieve class 

(mm)

Qs (calculated) 

(tons per day)

Qs (measured) 

(tons per day)

Qs (calculated) 

Q, (measured)

0.125-0.177 

0.177-0.250 

0.250-0.350 

0.350-0.500 

0.500-0.707 

0.707-1.00

859

1,724

747

118

36

6.9

1,194

937

713

203

25

0

0.72

1.84

1.05

.58

1.44

Total...... 3,491 3,072 1.14

In run 1, two calculations of the sediment-transport 

rate were possible because of the overlap of the green and 

yellow 0.250- to 0.350-mm sieve classes and the yellow 

and red 0.500- to 0.707-mm sieve classes. The maximum 

value given in table 10 was obtained by using the 0.250- 

to 0.350-mm sieve class of green quartz and the 0.500- 

to 0.707-mm sieve class of yellow quartz as tracers for 

the 0.250- to 0.350-mm and 0.500- to 0.707-mm sieve 

classes of bed material, respectively. The minimum value 

was obtained by using the 0.250- to 0.350-mm sieve class 

of yellow quartz and the 0.500- to 0.707-mm sieve class 

of red quartz as tracers for the 0.250- to 0.350-mm and 

0.500- to 0.707-mm sieve classes of bed material, respectively. The maximum value was about 6.7 percent larger 

than the minimum value.

The maximum and minimum calculated sedimenttransport rates are 62 and 52 percent larger than the 

sediment-transport rate measured at the weir. The ratios 

of the calculated sediment-transport rates to the measured 

sediment-transport rates for the various sieve classes 

are included in table 10 and each ratio is greater than 1.0 

for all size classes with the exception of the 0.350- to 

0.500-mm sieve class of yellow quartz.

Several factors could contribute to the fact that the 

calculated sediment-transport rates were almost all 

larger than the measured sediment-transport rates. 

Probably the key factor is the assumption inherent in 

equation 10 that all of the fluorescent tracer material 

injected is sampled as it passes through the measurement 

section. However, sampling at any cross section must be 

limited to a reasonable number of points with linear 

interpolation assumed valid between the points. A large 

quantity of fluorescent material could pass unsampled 

between two sampling positions or could pass through a 

sampling position while samples were being obtained at 

another position. These problems would be most important for high-velocity flows where the fluorescent material 

is moving very rapidly. In addition, a quantity of the 

fluorescent material may be trapped within the study 

reach temporarily, or sampling may be terminated before 

the fluorescent tracer material has passed completely 

through a study reach. All these factors would result in
130 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

low values of the areas, A(z), under the concentration 

as a function of time curves and, hence, high values for 

the calculated sediment-transport rates.

In run 1 the failure to sample at z = 30 feet may have 

caused some reduction of the areas under the A (z) as a 

function of z curves. In the absence of data at z = 30 feet, 

the areas were assumed to vary linearly with z between 

z = 23 feet and z=37 feet. A consideration of figure 20 

suggests that the areas at z = 30 feet could be larger than 

these interpolated values without resulting in unusual 

A(z) versus z relations. However, it is believed that 

these possible errors in the areas would not be large 

enough to account for all of the difference between the 

calculated and measured sediment-transport rates in 

run 1.

An additional factor that must be considered is the 

accuracy of the sediment-transport rates as measured at 

the weir. The basis of the weir operation is that all the 

sediment is suspended by the action of the baffles as the 

sediment passes over the weir and the sampler nozzle 

traverses the entire depth of flow at the weir crest. It is 

essential that all of the sediment be suspended and that 

the suspended sediment be sampled accurately. Errors 

in the sediment concentrations determined from the 

depth-integrated samples may occur if the intake velocity 

of the sampler differs significantly from the stream 

velocity. If the transit rate is too slow, overfilled sample 

bottles will result and the samples must be discarded. 

If the transit rate is too rapid, then the intake velocities 

are less than the stream velocities and the measured 

sediment concentrations are greater than the true sediment concentrations. The effect of an incorrect intake 

velocity increases with particle diameter (U.S. InterAgency Committee on Water Resources, 1941, fig. 14) 

and is very important for particles in the sand-size range.

In run 2, the calculated sediment-transport rate was 

about 14 percent larger than the measured rate. The 

good agreement, however, was fortuitous, as is shown by 

the ratios of the calculated to the measured sedimenttransport rates given in table 11. Two of the ratios were 

less than 1.0, and this negative deviation balanced the 

positive deviations for the other three sieve classes. 

There are no apparent reasons why the ratios for the 

0.125- to 0.177-mm and 0.350- to 0.500-mm sieve classes 

should be less than 1.0. However, when the ratio of the 

measured sediment-transport rate for run 1 to the measured rate for run 2 was calculated for the different sieve 

classes, it was found that the ratio values were between 

1.27 and 1.32 with the exception of the ratio for the 

0.350- to 0.500-mm sieve class. This ratio was 1.76 and 

the large difference for the 0.350- to 0.500-mm sieve class 

suggests the possibility of an error in the measured sediment-transport rates for this sieve class. Also note that the

Qs (calculated)/()s (measured) ratio for this sieve class 

was less than 1.0 in both runs.

The mean deviations, regardless of sign, of the calculated sediment-transport rates from the measured sediment-transport rates for the different sieve classes were 

51 and 41 percent for runs 1 and 2, respectively.

DEPTH-INTEGRATED SAMPLES AT THE WEIR

The calculation of the sediment-transport rate from 

the fluorescent tracer concentrations of the depthintegrated samples required a slightly different procedure than was used for the "dustpan" samples from 

cross section D. Because the amount of sand in the depthintegrated samples was small and, consequently, because the number of fluorescent particles in each size 

split would have been very small, the depth-integrated 

samples generally were not sieved into size classes. 

Because the samples were not sieved, only the total 

number of fluorescent particles of each color was obtained for each sample. The concentration of fluorescent 

material for these samples, therefore, was defined as the 

number of particles of a specific color per gram of sediment in the sample. Generally the 14 samples obtained 

across the weir for each sample time were composited 

to give one sample for that particular time.

In addition to requiring the modification of the definition of fluorescent tracer concentration, the small size 

of the depth-integrated samples necessitated two assumptions. First, it was assumed that the fluorescent 

particles were sampled at the weir in the same proportion 

as that at which the particles were injected. Second, it 

was assumed that the sieve-size distribution of the depthintegrated samples at the weir did not change with time 

during the run.

With these assumptions, it may be shown that the 

equation for the calculation of the sediment-transport 

rate of size class / from the concentrations of fluorescent 

tracers in the depth-integrated samples has the form

where

A" 

A'=\"C' (t)dt.

(11)

(12)

Equation 11 is similar in form to equation 10 but has the 

following differences. First, the weight of fluorescent 

tracer injected, W, has been replaced by N, the number 

of fluorescent particles of a specific color injected, and 

Pi is the fraction of the total weight of sediment in the 

sample that is in size class i. Second, A(z] has been replaced by A', which was accomplished by replacing in 

equation 3 the concentration, C, as grams of fluorescent 

tracer per gram of sediment by C", the concentration as
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 131

number of fluorescent particles per gram of sediment. 

Third, the integration across the channel width has been 

accomplished by the averaging effect of compositing a 

set of samples taken across the weir; hence the transport rate, Qsi, is the total transport rate for size class i 

for the cross section, and the concentration is a mean 

concentration, indicated by the overbar, for the cross 

section. Details of the development of equation 11 and 

a discussion of the two assumptions are presented in 

appendix C.

The variation with time of C' for the three colors of 

quartz used in run 1 and the quartz, garnet, and monazite 

tracers used in run 2 are presented in figures 28 and 29, 

respectively. The concentrations plotted in figures 28 

and 29 are relative concentrations, C'r (t); that is, each 

concentration for a given color or specific gravity has 

been divided by the area under the curve A'. Thus, 

Cr(t) is equal to C' (t)/A f where A' is defined by equation 

12.

The sediment-transport rates for the different sieve 

classes of fluorescent quartz were calculated from equation 11, and the results are summarized in tables 12 and 

13 for runs 1 and 2, respectively. The N values were 

determined from the quantities of fluorescent materials 

injected (table 2) and the numbers of fluorescent particles 

per gram of fluorescent material (table 6). The p, values 

were determined from the sieve-size distributions for the

TABLE 12. Summary of the calculation of the sediment-transport rate, 

depth-integrated samples at the weir, run 1

Color of quartz Sieve class 

(mm)

Qs (calculated) 

(tons per day)

Q, (measured) 

(tons per day)

Green

Yellow

Red

0.125-0.177 

0.177-0.250 

0.250-0.350

0.250-0.350 

0.350-0.500 

0.500-0.707

0.500-0.707 

0.707-1.00 

>1.00

2,403

1,889

1,463

451

174

16

3

0

0

1,515

1,191

922

922

357

33

33

0

0

Total (maximum), 

(minimum).

5,945

4,920

4,018

TABLE 13. Summary of the calculation of the sedimenttransport rate, depth-integrated samples at the weir, 

run 2

Quartz

sieve class

(mm)

Qi (calculated) 

(tons per day)

Qs (measured) 

(tons per day)

0.088-0.125.. 

0.125-0.177.. 

0.177-0.250.. 

0.250-0.350.. 

0.350-0.500.. 

0.500-0.707.. 

0.707-1.00...

890

1,050

824

627

178

22

0

1,013

1,194

937

713

203

25

0

Total. 3,591 4,085

depth-integrated samples (fig. 41). The A' values were 

determined for each color of fluorescent quartz tracer 

by plotting C' as a function of time and measuring the 

area under the curve with a planimeter (figs. 28 and 29).

In run 1, only the three sieve classes of each of the three 

colors contributed a significant number of fluorescent 

particles to the total number of particles of each color 

injected. As with the calculation of the sediment-transport 

rate from the "dustpan" sample concentrations, two 

answers were possible because of the overlap of the green 

and yellow 0.250- to 0.350-mm sieve classes and the yellow 

and red 0.500- to 0.707-mm sieve classes. The maximum 

of the two calculated results is about 48 percent larger, 

and the minimum is about 22 percent larger, than the 

sediment-transport rate measured at the weir. The big 

difference between the two calculated values is caused 

by the large difference between the sediment-transport 

rates predicted for the 0.250- to 0.350-mm sieve class of 

green quartz and the 0.250- to 0.350-mm sieve class of 

yellow quartz.

There is some basis for selecting the minimum of the 

two results as the more accurate. The results presented 

in table 1 show that the median fall diameter of the 0.250- 

to 0.350-mm sieve class of the yellow quartz was essentially identical with that of the natural bed material, 

whereas the median diameter of the 0.250 to 0.350-mm 

sieve class of the green quartz was about 17 percent smaller. This suggests that the 0.250- to 0.350-mm sieve class 

of the yellow quartz is the better of the two "tracers" for 

the 0.250- to 0.350-mm sieve class of the natural bed 

material. Large differences exist among the median 

fall diameters for the 0.500- to 0.707-mm sieve classes of 

yellow and red quartz and the natural bed material. Of 

the yellow and red quartz fall diameters, the red quartz 

median fall diameter is nearest to the median fall diameter of the natural bed material. The contribution of this 

sieve class to the total sediment-transport rate is less than 

1 percent, however.

In run 2, the 0.088- to 0.125-mm sieve class contributed 

almost 6 percent of the total number of quartz tracer 

particles injected. Therefore, it was necessary to consider this sieve class in addition to the six sieve classes 

that were considered in the analysis of the "dustpan" 

samples. The problem of differentiating between the 

small particles and chips or flakes of dye from the large 

particles could not be eliminated but was reduced as 

much as possible by careful counting of the fluorescent 

particles in the depth-integrated samples. The calculated sediment-transport rate for particles larger than 

0.088 mm was about 12 percent smaller than the sediment-transport rate measured at the weir.

Because of the two assumptions necessary in the 

analysis of the fluorescent tracer concentrations of the

TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 133

4.00

3.00-

2.00

1.00

Monazite

2.00

1.00 -

Garnet

2.00

1.00 -

Quartz

1000 1100 1200 1300 1400 

TIME, IN HOURS

1500 1600 1700

FIGURE 29. Variation with time of the relative mean fluorescent tracer concentrations of the depth-integrated samples at the weir, run 2.
134 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

depth-integrated samples, the ratio of the measured-tocalculated sediment-transport rates for each sieve class 

of a specific color of tracer was a constant. This can be 

shown as follows. The measured sediment-transport rate 

for size class i is

QSi (measured) = Qspi, (13)

where Qs is the total measured sediment-transport rate. 

The ratio for size class i is

(14)

QSf (measured) _

()s. (calculated)" N

For a specific color of fluorescent tracer in a specific 

experiment, all the factors on the right-hand side of 

equation 14 are constant, and thus the ratio of QSi (measured)/^,, (calculated) is constant for all size classes.

VELOCITIES OF THE CENTROIDS OF THE 

TRACER MASSES

The velocities of the centroids of the tracer masses 

were determined from the data of mean concentration, 

C, versus time from cross section D.

The data of fluorescent tracer concentration versus 

time for each sieve class at the various lateral positions 

at cross section D were combined to give the mean concentration, C(t). The mean concentration for a specific 

sieve class at time t is given by

z=B

C(z,

(15)

where C(z, t) is the concentration at time t at lateral 

position z where z is measured from the right bank, Az is 

the width increment over which C(z, t) is assumed to be 

the concentration, and B is the channel width.

In run 1, the sampling positions were not equally 

spaced, and one position near the centerline was omitted 

through an error in sampling procedure. As a result, 

the sampling position was not always at the center of the 

Az increment. The maximum displacement of a sampling 

position from the center of a width increment was 2 feet 

for the two center sampling positions. Because the 

positioning of the samplers at the different sample times 

was subject to an error of the order of ± 0.5 foot, the

2-foot displacement is not considered significant. Thus, 

equation 15 for run 1 is

10C7 (Q + 10C23 (Q + 10C37 (0

79 (16)

where 79 is the channel width, in feet, at cross section D.

In run 2, the sampling locations were equally spaced

at 6-foot intervals and equation 15 for run 2 has the form

+C24 (f) +C30 (0 +C42 (Q

79

79 (17)

The mean concentrations at cross section D for the 

various sieve classes and specific gravities of tracer 

materials were calculated from equations 16 and 17 

for runs 1 and 2, respectively.

The mean concentration values calculated from equations 16 and 17 were normalized by dividing by the area 

under the curve of mean concentration versus time to 

give a relative mean concentration. The relative mean 

concentration, Cr, is defined by

C(t} /"

Jo

(18)

The relative mean concentration values as a function of 

time for the various sieve classes of quartz tracers used 

in run 1 are presented in figures 30, 31, and 32.

The relative mean concentration values as a function of 

time for the quartz, garnet, and monazite tracers used in 

run 2 are presented in figures 33, 34, and 35, respectively.

The centroid velocities were calculated from

v= 700

(f-Af)3600' (19)

where V is the velocity of the centroid of the tracer mass, 

in feet per second; 700 is the distance, in feet, between 

the injection point and cross section D; t is the mean time, 

in hours, or the time required for the centroid of the 

tracer mass to move from the injection point to cross 

section D; and A£ is the time difference, in hours, between 

the start of the experiment and the mean injection time 

for a given sieve class or specific gravity of tracer material.
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 135

2.00

1.00

EXPLANATION

Yellow quartz 

0.500-0.707 mm

2.00

1.00-

EXPLANATION

Yellow quartz 

0.350-0.500 mm

3.00

2.00

1.00

EXPLANATION

Yellow quartz 

0.250-0.350 mm

0

1300 1400 1500 1600 1700 

TIME, IN HOURS

1800 1900 2000

FIGURE 30. Variation with time of the relative mean concentration at cross section D of the 0.250- to 0.350-mm, 0.350- to 0.500-mm, and 0.500-

to 0.707-mm sieve classes of yellow quartz, run 1.
m 

°o X

?8 C =>

RELATIVE MEAN FLUORESCENT TRACER CONCENTRATION, Cr (t)

i-1 ro u> .1^

§

b b b

o o o o

r

m 

p ^ X - O T|

-$ r

I (D v> 

P= ^

hon ^-

°!5

I N o
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 137

3.00

1300 1400 1500 1600 1700 

TIME, IN HOURS

1800 1900 2000

FIGURE 32. Variation with time of the relative mean concentration at cross section D of the 0.500- to 0.707-mm, 0.707- to 1.00-mm, and > 1.00-mm

sieve classes of red quartz, run 1.
138 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

2.00

4.00

3.00

2.00

1.00

EXPLANATION

Quartz 

0.125-0.177 mm

1200 1400 1600 1800 

TIME, IN HOURS

2000 2200 2400

FIGURE 33. Variation with time of the relative mean concentration
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 139

4.00

3.00

2.00

y i.oo

EXPLANATION

Quartz 

0.707-1.00 mm

2.00

1.00

EXPLANATION

Quartz 

0.500-0.707 mm

2.00

1.00

EXPLANATION

Quartz 

0.350-0.500 mm

1200 1400 1600 1800 

TIME, IN HOURS

2000 2200 2400

at cross section D of the six sieve classes of quartz tracer, run 2.
140 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

0.60 i

0.40

EXPLANATION

Garnet 

0.177-0.250 mm

0.20

0.80,

0.60

EXPLANATION

Garnet 

0.125-0.177 mm

0.40

0.20

1000 1200 1400 1600 1800 

TIME, IN HOURS

2000 2200 2400

FIGURE 34. Variation with time of the relative mean concentration at cross section D of the five sieve classes of garnet tracer, run 2 (classes

3 5 on opposite page).
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, rLAT-BED CONDITION 141

0.40

l<o 0.20 -;

0.20

< 0.20

EXPLANATION

Garnet 

0.250-0.350 mm

1200 1400 1600 1800 

TIME, IN HOURS

2OOO 2200 2400

The mean time, or t values, were calculated from 

( X tC(t)dt

T JO

C(t)dt

= 

Jo

= tCr (t)dt, (20)

where C is the mean concentration at cross section D as 

calculated from equation 15. The times, t and ?, are relative to the time at which the experiment was begun.

Mean time values were calculated from equation 20 for 

each sieve class and specific gravity of tracer material. 

The integrals were evaluated by measuring the areas 

under the appropriate curves with a planimeter. For the 

purpose of standardizing the calculations, the C(t) as a 

function of t curves for the different sieve classes and 

specific gravities were truncated at the time at which the 

mean concentration for a particular sieve class decreased 

to 1.0 percent of the maximum mean concentration for 

that sieve class. The initial sharp peaks in the garnet and 

monazite curves (figs. 34 and 35) were disregarded in the 

determination of the maximum mean concentrations. For 

the quartz tracer^ thsse times occurred within the duration of both of the experimental runs. For the garnet and 

monazite tracers used in run 2, an extrapolation was 

required. The maximum extrapolation required was 2.0 

hours for the 0.177- to 0.250-mm sieve class of garnet. The 

mean extrapolation time for the five sieve classes of garnet 

and the four sieve classes of monazite was 0.67 hour, 

or about 5 percent of the total time interval of run 2.

The calculation of the centroid velocities from equation 

19 requires some justification because this equation 

assumes that the fluorescent tracer materials were deposited on the bed of the channel at the injection point. 

However, because the fluorescent tracer materials were 

dumped at the water surface, they were carried some 

distance downstream by the flow before deposition on 

the channel bed. Loyacano (1967) found in some qualitative experiments that the initial fall velocity of groups 

of particles was four to seven times larger than the 

fall velocity of the single particles because of the tendency of the particles to fall as a group. Because of the 

very large injection rates used in the fluorescent tracer 

experiments and because of the relatively shallow 

depth of flow in the study reach (less than 3 feet), it was 

assumed on the basis of Loyacano's work that the tracer
142 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

0.20 r

EXPLANATION

Monazite 

0.350-0.500 mm

0.20

0.20

EXPLANATION

Monazite 

0.177-0.250 mm

0.60 r

0.40

0.20

EXPLANATION

Monazite 

0.125-0.177 mm

1000 1200 1400 1600 1800 

TIME, IN HOURS

2000 2200 2400

FIGURE 35. Variation with time of the relative mean concentration at cross section D of the four sieve classes of monazite tracer, run 2.
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 143

materials fell rapidly to the bed surface. Hence, the 

distance traveled by the fluorescent material before 

deposition on the bed surface was assumed negligible 

with respect to the 700 feet between the injection point 

and cross section D.

The centroid velocities calculated from equation 19 

and the t, A£, and the £ 0 . 0 i values are summarized in tables 

14 and 15 for runs 1 and 2, respectively. The £0.oi value 

is the time interval required for the mean concentration 

at cross section D to decrease to 1.0 percent of the 

maximum mean concentration.

The centroid velocities for the various sieve classes are 

plotted as a function of median fall diameters of the sieve 

classes in figures 36 and 37 for runs 1 and 2, respectively. 

The vertical dashed lines represent the size limits of the 

sieve class used in the analysis of the samples, and the 

numbers correspond to the sieve-class numbers given 

in the tables.

TABLE 14. Summary of the t. At, to.oi, and V data, run 1

Color

Green

Yellow

Red

Sieve class

(mm)

(D

(2)

(3)

(3)

(41

(5)

(5)

(6)

(7)

0.125-0.177

0.177-0.250

0.250-0.350

0.250-0.350

0.350-0.500

0.500-0.707

0.500-0.707

0.707-1.00

> 1.00

Median fall

diameter

(mm)

0.150

.189

.231

.271

.358

.452

.539

.613

.839

fooi

(hours)

1.33

1.58

1.92

3.53

2.78

2.63

2.65

2.67

2.58

t

(hours)

0.183

.273

.320

.596

.558

.593

.565

.564

.546

A^

(hours)

0.023

.023

.023

.062

.062

.062

.096

.096

.096

V

(fps)

1.22

.778

.655

.364

.392

.366

.415

.415

.432

TABLE 15. Summary of the t. At, tn .oi, and V data, run 2

Mineral

Quartz

Garnet

Monazite

Sieve class Median fall 

(mm) diameter 

(mm)

(D

(2)

(31

(4)

(5)

(6)

(1)

(2)

(3)

(4)

(5)

(D

(2)

(31

(4|

0.125-0.177

0.177-0.250

0.250-0.350

0.350-0.500

0.500-0.707

0.707-1.00

0.125-0.177

0.177-0.250

0.250-0.350

0.350-0.500

0.500-0.707

0.125-0.177

0.177-0.250

0.250-0.350

0.350-0.500

0.152

.204

.289

.420

.541

.694

.232

.300

.405

.578

.690

.235

.305

.484

.721

(hours)

1.85

7.37

7.00

5.50

1.97

1.20

15.3

16.0

14.4

14.3

14.4

14.4

14.6

14.4

14.3

t 

(hours)

0.310

1.55

.992

.952

.521

.401

8.70

10.22

9.84

8.24

7.39

7.20

8.35

7.52

8.15

A/ 

(hours)

0.017

.017

.017

.017

.017

.017

.043

.043

.043

.043

.043

.061

.061

.061

.061

V

(fps)

0.664

.127

.199

.208

.385

.506

.0224

.0191

.0198

.0237

.0264

.0272

.0235

.0261

.0240

Curves for the quartz tracer materials of runs 1 and 2 

having the centroid velocity as a function of median fall 

diameter are similar in shape. The curves are approximately U-shaped, with the maximum velocities occurring 

fc. the smallest particles and the minimum velocities 

occurring for those particles with fall diameters approximately the same as or slightly larger than the fall diameters of the natural bed-material particles comprising

the largest part of the bed-material transport. The 

maximum centroid velocities observed were for the 0.125- 

to 0.177-mm sieve class of quartz tracer, and these were 

approximately 26 and 16 percent of the mean water 

velocity in runs 1 and 2, respectively.

In run 1, the centroid velocities for the large particles 

were only slightly larger than the minimum centroid 

velocity. In run 2, however, the centroid velocity for the 

0.707- to 1.00-mm sieve class was about four times larger 

than the minimum centroid velocity and was about 76 

percent of the centroid velocity for the 0.125- to 0.177-mm 

sieve class of quartz tracer. This large increase of the 

centroid velocity with fall diameter for the large particles 

in run 2 can be explained by the fact that the large 

particles project into the flow more than the small particles. Other investigators (Chang, 1939; Sundborg, 1956; 

Meland and Norrman, 1966) have noted and discussed 

the tendency for the large particles to move with the 

largest velocity. It is expected that the particle velocity 

for a specific flow condition will continue to increase with 

particle fall diameter until the effect of increasing surface exposed to the flow, proportional to the square of the 

particle diameter, is exceeded by the effect of increasing 

mass, proportional to the cube of the diameter. Above 

this size, the velocity of the particle will decrease with 

increasing diameter.

i.O

Q

8 1.0

LU

C/3

g 0.8

0.

H

LU

H! 0.6

- 0.5 

Q 0.4

O

(-

LU °' 3

0

LU

I 

1-

0 0.2

Io

0

-1

LU

>

n.i

-

-

-

-

(1)

\\

« (D *

 i 

V

(2^S. Nta) c*\

 Size-"- 

limit of 

indicated 

sieve 

class

~- (2) 

EXPLANATIOf

Quartz

 Green

A Yellow

 Red

i

 i 

(

(3) *^"^^^

 (3) -

si

1 

4) 

k^(5)

 (4) *

i

 i

(5) (6)

 -

« (5) *

i

i

-

-

-

(7)

 (6) - 

-

i

0.1 0.2 0.3 0.4 0.5 0.6 0.8 

MEDIAN FALL DIAMETER, IN MILLIMETERS

1.0

FIGURE 36. Variation with fall diameter of the velocities of the centroids of the tracer masses, run 1. Numbers in parentheses are sieve 

class numbers; see tables 7 and 8.
144 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

The observation that the centroid velocities for the 

large red quartz particles in run 1 were only slightly 

larger than the minimum centroid velocity can be explained by the fact that these particles moved toward the 

right bank and some were trapped temporarily. This 

would cause the centroid velocities of the red quartz 

particles to be less than if these particles had moved 

down the center of the channel without interference.

0.80

EXPLANATION

 Quartz 

A Garnet

 Monazite

0.01

0.1 0.2 0.3 0.4 0.5 0.6 0.8 

MEDIAN FALL DIAMETER, IN MILLIMETERS

FIGURE 37. Variation with fall diameter of the velocities of the centroids of the tracer masses, run 2. Numbers in parentheses are sieve 

class numbers; see tables 7 and 8.

Centroid velocities for the small particles were large 

in both runs because these particles apparently spent a 

greater proportion of the time moving as suspended material than did the natural bed-material particles composing the largest part of the bed-material transport. 

It is expected that the centroid velocity will continue to

increase for decreasing particle fall diameter until the 

silt and clay size ranges are reached where the particles 

move with the mean water velocity.

The curve of centroid velocity versus fall diameter for 

the garnet was also U-shaped, but that of the monazite 

showed little relation to fall diameter. Also, the centroid 

velocities were about an order of magnitude less than the 

centroid velocities for the quartz. The concept of hydraulic equivalence (Rubey, 1933, Rittenhouse, 1943) 

suggests that particles having equal fall diameters tend to 

be of equivalent hydraulic value. The centroid velocities 

in figure 37 are plotted as a function of median fall diameter; hence, it would appear that the concept of hydraulic 

equivalence was not applicable to the comparison of 

the centroid velocities of quartz, garnet, and monazite 

for the high-velocity flat-bed condition.

However, if the difference between the behavior of 

the quartz particles and the heavy-mineral particles is 

attributed to the specific gravity effect, then the question 

may be asked as to why the denser, monazite particles 

moved about 20 percent faster than the garnet particles 

for the most of the fall-diameter range. The monazite was 

about 17 percent denser than the garnet, and the garnet 

was about 54 percent denser than the quartz. Because 

the difference in specific gravity between the garnet and 

monazite was small, the apparent anomaly may have 

been caused by shape differences.

None of the lead tracer particles were found in any 

of the "dustpan" samples at cross section D. The last 

set of samples was obtained 22 hours after injection; 

hence, the centroid velocity of the lead particles was 

something less than 700/22X3600, or 0.0088 foot per 

second. However, the centroid of the 0.707- to 1.00-mm 

sieve class of quartz tracer particles, which has a median 

fall diameter only slightly smaller than the median 

fall diameter of the 0.177- to 0.250-mm sieve class of lead 

(see table 1), moved through cross section D about 

0.4 hour after injection of the fluorescent materials. 

This corresponds to a centroid velocity of 0.506 foot 

per second. As before, it would appear that the concept of hydraulic equivalence was not applicable to 

the comparison of the centroid velocities of quartz and 

lead-tracer particles of comparable fall diameter for the 

high-velocity flat-bed condition.

Approximately fifty 6-inch core samples were obtained 

over about the center third of the channel at cross sections A, B, C, and 15, 40, and 65 feet downstream from 

the injection point. These samples were obtained about 

21.5 hours after the injection of the fluorescent tracer 

materials in run 2 and were divided into two 3-inch segments. These samples, both the top and bottom segments, 

contained essentially no quartz tracer particles. Two of 

the top segments contained an appreciable number of
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 145

garnet and monazite particles., and six top segments 

contained a few garnet and monazite particles. All the 

other segments of the core samples contained very few 

fluorescent particles. These results indicate that there 

was no general tendency for either the quartz or the 

heavy-mineral tracer particles to be exchanged with that 

part of the bed material not in transport. This is in agreement with the observation that the bed surface below 

the moving layer of sediment for the flat-bed condition 

of alluvial-channel flow is very firm.

LONGITUDINAL-DISPERSION CHARACTERISTICS OF THE 

TRACER MATERIALS

The longitudinal-dispersion coefficient, Kx , can be 

calculated from the rate of change of the variance of the 

concentration as a function of time curve with distance 

downstream (Sayre and Chang, 1968). In the fluorescent 

tracer experiments, meaningful data were obtained only 

at cross section D because of the rapid rate at which the 

tracer material moved through the study reach. Therefore, a true longitudinal-dispersion coefficient could not 

be calculated. However, the variance, erf, of the mean 

concentration as a function of time curves for the different sieve classes and specific gravities at cross section D 

was used as a measure of the longitudinal dispersion 

between the injection point and cross section D. For a 

valid comparison, this procedure assumes that the initial 

period required for the establishment of the linear variation of the variance with distance is the same for all sieve 

classes and specific gravities of tracer minerals.

The variance, of, is given by

0-7 =j;t2C(t)dt

 -t 2 . (21)

where t is given by equation 20. The integrals were 

evaluated by measuring the areas under the appropriate 

curves with a planimeter. As in the t calculations, the 

t 2C versus t curves were truncated at the times at which 

the mean concentration decreased to 1.0 percent of the 

maximum mean concentration. These time values, designated £0.01, are summarized in tables 14 and 15 for runs 

1 and 2, respectively.

The variances of the curves of mean concentration at 

cross section D versus time were calculated from equation 21, and the values for the various sieve classes and 

specific gravities are summarized in tables 16 and 17 

for runs 1 and 2, respectively. The variances are plotted 

as a function of the median fall diameters of the sieve 

classes in figures 38 and 39 for runs 1 and 2, respectively. 

The vertical dashed lines represent the size limits of the

sieve classes, and the numbers correspond to the sieveclass numbers given in the tables.

TABLE 16. Summary of the crj values of the mean concentration at 

cross section D as a function of time data, run 1

Color

Green

Yellow

Red

Si

(D

(2)

(3)

(3)'

(4)

(5)

(5)

(6)

(7)

ieve class

0.125-0.177

0.177-0.250

0.250-0.350

0.250-0.350

0.350-0.500

0.500-0.707

0.500-0.707

0.707-1.00

>1.00

fT-t (hours-)

0.0358

.0455

.0810

.356

.200

.165

.149

.170

.153

TABLE 17. Summary of the 07 values of the mean concentration at 

cross section D as a function of time data, run 2

Mineral

Quartz

Garnet

Monazite

Si

(1)

(2)

(3)

(4)

(5)

(6)

(D

(2)

(3)

(4)

(5)

(1)

(2)

(3)

(4)

ieve class 

(mm)

0.125-0.177

0.177-0.250

0.250-0.350

0.350-0.500

0.500-0.707

0.707-1.00

0.125-0.177

0.177-0.250

0.250-0.350

0.350-0.500

0.500-0.707

0.125-0.177

0.177-0.250

0.250-0.350

0.350-0.500

<rj (hours 2 )

0.120

3.35

2.23

1.70

.0762

.0423

12.9

11.6

8.25

7.73

8.86

13.0

10.3

11.4

13.3

The variation of the variances with fall diameter should 

be approximately the inverse of the variation of the centroid velocities with fall diameter. This behavior was expected because the more rapidly a slug of tracer material 

of a specific size moves through the study reach, the less 

opportunity that slug has for dispersing in the longitudinal 

direction. Figures 38 and 39 show that the variation of the 

variance, of, with fall diameter for the quartz tracer materials in both runs was approximately the inverse of the 

variation of the centroid velocities with fall diameter presented in figures 36 and 37.

The maximum of values occurred for particles with 

diameters approximately the same as or slightly larger 

than the diameters of the particles comprising the bulk of 

the natural bed material in transport. Minimum erf values 

occurred for the largest and smallest particles within the 

fall-diameter range considered. The failure of the cr 2t 

values for the 0.707- to 1.00-mm and > 1.00-mm sieve 

classes of red quartz to continue to decrease with increasing particle diameter (fig. 38) may be explained by the 

same reasoning applied to the failure of the centroid
146 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

velocities for these sieve classes to increase with fall 

diameter. Both the displacement of the red quartz particles toward the region of small velocities near the bank 

and the temporary entrapment of some of the red particles along the bank would tend to increase the variance 

over that expected, had the red quartz particles moved 

down the center of the channel.

One minor discrepancy in the inverse relation between 

the of as a function of fall diameter and Fas a function of 

fall-diameter curves for the quartz tracer particles in run 

2 is that the of values for the 0.500- to 0.707-mm and 

0.707- to 1.00-mm sieve classes of the quartz tracer were 

less than erf for the 0.125- to 0.177-mm sieve class of 

quartz. The centroid velocity of the 0.125- to 0.177-mm 

sieve class of quartz exceeded the centroid velocities for 

the 0.500- to 0.707-mm and 0.707- to 1.00-mm sieve classes 

of quartz, however.

The variances of the garnet and monazite varied with 

fall diameter in the same manner as the centroid velocities, as a comparison of figures 37 and 39 shows. In each

0.40

CO

o:

D 

O 

I 0.30

0.20

o.io

0.08

UJ

z 0.06 

O

H 0.05 

<

a:

H

0.04

0.03

0.02

0.011 

0.1

I

l« Size-H

] limit of

indicated

sieve

class

(2)

(3P I r

EXPLANATION

Quartz

 Green

A Yellow

 Red

0.2 0.3 0.4 0.5 0.6 0.8 

MEDIAN FALL DIAMETER, IN MILLIMETERS

1.0

FIGURE 38. Variation with fall diameter of the variances of the mean 

concentration as a function of time curves at cross section D, run 1. 

Numbers in parentheses are sieve class numbers; see tables 7 and 8.

instance, however, the variation of either of or V with 

fall diameter was much less for the garnet and monazite 

than for the quartz. The centroid velocity and the variance, 

of, for the quartz tracer used in run 2 varied with fall 

diameter about 420 and 780 percent, respectively, from 

the minimum to the maximum value. The centroid velocity and the variance for the garnet varied with fall diameter about 38 and 67 percent, respectively, and these

20.0

0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 

MEDIAN FALL DIAMETER, IN MILLIMETERS

FIGURE 39. Variation with fall diameter of the variances 

of the mean concentration as a function of time curves 

at cross section D, run 2. Numbers in parentheses are 

sieve class numbers; see tables 7 and 8.
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 147

quantities for the monazite varied with fall diameter 16 

and 33 percent, respectively, from the minimum value 

to the maximum value. These results and the fact that the 

cr'f values for garnet and monazite were about an order 

of magnitude larger than 07 for quartz particles of comparable fall diameter indicate a distinct difference in 

behavior between the quartz particles and the garnet 

and monazite particles. The differences in longitudinaldispersion characteristics indicated in figure 39 are seen 

clearly in the relative mean concentration as a function 

of time plots, figures 33, 34, and 35. One additional 

difference between figures 37 and 39 is that the o-j? values 

for garnet generally fall between the values for quartz 

and monazite, whereas the lvalues for monazite generally 

fall between the V values for quartz and garnet. This 

difference, however, probably is not significant because 

of the small differences between these quantities for the 

garnet and monazite. It is concluded that neither fall 

diameter nor fall diameter and specific gravity are 

sufficient to explain the differences in cr'f for the quartz, 

garnet, and monazite tracers in run 2.

EVALUATION OF THE FLUORESCENT 

TRACER TECHNIQUE

With the experience gained in the planning and execution of the two experiments and the analysis of the results, 

it is possible to evaluate the application of the fluorescent 

tracer technique to studies of sediment movement. Four 

basic steps are involved in the fluorescent tracer technique. These are the preparation of the tracer materials, the injection of the tracer materials into the study 

reach, the sampling of the tracer masses as they move 

through the study reach, and the analysis of the samples.

The first step in the preparation of the tracer materials 

is to select the material to be coated with the fluorescent 

dye. At least three different sources of material may be 

used. The most obvious source is sediment taken from 

the study reach. This material has the advantage of relatively low cost, but it may have some significant disadvantages. The bed material can range widely in shape and 

specific gravity for a given sieve size. The use of such material makes it difficult, or impossible, to determine the 

effect of size alone on sediment velocity or dispersion, if 

considerable quantities of mica or heavy minerals are 

present. If one could collect and dye a sample representing the sieve-size distribution of the total sand in 

transport and then return it to the stream before the size 

distribution changed, then such a tracer should be excellent for determining sediment-transport rate. However, 

except under ideal circumstances, this approach is not 

feasible. Instead, a sample of bed material would normally be used. Such bed material does not truly represent the size, shape, or specific gravity distribution of the

sediment in transport. To some extent it represents a lag 

deposit. The greater the difference in characteristics of 

bed sediment and sediment in transport, the greater will 

be the error in estimating the sediment-transport rate.

A second source is material from a different stream. 

However, such material, unless it closely matches the 

sediment in the stream under study, is useful mainly for 

reconnaissance work. Its usefulness in determining the 

effect of size, shape, and specific gravity on transport will 

depend on how uniform these characteristics are in a particular sieve size. In this study, coated material from another stream was used for reconnaissance in run 1 

because it was available from a previous investigation.

A third source, and probably the best for many research 

studies, is a material with little variation in shape or 

specific gravity. Thus, one can learn how a material of 

known characteristics moves in a stream under particular 

flow conditions. Ottawa sand and other similar products 

are composed of clean well-rounded quartz sand with 

very few heavy minerals. Such sand is commercially 

available in large quantities at very reasonable price. In 

fact, total cost to buy the sand and dye can be less than 

lOc per pound. Because 1 pound of the fluorescent sand 

can "tag" 5,000 to 10,000 pounds of moving stream sand, 

the cost of tracer is a negligible part of the expense of a 

tracer experiment.

The quartz sand used in the second, and main, run of 

this study was Ottawa silica sand of uniform shape and 

specific gravity.

The problem of obtaining uniform material of specific 

gravity and (or) shape greatly different from quartz, but 

yet resembling the type of material that might be found in 

a stream, is a major one. Although heavy-mineral concentrates and lead shot were used in this experiment, synthetic materials whose characteristics can be closely 

controlled probably should be used.

The method of applying the fluorescent dye to the particles developed by Kennedy and Kouba (1970), and used 

in the present study with slight modification, produced a 

good, abrasion-resistant fluorescent coating. There was 

apparently no difficulty with loss of the dye coating in the 

stream; however, sieving of the samples resulted in some 

chips of dye from large particles that limited the analysis 

of the samples to particles larger than 0.125 mm.

The resultant coating was nonwetting, and this characteristic complicated the injection process. A detergent 

had to be added to the fluorescent material or the fluorescent material had to be injected as a slurry to which detergent had been added. These precautions were necessary to insure that the fluorescent particles did not clump 

together because of the surface effects of the coating. 

Further work toward the development of an abrasionresistant fluorescent coating that is wettable is necessary.
148 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

On the other hand, there is need occasionally for fluorescent coatings that will decompose after a specific 

time interval so that a stream or river is not contaminated 

permanently with the fluorescent tracer particles. Previous work on this type of coating as well as on other types 

of permanent coatings has been summarized by Ingle 

(1966), and Teleki (1966) has presented a detailed review 

of the various types of fluorescent dyes and coating processes. Whatever the type of coating, however, it must be 

remembered that the primary requirement of any coating is that the tagged particles of a specific size behave 

identically with the natural sediment particles of the 

same size. If a range of particle sizes is considered, then 

the size distribution within a particular size range must 

approximate the distribution of natural sediment particles in this size range that are in transport. This does not 

necessarily mean, of course, that sediment from the 

stream must be the material used in the preparation of 

the tracers.

The injection of the fluorescent materials into the study 

reach must satisfy the following conditions:

1. The location of the injection point relative to the 

sampling point must be known accurately.

2. If an instantaneous-slug injection is used, the time 

required for the injection process must be negligible 

compared with the time scale of the sediment motion.

3. If an intermittent-slug injection is used as an approximation of the true continuous injection process, the 

time interval between injections should be negligible compared with the time scale of the sediment 

motion.

4. The injection process should disturb the natural sediment-transport process at the injection point as 

little as possible.

Some difficulty was experienced with the injection 

tube used in the present study, but it is believed that the 

procedure of simply dumping the fluorescent material 

into the channel at as high a rate as possible reasonably 

approximated an instantaneous point source of fluorescent material. However, because the tracer particles 

did move so rapidly for the high-velocity flat-bed condition, several advantages would have been gained by the 

use of a continuous point-source injection. For example, 

a better evaluation of the lateral-dispersion characteristics of the tracers would have been possible, and the 

calculation of the sediment-transport rates would have 

been simplified. Similarly the possibility of failing to 

sample a fast-moving slug of tracer material would have 

been eliminated.

Various types of injection procedures have been discussed in the literature, and these procedures range 

from water-soluble containers discussed by De Vries 

(1966) and Lean and Crickmore (1963) to the elaborate 

constant-injection apparatus that was used for a period

of 6 weeks by Crickmore (1967). However, further work 

is needed in the development of injection processes.

The type of sampling required in a fluorescent tracer 

experiment in general depends upon the bed configuration in the study reach. If a dune bed exists, then core 

samples are necessary to define the spatial distribution 

of fluorescent material within the study reach. In the 

present study, the high-velocity flat-bed condition 

existed. Samples of the bed material moving near the 

bed surface were desired because large samples could 

be obtained rapidly at this location and because these 

samples should contain some of the large bed-material 

particles in transport. The "dustpan" sampler described 

previously and used in the present study appeared to be 

an acceptable device for obtaining these samples.

Analysis of the samples requires a determination of the 

number of fluorescent particles of each color in each 

sieve class of each sample. In the present study, the 

numbers of fluorescent particles were determined by a 

manual counting process. The manual counting process 

is a simple procedure, and only a minimum amount of 

equipment is required. Although the statistical analysis 

(C. F. Nordin, Jr., written commun., 1968) simplified 

greatly the counting process, the manual counting procedure was time consuming because the length of time 

any one individual could spend counting particles was 

limited by the tedium of the process. Automatic electronic devices for counting the number of fluorescent particles have been described by De Vries (1967) and Teleki 

(1967). An electronic counter has the obvious advantage 

of convenience and ease of sample analysis. Disadvantages are the expense and the careful calibration and 

maintenance of the instrument that are required to obtain accurate concentrations. If two or more different 

fluorescent dyes are used, care must be taken to insure 

that the spectra of the dyes are displaced sufficiently so 

the different colors can be distinguished by the instrument with the use of the proper filters.

The problem of differentiating between chips or flakes 

of dye from large particles and actual fluorescent particles 

for the small-diameter sieve classes was encountered in 

this study. Because of this problem, the smallest diameter sieve class considered was the 0.125- to 0.177-mm 

sieve class. It was impractical to attempt to distinguish 

visually between particles and chips in the 0.088- to 

).125-mm sieve class.

However, the 0.062- to 0.088-mm and 0.088- to 0.125-mm 

sieve classes often may be of importance, as they were in 

the present study because they contributed about 27 

percent of the total sediment transport of particles larger 

than 0.062 mm. A way of eliminating the problem of 

chips and flakes in these sieve classes is to use one color 

of dye specifically for each of these two sieve classes. 

After the preparation of the fluorescent materials, the ma-
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 149

terial for each sieve class should be carefully resieved to 

remove all material outside the desired sieve range. Care 

should be taken also in the preparation of the fluorescent 

materials to insure that the size distributions within each 

sieve class of material are approximately the same as the 

size distributions within that sieve class of the bed material in transport.

It is concluded that the fluorescent tracer technique is 

a simple and sensitive experimental method for studying 

the movements of groups of particles either in a natural 

channel or in a laboratory alluvial channel. However, considerable improvement in technique in each of the four 

basic steps is still necessary.

SUMMARY

A fluorescent tracer technique was applied to the study 

of the rates of transport and dispersion of sediment 

particles of various sizes and specific gravities for the 

high-velocity flat-bed condition of alluvial-channel flow. 

Two runs were completed in the Rio Grande conveyance 

channel near Bernardo, N. Mex., and the following statements summarize the knowledge gained from these two 

experiments.

1. The centroid velocity of the 0.125- to 0.177-mm sieve 

class of sand was 1.2 fps in run 1 when the mean water 

velocity was 4.66 fps and 0.66 fps in run 2 when the mean 

water velocity was 4.05 fps. Thus, the fine sand moved 

about 16 to 26 percent of the mean water velocity.

2. The centroid velocity of the quartz tracer particles 

varied with particle size. In the size range from 0.125 to 

1.0 mm, the minimum velocity occurred for a particle 

size slightly larger than the median diameter of the bed 

material (about 0.2 mm). Both the larger and the smaller 

particles moved faster. In run 1, the tendency of the 

large particles to follow the thalweg of the channel 

distorted the U-shaped velocity-diameter relation.

3. Garnet and monazite particles moved at velocities 

about an order of magnitude less than the velocities of 

quartz particles of equivalent fall diameter. Thus, the 

concept of hydraulic equivalence based on fall diameter 

is not applicable to sand-size particles under the conditions of this experiment.

4. At least two factors were important in producing 

lateral mixing of the tracer particles. These are turbulent 

fluctuations in the flow and the effect of the thalweg of 

the channel.

5. The large and heavy particles tended to folio-v the 

thalweg of the channel even though the channel was 

approximately straight and the flow lines at the surface 

appeared to follow the alinement of the channel.

6. Lateral mixing was greatest for the smallest quartz 

tracer particles and was approximately the same as that

for a water-soluble fluorescent dye. Lateral mixing decreased with increasing size of quartz tracer in run 2 

when the effect of the thalweg was minimized. The large 

particles mixed the least because they spent a greater 

proportion of the time resting on or moving along the bed 

surface than did the small particles.

7. Longitudinal mixing of the quartz tracer particles 

as related to particle size showed an approximately 

reciprocal relation to that observed for centroid velocity 

as a function of particle size; that is, the slower the sand 

moved, the greater was the longitudinal mixing.

8. The rapid rate of movement of the quartz tracers 

through the study reach made it difficult to obtain an 

accurate record of the passage of the tracer mass. Failure 

to sample the complete tracer mass will result in calculated values of the sediment-transport rate that are too 

large, as occurred in this study. A continuous injection of 

fluorescent tracer would have been preferable for the flow 

conditions of this study.

9. The fluorescent tracer technique has great potential 

as a tool for the study of movements of sediment. Further 

development of equipment and techniques is needed, 

however.

LITERATURE CITED

Chang, Y. L., 1939, Laboratory investigation of flume traction and

transportation: Am. Soc. Civil Engineers Trans., v. 104,

p.1246-1313. 

Crickmore, M. J., 1967, Measurement of sand transport in rivers with

special reference to tracer methods: Sedimentology, v. 8, no. 3,

p. 175-228. 

DeVries, M., 1966, Application of luminophores in sand transport

studies: Delft Hydraulics Lab. Pub. 39, 86 p., Delft, Netherlands. 

 1967, Photometric counter for fluorescent tracers: La Houille

Blanche, no. 7, p. 717-722.

Fischer, H. B., 1967, Transverse mixing in a sand-bed channel, in 

Geological Survey research, 1967: U.S. Geol. Survey Prof. Paper 

575-D, p. D267-D272.

Gonzalez, D. D., Scott, C. H., and Culbertson, J. K., 1969, Stagedischarge characteristics of a weir in a sand-channel stream: 

U.S. Geol. Survey Water-Supply Paper 1898-A, 29 p.

Guy, H. P., and Norman, V. W., 1970, Field methods for measurement 

of fluvial sediment: U.S. Geol. Survey Techniques Water-Resources 

Inv., Book 3, Chap. C2,59 p.

Harris. D. D., and Richardson, E. V., 1964. Stream gaging control 

structure for the Rio Grande conveyance channel near Bernardo, 

New Mexico: U.S. Geol. Survey Water-Supply Paper 1369-E, 

p. 123-154.

Hubbell, D. W., 1964, Apparatus and techniques for measuring bedload: U.S. Geol. Survey Water-Supply Paper 1748, 74 p.

Ingle, J. C., Jr., 1966, The movement of beach sand: New York, Elsevier 

Pub. Co., 221 p.

Kennedy, V. C., 1968, Fluorescent sand as a tracer of fluvial sediment 

movement: Geol. Soc. America Spec. Paper 101, p. 108-109.

Kennedy, V. C., and Kouba, D. L., 1970, Fluorescent sand as a tracer 

of fluvial sediment: U.S. Geol. Survey Prof. Paper 562-E, 13 p.

Lean, G. H., and Crickmore, M. J., 1963, Methods for measuring sand 

transport using radioactive tracers, in Symposium on the appli-
150 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

cation of radioisotopes in hydrology: Tokyo, Internal. Atomic

Energy Agency, p. 111-131. 

 1966, Dilution methods of measuring transport of sand from

a point source: Jour. Geophys. Research, v. 71, no. 24, p. 5843-5855. 

Loyacano, J. N., 1967, Fall velocity of sand particles in turbulent

flume flow: Fort Collins, Colo., Colorado State Univ. Dept. Civil

Eng. unpub. M.S. thesis. 

Meland, N., and Norrman, J. O., 1966, Transport velocities of single

particles in bed-load motion: Geog. Annaler, v. 48, ser. A, p.

165-182. 

Rittenhouse, G., 1943, Transportation and deposition of heavy minerals:

Geol. Sue. America Bull., v. 54, p. 1725-1780. 

Rubey, W. W., 1933, The size-distribution of heavy minerals within a

water-laid sandstone: Jour. Sed. Petrology, v. 3, no. 1, p. 3-29. 

Sayre, W. W., and Chang, F. M., 1968, A laboratory investigation of

open-channel dispersion processes for dissolved, suspended, and

floating dispersants: U.S. Geol. Survey Prof. Paper 433-E, 71 p.

Sundborg, Ake, 1956, The river Klaralven a study of fluvial processes:

Geog. Annaler, v. 38, p. 127-316. 

Teleki, P. G., 1966, Fluorescent sand tracers: Jour. Sed. Petrology, v. 36,

no. 2, p. 468-485.

 1967, Automatic analysis of tracer sand: Jour. Sed. Petrology, 

v. 37, no. 3, p. 749-759.

U.S. Inter-Agency Committee on Water Resources, 1941, Laboratory 

investigations of suspended sediment samplers, in A study of methods used in measurement and analysis of sediment loads in streams: 

Washington, U.S. Govt. Printing Office, Rept. 5, 99 p.

 1957a, The development and calibration of the visual-accumulation tube, in A study of methods used in measurement and analysis 

of sediment loads in streams: Washington, U.S. Govt. Printing 

Office, Rept. 11, 109 p.

 1957b, Some fundamentals of particle size analysis, in A study of 

methods used in measurement and analysis of sediment loads in 

streams: Washington, U.S. Govt. Printing Office, Rept. 12, 55 p.
APPENDIXES
152 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

APPENDIX A-DISCUSSION OF THE WASHING EFFECT

Because of the flow through the "dustpan" sampler during the collection of the sample, some of the fines may 

have been preferentially washed from the sample. This 

effect is not of concern if the tracer particles of a specific 

sieve diameter behave exactly as nontagged particles of 

the same diameter, as is assumed to be true for the quartz 

tracer particles. For the garnet and monazite, however, 

the natural bed material in a specific sieve class would be 

of a smaller median fall diameter than that of the garnet 

or monazite in the same sieve class because of the specific 

gravity difference. Thus, if the washing effect were related to fall diameter, the concentrations of the garnet and 

monazite would be affected. The purpose of this appendix 

is to discuss briefly some observations concerning the 

washing effect. These observations are based primarily on 

the size distributions of various types of samples collected 

in runs 1 and 2.

The median diameter, cfeo, and the gradation, o% for the 

size distributions of various types of samples obtained in 

runs 1 and 2 are presented in table 18. The median diameter, c4o, is defined as the diameter for which 50 percent

TABLE 18. Comparison of the median diameters and the gradations 

of the size distributions of selected "dustpan," core, and depthintegrated samples

Type of 

sample

Do......................

Do......................

Do......................

Do......................

Do......................

Do......................

Core bottom 3 in .........

Run

. 2

. 2

7

7

. 2

. 2 . 

7

. 2 .

Composite over channel 

50 feet upstream of D. 

3 Dec. 15.

Time

1326 

1015 

1542 

1604

1655 

1701 

1638 

1552

1620 

1605 

1623 

1634

 '0830 

. .do 3 .

3 0815 

.. .do 3 . . 

:> 0845 

...do 3 .

width.

Method 

of 

analysis

Sieve 

.....do..... 

VA tube

Sieve 

.....do......

.....do......

....do...... 

.....do......

.....do......

.....do......

.....do......

.....do...... 

....do...... 

.....do......

.....do......

Cross 

section

Weir 

'.'.'."do.'.'.""

B

....do......

....do......

DD 

....do......

.....do......

4

....do......

B

.....do...... 

C 

....do.......

Lateral position 

(feet from 

right bank)

C) 

C) (') 

C)

35 

35 

35 

35

37 

36 

36 

36

36 

36 

35 

35 

35 

35

rfw 

(mm)

0.168 

.164 

.176 

.170

.185 

.251 

.245 

.258

.172 

.270 

.280 

.283

.193 

.201 

.208 

.202 

.206 

.184

(7

i.60 

1.57 

1.54 

1.48

1.46 

1.28 

1.27 

1.27

1.45 

1.33 

1.34 

1.36

1.44 

1.46 

1.38 

1.52 

1.47 

1.51

of the sediment by weight is finer. The gradation, cr, is defined as 1/2(d84/d5Q + d5 o/di6), where d$4 and d^ are, respectively, the diameters for which 84 and 16 percent of 

the sediment by weight are finer.

At the centerline of cross section B, the median sieve 

diameter of a 6-inch core sample was 0.185 mm and the

gradation, o% was 1.46. The mean median diameter of 

three "dustpan" samples obtained at the same point at 

about the same time was 0.251 mm, and the mean gradation was 1.27. Similar results were obtained at cross section D. A comparison of the median diameters of the 

"dustpan" samples with the median diameters of the 

depth-integrated samples and the top and bottom 3-inch 

segments of the core samples showed that the median 

diameters of the "dustpan" samples were about 25 to 40 

percent larger than the median diameters of the other 

samples. Also the gradations of the "dustpan" samples 

were less than the gradations of the other samples, indicating more uniform size distributions. These observations would be expected if some of the fine material had 

been washed from the "dustpan" samples.

However, other factors could contribute to the observation that the "dustpan" samples contained coarser material than did the other types of samples. As was discussed previously, it was found in the fluorescent tracer 

experiments that particles larger than the median size 

of material in the bed moved faster than the median-size 

particles did. Thus, the material in the "dustpan" would 

tend to become enriched with the larger particles. Also, 

the fact that the "dustpan" samples were obtained on the 

bed surface emphasized the coarser material.

The results presented in table 18 show that the median 

diameters and gradations for "dustpan" samples obtained 

at different times at the same position are essentially 

identical. However, there is a slight difference between 

the results at cross sections B and D, Because the 

calculations, described previously, of the quantities V, t, 

erf, f, and of involve ratios of concentration integrals, 

the effect of the washing depends on how much the washing varies with time and position at cross section D.

The die, <4o, t/84 , and cr values for sieve-size distributions for "dustpan" samples obtained at cross section D 

at lateral positions of 18, 30, 42, and 54 feet for times 

near the beginning, the middle, and the end of run 2 are 

tabulated in table 19 to show the variation of the size 

distributions with time and position.

The results presented in table 19 show that di& varies 

little with either time or position, fl?50 shows increased 

variation, and d$4 shows the greatest variation with time 

and position. The mean values of d$4 and cr for cross section D vary little with time; however, these quantities at 

a specific position do vary appreciably with time. Also, 

the d»4 values for the sampling positions in the right-hand
part of the channel (2= 18 and 2 = 30) are, with one exception, larger than the c?84 values for 2 = 42 and 2=54. 

This means that the samples from the right-hand part of 

the channel contained more coarse material than the 

samples from the left-hand part of the channel. This observation is in agreement, as was discussed previously, 

with the observed behavior of the large quartz tracer 

particles.

To summarize this discussion of the washing effect, the 

results in table 18 show that the median diameters of the 

"dustpan" samples are larger than the median diameters 

of other types of samples. This could be the result of 

washing of the fines from the "dustpan" sampler or the 

several factors that tend to increase the numbers of large 

particles in the "dustpan" samples. The results in table 19 

suggest that if washing of the fines is occurring, then the 

effect is essentially uniform with respect to time and position at cross section D.

T TRACER PARTICLES, FLAT-BED CONDITION

TABLE 19. Comparison of the die,

Approximate 

time

1015

1700

2400

"dustpan" samples at

Particle 

diameter 

z=18

da 0.225

d50 .311

dM .424

a 1.37

dw .199

d50 .281

dM .450

o- 1.50

dw .212

d-M .289

d84 .393

o- 1.36

dso, d»4, and <j

cross section D,

153

values for selected

run 2

Diameter (mm) or gradation at

z = 30

0.214

.300

.441

1.44

.213

.307

.467

1.48

.223

.329

.498

1.50

z = 42

0.210

.291

.407

1.39

.190

.253

.327

1.31

.201

.262

.323

1.26

z = 54

0.220

.283

.352

1.26

.223

.304

.418

1.36

.240

.323

.422

1.33

Mean

0.217

.296

.406

1.36

.206

.286

.416

1.41

.219

.301

.409

1.36

Mean .212 .217 .200 .228

.294 .312 .269 .303

.422 .469 .352 .397

1.41 1.47 1.32 1.32

APPENDIX B-DETERMINATION OF THE WEIGHTING FACTORS

The weighting factors, w(z), defined by equation 9 

were determined from a set of depth-integrated samples 

obtained at the weir. A set of samples obtained near the 

beginning of each run was used in the determination of 

the w(z) values because most of the quartz tracer moved 

through the measurement section during the early part of 

each run. Both the water discharge and the sediment concentration at each vertical were necessary in the computation of the weighting factors. The procedure was as 

follows.

The sediment concentration, C*(2), for 5-foot intervals 

from 2=5 feet to 2=70 feet was determined from the 

depth-integrated samples. The asterisk is added to differentiate the standard sediment concentration, expressed 

as milligrams of sediment per liter of water-sediment 

mixture, from the fluorescent tracer concentration. The 

sampling transit rate was relatively uniform at all verticals; therefore, the distribution of water weights in the 

samples across the weir was the same as the distribution 

of water discharge across the weir. The water-discharge 

distribution was represented by Tz where

__ net weight at vertical 2 

sum of the net weights (B-l)

The weight of the sand was not subtracted from the net 

weights of the depth-integrated samples because the 

sand weight was less than 0.5 percent of the total weight at 

each vertical.

The incremental water discharge at each vertical, 

q(z), was calculated from

q(z) = TzQ, (B-2)

where Q is the measured total water discharge.

The incremental sediment-transport rate, q K (z], was 

calculated from

where y is the specific weight of the water-sediment 

mixture. The mean unit sediment-transport rate, qs (z), 

was obtained from

 

q(z)C*(z) ~~~ (B"4)

where 14 is the total number of verticals at 5-foot intervals between 2 = 5 feet and 2 = 70 feet. The weighting 

factor, w(z), is given by

w(z} _, ~ = S "

y

14 q(*)C*(z)

(B-5)
154 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Two additional assumptions were necessary in the application of the weighting factors obtained from equation 

B 5 to data obtained at cross section D. First, it was 

assumed that the variation of the weighting factor with 

lateral position was the same at cross section D as at the 

weir; second, it was assumed that the weighting factor 

at a given lateral position applied to all size classes of 

material. The shift of the large particles toward the right 

bank suggests that the second assumption was not exactly 

true for all sizes; however, the contribution of the large 

sizes to the total sediment-transport rate was insignificant. 

The weighting factors obtained from the depth-integrated samples for runs 1 and 2 are presented in figure 

40. The distribution of the weighting factors across the 

channel was similar for the two runs.

3.00

0 10 20 30 40 50 60 

DISTANCE FROM RIGHT BANK (z), IN FEET

Fl(,URE 40. Variation with lateral position of the sediment-transport 

weijihtin-!; factors, run« 1 and 2.

APPENDIX C-CALCULATION OF THE SEDIMENT-TRANSPORT RATES FROM THE DEPTHINTEGRATED SAMPLES AT THE WEIR

Because the depth-integrated samples from the weir 

were small, the samples generally were not sieved into 

size classes; and because these samples were not sieved, 

only the total number of fluorescent particles of each 

color was obtained for each sample. Thus, two assumptions were necessary to permit the calculation of the 

sediment-transport rates from the numbers of fluorescent particles in the depth-integrated samples. These assumptions and the development of the equation for the 

calculation of the sediment-transport rate are discussed 

in the following paragraphs.

First, it was assumed that the fluorescent particles 

were sampled at the weir in the same proportion at which 

the particles were injected. For example, in run 1 the number of green quartz particles injected was 23.0 X 108 , 

27.9 X108 , and 12.0 X 108 for the 0.125- to 0.177-mm, 

0.177- to 0.250-mm, and 0.250- to 0.350-mm sieve classes, 

respectively. Therefore, it was assumed that 36.6 percent 

of the green particles in any sample were from the 0.125- 

to 0.177-mm sieve class, 44.3 percent were from the 0.177- 

to 0.250-mm sieve class, and 19.1 percent were from the 

0.250- to 0.350-mm sieve class. This assumption should be 

valid if all of the sediment is suspended by the weir and if 

the depth-integrated sampler functions properly; that is, 

each size of sediment is sampled in direct proportion to 

the amount of that size in transport. A problem exists with 

the fluorescent tracers, however, because the instantaneous type of injection was used. The fastest-moving particles would be sampled first, and the slowest would be

sampled last. This problem was not too great in run 1, 

where, as was discussed previously, the variation of centroid velocity for the sieve classes within a specific color of 

tracer was not large. In run 2, however, quartz particles of 

all sizes were coated one color, and, as was discussed previously, the fastest moving particles were the largest and 

the smallest particles. Thus, it is expected that the quartz 

tracer particles sampled first were predominately the 

large and the small particles and that those sampled last 

were the medium-sized quartz tracer particles. As a result, some deviations from this assumption might occur in 

run 2.

Second, it was assumed that the sieve-size distribution 

of the depth-integrated samples at the weir did not change 

with time. If this assumption is valid, then size distributions determined for one sample in each run could be 

used for all of the depth-integrated samples. Figure 41 

shows the sieve-size distributions of two depth-integrated 

samples, one from each run, obtained at the weir; and 

figure 42 shows the visual-accumulation-tube size distributions of two other depth-integrated samples, one from 

each run, obtained at the weir. The sieve-size distributions 

of the two depth-integrated samples presented in figure 41 

are essentially identical, even though the time interval 

between the samples was about 21 hours. Also, the visualaccumulation-tube size distributions presented in figure 

42 are similar for two other samples obtained about 24 

hours apart. These distributions differ slightly from the 

sieve-size distributions, particularly at the large diameter
TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 155

end of the distributions. This difference was not considered significant, however. On the basis of these size 

distributions, therefore, the second assumption was considered to be valid. The sieve-size distributions presented 

in figure 41 were used in the calculations in preference to 

the visual-accumulation-tube distributions presented in 

figure 42 because the size distributions of the fluorescent 

tracer materials were determined by sieve analysis.

If the sediment-transport rate is assumed to be independent of time, then the equation for the calculation of 

the sediment-transport rate from the fluorescent tracer 

concentrations of the depth-integrated samples has the 

form

EXPLANATION

Sample time

(hr) 

1 1326

1015

0.2 0.3 0.4 0.6 

DIAMETER, IN MILLIMETERS

1.0

FIGURE 41. Sieve-size distributions of two depth-integrated samples 

obtained at the weir.

0.1 0.2 0.3 0.4 0.5 

DIAMETER, IN MILLIMETERS

FIGURE 42. Visual-accumulation-tube size distributions 

of two depth-integrated samples obtained at the weir.

tracer injected, W, has been replaced by N, the number 

of fluorescent particles of a specific color injected, 

second, the concentration, C, as grams of fluorescent 

material per gram of sediment, has been replaced by 

C', the concentration as number of fluorescent particles 

per gram of sediment; third, the integration across the 

channel width has been accomplished by the averaging 

effect of compositing a set of samples taken across the 

weir; hence, the transport rate, Qs, is the total transport 

rate for the cross section, and the concentration is a mean 

concentration, indicated by the overbar, for the cross 

section.

If n(t] is the total number of fluorescent particles of a 

specific color in a sample at time t and if W(t} is the
156 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

total weight of sediment in the sample, then A', the integral in equation C 1, can be written

i'=f~i£r(

Jo W(t)

dt. (C-2)

With the two assumptions discussed previously, 

equation C 2 can be written for a specific size class i, 

or

A'; = dt, (C-3)

where p\ is the fraction of the total weight of sediment in 

the sample that is in size class i, and NI is the total 

number of fluorescent particles of size class / of a specific color injected at the beginning of the experiment. 

The quantity Nt/N is a constant for a specific experiment, and pi is independent of time because of the 

second assumption. Therefore

A't =- n(t) dt.

>,-Jo W(t) 

By comparing equations C-4 and C-2, it follows that

(C-4)

NPi

(C-5)

If equation C 1 is written for size class i, the result is 

Ni = Q*(A't* (C-6)

f x -

i;= c;

Jo

(t)dt. (C-7)

By combining equations C~6 and C 5 and rearranging, 

it follows that

Q*i=-r- (C-8)

,T

Equation C 8 is equation 11, which was used to calculate the sediment-transport rates for the different sieve 

classes from the numbers of fluorescent particles of each 

color in the depth-integrated samples. Because of the 

two assumptions, only one integral evaluation was 

necessary for each color of tracer particle.

U. S. GOVERNMENT PRINTING OFFICE : 1971 OL - 405-770