Response of a Laboratory 

Alluvial Channel to 

Changes of Hydraulic and 

Sediment -Transport 

Variables

GEOLOGICAL SURVEY PROFESSIONAL PAPER 562-D
Response of a Laboratory 

Alluvial Channel to 

Changes of Hydraulic and 

Sediment -Transport 

Variables

By R. E. RATHBUN, H. P. GUY, and E. V. RICHARDSON

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 562-D

A comparison of the feed and recirculation 

systems of flume operation for laboratory studies 

of sediment transport and resistance to flow

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1969
UNITED STATES DEPARTMENT OF THE INTERIOR 

WALTER J. HIGKEL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

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

Washington, D.C. 20402 - Price 40 cents (paper cover)
CONTENTS

Abstract _ ________________________________________

Introduction. ______________________________________

General procedures for laboratory alluvial channel 

experiments. __ ___________________________________

Experimental apparatus and procedure._______________

Apparatus.____________________________________

Bed material.__________________________________

Procedure__ __________________________________

Comparison of the feed and recirculation systems_______

Sediment-transport rate.____--___--__---_-______

Water-surface slope.____________________________

Page

Dl

1

3

5

5

7

7

9

9

10

Page 

Comparison of the feed and recirculation systems 

Continued

Depth of flow.._____________________ Dll 

Velocity.___--____----_-______----------------_ 11

Responses of the flume to changes of the hydraulic and 

sediment-transport variables_____--------_---_-____ 13

Advantages and disadvantages of the feed and recirculation systems------------------------------------- 28

Summary.---_-------__--_------------------------- 30

Limitations and recommendations______--_____--_____ 31

Literature cited ________________________________ 31

ILLUSTRATIONS

Page

FIQTTBE 1. Schematic diagrams of the recirculation and feed systems of flume operation for alluvial channel experiments. D2 

2. Schematic diagram of the experimental flume and associated equipment used in this study.--------------- 6

3-21. Graphs showing:

3. Variation with time of several variables in run 6____________________________----__- --- 8

4. Comparison of the unit sediment-transport rate when a change is made from the recirculation system

to the feed system, runs l-ll_________________________________-_______------------------ 11

5. Comparison of the unit sediment-transport rate when a change is made from the feed system to the

recirculation system, runs 3-6 and 8-ll_----___-_____-_____----_------------------------- 12

6. Comparison of the water-surface slope for the recirculation and feed systems, runs l-ll__-----_-__- 13

7. Comparison of the mean depth of flow for the recirculation and feed systems, runs 1-11 ________ 14

8. Comparison of the mean velocity of flow for the recirculation and feed systems, runs 1-11 15 

9-11. Response of the feed system to:

9. An increase in sand-bed slope, run 12b_____________________-_______------------------ 17

10. A decrease in sand-bed slope, run 13_______________________-_______-__---_----------__ 18

11. An increase in sediment-feed rate, run 14b________________-_________----------------- 19

12. Response of the recirculation system to a decrease in sand-bed slope, run 15-__________-_---_-.---- 20

13. Response of the feed system to a decrease in sediment-feed rate, run 16.___________-__-----------_ 21

14-16. Response of the recirculation system to:

14. An increasing sediment-transport rate, run 17b-____________________ _____ ___- 22

15. An increase in sand-bed slope, run 18-__________---_-______--_------------------------ 23

16. A decreasing sediment-transport rate, run 19_-_-___-_--_---------------------------- 24

17. Response of the feed system to an increase in the tail-water depth, run 20 _____________---__--_ 25

18. Response of the recirculation system to a decrease in the tail-water depth, run 21________-_-_-__--- 26

19. Response of the lecirculation system to an increase in the tail-water depth, run 22________--___-- 27

20. Response of tiu. teed system to a decrease in tail-water depth, run 23______________------_--- 28

21. Mean velocity versus unit water discharge-slope product relations_..____________----_--------- 29

TABLES

Page 

TABLE 1. Summary of experimental data for runs l-ll___-_____________________-_______-- ---- D10

2. Comparison of the responses of the feed and recirculation systems to changes of sand-bed slope, tail-water

depth, and sediment-transport rate when water discharge is constant ____________-_-------------- 16

3. Summary of experimental data for runs 12-23-____-----__-__-------____-___-_---__--------- ---- 16

4. Summary of the least squares values of log« a and 6_____________-____------------------------------- 27

in
IV CONTENTS

SYMBOLS

Symbol

a Constant in 'the relation between V and qS.

6 "Least squares" slope of V versus qS relation.

Bf Bed configuration.

Cf Concentration of fine material, in milligrams per liter.

C t Concentration of sediment in the flow, in milligrams per liter.

D Mean depth of flow, in centimeters.

d Representative particle size in terms of fall diameter, in millimeters.

dso Median particle size of the sediment, in millimeters.

du Particle size for which 16 percent of the sediment by weight is finer, in millimeters.

ds4 Particle size for which 84 percent of the sediment by weight is finer, in millimeters.

e Base of the natural logarithm, 2.718.

F Proude number, equals Vf-JgD'.

f Darcy-Weisbach resistance coefficient, equals SgDS/V2 .

g Acceleration of gravity, equals 980 centimeters per second per second.

K Constant.

loge Logarithm to the base e, or the natural logarithm.

Q Discharge of water-sediment mixture, in liters per second.

Q, Sediment-transport rate, in grams per second.

q Unit discharge of water-sediment mixture, in liters per second per meter.

q. Unit sediment-transport rate, in grams per second per meter.

S Slope of the energy grade line, equal to the water-surfac'e slope at equilibrium, in meters per meter.

Se Shape factor for the cross-section.

Sj, Shape factor for the sediment particles.

T Time, in seconds.

V Mean velocity, based on continuity principle, in centimeters per second.

w Pall velocity of median particle size of the sediment, in centimeters per second.

W Width of flume, in centimeters.

7 Specific weight of water, in grams per cubic centimeter.

p Mass density of the water, in grams per cubic centimeter.

p. Mass density of the sediment, in grams per cubic centimeter.

<r A measure of the gradation of the sand, equals - ( -3^+-^ ) 	2 \oia ago/ 

$ Function of. 

v Kinematic viscosity of the water, in square centimeters per second.
SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

RESPONSE OF A LABORATORY ALLUVIAL CHANNEL TO CHANGES OF HYDRAULIC AND

SEDIMENT-TRANSPORT VARIABLES

By E. E. EATHBUN, H. P. GUY, and E. V. EICHARDSON

ABSTRACT

The feed and recirculation systems of flume operation were 

compared in a series of experiments conducted in a tilting 

plastic flume 10 meters long, 20 centimeters deep, and 20 centimeters wide. No significant differences were observed in the 

mean values of the sediment-transport rate, water-surface slope, 

depth of flow, and mean velocity for the two systems in the 

equilibrium steady state.

The responses of the laboratory alluvial channel with a constant water discharge to changes of sand-bed slope, tail-water 

depth, and sediment-transport rate were determined. The results 

observed were: (1) For the feed system, changes of the sedimentfeed rate resulted in new equilibrium values of the water-surface slope, depth of flow, and sediment-transport rate; (2) for 

the feed system, changes of the sand-bed slope and to the tailwater depth resulted in the flume system returning to the 

equilibrium values of the water-surface slope, depth of flow, 

and sediment-transport rate that existed before the change; (3) 

for the recirculation system, changes of the sand-bed slope and 

tail-water depth resulted in new equilibrium values of the watersurface slope, depth of flow, and sediment-transport rate; and 

(4) for the recirculation system, changes of the sediment-transport rate resulted in continually changing nonequilibrium conditions, and equilibrium conditions were established only when the 

external feeding or extracting of sediment was terminated. The 

second and third results do not indicate a true difference between the feed and recirculation systems because in the feed 

system both the water discharge and the sediment-transport rate 

were controlled, whereas only the water discharge was controlled in the recirculation system.

The recirculation system has the advantage of ease and 

economy of operation, and the feed system has the advantage of 

direct quantitative control of the sediment-transport rate.

INTRODUCTION

For many years man has attempted to understand the 

phenomena of sediment transport and resistance to flow 

in alluvial channels. In an effort to understand these 

phenomena, numerous laboratory experiments have been 

conducted in open-channel flumes with a sand bed. These 

experiments attempted to simulate a natural alluvial 

channel under laboratory conditions where the different

variables could be controlled or varied as desired. One of 

the first and most extensive of these investigations was 

by Gilbert (1914), who studied the transport rates of a 

number of sands under a variety of flow conditions.

One of the problems that confronts investigators in 

flume studies is the replacement of the sediment removed 

from the flume by the flowing water. Two general procedures have been developed for providing a supply of 

sediment at the inlet of the flume. These are the sandfeed system, or feed system, and the recirculation system. In the feed system, the general operating procedure 

is to catch the water-sediment mixture leaving the 

downstream end of the flume, remove the sediment, and 

recirculate the water to the upstream end of the flume, 

where sediment is fed into the flow at the desired rate. 

In the recirculation system, the water-sediment mixture 

leaving the downstream end of the flume is recirculated 

to the upstream end of the flume. Figure 1 shows 

schematic diagrams of the general arrangement of the 

feed and recirculation systems of flume operation.

Early investigators were forced to use the feed system 

in their flume studies because they lacked equipment to 

pump water-sediment mixtures. All the studies completed through about 1940, the results of which were 

compiled by Johnson (1943), used the feed system. 

After the development of pumps which could pump 

water-sediment mixtures, later investigators almost exclusively used the recirculation system in laboratory 

studies of sediment transport and resistance to flow. 

These studies included the works of Einstein (1950) and 

Barton and Lin (1955), the extensive series of experiments completed by Simons and Eichardson and summarized by Guy, Simons, and Eichardson (1966), and 

the work of Brooks (1958), Laursen (1958), Kennedy 

(1961), Kennedy and Brooks (1965), Eaudkivi (1967), 

and Vanoni and Hwang (1967). Williams (1967) used 

the feed system.
D2 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

- Shaker (for feeding dry sediment)

Calibrated orifice

Elevator (for feeding wet sediment)

FEED SYSTEM

w.

Hydraulic sediment return

RECIRCULATION SYSTEM Pump

Waste

FIQUBE 1. Schematic diagrams of the recirculation and feed systems of flume operation for alluvial channel experiments.

For the feed system, both the wet and the dry methods are shown.

The use of the two types of flume systems has raised 

the question of the comparability of results obtained 

from the feed system with results obtained from the recirculation system. Are the equilibrium conditions established by the two systems the same and are the 

relations among the variables at equilibrium the same? 

It is important also to consider how the feed and recirculation systems respond to a change of a given 

controlled variable such as depth of flow, slope, water 

discharge, or sediment-transport rate and the time interval required to reach equilibrium conditions after a 

change has been imposed on the system.

The purpose of this report is to describe the results 

of a study in which the equilibrium values of the sediment-transport rate, water-surface slope, depth of flow, 

and mean velocity were compared for the feed and 

recirculation systems, and the responses of several dependent variables to a change in a specific independent

variable were determined for the feed and recirculation 

systems of flume operation for alluvial channel flume 

experiments.

This report is divided into seven sections. The first 

section gives the general procedures for flume experiments and the various combinations of independent and 

dependent variables that have been used. The second 

section describes the experimental apparatus and procedures. The third section compares the feed and recirculation systems under equilibrium conditions. The 

fourth section describes the responses of the laboratory 

alluvial channel to a change in one of the independent 

variables. The fifth section discusses the advantages and 

disadvantages of the feed and recirculation systems of 

flume operation. The sixth section is a summary of the 

results and conclusions. The seventh section discusses 

the limitations of the present study and recommendations for future studies.
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D3

GENERAL PROCEDURES FOR LABORATORY 

ALLUVIAL CHANNEL EXPERIMENTS

The extent and usefulness of laboratory studies of 

sediment transport and resistance to flow may be limited 

by (1) the ranges of variable values for a given flume 

system (2) the large number of variables and the dependencies and interdependences among them, (3) the 

ability or inability to control or eliminate the effects of 

certain variables, and (4) the order and importance of 

the questions to be answered. These limitations are 

applicable to both the feed and the recirculation systems 

of flume operation.

The variables to be considered in flume experiments 

include those that describe the characteristics of the 

flow, the fluid, the sediment, the geometry of the system, and the variations in these quantities with time. 

The important variables are as follows:

*I7, Q, Q*, 8, D, V, O, 0t, W, Bf, d, w, tr, <7, y, Of, S0 8# 

ft*]=0. (1)

Simons and Eichardson (1966) have discussed in detail 

the effect that many of these variables have on resistance 

to flow in alluvial channels.

Under controlled laboratory conditions many of these 

variables can be maintained at constant values. Thus, 

for a study in a given flume that uses a specific liquid 

(water) at a constant temperature and a specific sediment, the variables describing the sediment (d, to, tr, $P, 

ps ) , the fluid (y, p) , and the flume (TP, Sc ) have constant 

values. The shape factor for the cross section, $c, is constant because the average shape of the cross-sectional 

area of the flow is rectangular. At a specific location, 

one dimension of the rectangle changes with time, and 

this variation is accounted for by the depth of flow. The 

acceleration of gravity, <7, has a constant value, and the 

concentration of fine sediment, C^ is generally zero. 

The fine-sediment concentration is important because 

Simons, Richardson, and Haushild (1963) found that 

the fine-sediment concentration significantly affected 

the coarse-sediment-transport rate and resistance to 

flow.

Experimenters have usually studied the equilibrium 

condition where the mean values of the variables are 

independent of time. Equilibrium flow in a laboratory 

flume is defined as the condition where the time-average water-surface slope is approximately constant 

and is equal to the time-average sand-bed-surface slope, 

and where the sediment-transport rate is approximately 

independent of time. The word "approximately" was 

used in this definition because investigators have noted 

(Simons and others, 1963; Rathbun and Guy, 1967) that 

the observed values of water-surface slope, depth of

flow, and sediment-transport rate vary considerably 

about the means of the observed values for a given 

equilibrium condition, especially when the bed forms 

are dunes or antidunes.

Under the restrictions of a specific flume, a specific 

liquid, and a specific sediment and when mean values of 

the variables are obtained for equilibrium-condition experiments so that time is eliminated as a variable, the 

list of variables is reduced to

+[Q9 Q.,8,D,V,Ot,Bf-]=Q. (2)

If certain fundamental relations that exist among the 

variables are used, the list of variables can be reduced 

further. The mean velocity is given by the law of continuity, or

v-m- (3)

The mean sediment concentration is given by

(4)

where K is a constant whose value depends on the system of units used. The resistance to flow is often represented by the Darcy-Weisbach resistance coefficient, /. 

Simons and Richardson (1966) stated that

, d, <o, tr, (5)

and that the bed configuration may be substituted for 

the resistance coefficient to give

Bf=<l>[S, D, d, to, tr, 17, (6)

Equation 6 does not say that the bed configuration is a 

unique or single-valued function of these variables but 

only that the bed configuration is some unknown function of these variables.

By using equations 3, 4, and 6, the list of variables 

can be reduced to

The experimenter usually selects from these four variables the variables to be independent and the variables 

to be dependent for his particular study. An independent variable is defined as a condition imposed on the 

system, whereas the dependent variable is defined as the 

condition that results when equilibrium is established.

In the feed system, the water discharge and the sediment-transport rate are usually controlled independent 

or imposed variables, and the depth of flow and watersurface slope are the dependent variables. This system 

was employed by Gilbert (1914), and the terms "sand-
D4 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

feed" or "feed" have been associated generally with experiments in which the sediment-transport rate is an 

independent variable. In the studies of the U.S. War 

Department, Army Corps of Engineers, however, 

(1935), water discharge and water-surface slope were 

independent variables and sediment-transport rate and 

depth of flow were the dependent variables, even though 

the feed system was used, because sediment was fed into 

the upper end of the flume at a rate just sufficient to balance the sediment-transport rate.

Williams (1967) used a feed system in which the sediment-transport rate and the depth of flow were the independent variables and water discharge and water-surface slope were the dependent variables. The water 

depth was controlled at the desired value by adjustment 

of the water discharge, and equilibrium occurred 

through changes of the water-surface slope and bed 

roughness.

In recirculation systems, the water discharge is usually an independent variable and the sediment-transport 

rate is a dependent variable. Either the depth of flow or 

the water-surface slope can be selected as the second independent variable. Simons and Kichardson (Simons 

and others, 1961) preselected the water-surface slope 

only approximately; thus, slope was an independent 

variable within limits, and the depth of flow was a dependent variable. The water-surface slope was set at the 

beginning of the run by adjusting the tailgate, and 

equilibrium conditions occurred through adjustments in 

the depth of flow, sediment-transport rate, bed roughness, and, to some extent, slope. For the water-surface 

slope to have been a truly independent variable, the tailgate adjustments to maintain the preselected slope 

would have had to be continued until equilibrium had 

been established. Simons and Richardson (Guy and 

others, 1966) also used other combinations of the independent and dependent variables.

Most of the other investigators using the recirculation 

system, such as Brooks (1958), Laursen (1958), and 

Stein (1965), have used the water discharge and the 

depth of flow as the independent variables and the water-surf ace slope and the sediment-transport rate as the 

dependent variables. These investigators found it more 

convenient to use depth of flow as an independent variable than water-surface slope because their recirculation 

systems were closed with respect to the quantity of water in the system. Therefore, the depth of flow was determined by the amount of water in the system at the 

start of the experiment. Simons and Richardson 

(Simons and others, 1961) added or wasted water to 

maintain a constant head in an open tailbox.

Another method of flume operation, which in theory 

would be possible but in reality may not be practical, is

the operation of a recirculation system with the sediment-transport rate as an independent variable. Water 

discharge and sediment-transport rate would be the independent variables, and the depth of flow would be 

adjusted by the investigator to give a predetermined 

sediment-transport rate, and equilibrium would occur 

through the adjustments of the depth of flow, watersurface slope, and bed roughness. Although the depth 

of flow is adjusted by the operator of the flume, it is in 

theory a dependent variable because the final or equilibrium value of the depth is inconsequential.

Other combinations of the independent and dependent variables are possible because the four fundamental 

variables $, /$, Z>, and Q8 when used as two independent 

and two dependent variables, yield a total of six different combinations. Not all these combinations have been 

used in practice.

There are complications in the planning of flume experiments and in the interpretation of the results. Measurements of sediment-transport rates and resistance to 

flow in alluvial channel flumes by Brooks (1958) and 

Simons and Richardson (1966) have revealed certain 

nonunique relations among the variables. The word 

"unique" implies that there is only one value for the 

dependent variable corresponding to a given value of 

the independent variable. Brooks (1958) reported "that 

neither the velocity nor the sediment discharge concentration could be expressed as a single-valued function, 

of the bed shear stress, or any combination of depth and 

slope, or bed hydraulic radius and slope." Although the 

relations among the variables are nonunique when the 

broad spectrum of bed forms is considered, there is, as 

pointed out by Simons and Richardson (1966), a unique 

relation among the variables for a given bed 

configuration.

Kennedy and Brooks (1965) considered the question 

of which combinations of the independent and dependent variables yield unique functional relations among 

the variables and which combinations yield multiplevalued relations for certain ranges of the variables. A 

brief summary of their conclusions and the investigators who have used the various combinations of variables is:

Variables

Independent Dependent Unique Investigator

Q,QS . S,D...... Yes__..__ Gilbert (1914).

Q,S. ..._-- QS,D- No_..._- U.S. War Dept. (1935),

Simons, Richardson, and 

Albertson (1961).

D,S . Q,Q...... No_--__- Simons and Richardson

(1966).

Q,D--.-_ Q,,S..... Yes____ Brooks (1958); Laursen

(1958); Kennedy and 

Brooks (1965); Stem 

(1965).

Q,,D...... Q,S...... Yes___ Williams (1967).
RESPONSE OP CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D5

It is assumed in this summary that the properties of 

the fluid and the sediment, the acceleration of gravity, 

and the flume width are constant. The mean velocity 

and the resistance to flow as represented by the DarcyWeisbach resistance coefficient are not included in the 

list of dependent variables because they are functions 

of the four fundamental variables. The combination of 

independent and dependent variables used by Williams 

(1967) has been added to the results of Kennedy and 

Brooks (1965). The other possible combination is with 

Qa and S as the independent variables. It is expected 

that this combination would yield multiple-valued results. The method of designing flume experiments should 

not be confused with the analysis of the data. In data 

analysis, only one dependent variable is allowable, and 

it can be any of the variables given in equation 7.

The flume capabilities also can impose limitations on 

the dependent and independent variables. For example, 

in the data of Simons and Richardson (in Guy and 

others, 1966), the maximum depth of flow that would 

occur on the steep slopes was limited by the maximum 

water discharge capacity of the pump.

The existence of nonunique relations among the variables for certain combinations of the independent and 

dependent hydraulic and sediment-transport variables 

in flume studies is important because nonunique relations among the variables also occur in natural sandchannel streams. Dawdy (1961) has shown that the 

relation between stage and discharge is discontinuous 

for many sand-channel streams. Furthermore, Kennedy 

and Brooks (1965) believed that "rivers naturally fall 

into the range of variables (slope, depth, velocity) 

where relationships are multiple-valued due to changes 

in bed forms."

Because of the two types of flume systems and because 

of the freedom which the experimenter has in selecting 

the independent variables, questions have arisen as to 

the comparability of results obtained with the feed 

system and results obtained with the recirculation system. It is well known that differences exist among the 

flume data of the various investigators. Some of these 

differences may be the result of differences in the characteristics of the flumes and sediments used. Other differences may result from variations in operational 

procedures including the obtainment of data before 

equilibrium was attained. Blench (1962) has stated that 

the recirculation system is suitable for qualitative work 

but that he has reverted to the feed system for quantitative studies. As justification he cited difficulties with 

steady pumping of the water-sediment mixture and the 

tendency for long term oscillations in the amount of 

sediment transported or discharged by the flume. He 

did, however, note that the recirculation system "pro351-258 O 69 2

duces very realistic river behavior even with steady 

discharge."

Maddock (1968) has suggested that when water discharge and sediment-transport rate are independent 

variables, as in the feed system, then

where q is the unit discharge, or Q/W. When water discharge and slope are the independent variables, as in 

the recirculation system, he proposed

Foc(^) 0- 4 (9)

Equations 8 and 9 suggest that the relations among the 

variables #, F, and 8 are different for the feed and r&- 

circulation systems of flume operation.

The discussion of the feed and recirculation systems 

of flume operation has thus far been limited to a consideration of the equilibrium characteristics of the 

systems. It is important to consider also how these two 

systems of flume operation respond when nonequilibrium conditions are imposed upon the systems in 

equilibrium. A general qualitative expression relating 

the variables for alluvial channel flow has been proposed 

by Lane (1955). This expression has the form

Q8d « QJS. (10)

In addition to being an equilibrium expression, equation 

10 indicates qualitatively the responses of the variables 

to nonequilibrium conditions. For example, if a recirculation system is used with a given sediment and a constant water discharge, then equation 10 predicts that 

the water-surface slope varies directly as the sedimenttransport rate. If the sediment-transport rate is also 

constant, as is possible in the feed system, then equation 

10 predicts that the water-surface slope is uniquely 

determined and the water-surface slope at equilibrium 

will be the one corresponding to the specific Q and $8 , 

regardless of what other changes are imposed on the 

system. This result predicted by equation 10 is in agreement with the result of Kennedy and Brooks (1965) 

that for a given flume with a given sediment, D and S 

are uniquely determined when Q and Qa are the independent variables.

EXPERIMENTAL APPARATUS AND PROCEDURE 

APPARATUS

The experimental runs for this study were made in 

a tilting plastic flume 10 meters long, 20 cm (centimeters) wide, and 20 cm deep. The flume could be operated either as a recirculation system in which both the 

water and sediment were recirculated from the downstream end of the flume to the upstream end or as a feed
D6 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

system in which only the.water was recirculated. In the 

feed system, the sediment transported from the end of 

the flume was removed with a screened trap, dried, and 

returned to the flow at a constant rate by a vibrating 

sediment feeder. Though the sediment was fed in the 

dry condition, it was assumed to be thoroughly wetted 

upon entrance to the flume at the headbox. Figure 2 

shows a diagram of the flume and associated equipment.

The slope of the flume could be varied from 0 to 0.085 

meters per meter, and the discharge range was from 

0 to approximately 100 liters per second per meter of 

width. The water depth and the backwater curve at 

the downstream end of the flume were controlled either 

with a tailgate or by the water level in the tailbox. 

Longitudinal locations in the flume were referenced to 

stations at 1-meter intervals along the flume; station 1 

was 50 cm downstream from the flume entrance.

Water discharges were determined by means of a 

calibrated orifice meter equipped with a water-air 

manometer. The orifice was in the return pipe of the 

flume. Water temperatures were measured with a mercury thermometer. In the first several runs, the water 

temperature was approximately that of the laboratoryair temperature. In later runs, a water heater and an 

electronic temperature controller were used to maintain 

a constant water temperature of 24.0°C. In the summer, 

the laboratory-air temperature sometimes exceeded 

24° C and it was necessary to add cold water periodically 

to keep the water temperature at about 24°C.

The water-surface slope was determined from the 

readings of a series of 11 piezometers with taps positioned at 1-meter intervals along the centerline of the 

flume bottom. The initial 2-meter section of the flume 

was affected by entrance conditions and was not considered in the determination of the water-surface slope.

The taps were connected with plastic hoses of equal 

lengths to the piezometer tubes at a central location. To 

prevent the sediment from entering the hoses, the tap 

openings were covered with small squares of stainless 

steel screen with openings of about 0.2 mm. The water 

levels in the piezometer tubes were an accurate reproduction of the water-surface elevations along the flume 

and quickly changed when the water level in the flume 

changed. Water-surface slopes were determined from 

the elevations of the water columns in the piezometers 

by plotting the elevation against the longitudinal location and drawing a straight line of "best fit". Comparable results were obtained by applying a simple "least 

squares" procedure to the readings.

The slope of the flume bottom (not necessarily the 

same as the slope of the surface of the sand bed) was 

determined from two stilling wells attached to the outside of the flume 9 meters apart at stations 1 and 10. 

The heights of these wells were adjustable so that the 

water level in each well could be positioned at exactly 

the same elevation as the bottom of the flume. These 

wells were connected by plastic hoses to tubes on the 

piezometer board. The difference in water level of these 

two tubes divided by the distance between the stilling1 

wells was the flume-bed slope.

The depth of flow was determined by measuring the 

difference in elevation between the water surface and 

the sand-bed surface with a point gage. The mean depth 

of flow was the average of measurements at several locations; the number of measurements depended upon 

the bed form.

Total sediment-transport rates were determined by 

sampling with a trap at the tailbox of the flume. This 

trap had rigid plastic sides and a bottom and a back 

of stainless steel screen which had openings small enough

Flex tubing /|Tailbox|-

 ir- - / *f* j n i """~"M__

Variable-speed Pump 

motor

FIGURE 2. Schematic diagram of the experimental flume and associated equipment used in this study.
RESPONSE OP CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D7

to trap the sediment. The trap fit in the tailbox of the 

flume so that all the water-sediment mixture leaving 

the flume passed into the trap. The amount of sediment 

transported from the end of the flume in a given time, 

and hence the sediment-transport rate, was thus determined. When the recirculation system was used, the 

vibrating sediment feeder was used to replace an amount 

of sediment equal to the sediment trapped so as to maintain a constant amount of sediment in the system. For 

the first sample of a recirculation system run, it was 

necessary to estimate the feed rate for the sediment 

feeder. Thereafter, when a sample of the sediment in 

transport was taken, the feed rate was set at the sediment-transport rate determined from the previous sample; thus, the flume was operating with either a small 

deficiency or a small excess of sediment from one sample 

period to the next. The amount of sediment in any given 

sample, however, was insignificant when compared with 

the amount of sediment in the flume.

The volume of sediment collected in the trap was 

measured in a graduated cylinder. The relation between 

the volume of wet sediment and the dry weight of the 

sediment was determined by calibration. The wet sediment had a mean bulk density of 1.677 grams per cubic 

centimeter. Use of this procedure permitted a rapid determination of the sediment-transport rate.

When the feed system was used, the trap was left in 

the tailbox and all the sediment leaving the end of the 

flume was trapped. The sediment was siphoned from the 

trap into measuring containers placed in a small tank. 

The water removed by the siphon was returned from the 

small tank to the tailbox of the flume by means of a 

small pump; the discharge of the pump was adjusted 

to keep a constant water depth in the tailbox and, consequently, a constant head on the flume pump.

Sediment was fed at a constant rate with the vibrating sediment feeder. The feed rate was checked periodically by measuring the volume of dry sediment fed over 

a given time interval. Volume of sediment was converted 

to the weight of sediment using the bulk density of the 

dry sediment, which was found to be 1.563 grams per 

cubic centimeter. The sediment-feed and sediment-transport rates were rapidly determined by the volumetric 

measurement procedure, and a rapid comparison, of the 

two rates was therefore possible. One obvious criterion 

for equilibrium in the feed system is that the sedimenttransport rate equals the sediment-feed rate.

BED MATERIAL

The sediment used in this study consisted of wellrounded quartz particles having a median fall diameter, 

^50, of 0.30 mm and a median fall velocity of 4.4 cm per

sec (centimeters per second). The gradation of the sediment, o-, was 1.26.

PROCEDURE

The first part of this study consisted of the comparison of the feed and recirculation systems of flume operation under equilibrium conditions. The general procedure consisted of selecting the water discharge and the 

water-surface slope. The initial depth of flow was fixed 

approximately by the amount of water in the flume system in the early experiments when the water level in 

the tailbox served as the downstream control of the 

depth. As equilibrium conditions were approached and 

the water depth in the flume increased or decreased, the 

amount of water in the tailbox was increased or decreased so that the water level in the tailbox remained 

constant. In later runs, an adjustable tailgate was used 

to obtain the desired depths. Again the water level in 

the tailbox was maintained at a constant level. Equilibrium conditions were established using the recirculation 

system because the hydraulic sediment return of the recirculation system was much simpler to use than the 

mechanical return of the feed system and the supply of 

dry sediment for the feed system was limited. Equilibrium was considered established when the depth of flow 

was approximately uniform along the flume (excluding 

the section affected by the entrance conditions) and 

when the water-surface slope and sediment-transport 

rate were approximately independent of time. The determination of the establishment of equilibrium was 

somewhat arbitrary because the flume system asymptotically approached equilibrium conditions. As Laursen 

(1958) has noted, the final decision as to whether equilibrium has been established depends considerably on 

the judgment of the flume operator.

After equilibrium was established, a number of 

measurements of the water discharge, depth of flow, 

water-surface slope, sediment-transport rate, and water 

temperature were made. The number of measurements 

depended roughly on the magnitude of the variation 

with time of the variables. Figure 3 shows how the 

values of the variables varied with time for run 6. For 

water discharge, depth of flow, and water-surface slope, 

the deviations of the measured values from the mean 

values are shown in the lower part of the figure, and 

the measured sediment-transport rates are shown in the 

upper part. It is apparent that the values of observed 

slope show the greatest deviations from the mean and 

that the values of the water discharge deviate the least 

from the mean. The sediment-transport rate apparently 

was more uniform for the feed system than for the 

recirculation system. However, the sampling times 

were longer for the feed system than for the recircula-
D8 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Recirculation - Feed

15

10

-10

-15' 

0800

ycf

\ ^ \ I \ i 

\^" \ ' 'k

EXPLANATION ° 1 / 

n Discharge 11

A Depth g ~~ 

o Slope

1000 1200 

12-28-65

1400 1600 1700 0800 1600 1700

TIME, IN HOURS

FIGUBE 3. Variation with time of sediment-transport rate, water-surface slope, mean depth of flow, and water discharge in run 6.

tion system, and there was a greater tendency for the 

oscillations in the sediment-transport rate to be averaged 

for the feed system.

After the collection of sufficient data to define the 

equilibrium conditions for the recirculation system, the 

change to the feed system was made. The water discharge and sediment-feed rate were set equal to the 

mean equilibrium values of the water discharge and 

sediment-transport rate for the recirculation system. 

Measurements of the water discharge, depth of flow, 

water-surface slope, sediment-transport rate, water 

temperature, and sediment-feed rate were continued until sufficient data were obtained to define the equilibrium 

conditions for the feed system. These measurements were 

begun as soon as the change to the feed system was 

completed so that measurements would be obtained during the transition to the new equilibrium conditions if

the change to the feed system resulted in new hydraulic 

and sediment-transport conditions.

After the completion of the feed system part of the 

experiment, the usual procedure was to revert to the 

recirculation system and to continue the hydraulic and 

sediment-transport measurements. The purpose of this 

procedure was to permit a comparison of the sedimenttransport rate under conditions where the sedimenttransport rate was an independent or controlled variable 

before the change and a dependent variable after the 

change. The measurements were begun as soon as the 

change in the method of operation was completed, and 

the measurements were continued until sufficient data 

were obtained to define the equilibrium conditions for 

the recirculation system.

The second part of this study was to determine the 

responses of the laboratory flume systems to changes
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D9

that caused nonequilibrium conditions, with the water 

discharge maintained at a constant value. The runs 

consisted in general of three parts: (1) establishment 

of equilibrium conditions; (2) imposition of a change, 

resulting in nonequilibrium conditions; and (3) reestablishment of equilibrium. The change imposed upon the 

system consisted of either increasing or decreasing the 

sand-bed slope by raising or lowering the upper end of 

the flume, either increasing or decreasing the tail-water 

depth at the downstream end of the flume by adjusting 

the tailgate, or increasing or decreasing the amount of 

sediment transported by changing the sediment-feed 

rate for the feed system and by adding sediment to the 

recirculating system or extracting a portion of the recirculating sediment. These changes were imposed upon 

both the feed and recirculation systems in a total of 12 

experimental runs. The runs were completed in a sequence such that a run that resulted in increased values 

of the water-surface slope and sediment-transport rate 

was followed by a run that was expected to yield decreased values of the water-surface slope and sedimenttransport rate. The equilibrium conditions established 

at the conclusion of one run served as the initial equilibrium conditions for the next run.

Numerous measurements of the water discharge, 

water-surface slope, depth of flow, sediment-transport 

rate, and water temperature were made for both the 

nonequilibrium conditions and the equilibrium conditions. The sediment-feed rate was also checked periodically in the feed system runs. During the initial stages 

of each run when the nonequilibrium conditions prevailed, measurements of the variables were completed 

as rapidly as possible. It required about 1 minute to read 

and record the readings of the 11 piezometers used to 

determine the water-surface slope, the reading of the 

manometer used to determine the water discharge, and 

the reading of the thermometer used to determine the 

water temperature. The depth of flow was determined 

from 18 measurements of the water-surface elevation 

and 18 measurements of the sand-bed elevation at 0.5- 

meter intervals along the flume centerline. The initial 

2-meter section of the flume was affected by entrance 

conditions and was not considered in the determination 

of the depth of flow. The measurement of the depth 

of flow required about 9 minutes. For feed-system runs, 

the determination of the sediment-feed rate required 

about 2 minutes. Thus, a complete set of measurements 

of the variables could be obtained in about 10 minutes 

for recirculation-system runs and in about 12 minutes 

for the feed-system runs. The sediment-transport rate 

determinations in the recirculation-system runs were 

made concurrently with the other measurements. In the 

feed-system runs, all the sediment transported from the

end of the flume was collected continuously (divided 

into discrete increments of time), and the sediment 

volumes and the corresponding sediment-transport rates 

were determined after the completion of a run.

The magnitudes of the changes imposed upon the 

systems during these experimental runs and the durations of the runs were such that significant changes occurred in the sediment-transport rate, the water-surface slope, and the depth of flow. Significant changes 

generally did not occur in the resistance to flow as represented by the Darcy-Weisbach resistance coefficient. 

The water-discharge used in runs 12 and 13 was about 

10 percent larger than the approximately constant water 

discharge used in runs 14-23.

COMPARISON OF THE FEED AND RECIRCULATION

SYSTEMS

In the first part of this study, the feed and recirculation systems were compared under equilibrium conditions in 11 experimental runs that covered a wide range 

of flow conditions with bed forms ranging from ripples 

to antidunes. The mean values of the measured variables 

at equilibrium flow conditions and the parameters computed from the measured variables are given in table 1. 

The variations of the variables about their mean values 

were essentially the same for the two systems. Comparison of the measured variables and the calculated 

parameters is as follows.

SEDIMENT-TRANSPORT RATE

The sediment-transport rate should be one of the 

more sensitive indicators of any possible differences between the feed and recirculation systems. In the procedure employed in runs 1-11, the mean equilibrium 

sediment-transport rate for the recirculation system was 

used as the sediment-feed rate when the change from 

the recirculation system to the feed system was made. 

If differences between the two systems had existed, the 

equilibrium conditions established in the recirculation 

part of the run would have been disturbed, and different 

values of the water-surface slope, depth'of flow, and bed 

roughness would have resulted. Because the sedimentfeed rate was fixed, and, hence, the sediment-transport 

rate, a new permanent equilibrium condition could not 

be established. Differences between the two flume systems would have been reflected in changing conditions 

and an inability to establish equilibrium. Changing conditions were not observed in any of the 11 runs, and the 

equilibrium conditions of the recirculation system did 

not change within the limits of experimental variation 

or error when the change to the feed system was made. 

Figure 4 is a comparison of the unit sediment-transport
D10 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 

TABLE 1. Summary of experimental data, for runs 1-11

Run number Operational system Discharge M 

(1/sec/m)

l______---______-_- _ Recirculation_ __________ 30.4

Feed ____________ 30.2

2____________________ Recirculation. __________ 37. 5

Feed__ __ _ ___ __ __ 37.4

3__. _______ _________ Recirculation. __________ 22.4

Feed___________________ 22.7

Recirculation_ __________ 22. 2

4____ _._ __ Recirculation. ___ __ ___ 32.8

Feed.. ____ _ __ _____ 32.6

Recirculation ___________ 32. 5

5______-________- ___ Recirculation. _________ 24.6

Feed... ________________ 24.7

Recirculation___________ 24. 6

6______ _____________ Recirculation_ ________ 37.0

Feed _ ___ ____ __ _ _ 37.0

Recirculation _______ ___ 37. 2

7___----_____________ Recirculation. __ _______ 19.7

Feed__. _ __._.___...__ 19.7

8___---_-_--_________ Recirculation. ______ ___ 149

Feed _ ___ _ ______ __ 14.9

Recirculation. __________ 15. 0

9______ _____________ Recirculation- _______ __ 25.2

Feed.. ___ _____ ___ 24.9

Recirculation. __________ 24 9

10_ __________________ Recirculation. __________ 17. 5

Feed ___ ____ ______ 17.6

Recirculation _______ ___ 17. 5

 11___________________ Recirculation- ________ _ 29.4

Feed _______ ___ 28.6

Recirculation. _ ___ ___ 27. 8

rate for the recirculation system with the unit sedimenttransport rate for the feed system when a change is 

made from the recirculation system to the feed system. 

The mean sediment-transport rates for each run fall on 

both sides of, but near, the line of perfect agreement. 

The size of the rectangle about each point represents the 

confidence limits at the 95 percent level of significance 

of the mean values used to establish the point. 

In eight of the 11 runs (runs 1, 2, and 7 are the exceptions) , a change was made from the feed system to the 

recirculation system with only the water discharge held 

constant. Under these conditions, the sediment-transport rate changed from an independent variable to a 

dependent variable, and the water-surface slope, depth 

of flow, bed roughness, and sediment-transport rate 

were free to change if differences existed between the 

feed and recirculation systems. Figure 5 is a comparison of the unit sediment-transport rate for the recirculation system with the unit sediment-transport rate 

for the feed system when a change is made from the feed

Mean Water-surface Sediment transport

(cm) (cm/sec) (m/m) (° C) Bate Concentra- 

(g/sec/m) tion (mg/1)

5. 97 50. 9 4 13 19. 8 26. 9 885 

6. 10 49. 6 3. 90 21. 1 24 2 798

7.42 50.5 3.22 20.4 20.6 550 

7. 71 48. 6 3. 50 20. 8 16. 7 446

4 50 50. 0 5. 28 20. 7 19. 8 875 

4.70 48.4 4.67 20.5 28.8 1,270 

442 50.2 487 21.0 20.6 925

5.32 61.4 6.08 20.4 55.0 1,680 

5. 50 59. 4 5. 51 21. 1 50. 0 1, 540 

5. 14 63. 2 5. 90 21. 5 52. 9 1, 630

5. 63 43. 8 3. 06 24 3 13. 0 529 

5. 72 43. 2 3. 30 24 7 15. 7 637 

5.83 42.2 2.92 25.0 11.7 474

8. 41 44 2 2. 40 25. 2 12. 4 335 

8. 59 43. 1 2. 31 25. 1 11. 8 318 

8. 63 43. 0 2. 25 25. 4 11. 9 320

6. 05 32. 6 2. 12 24 6 2. 74 139 

6. 12 32. 1 2. 06 23. 9 2. 73 139

470 31.7 2.74 242 2.71 182 

4 74 31. 5 2. 74 23. 9 3. 28 220 

4 84 31. 0 2. 83 24 1 3. 08 234

3. 99 62. 8 7. 83 21. 0 69. 0 2, 750 

4 14 60. 4 7. 78 21. 2 84 2 3, 380 

400 62.4 7.82 21.0 65.2 2,610

4 59 38. 2 3. 24 24. 0 8. 59 490 

4 59 38. 4 3. 19 24 0 8. 59 488 

4 60 38. 1 3. 20 24 0 9. 00 514

3. 87 76. 1 8. 96 24 0 146 4, 960 

3.80 75.4 8.78 240 140 4,890 

3.70 75.2 9.40 24.0 145, 5,210

system to the recirculation system. The mean sedimenttransport rates for each run fall on both sides of, but 

near, the line of perfect agreement. It can be concluded 

on the basis of the results presented in figure 5 that no 

significant differences at the 95 percent level of significance exist between the sediment-transport rate for the 

recirculation system and the sediment-transport rate 

for the feed system.

WATER-SURFACE SLOPE

The results of the comparison of the mean values of 

the water-surface slope for the recirculation and feed 

systems are shown in figure 6. Values of the water-surface slope for runs 1, 3, 4, and 11 were slightly larger 

for the recirculation system than for the feed system 

and values of the water-surface slope for runs 2 and 5 

were smaller for the recirculation system than for the 

feed system. The differences in water-surface slopes 

were not significant at the 95 percent level of 

significance.
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES Dll

200

100

4 6 8 10 20 40 60 80 100 

SEDIMENT-TRANSPORT RATE (FEED SYSTEM), IN GRAMS PER SECOND PER METER

200

FIGURE 4. Comparison of the unit sediment-transport rate when a change is made from the recirculation system to the feed

system, runs 1-11.

DEPTH OF FLOW

The results of the comparison of the mean values of 

the depth of flow for the recirculation and feed systems 

are shown in figure 7. Mean depth of flow values were 

in general slightly smaller for the recirculation system 

than for the feed system. The differences in depths of 

flow were not significant at the 95 percent level of 

significance.

VELOCITY

The mean velocity was computed from the equation 

of continuity, equation 3. Because the water discharge 

was controlled within very narrow limits, the flume 

width was constant, and the depths of flow were, in general, slightly smaller for the recirculation system than 

for the feed system, the mean velocities were slightly 

larger for the recirculation system than for the feed
D12

1000

800

600

400

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

200

£100 

w

80

60

40

20

h- 

< 10

U. 8

o

0_

w c 

z 6

< 

a:

71

-X-fI I I

4 6 8 10 20 40 60 80 100 200 

SEDIMENT-TRANSPORT RATE (FEED SYSTEM), IN GRAMS PER SECOND PER METER

400 600 800 1000

FIGUBE 5. Comparison of the unit sediment-tnansport rate when a change is made from the feed system to the redrculation

system, runs 3-6 and 8-11.

system, as figure 8 shows. The differences in mean velocities were not significant at the 95 percent level of 

significance.

Agreement between derived parameters, such as the 

Darcy-Weisbach friction factor, as defined by equation 

5, and the stream power (yDSV) was found for the two 

systems. Agreement was expected because of the agreement between water-surface slope, depth of flow, and

mean velocity values for the two systems. On the basis 

of these results and the results shown in figures 5-8, 

we conclude that no significant differences at the 95 

percent level of significance exist between the equilibrium values of the sediment-transport rate, water-surface slope, depth of flow, mean velocity, Darcy-Weisbach 

resistance coefficient, and stream power for the recirculation system and for the feed system.
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D13

10

567 

WATER-SURFACE SLOPE (FEED SYSTEM)X1Q3

10

FIGUBE 6. Comparison of the water-surface slope for the recirculation and feed systems, runs 1-11.

RESPONSES OF THE FLUME TO CHANGES OF THE 

HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES

The second part of this study consisted of determining' the responses of the feed and recirculation systems 

of flume operation to three types of changes that caused 

nonequilibrium hydraulic and sediment-transport conditions in the flume. A series of 12 experimental runs

(runs 12-23) was completed, and the qualitative results 

of these runs are given in table 2. A summary of the 

equilibrium values of the variables for each run is given 

in table 3. The bed forms for these runs were transition 

(Task Committee on Bed Forms in Alluvial Channels, 

1966), and the Froude number (F=V/(gD)°- 5 ) ranged 

from 0.58 to 0.86. The unit sediment-transport rate qs,

351-258 O 69 '3
D14

10

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

<n 

LJ 8

I

LU 5 

Q

 1

/

45-1

n % / 1

5

456789 

DEPTH OF FLOW (FEED SYSTEM), IN CENTIMETERS

FIGTJBE 7. Comparison of the mean depth of flow for the recirculation and feed systems, rons 1-lL

10

ranged from 13.2 to 53.7 grams per second per meter 

and were in the middle of the range of unit sedimenttransport rates for runs 1-11.

Numerous measurements of the different variables 

were obtained during the periods of nonequilibrium 

conditions as well as during the periods of equilibrium

conditions. Results from these experiments are shown 

in a figure for each run (figs. 9-20 for runs 12-23, respectively). The following comments are applicable to 

these figures:

1. The rate of sediment transport from the end of the 

flume is represented by the use of block diagrams.
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D15

86

78

70

62

54

46

38

30

30 38 46 54 62 70

MEAN VELOCITY OF FLOW (FEED SYSTEM), IN CENTIMETERS PER SECOND

78 86

FIGUBE 8. Comparison of the mean velocity of flow for the recirculation and feed systems, runs 1-11.

With the feed system, a continuous record (divided 

into discrete increments) of the sediment-transport rate was obtained.

2. The triangles represent measurements of the sediment-feed rate for the feed system.

3. The horizontal lines and the numbers near the ordinate scale represent the variable values for the

equilibrium that existed prior to the change 

imposed upon the system.

4. During nonequilibrium and equilibrium conditions, 

the depth of flow values are the average of 18 observations at 0.5-meter intervals over the section of 

the flume from station 2.5 to station 11. During 

nonequilibrium conditions, local depth differences
D16 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 2. Comparison of the responses of the feed and recirculation systems to changes of sand-bed slope, tail-water depth, and sedimenttransport rate when water discharge is constant

Method of 

operation 

and ran

Response

Variable changed

Water-surface slope Depth of flow

Rate of

Sediment-transport rate approach to Equilibrium 

equilibrium conditions 

conditions

Recirculation,

run 18. 

Recirculation,

run 15. 

Feed, run 12b..

Feed, run 13...

Recirculation,

run 17b 

Recirculation,

run 19.

Recirculation,

run 22. 

Recirculation,

run 21.

Slope increased by raising

upstream end of flume. 

Slope decreased by lowering

upstream end of flume. 

Slope increased by raising

upstream end of flume. 

Slope decreased by lowering

upstream end of flume.

Sediment-transport rate

increased by adding sand 

with feeder to recirculating 

system.

decreased by extracting a 

portion of the recirculating 

sediment.

increased by increasing 

sediment-feed rate.

decreased by decreasing 

sediment-feed rate.

Tail-water depth increased

by adjusting tailgate.

by adjusting tailgate.

by adjusting tailgate.

by adjusting tailgate.

Increased.. ___ ...........

Decreased ....................

and then returned to value 

existing before flume was 

raised.

and then returned to value 

existing before flume was 

lowered.

sediment was added.

sediment was extracted.

sediment-transport rate 

equaled sediment-feed rate.

sediment-transport rate 

equaled sediment-feed rate.

and then returned to value 

existing before depth was 

changed.

and then returned to value 

existing before depth was 

decreased.

and then returned to value 

existing before flume was 

raised.

and then returned to value 

existing before flume was 

lowered.

sediment was added.

sediment was extracted.

sediment-transport rate 

equaled sediment-feed rate.

sediment-transport rate 

equaled sediment-feed rate.

and then returned to value 

existing before depth was 

increased.

and then returned to value 

existing before depth was 

increased.

Decreased __ . _ .. ........

Sediment-transport was

initially larger and then 

returned to value existing 

before flume was raised.

initially smaller and then 

returned to value existing 

before flume was lowered.

increased as long as 

sediment was added.

transport rate decreased, 

total sediment-transport 

rate decreased as long as 

sediment was extracted.

increased until it equaled 

sediment-feed rate.

decreased until it equaled 

sediment-feed rate.

initially smaller and then 

increased until it equaled 

sediment-feed rate.

initially larger and then 

decreased until it equaled 

sediment-feed rate.

Rapid

.....do.......

Slow.......

.....do.......

Slow.......

.....do... ....

.....do.......

.....do.......

Rapid. ......

.....do ....

.....do ....

Do.

Do.

Changing.

Do.

Do.

New.

Do.

Original.

Do.

TABLE 3. Summary of experimental data for runs 12-

Run Change imposed on system

12a

12b ___ _ Increase flume slope ___

14b______ Increase feed rate. _____

15 __ ___ Decrease flume slope. __ _

16. _ _ _ _ Decrease feed rate. _______

I7b__ _ _ Add sediment. __ ____ ___

18 ___ __ Increase flume slope. _ _

19 _ _ _ _ _ Extract sediment- _ ______

20_ ______ Increase depth. __ __ _

22_ _ _ _ _ _ Increase depth. __________

23 ______ Decrease depth __ ____ _

Operational system

__ _ Recirculation. ...

___ Feed _ ___ ____

___ _ Recirculation ____

_ _ Feed ___ __ _

__ _ Feed ___ _ _____

do

do

_ ___ Feed. _ _ __ _

_ _ _ _ _ Recirculation

. _._ Feed _ ___ . ___

Discharge 

(1/sec/m)

__ 24.5

__ 24.7

__ 24.5

__ 22.4

__ 22.2

__ 22.4

22.3

__ 22.4

__ 22.3

__ 22.2

__ 22.3

__ 22.2

__ 22.2

__ 22.4

22.3

Mean Water- Flume-bed 

depth surface slope X 103 

(cm) slope X 103 (m/in) 

(m/m)

5.64 

5.40 

5. 56 

4. 55 

4.31 

4. 62 

5.00 

5.01 

4. 60 

4.28 

4. 62 

4.50 

4.06 

4. 58 

4.45

3. 10 

3.15 

3. 16 

4.62 

5.91 

4.84 

3.67 

3.64 

4.95 

5.97 

4. 67 

4. 84 

6.64 

4.78 

4. 85

3.09 

4.72 

3. 12 

4. 76 

4. 76 

3.53 

3. 53 

3.73 

3.73 

4.72 

4.72 

4.72 

4.72 

4. 72 

4.72

Tempera- Sediment transport

(° C) Rate Concentra- 

(g/sec/m) lion (mg/1)

24.0 

23.8 

24.9 

24.0 

24. 0 

24.4 

24. 6 

24.7 

25.2 

24.5 

24.6 

25.6 

24. 2 

24. 1 

24.0

13.2 

13.4 

13.2 

28.0 

39.5 

29. 1 

15.2 

17.0 

32. 1 

44.2 

27. 1 

28. 1 

53.7 

29.0 

28. 6

539 

544 

539 

1,250 

1,780 

1,300 

681 

760 

1,440 

2,000 

1,210 

1,260 

2,420 

1,300 

1,280

(in the upstream or downstream flume section most 

affected by the change) were greater than differences shown by the data in the figures. 

5. During nonequilibrium conditions, an abrupt change 

or break in the water-surface slope sometimes 

occurred during the initial stages of a run. This

break occurred either in the upstream or downstream section of the flume, the location depending 

on the type of change imposed on the system. When 

a break was observed, the water-surface slope 

calculation was based on the longer of the two 

sections. The shorter section was usually 2-3 meters
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D17

in length. Initial slope differences, therefore, were 

greater than the differences shown by the data in 

figures 9-20.

6. For equilibrium conditions, water-surface-slope 

values were determined from the water-surface 

elevations measured by the 10 piezometer taps 

between stations 2-11.

7. The determination of when equilibrium had been 

established was based on the manner in which the 

depth of flow, water-surface slope, and sedimenttransport rate varied with time. In the feed system, 

the agreement of the sediment-transport rate with 

the sediment-feed rate was also a necessary criterion for equilibrium.

Runs 12-23 are discussed in detail in the following 

paragraphs. The water discharge was a constant or 

independent variable and the water-surface slope, depth 

of flow, and the bed roughness were dependent variables 

in all the runs. The sediment-transport rate was an 

independent variable in the feed system runs and in 

two of the recirculation system runs (lYb and 19) and 

was a dependent variable in the other four recirculation 

system runs.

Run 12 (increase slope, feed system). In run 12b, 

after establishment of equilibrium conditions with the 

recirculation system in run 12a, the sand-bed slope was 

increased about 50 percent by raising the upper end of 

the flume, and the feed system was used with a sediment-feed rate equal to the mean equilibrium value 

of the sediment-transport rate for run 12a. Figure 9 

shows graphically the variation with time of the several 

variables during run 12b. The increase in sand-bed slope 

caused degradation of the sand bed in the upstream 

section of the flume; the degradation resulted in a 

flattening slope and a gradual approach to the final 

equilibrium value of the water-surface slope. The initial 

sediment-transport rate was larger and the initial mean 

depth of flow was shallower than the final equilibrium 

values of these variables. The final equilibrium values 

of the water-surface slope, depth of flow, and sedimenttransport rate, however, were within 4.3 percent of the 

equilibrium values of these variables that existed before 

the change in sand-bed slope. The maximum difference 

between initial and final equilibrium values was for the 

depth of flow. About 6 hours was required to achieve 

equilibrium after the change in slope.

Rim 13 (decrease slope, feed system). In run 13 

the sand-bed slope was decreased about 50 percent by 

lowering the upper end of the flume, and the feed system was used with the same water discharge and the 

same sediment-feed rate as in run 12b. Figure 10 shows 

graphically the variation with time of the several variables during run 13. The decrease in sand-bed slope resulted in aggradation in the upstream section of the 

flume, and the sediment-transport rate was less than the 

sediment-feed rate. The initial depth of flow was 

deeper than the final equilibrium value. As the sand bed 

aggraded in the upstream section of the flume, the watersurface slope increased, the depth of flow decreased, and 

the sediment-transport rate increased until equilibrium 

conditions were established. The final equilibrium values 

of the water-surface slope, depth of flow, and sediment-transport rate were within 3.0 percent of the equilibrium values of these variables that existed before 

the change in sand-bed slope. About 8.2 hours was required to achieve equilibrium after the change in slope. 

Run 14 (increase sediment-feed rate, feed system) . 

In run 14b, after establishment of equilibrium conditions with the recirculation system in run 14a, the sediment-feed rate was set at a value 1.35 times the mean 

equilibrium value of the sediment-transport rate for run 

14a. Figure 11 shows graphically the results of run 14b. 

The increased sediment-feed rate caused aggradation 

in the upstream section of the flume; the aggradation 

caused the slope to increase gradually, the mean depth 

of flow to decrease, and the sediment-transport rate to 

increase. The process of increasing slope, decreasing 

depth, and increasing sediment-transport rate contintz cc ft 0 K 25.0

24.0

23.5

DEPTH OFFLCIN CETIMETE

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1000 1100 1200 1300 1400 1500 16001700 10001100 1200 1300 

5-12-66 5-13-66 

TIME, IN HOURS

FIGURE 9. Response of the feed system to an increase in sandbed slope, run 12b.
D18 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

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5-16-66 5-27-66 5-31-66

TIME, IN HOURS 

FIOITBB 10. Response of the feed system to a decrease in sand-bed slope, run 13.

ued until the sediment-transport rate approximately 

equaled the sediment-feed rate 'at which time the slope 

and depth had also attained approximately constant 

values. The fluctuations of the variable values about the 

mean equilibrium values, which are indicated by the 

solid lines and the numbers near the right ordinate in 

figure 11, should be noted. Equilibrium was reached in 

about 7.5 hours after the increase in sediment-feed rate. 

The water-surface slope was 28 percent larger, the depth 

of flow was 5.3 percent less, and the mean bed-surface 

elevation was 0.42 cm higher than the equilibrium values of these variables that existed before the increase in 

sediment-feed rate.

Rum 15 (decrease slope, retirculation system). In 

run 15 the sand-bed slope was reduced about 26 percent 

(from 0.00476 to 0.00353 m per m) by lowering the upper 

end of the flume. The recirculation system was used, and 

new equilibrium conditions were established almost immediately. The rapid response of the recirculation system to the decrease in flume slope is shown by the data 

presented in figure 12. The water-surface slope was 18

percent less, the depth of flow was 7.2 percent larger, 

and the sediment-transport rate was 26 percent less than 

the equilibrium values of these variables that existed 

before the decrease in sand-bed slope.

Run 16 (decrease sediment-feed rate, feed system) . 

In run 16 the sediment-feed rate was reduced to about 

48 percent of the mean sediment-transport rate for the 

equilibrium conditions at the end of run 15. Because 

the sediment-transport capacity of the flume system was 

larger than the sediment-feed rate, degradation occurred in the upstream section of the flume. The degradation caused the water-surface slope to decrease and the 

depth of flow to increase. The slope continued to decrease, and the depth increased until the sedimenttransport rate had decreased to a rate equal to the sediment-feed rate. The mean sand-bed surface elevation 

decreased 0.75 cm during the run. The variation with 

time of the several variables during run 16 is shown in 

figure 13. Equilibrium was obtained about 9.2 hours 

after the decrease in sediment-feed rate. The watersurface slope was 24 percent less and the depth of
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES

50

D19

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OF DEPTH FLO R-SURFACE CENTIMETEF )PEX103 IN Ol O1 4ibi COi 

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6-9-66 6-13-66 I 6-17-66

TIME, IN HOURS

. ^Response of the feed system to an increase in sediment-feed rate, run 14b.

flow was 7.6 percent larger than the equilibrium values 

of these variables that existed before the decrease in 

sediment-feed rate.

Rim 17 (increase sediment-transport rate, recirculation system). Bun 17b was made after equilibrium 

conditions were determined using the recirculation system in run 17a. In run 17b sediment at a rate equal to 

about 65 percent of the equilibrium sediment-transport 

rate of run I7a was added continuously to the recirculating system by feeding sediment into the tailbox with 

the sediment feeder. Because the amount of sediment 

transported from the downstream end of the flume is 

usually the input to the upstream end of the flume in 

a recirculation system, the sediment added to the system resulted in a larger input of sediment at the flume 

inlet. This sediment input exceeded the sediment-transport capacity of the flume for the given hydraulic conditions and aggradation occurred. The aggradation

caused the slope to steepen, the depth of flow to decrease, and the sediment-transport rate to increase. As 

the sediment-transport rate increased, the sediment 

input at the flume inlet increased, and the cycle of 

adjustment of the water-surface slope and depth of 

flow in response to the increasing sediment-transport 

rate continued. The result was a flume system of changing hydraulic and sediment-transport conditions, and 

it was impossible to achieve equilibrium conditions as 

long as sediment was being added to the system.

The addition of sediment was terminated after 4.25 

hours of operation. During the period of adding sediment, the water-surface slope increased 36 percent and 

the sediment-transport rate increased 89 percent, 

whereas the depth of flow decreased 8.0 percent with 

respect to the equilibrium values of these variables that 

existed at the start of run 17b. Equilibrium conditions 

were assumed established about 1.7 hours after the ces-
D20 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Equilibrium 

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6-20-66 6-21-66

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1400 16

TIME, IN HOURS 

FIGURE 12. Response of the recirculation system to a decrease in sand-bed slope, run 15.

sation of the addition of the sediment; however, the 

data indicated that equilibrium was established almost 

immediately after the addition of sediment was 

stopped. The variation with time of the several variables in run 17b is shown graphically in figure 14. The 

mean bed-surface elevation increased 0.81 cm during 

the run.

It is interesting to speculate on the final condition of 

the system if the addition of the sediment had been 

continued. The final condition probably would have 

been one of large sediment-transport rate with flow in 

the upper regime; the final condition would have depended on the water discharge.

Rwi 18 (increase slope, recirculation system). In 

run 18 the flume slope was increased about 26 percent 

(from 0.00373 to 0.00472 m per m) by raising the upper 

end of the flume. The change for run 18 was the converse of the change for run 15, and, as in run 15, equilibrium conditions were established immediately. The 

increase in flume slope caused a 21 percent increase in 

water-surface slope, a 38 percent increase in sedimenttransport rate, and a 7 percent decrease in depth of 

flow with respect to the equilibrium values of these 

variables that existed before the increase in flume slope. 

The data from run 18 are shown in figure 15.

Rum, 19 (decrease sediment-transport rate, recircular 

tion system). The change for run 19 was the converse
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D21

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TIME, IN HOURS

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6-27-66

1600 1800

PIGUEE 13. Response of the feed system to a decrease in sediment-feed rate, run 16.

of the change for run lYb. A proportional sediment trap 

was placed in the tailbox of the flume so that about 

one-third of the sediment transported from the end of 

the flume was trapped and removed from the system. 

Thus the amount of sediment returned to the upstream 

end of the flume was decreased. Degradation occurred 

because the sediment input to the flume was less than 

the sediment-transport capacity of the flume for the 

given conditions. The degradation caused a decreasing 

slope, an increasing depth of flow, and a reduced 

amount of sediment transported. Because about onethird of the sediment transported was removed continuously from the flume system, the input to the flume was 

reduced continuously also, and the cycle of change and 

adjustment in the variables was repeated. As in run 

lYb, equilibrium conditions could not be established. 

However, when the extraction of sediment was discontinued after 3.7 hours of operation, equilibrium was 

established almost immediately. The variation with

time of the several variables in run 19 is shown graphically in figure 16. The data shown for the sedimenttransport rate during nonequilibrium conditions of the 

system are the rates of extracting sediment, whereas the 

data shown for the equilibrium conditions of the system are the total sediment-transport rates. During the 

period of extracting sediment, the water-surface slope 

decreased 22 percent, the sediment-transport rate decreased 39 percent, and the depth of flow increased Y.9 

percent with respect to the equilibrium values of these 

variables that existed at the time the extraction of 

sediment was begun. The mean sand-bed elevation, decreased O.Y9 cm during run 19.

It is interesting to speculate on the final condition of 

the system if the extraction of sediment had been continued. Kathbun and Guy (196Y) found that the mean 

velocity for cessation of motion on a ripple bed for the 

sediment used in this study was about 10.4 cm per sec. 

For the water discharge used in run 19 (22.3 1 per sec
D22 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

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0900 HOG 1300 1500 17001800 1000 1200 1400 

7-18-66 7-19-66 

TIME, IN HOURS

1600 1800

FIGTJBE 14. Response of the recirculation system to an increasing sediment-transport rate, run 17b.

per m), this velocity would require a depth of flow of 

about 21 cm, which is more than the depth capacity of 

the flume. Thus the final conditions would have been a 

low sediment-transport rate, a deep depth of flow, and a 

flat slope. It is assumed that the sediment bed in the 

flume is thick enough that the bottom of the flume would 

not be exposed as degradation of the sediment bed occurs. Exposure of the flume bottom would be the more 

likely limiting condition.

Run W (increase depth, feed system). In run 20 the 

tailgate was adjusted to increase the tail-water depth, 

and the feed system was used. The data are shown in 

figure 17. As with changes in flume slope for the feed 

system, the feed system was expected to return to the 

equilibrium conditions that existed before the change 

in tail-water depth. The final equilibrium values of the 

variables were within 3.7 percent of the values of the 

variables that existed before the change in tail-water

depth. The maximum difference was for the sedimenttransport rate. About 11.5 hours of operation after the 

increase in tail-water depth was necessary for the establishment of equilibrium.

Rim 21 (decrease depth, recirculation system). In 

run 21 the tailgate was adjusted to decrease the tailwater depth, and the recirculation system was used. 

Equilibrium was established in about 0.5 hour. The 

decrease in tail-water depth caused a 37 percent increase 

in water-surface slope, a 9.8 percent decrease in depth 

of flow, and an 85 percent increase in the sedimenttransport rate with respect to the equilibrium values 

that existed before the decrease in tail-water depth. The 

data for run 21 are shown in figure 18.

Run 22 (increase depth, recirculation system). Run 

22 was the converse of run 21. As expected, new equilibrium conditions were developed. Because it was 

desired to return to approximately the same equilibrium
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D23

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1100 1700 1900

7-20-66 

TIME, IN HOURS

FIGUBE 15. Response of the recirculation system to an increase 

in sand-bed slope, run 18.

conditions that existed at the start of run 21, one large 

tailgate adjustment was made initially, and two smaller 

adjustments were made later. Equilibrium was established after the large adjustment in about 0.75 hour, 

and equilibrium was established almost immediately 

after the two smaller adjustments. The data for run 22 

are shown in figure 19. The first small adjustment of the 

tailgate was at 1528 hours on the first day, and the 

second was at 0806 hours on the second day. The fact 

that these tailgate adjustments were made are evident 

from the changes in the sediment-transport rate and in 

the water-surface slope. The adjustments to the tailgate caused a 28 percent decrease in the water-surface 

slope, a 12.8 percent increase in the depth of flow, and a 

46 percent decrease in the sediment-transport rate with 

respect to the equilibrium conditions that existed prior 

to the increase in the tail-water depth.

Rim 23 (decrease depth, feed system). Run 23 is the 

converse of run 20. The tailgate was adjusted to decrease 

the tail-water depth, and the feed system was used. This 

adjustment resulted initially in the rapid degratation in 

the downstream section of the flume and a very large 

sediment-transport rate. Figure 20 shows the increased 

sediment-transport rate, the increased water-surface 

slope, and the decreased depth of flow that existed in the 

initial stages of the run. Because the sediment-feed ratte 

was considerably less than the sediment-transport 

capacity for the conditions in the flume, the initial 

rapid degradation in the downstream section of the 

flume changed to degradation in the upstream section 

of the flume and aggradation in the downstream section. 

This degradation and aggradation resulted in a decreasing slope, a decreasing sediment-transport rate, and an 

increasing depth. These variables continued to change 

until conditions were reached at which the sedimenttransport rate equaled the sediment-feed rate. The variation with time of the several variables in run 23 is 

shown graphically in figure 20. The final equilibrium 

values of the variables were within 2.8 percent (maximum difference was for the depth of flow) of the 

equilibrium values of the variables that existed before 

the adjustment of the tailgate. Because of the degradation during the initial period of the run, the mean bedsurface elevation decreased 0.98 cm.

The results of runs 12-23 are summarized as follows:

1. For the feed system, changes of the sediment-feed 

rate resulted in new equilibrium values of the 

water-surface slope, depth of flow, and sedimenttransport rate (runs 14b, 16).

2. For the feed system, changes of the sand-bed slope 

and tail-water depth resulted in the flume system 

returning to the equilibrium values of the watersurface slope, depth of flow, and sediment-transport rate that existed before the change (runs 12b, 

13,20,23).

3. For the recirculation system, changes of the sand-bed 

slope and tail-water depth resulted in new equilibrium values of the water-surface slope, depth 

of flow, and sediment-transport rate (runs 15,18, 

21,22).

4. For the recirculation system, changes of the sediment-transport rate resulted in continually changing nonequilibrium conditions. Equilibrium 

conditions were established only when the external 

feeding or extracting of sediment was terminated. 

When the feeding or extracting of sediment was 

stopped, new equilibrium values of the watersurface slope, depth of flow, «and sedimenttransport rate were obtained (runs 17,19).
D24 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

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Extracted sediment only

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Stop sediment extraction 

 RecirculationI_______________I

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7-21-66

1700 0800 1000 1200 1400 1600 1800

7-22-66 

TIME, IN HOURS

FIGURE 16. Response of the recirculation system to a decreasing sediment-transport rate, run 19.

The feed and recirculation systems apparently responded differently to changes in sand-bed slope and 

tail-water depth. This apparent difference is not a true 

difference when the interrelations among the variables 

are considered. In the feed system, both the water discharge and the sediment-feed rate were fixed or independent variables. When Q and Qs are the independent 

variables, the variables are uniquely related (Kennedy 

and Brooks, 1965), and $, Z>, and bed roughness can 

have only single values for the fixed values of Q and 

Qs. In the recirculation system, Q and S were usually 

the independent or controlled variables as equilibrium 

was established to begin a run. When the sand-bed slope 

or tail-water elevation was changed, only the water discharge was controlled, and all other variables were free

to adjust to new values. If the depth of flow had been 

controlled in addition to the water discharge when the 

sand-bed slope was changed, then the variables would 

be uniquely related (Kennedy and Brooks, 1965) and 

could not permanently change in value. If slope had 

been fixed in addition to water discharge when the tailwater depth was changed, unique relations would not 

exist among the variables (Kennedy and Brooks, 1965), 

and permanent changes in value may or may not occur. 

The responses of the feed and recirculation systems 

to changes of sand-bed slope, tail-water depth, and sediment-transport rate were predicted qualitatively by the 

proportionality among the variables Q, Q8<> d, and S 

proposed by Lane (1955). In the present study, the 

water discharge was constant, and d was constant be-
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D25

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Feed Feed

0800 1000 

7-25-66

1200 0900 1100 1300 0900 

7-26-66

1100 1300 

7-29-66

1500 1200 

3-66

TIME, IN HOURS 

FIGUBE 17. Response of the feed system to an increase in the tail-water depth, run 20.

1400 1600 

8-3-66

cause a uniform sediment was used. When d and Q are 

constant, the proportionality of Lane (1955) predicts 

that the sediment-transport rate and the water-surface 

slope are directly related. A comparison of the direct 

proportionality of Qs and 8 with the results of runs 

12-23 is:

1. In run 14b, 8 increased when Q8 was increased by 

increasing the sediment-feed rate; and in run 16, 

8 decreased when Qs was decreased by decreasing 

the sediment-feed rate.

2. In runs 12b, 13, 20, and 23, Q8 was constant, and the 

flume slope or tail-water depth was changed to 

cause nonequilibrium hydraulic and sedimenttransport conditions. 8 initially deviated from its 

equilibrium value but returned after the reestablishment of equilibrium conditions to its equilibrium value that existed prior to the change.

3. In runs 15 and 22, Qa was decreased by changes to 

the sand-bed slope and tail-water depth, and 8 decreased in both runs. In runs 18 and 21, Q8 was 

increased by changes to the sand-bed slope, and 

tail-water depth and 8 increased in both runs.

4. In run lYb, Qa and 8 increased continuously as sediment was added to the recirculation system. In 

run 19, Q8 and 8 decreased continuously as sediment was extracted from the recirculation system.

In the operation of both feed and recirculation systems, the depth of flow and the water-surface slope 

can be changed by adjustments of the flume slope, or 

the tailgate at the downstream end of the flume, or of 

both. These adjustments, however, do not exclude 

changes in the depth of flow and the water-surface 

slope resulting from changing hydraulic and sedimenttransport conditions in the flume. Runs 12-23 showed 

that changes in the depth of flow and the water-surface 

slope can occur with no adjustment to the tailgate (runs 

14b, 15, 16, I7b, 18, 19) and with no adjustment to the 

tailgate or the flume slope (runs 14b, 16,17b, 19). Depth 

adjustments can occur only in flume systems that 

operate with a constant-head tailbox. If the flume system 

is closed with respect to the quantity of water, then 

depth adjustments cannot occur.

The experimental data were used to determine if, 

as suggested by Maddock (1968), the relation between
D26 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

-Equilibrium 

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TIME, IN HOURS

FKTOBE. 18. Response of the recirculation system to a decrease in the tail-water

depth, run 21.

mean velocity F, and the unit water discharge-slope 

product, qS, for the feed system significantly differs 

from this relation for the recirculation system. jRecall 

equations 8 and 9 (p. D5). Because q=VD, the qS 

product differs from stream power, yVDS, only by the 

presence of the constant y in the stream power relation. 

Equations 8 and 9 were put in the general form

V=a (11)

If logarithms are taken, the result is

loge V= loge a + b loge ( qS) . ( 12)

Least squares procedures were used in applying the 

experimental data to equation 12 to determine the values 

of the constants b and loge a. Six different combinations

of the data were used and the results are summarized 

in table 4. The first three entries are the results of using 

the experimental data from runs 1-11, in which the 

equilibrium conditions for the feed and recirculation 

systems were compared. The first entry is for the overall 

mean values of V and qS for runs 1-11, in which the 

mean values of these variables for each part of the run 

(recirculation, feed, and recirculation) were weighted 

in accordance with the number of observations of each 

variable in each part. For the recirculation runs (entry 

2), the mean values were weighted in proportion to 

the number of observations made for each of the two 

recirculation parts of the run. In the last three entries, 

the mean values of V and q/S for the equilibrium conditions obtained in runs 12-23 were included with the
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES

601 n i i 

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500 1000 1400 1600

TIME, IN HOURS 

FIGTJEE 19. Response of the recirculation system to an increase in the tail-water depth, run 22.

mean values from runs 1-11. For the "overall" entry 

(entry 4), the mean equilibrium values for each of the 

runs 1-23 were used, regardless of whether the method 

of operation was feed or recirculation. Only data for 

feed-system runs were used in entry 6 and only data 

for recirculation-system runs were used in entry 5.

TABLE 4. Summary of the least squares values of loge a and b

1

2 

3 

4 

5 

6

Entry Runs included

______ Overall, 1-11 !_______.

______ Feed, 1-11. _ ________

______ Overall, 1-23 !_ _______

_ ____ Recirculation, l-23_ _.

.--___ Feed, 1-23 __ ________

log. a

... 1. 852±0. 171

._. 1. 841±0. 154

.-. 1. 860± 0.210

._ 1. 942 ±0. 145

__ 1. 885 ±0. 120

... 1. 915±0. 192

6

0 43±0. 04 

44 ±0. 03 

43 ±0. 05 

42 ±0. 03 

43 ±0. 03 

42 ±0. 04

i Overall implies mean values based on all runs, regardless of whether the system 

of operation was feed or recirculation.

Runs 1-11 and 12-23 were considered separately as well 

as together because runs 12-23 covered only a part of 

the range of hydraulic and sediment-transport conditions covered by runs 1-11. The possibility existed that 

the combination of all the experimental data might be 

biased toward the range of conditions covered by runs 

12-23 because of the large number of runs in this range. 

The results presented in table 4, however, show no significant differences between the V versus q/S relation 

for runs 1-11 and for runs 12-23.

The limits shown in table 4 for the b and \ogea values 

are based on the 95 percent confidence level of significance. The b or slope values range from 0.42 to 0.44, and 

no significant differences exist among the six values of 

&. The b values are not significantly different from 0.40, 

except the value for entry 2 (runs 1-11). This b value is
D28 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

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FLOW, DEPTHOF 

CENTIMETERS IN 

URFACE 

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TIME, IN HOURS 

FIGUBE 20. Response of the feed system to a decrease in the tail-water depth, run 23.

1600

just significantly different from 0.40 at the 95 percent 

confidence level but is not significantly different from 

0.40 at the 97.5 percent level. The differences between the 

feed and recirculation systems suggested by equations 

8 and 9 are not substantiated by the experimental data 

of this study. The logea values also do not differ significantly from each other.

Figure 21 shows the V versus q/S relations for the experimental data of this study. The circles are the data 

using the overall mean values of V and qS for all the 

runs. The solid line represents the least squares line for 

the data from overall mean (runs 1-23) values; these 

data had the maximum logea value and the minimum 5 

value. The dashed line represents the least squares line 

for the data using the recirculation (runs 1-11) values; 

these data had the maximum b value and the minimum

logea value. All the other least squares lines that represent the relations for other combinations of the data lie 

between these two. It may be concluded that the data 

of this study show that the relation between the mean 

velocity and the unit discharge-slope product for the 

feed system does not differ significantly from this relation for, the recirculation system.

ADVANTAGES AND DISADVANTAGES OF THE 

FEED AND RECIRCULATION SYSTEMS

From the experience gained in this study, in which 

both the feed and recirculation systems were used, it is 

possible to compare the two systems with respect to the 

advantages and disadvantages of each. As indicated in 

the preceding pages, the main difference between the 

two systems is the procedure by which the sediment is
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D29

UJ

Q. 60 

V)

cc

tf 50

40

>: 30

20

EXPLANATION

Experimental data.overall runs(1-23) 

Least squares, overall runs (1-23) 

Least squares, recirculation runs (1-11)

20 30 40 50 60 70 80 90100 200 300 400 

5 UNIT WATER DISCHARGE XSLOPE, (gs) X 103, IN LITERS PER SECOND PER METER

FIGURE 21. Mean velocity versus unit water discharge-slope product relations for the 

feed and recirculation systems of flume operation.

transported from the downstream end of the flume to 

the upstream end. This transport is accomplished hydraulically in the recirculation system, whereas some 

mechanical means of sediment return must be used in 

the feed system (fig. 1). The flume used in the present 

study was small, and the amount of sediment for operating the flume as a feed system was not excessive. Operation of a feed system for a large flume may not be practical, however. For example, the sediment-transport rate 

for upper regime flow conditions in an 8-foot-wide flume 

may be as much as 5.9 pounds per second per foot of 

width, or 2,035 tons per day for an 8-foot width.

An additional disadvantage of the feed system is that 

the sediment must be fed into the flume at a reasonably 

constant rate. Gilbert (1914) experienced considerable 

difficulty with his sand-feeding devices. He stated (p. 

23): "The hopper feeding was at best not sufficiently 

uniform to be used in measuring the load carried by the 

experimental stream." At large sediment-transport 

rates, Gilbert had to feed the sediment by hand. He 

filled a small box of known sediment capacity and 

emptied it at regular intervals. This procedure of handfeeding had the disadvantage of discontinuous sediment 

feeding but had the advantage of permitting a reasonably accurate determination of the sediment-feed rate. 

Gilbert (1914) summarized his experiences with sand 

feeding as follows (p. 241): "None of the devices we 

employed to feed debris to the current achieved uniformity. Those which depended on the flow of wet debris 

through an aperture failed because the proportion of 

water could not be kept constant. The others depended 

on handwork and experienced the irregularity usual to 

handwork."

In addition to the hopper-type sand feeder used by 

Gilbert (1914) and feeding sediment by hand, a third 

general type of sediment feeding procedure has been 

used. This third type is the elevator infeed system, and 

the procedure consists of placing wet sediment in a receptacle and then gradually raising the receptacle into 

the flow so that the sediment is removed by the water 

flowing over it. The elevator infeed system has the 

advantages that the sediment does not have to be dried 

and that little attention to the sediment feeder is necessary during a run. The elevator infeed system has the 

disadvantages that the length of time the feed system 

can be run without interruption is limited by the size 

of the infeed receptacle, and that there is no way of 

checking the sediment-feed rate during the run. Also 

voltage fluctuations and the decreasing load on the electrical drive system for the infeed receptacle may cause 

unknown variations in the sediment-feed rate.

In this study, a vibrating sediment feeder was used, 

and a reasonably constant sediment-feed rate could be 

obtained if certain precautions were observed. The sediment had to be completely dry, because even small 

amounts of moist sediment caused variations in the sediment-feed rate. Also the depth of sediment in the hopper had to be constant. The sediment depth in the hopper of the sediment-feeder was kept constant by using 

a large secondary storage bin which fed sediment directly into the hopper (fig. 2). The sediment had to be 

kept free of debris, which would also cause variations in 

the sediment-feed rate. Fluctuations in the voltage supply caused variations in the sediment-feed rate. The 

vibrating sediment feeder has the advantage that the 

sediment-feed rate can be checked easily at any time
D30 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

during the run. Even with modern equipment, however, 

obtaining a constant sediment-feed rate is difficult. 

Johnson (1942) recognized the limitations of feed systems and pointed out that the usefulness of the bed-load 

data in the summary of flume experiments that he compiled (1943) is limited by the effects of the various types 

of equipment and procedures used in feeding the 

sediment.

Difficulties with sediment feeding in the feed system 

can be eliminated by using the recirculation system in 

which the transported sediment is returned "hydraulically to the upstream end of the flume. There is some variation in the rate of return of the sediment to the upstream end of the flume because the rate at which the 

sediment is transported from the downstream end of 

the flume varies with time. This variation in the rate of 

return is an advantage because sediment-transport rates 

of natural alluvial channels also vary with time. Therefore, it should be possible to operate a recirculation system with a shorter flume than that necessary for a feed 

system because the naturally varying sediment-transport conditions are established almost immediately in 

the upstream section of the recirculation flume. In the 

feed system, however, some length of the upstream section of the flume is necessary for dampening of the manmade oscillations in the sediment-feed rate and for 

establishing the natural oscillations of sediment 

transport.

The feed system has the advantage that the sedimenttransport rate in the flume can be controlled directly. 

A specific sediment-transport rate can be obtained in the 

recirculation system only by trial and error.

No specific cost analysis of the two systems of flume 

operation was made during this study, but the following observations were made. First, the feed system 

required a larger supply of sediment than the recirculation system for continuous operation because dry sediment was necessary for the sediment feeder. Because the 

supply of sediment was limited, the length of time the 

feed system could be run without interruption was limited. An example is run 14b, the results of which are 

presented in figure 11. A total of 9 days was required to 

complete run 14b, in which the feed system was used. 

Operation of the flume was limited to 3 days with two 

3-day periods of no operation that were necessary for 

drying the sediment. Second, the feed system required 

constant attention with respect to removal of the trapped 

sediment, replacement of the water, and checks of the 

sediment-feed rate; the recirculation system required 

no attention other than that required to obtain the 

necessary measurements. Third, the recirculation system responded much more quickly to changes in the 

sand-bed slope, tail-water depth, and sediment-transport

rate than the feed system; therefore equilibrium could 

be established much more rapidly for a recirculation 

system than for a feed system as the hydraulic and sediment-transport parameters were varied in a series of 

experiments.

In summary, the recirculation system has the advantage of ease and economy of operation, whereas the feed 

system has the advantage of direct control of the sediment-transport rate.

SUMMARY

The feed and recirculation systems of flume operation 

for laboratory alluvial channel experiments were compared under a variety of hydraulic and sediment-transport conditions, and the responses of the laboratory 

flume systems to changes of the hydraulic and sedimenttransport variables were determined. The experiments 

for this study were conducted in a tilting plastic flume 

10 meters long, 20 cm wide, and 20 cm deep. This flume 

could be operated either as a feed system or as a recirculation system. The sediment had a median fall diameter 

$50, of 0.30 mm and a gradation o-, of 1.26.

The equilibrium conditions for the feed and recirculation systems were compared in a series of 11 runs that 

covered a wide range of flow conditions and a variety 

of bed forms from ripples to antidunes. The mean equilibrium values of the water-surface slope, depth of flow, 

velocity, and sediment-transport rate for the recirculation system were not significantly different at the 95- 

percent level of significance from the mean equilibrium 

values of these variables for the feed system.

The responses of the feed and recirculation systems 

of the laboratory flume to changes of sand-bed slope, 

tail-water depth, and sediment-transport rate were 

determined with the water discharge constant. Data 

from 12 experimental runs showed that:

1. For the feed system, changes of the sediment-feed 

rate resulted in new equilibrium values for the 

water-surface slope, depth of flow, and sedimenttransport rate.

2. For the feed system, changes of the sand-bed slope 

and the tail-water depth resulted in the return of 

the water-surface slope, depth of flow, and sediment-transport rate to the equilibrium values that 

existed before the change.

3. For the recirculation system, changes of the sandbed slope and tail-water depth resulted in new 

equilibrium values for the water-surface slope, 

depth of flow, and sediment-transport rate.

4. For the recirculation system, changes of the sediment-transport rate (by addition of sediment to 

the recirculating sediment or extraction of sedi-
RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D31

ment from the recirculating sediment) resulted in 

continually changing nonequilibrium conditions. 

Equilibrium conditions were established only when 

the external feeding or extracting of sediment was 

terminated. New equilibrium values for the watersurface slope, depth of flow, and sediment-transport rate were obtained when the feeding or 

extracting of sediment was stopped.

The results of the 12 runs suggest that the feed and 

recirculation systems responded differently to changes 

in sand-bed slope and tail-water depth. However, this 

difference is not a true difference when the interrelations 

among the variables Q, Qs, 8, and D are considered. If 

the sediment-feed rate, Qs, and the water discharge, Q, 

are constant, then the variables are uniquely related 

(Kennedy and Brooks, 1965), and $, Z>, and bed roughness can only have single values for the fixed Q and Qs. 

Thus, when the sand-bed slope or tail-water depth was 

changed, S and D had to return to the previous equilibrium values determined by the fixed Q and Qs. In the 

recirculation system, only the water discharge was 

maintained constant, and $, Z>, and Q8 were free to 

adjust to new values when the sand-bed slope or tailwater depth was changed.

The recirculation system has the advantages of ease 

and economy of operation because the sediment is 

returned hydraulically to the upstream end of the 

flume. Hydraulic return of the sediment requires no 

attention or effort on the part of the flume operator. For 

the feed system, the sediment must be separated from 

the flow, prepared for feeding, transported to the 

upstream end of the flume, and introduced continuously 

at a reasonably constant rate. The operator must attend 

the sediment-feeding mechanism throughout the duration of the experimental run. If dry sediment is 

required for the sediment-feeder, as it was in the present 

study, the length of time the flume can be operated 

depends upon the available supply of dry sediment. 

Also, the time between runs must be sufficiently long 

to permit the sediment to dry. Drying the sediment also 

requires additional handling of the sediment. The feed 

system has the advantage that the sediment-transport 

rate can be set directly, whereas in the recirculation 

system, a specific sediment-transport rate can be 

obtained only by trial and error. The recirculation system responded much more rapidly to changes in sandbed slope, tail-water depth, and sediment-transport rate 

than did the feed system.

The responses of the feed and recirculation systems 

of the laboratory flume to changes of sand-bed slope, 

tail-water depth, and sediment-transport rate were predicted qualitatively by the proportionality of Lane 

(1955).

LIMITATIONS AND RECOMMENDATIONS

One limitation of this study is that the experiments 

were conducted in a single flume and one sediment was 

used. The second limitation is that the determination of 

the responses of the feed and recirculation systems of 

flume operation to changes of variables was limited to a 

single water discharge. Similar results would be 

expected for other discharges, and perhaps the rate at 

which equilibrium was established would be faster or 

slower, depending upon whether the water discharge 

was larger or smaller than the water discharge used in 

this study.

The two limitations of the present study suggest the 

following subjects for further study: Similar experiments with a graded sediment; similar experiments 

with different water discharges; similar experiments 

with the imposition of large changes of the variables 

so that significant changes in the bed roughness occur; 

and experiments to test the response of a feed system 

with a constant sediment-feed rate to changes in water 

discharge.

LITERATURE CITED

Barton, J. R., and Lin, Pin-Nam, 1955, A study of sediment 

transport in alluvial channels: Colorado State Univ., Dept 

Civil Engineering Research Rept. 55JRB2, 43 p.

Blench, T., 1962, Discussion of resistance to flow in alluvial 

channels: Am. Soc. Civil Engineers Trans., v. 127, p. 956- 

963.

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

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

526-549.

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

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

Water-Supply Paper 1498-C, 16 p.

Einstein, H. A., 1950, The bed-load function for sediment transportation in open channel flows: U.S. Dept. Agriculture 

Tech. Bull. 1026, 71 p. [1951].

Gilbert, G. K., 1914, The transport of debris by running water: 

U.S. Geol. Survey Prof. Paper 86, 263 p.

Guy, H. P., Simons, D. B., and Richardson, E. V., 1966, Summary 

of alluvial channel data from flume experiments, 1956-61: 

U.S. Geol. Survey Prof. Paper 462-1,96 p.

Johnson, J. W., 1942, Discussion of formulas for the transportation of bed load: Am. Soc. Civil Engineers Trans., v. 107, 

p. 578-580.

 1943, Laboratory investigations on bed-load transportation and bed Toughness: U.S. 'Soil Conserv. Service Rept. 

SCS-TP-50, 116 p.

Kennedy, J. F., 1961, Stationary waves and antidunes in alluvial 

channels : Pasadena, California Inst. Technology Rept KHR-2, 146 p.
D32 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Kennedy, J. F., and Brooks, N. H., 1965, Laboratory study of 

an alluvial stream at constant discharge, in Proceedings of 

the Federal Inter-Agency Sedimentation Conference, 1963: 

U.S. Dept. Agriculture Misc. Pub. 970, p. 320-330.

Lane, E. W., 1955, The importance of fluvial morphology in 

hydraulic engineering: Am. Soc. Civil Engineers Proc., v. 

81, no. 745, 17 p.

Laursen, E. M., 1958, The total sediment load of streams: Am. 

Soc. Civil Engineers Proc., Jour. Hydraulics Div., v. 84, no. 

HY1, pt. 1, 36 p.

Maddock, Thomas, Jr., 1968, Discussion of recirculation and 

sand-feed type flume experiments: Am. Soc. Civil Engineers 

Proc. Jour., Hydraulics Div., v. 94, no. HY4, p. 1139-1147.

Rathbun, R. E., and Guy, H. P., 1967, Measurement of hydraulic 

and sediment-transport variables in a small recirculating 

flume: Water Resources Research v. 3, no. 1, p. 107-122.

Raudkivi, A. J., 1967, Analysis of resistance in fluvial channels: 

Am. Soc. Civil Engineers Proc., Jour. Hydraulics Div., v. 

93, no. HY5, p. 73-84.

Simons, D. B., and Richardson, E. V., 1966, Resistance to flow 

in alluvial channels: U.S. Geol. Survey Prof. Paper 422-J, 

p. J1-J61.

Simons, D. B., Richardson, E. V., and Albertson, M. L., 1961,

Flume studies using medium sand (0.45 mm) : U.S. Geol.

Survey Water-Supply Paper 1498-A, 76 p. 

Simons, D. B., Richardson, E. V., and Haushild, W. L., 1963,

Some effects of fine sediment on flow phenomena: U.S. Geol.

Survey Water-Supply Paper 1498-G, p. G1-G47. 

Stein, R. A., 1965, Laboratory studies of total load and apparent

bed load: Jour. Geophys. Research, v. 70, no. 8, p. 1831-

1842. 

Task Committee on Bed Forms in Alluvial Channels, 1966,

Nomenclature for bed forms in alluvial channels: Am. Soc.

Civil Engineers Proc., Jour. Hydraulics Div., v. 92, no.

HY3, p. 51-64. 

U.S. War Department, Army Corps of Engineers, 1935, Studies

of river bed materials and their movement, with special

reference to the lower Mississippi River: U.S. Army Corps

Engineers, Waterways Expt. Sta. Paper 17, 161 p. 

Vanoni, V. A., and Hwang, L. S., 1967, Relation between bed

forms and friction in streams: Am. Soc. Civil Engineers

Proc., Jour. Hydraulics Div., v. 93, no. HY3, p. 121-144. 

Williams, G. P., 1967, Flume experiments, transport of a coarse

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

O