A Study of Fluvial 

Characteristics and 

Hydraulic Variables 

Middle Rio Grande 

New Mexico

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1498-F

JAN 20 1964

v '**

&A

A Study of Fluvial 

Characteristics and 

Hydraulic Variables 

Middle Rio Grande 

New Mexico

By JAMES K. CULBERTSON and DAVID R. DAWDY

STUDIES OF FLOW IN ALLUVIAL CHANNELS

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1498-F

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1964
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

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

Washington, D.C. 20402
CONTENTS

Page

Symbols________________________________________________________ vi

Abstract___--_--_---_______-__-______-_____________________-___ Fl

Introduction._____________________________________________________ 1

Purpose and scope_____--____-________-_____-_______-__________ 1

Personnel and acknowledgments,-_______________________________ 3

Geographic location and description of reaches ________________________ 4

Definitions _______________________________________________________ 8

Measurement of hydraulic and sediment variables.____________________ 9

Water discharge.______________________________________________ 9

Concentration of suspended sediment.___________________________ 9

Suspended-sediment discharge_______-__-___-_______------_-_-- 9

Bed elevation _________________________________________________ 9

Slope determinations___--_-___--_______-__-___-_-___-___--_-- 10

Bed material________________________________________________ 12

Depth-discharge relations.___________________________________________ 13

Depth-discharge relations at individual stations.__________________ 14

Criteria for estimating regime of flow_____--_-__--_-_--__------__- 18

Relation of Chezy C to bed material.________________________________ 21

Other factors influencing roughness_________________________-__--___- 27

Relative roughness_ ___________________________________________ 27

Channel shape.________________________-__-_______-___----.--_ 28

Standard deviation of bed material._____________-___-___--_-_-_- 28

Suspended-sediment concentration__________________--_-_-__-_-__ 29

Summary of other factors influencing roughness.__________________ 29

Changes in bed elevation___________________________________________ 29

Sediment transport functions______________________________________ 36

Relation of sediment transport to shear____________________-_--_----_- 36

Modified Einstein method.____-___________-_-_._-_-___-_-_--------- 40

Bagnold theory__________________________________________________ 43

The Bagnold plot_.___-_--________________________----- 45

Critical stress 0^0 A--------------------------------------- 47

Characteristic applied tangential stress.___.__________-_--___- 48

Total transport function, <£.____________-___-__-_-_----__--- 49

Comparison between modified Einstein and Bagnold___________-___._-- 51

Conclusions and summary_-__________-_-___-___------------_------- 53

Tables of basic data and computed parameters._______________________ 55

Literature cited._-_______-__________-______-___-_-------_--_--_--- 73

Index. _____________________________________________----- 73

in
IV CONTENTS

ILLUSTRATIONS

Page 

FIGURE 1. Location map of middle Rio Grande___________________ F2

2. Sketch map of Rio Grande near Bernalillo reach_______ 6

3. Sketch map of Rio Grande near Belen, Casa Colorada

reach ____________.__________________ ___________._ 7

4. Rio Grande near Bernalillo reach, showing energy gradients. . __________________________________________ 11

5-13. Relation of velocity to hydraulic radius.

5. Rio Grande near Bernalillo-__-_---__-_-___-____ 15

6. Casa Colorada reach near Belen-________________ 16

7. San Francisco riverside drain near Bernardo. _ _ _ _ _ 17

8. Rio Grande at Socorro.________________________ 18

9. Rio Grande at San Antonio, January 1952-June

1953; October 1954-June 1955___________ 19

10. Rio Grande at San Antonio, July 1953-May 1954.. 20

11. Rio Grande at San Antonio, May-September 1954;

July-September 1955------------------------- 21

12. Galisteo Creek at Domingo-___-_-_-___-_-_--___ 22

13. Rio Puerco near Bernardo.________-___-_--__-__ 23

14. Garde's criteria for regimes of flow in alluvial channels. _ _ 24

15. Simons' criteria for regimes of flow in alluvial channels.-- 25

16. Variation of Chezy C with median diameter of bed material- _._--_______-________--___-____-___-___-___ 26

17. Relation of velocity to hydraulic radius for Rio Grande

at Cochiti-------__---_-----------_--------------- 26

18. Relation of velocity to hydraulic radius for Bernalillo

sections A-2 and F.------------------------------- 30

19. Changes in bed elevation during 1952 spring runoff,

Bernalillo reach.__________________________________ 33

20. Changes in bed elevation during 1957 and 1958 spring

runoff, Casa Colorada reach_______________________ 34

21. Schematic diagram showing friction head loss in open

channel flow._____________________________________ 35

22-25. Relation of suspended sands to hydraulic radius.

22. Bernalillo sections A-2 and F.------------------ 37

23. Bernalillo reach sections A-2 through F- ________ 38

24. Casa Colorada reach.__________________________ 39

25. Rio Grande at San Antonio.___-__-___-_-------_ 41

26. Comparison between computed total sediment loads at

Bernalillo sections A-2 and F_---------------------- 42

27. Relation between median diameter, B, and Bb __________ 44

28. Bagnold plot of Rio Grande data__------------------- 46

29. Bagnold relation for Casa Colorada reach_____________ 47

30. Comparison of Bagnold and modified Einstein computed

total sands-_________________________----_-------- 52

31. Comparison between modified Einstein and Bagnold total

transport.- _ _________________________-__-_-------- 53
CONTENTS

TABLES

Page 

TABLE 1. Energy gradients and water-surface slopes for the Rio

Grande near Bernalillo reach, 1952________________ F12

2. Energy gradients and water-surface slopes for Casa

Colorada reach____________________________________ 12

3. Median diameter of bed material, in millimeters, for the

Rio Grande at CochitL_________-_-______-__-__----. 25

4. Median diameter and Chezy C for the Rio Grande at

Cochiti____________________________-______-__--- 27

5-18. Basic data and computed parameters.

5. Rio Grande at Otowi Bridge, near San Ildefonso___ 55

6. Rio Grande at Cochiti________________________ 56

7. Galisteo Creek at Domingo__-__--__-_------_---_ 57

8. Rio Grande at San Felipe,______________________ 58

9. Rio Grande at Angostura heading near Algodones__ 59

10. Rio Grande near Bernalillo, section A-2, _________ 62

11. Rio Grande near Bernalillo, sections A, B, C, D, £"__ 63

12. Rio Grande near Bernalillo, section F. ___________ 64

13. Rio Grande near Bernalillo, section A-2 runoff

from tributary inflow__-----__--_-__---------- 65

14. Rio Grande near Bel en, Casa Colorada reach______ 66

15. Rio Puerco near Bernardo.__________-___--__--- 68

16. Rio Grande near Socorro reach____________-__--_ 69

17. Rio Grande at San Antonio. _-___-_--__-_------- 70

18. Rio Grande Floodway at San Marcial. ______----_ 71
SYMBOLS

Symbol Description Units 

A Area of channel_____________________________ sq ft

b Width of channel____________________-___-__- ft

C Chezy coefficient of discharge, (F/F*) T/g. Sub- 0 

script 1 and 2 indicate lower and upper regimes 

respectively.

Cm Concentration of measured suspended sediment ppm 

_ by weight.

C Concentration of measured suspended sediment by ppm 

volume.

CT Concentration of measured suspended sands ppm

(>0.062 mm) by weight. 

d Median diameter of bed material ______________ ft

D Average depth of flow_______-_-_-__-_-_-_---- ft *

/ Darcy-Weisbach friction factor equals 8 (F*/F) 2 _ 0 

F Froude number, V/-\/gD________-_-____-_____- 0

g Gravitational constant _______________________ ft per sec 3

ht Friction head loss_____________-______-_-____- ft

k Constant ___________________________________ 0

n Manning's coefficient of roughness_____________ ft 1/e

qa Total sediment discharge in Bagnold equation. _ Ib per sec per ft 

Q Discharge of water-sediment mixture.--------- cu ft per sec

Q, Discharge of measured suspended sediment----- tons per day

QT Discharge of computed total sediment.______ tons per day

R Hydraulic radius._________-__--__---__-_-___ ft

5 Slope of water surface, assumed to equal energy ft per ft

gradient, except where noted. 

T Water temperature..------------------------ °C

V Average velocity of flow___------------------- ft per sec

F* Shear velocity which is ^gDS or VTO/P -------- ft per sec

Z Elevation above an arbitrary datum___________ ft

y Specific weight of water, 62.5_______________ Ib per cu ft

y, Specific weight of sediment, 165.6_____--------- Ib per cu ft

AT, Difference between specific weights of sediment Ib per cu ft

and water, 103. 

v Kinematic viscosity________.__---__-_--__-- sq ft per sec

p Mass density of water, at 60°F equals 1.94---_-_ slug per cu ft 

pa Mass density of sediment, at 60°F equals 5.14___ slug per cu ft 

<£ Bagnold transport rate function <f» q,/bgp»d 0

Bb -\/Aysd/p. 

TO Tractive or shear force developed on the bed, Ib per sq ft

yDS'.

6 Bagnold shear function, or overall tangential stress 0

parameter=To/A78d + D(SCm/2.65d. 

w Fall velocity of sediment particles (median diam- ft per sec

eter of bed material).

VI
STUDIES OF FLOW IN ALLUVIAL CHANNELS

A STUDY OF FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES, MIDDLE RIO GRANDE, NEW MEXICO

By JAMES K. CULBERTSON and DAVID R. DAWDY

ABSTRACT

Extensive data concerning water discharge and suspended-sediment transport 

for many sand-be*d cross sections in the middle Rio Grande basin are analyzed. 

A discontinuity in the velocity-hydraulic-radius relations of these reaches is shown 

to occur, with velocity doubling for a constant depth. The roughness parameter, 

Chezy C, is relatively constant for discharges beyond the discontinuity, and mainly 

is a function of the size of bed material.

A discontinuity in the hydraulic-radius suspended-sand loads relation is shown 

to coincide with the discontinuity in depth discharge. Suspended-sand loads 

increase 8 to 10 times for a constant depth at the point of discontinuity.

The mechanics of scour and fill are studied, and it is indicated that contracted 

sections of a reach generally will scour on a rising stage and fill on the recession. 

The stream system apparently operates so as to maintain a constant energy 

gradient through a reach.

The suspended-sediment data for the middle Rio Grande are used to compute 

total loads according to the modified Einstein and the Bagnold methods. The 

modified Einstein method gives consistent results when applied to different cross 

sections of a single reach. The Bagnold method apparently predicts a correct 

shape for the shear-transport relation, but it is not as suited to field use at this 

time as is the modified Einstein method.

INTRODUCTION 

PURPOSE AND SCOPE

The purpose of this report is to present interrelations between 

hydraulic radius, median size of be4 material, channel-bed roughness, 

flow regime, mean velocity, and sediment transport for flow in sand 

channels of the middle Rio Grande in New Mexico. Data used were 

collected during the period 1952 to 1959 as part of a cooperative 

program between the U.S. Geological Survey and the U.S. Bureau of 

Reclamation to study sediment transport hi the middle Rio Grande.

Observations were made at eight stations on the main stem of the 

Rio Grande. The stations presented are in that reach of the Rio 

Grande from Otowi Bridge near San Ildefonso to San Marcial, N.

Fl
F2 STUDIES OF FLOW IN ALLUVIAL CHANNELS

COLORADO 

NEW MEXICO

-'

f

V

Rio Puerco fctSan Francisco Riverside Drain 

Bemardo

SOCORRO 

Socorro Reach 

San Antonio 

San Marcial

S

NEW MEXICO 

TEXAS

FIGURE 1. Location map of the middle Rio Grande.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F3

Mex., approximately 180 miles (fig. 1). The study sites at three stations were reaches of approximately 1% miles each. The Rio Grande 

near Bernalillo reach includes 7 sections, the Rio Grande near Belen, 

Casa Colorado reach, 10 sections, and the Rio Grande near Socorro 

reach, 4 sections. Rates of flow ranged from 2,000 cfs (cubic feet per 

second) to 10,000 cfs; frequencies of discharge being from that equaled 

or exceeded 50 percent of the time to that equaled or exceeded 10 

percent of the time.

Most of the observations listed in this report represent spring 

runoff from the headwaters of the Rio Grande in Colorado, some minor 

tributaries in northern New Mexico, and runoff from the Rio Chama. 

The Rio Chama is the largest contributor of tributary inflow above the 

Rio Grande at Otowi Bridge station.

Several measurements representing flow from the Rio Puerco are 

shown for the Rio Puerco near Bernardo, the Rio Grande near Socorro, 

and the Rio Grande at San Antonio stations. Some storm runoff 

data for the Galisteo Creek at Domingo also are included.

Data observed for most of the stations include (1) stream depths 

and velocities, (2) samples of suspended sediment, (3) samples of the 

bed material, (4) water temperature, and (5) water-surface slope. 

Slopes are not available for all observations.

Hydraulic characteristics at each station are discussed, and flow 

regime based on discontinuities in the- stage-discharge relation and 

visual observation of water surface appearance are noted. Sedimenttransport characteristics are described for each station and related 

to hydraulic variables and regimes of flow. Most of the total-load 

computations represent upper-flow regimes, that is, plane bed, standing wave, or antidune bed configuration; however, several computations are shown for lower-regime flows or dune bed configuration. 

The relation between F*/w and V*dfv is used to compare forms of 

bed roughness found in the Rio Grande with those found in flume 

studies. The relation between the roughness parameters, Manning's n 

and Chezy's C, and median diameter of bed material is shown to be 

well defined for stations studied in the Rio Grande basin.

Total sediment loads are computed by using the modified Einstein 

method and the Bagnold method. Also, field data are used to test the 

interrelation of Bagnold's total-transport and shear functions.

PERSONNEL AND ACKNOWLEDGMENTS

This report was written under the supervision of J. M. Stow, 

district chemist, Albuquerque District, Quality of Water Branch. 

Field and laboratory work was under the supervision of W. G. Bratschi, 

succeeded by J. K. Culbertson, hydraulic engineer, Geological Survey. 

F. C. Ames and G. L. Oakland of the Geological Survey assisted

690-231 O 63 2
F4 STUDIES OF FLOW IN ALLUVIAL CHANNELS

materially in setting up the field investigations. R. W. Fife, chief 

of the Hydrology Section, and E. L. Pemberton, head of the Sedimentation Section, both of the Albuquerque Bureau of Reclamation Office 

planned and supervised the data collection program for the Bureau at 

field level.

C. F. Nordin, Jr., hydraulic engineer, Geological Survey, aided 

materially in the planning and beginning of this report.

GEOGRAPHIC LOCATION AND DESCRIPTION OF REACHES

The Otowi Bridge station is located at the lower end of an alluvial 

reach, which includes the lower Rio Chama (fig. 1). Alluvium 

apparently has accumulated in the Rio Grande between the mouth of 

the Chama and the Otowi Bridge location as the result of flow from the 

Rio Chama. Immediately downstream from the Otowi station the 

Rio Grande enters a narrow gorge, which confines the river channel. 

Although no data are available, it is believed that little or no aggradation or degradation occurs within the reach between the Otowi Bridge 

and Cochiti stations. Data for Otowi Bridge are shown in table 5.

At Cochiti the river channel and flood plain widen considerably 

and the river channel becomes characteristic of that of a sand-bed 

stream. However, large gravel and rock are predominant bed materials at discharges higher than the approximate median frequency 

discharges at this station, which is located approximately 1 mile below 

the Cochiti diversion dam. The dam does not appear to trap any 

appreciable sand loads. Data for the Cochiti station are shown in 

table 6.

Eight miles below Cochiti the Galisteo Creek empties into the 

Rio Grande. The Galisteo is a large contributor of sediment to the 

Rio Grande. Galisteo Creek did not contribute to the spring runoff 

flows that are described in this report; however, some data on flashflood events are presented (table 7).

The San Felipe station is approximately 7 miles downstream from 

the mouth of Galisteo Creek. Tonque Arroyo empties into the Rio 

Grande immediately upstream from the San Felipe station. This 

arroyo runs only infrequently and did not contribute to the spring 

runoff events covered in this report. The river channel at the San 

Felipe station is narrow, being confined by a volcanic talus slope on 

the right bank and fairly stable clay banks on the left. Velocities are 

relatively high, and bed material in the sand range, which is brought 

in by Galisteo Creek and Tonque Arroyo, apparently is moved on past 

the station. There is little evidence of general aggradation at this 

site. Samples of bed material taken at the San Felipe station during 

high discharges showed sparse quantities of sand-size particles. Data 

for the San Felipe station are shown in table 8.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F5

Angostura diversion dam is approximately 5 miles downstream 

from the San Felipe station and forms the headworks for the Albuquerque main canal. Data were collected in the Rio Grande above 

the heading, in the settling basin immediately below the heading, 

in the wasteway return to the river, and in the Albuquerque main 

canal (table 9) as part of a study by the U.S. Bureau of Reclamation 

to determine the trap efficiency of the settling basin.

The Jemez River empties into the Rio Grande, 8 miles downstream 

from the San Felipe station. The Jemez River brought large sediment loads into the Rio Grande before the completion of Jemez 

Canyon Reservoir, which is approximately \% miles upstream from 

the mouth. Operation of this reservoir controlled all spring runoff 

from the Jemez River during the period covered by this report, and 

only minor releases were made during periods of observations. Approximately 500 cfs was released for a short period on June 18, 1959. 

The rise in suspended-sediment concentration can be noted in the 

data table for the Bernalillo section A-2 station (table 10).

The Rio Grande near Bernalillo station, referred to in this report as 

Bernalillo section A-2,, is located at a comparatively narrow point 8 

miles downstream from the mouth of Jemez River. The right bank 

is a high bluff composed of a calcareous sandstone. The left bank 

consists of a silty clay that is stabilized by salt cedar, cottonwoods, 

and range grasses. Width of the river channel at this point has 

remained at 270 feet ±3 feet at all discharges above about 1,000 cfs 

for several years. The Bernalillo section F is 8,240 feet downstream 

from the Bernalillo section A-2. Section F is comparatively wide 

with varying widths for all discharges. A section of this report is 

devoted to the observed differences in hydraulic and fluvial characteristics between these two stations (tables 10-13). A sketch map of 

the Bernalillo reach is shown in figure 2.

The next stations in downstream order below the Bernalillo stations 

are (1) Rio Grande at Albuquerque, (2) Rio Grande at Belen, and (3) 

Rio Grande near Bernardo. These three stations are measured from 

bridges. No data for these stations are discussed, because the 

hydraulic conditions caused by the bridge structures are extremely 

complicated. The Bernardo station is approximately 65 miles downstream from the Bernalillo station. There is no large tributary inflow 

in this 65 mile reach.

Approximately 7 miles downstream from the Rio Grande at Belen 

is the Casa Colorada reach. This reach of about 3% miles is of particular interest because of recent channel rectification work by the 

Bureau of Reclamation. Kelner jetties were used extensively through 

this reach in an effort to re aline the river channel and to control bank 

erosion. A great deal of effort has gone into a thorough study of the
STUDIES OF FLOW IN ALLUVIAL CHANNELS

A-2 (cableway)

Section A-3

r

Section M

_ _ _ _J

2500 

I

5000 FEET

FIGUSE 2. Sketch map of the Rio Grande near Bernalillo reach.

reach before and after installation of the jetties. A model of the 

entire reach was constructed for study at the hydraulic laboratory 

of the Bureau of Reclamation in Denver, Colo. Total-load data 

and other hydraulic measurements were collected throughout the
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F7

upper \yz miles in the prototype reach by the Geological Survey. 

Hydraulic and sediment variables are shown in table 14. A sketch 

map of the Casa Colorada reach is shown in figure 3.

Three miles downstream from the Rio Grande near Bernardo station is the mouth of the Rio Puerco. The Rio Puerco has the largest 

tributary drainage area to the Rio Grande in New Mexico and yields 

great quantities of sediment. Sediment concentrations in excess of 

400,000 ppm (parts per million) by weight have been recorded at the 

Rio Puerco near Bernardo station. Some data are shown for this 

station in table 15.

Approximately 9 miles downstream from the mouth of the Rio 

Puerco is the mouth of the Rio Salado. The Rio Salado is similar to

Note: Stationing is in river 

miles above Elephant 

Butte Dam

Above Bosque Bridge

I__I

8000 FEET 

__1

FIGURE 3. Sketch map of the Rio Grande near Belen, Casa Colorada reach.
P8 STUDIES OF FLOW IN ALLUVIAL CHANNELS

the Rio Puerco in that it is an intermittent stream yielding large 

quantities of sediment. Two miles below the Rio Salado is San 

Acacia diversion dam. No data are presented for the Rio Grande 

at San Acacia station, which is 0.7 mile downstream from the diversion dam.

Some data are presented in table 16 for a 1-mile reach of the Rio 

Grande near Socorro. This reach is about 16 miles downstream 

from the San Acacia station. There is no station near this reach 

of the Rio Grande.

The next station downstream from Socorro reach is the Rio Grande 

at San Antonio. San Antonio is about 28 river miles from the San 

Acacia station. Data are presented for this station in table 17.

The Rio Grande at San Marcial station is another 21 miles below 

San Antonio and is the southernmost station covered by this report. 

Data for the Rio Grande at San Marcial station are shown in table 18.

DEFINITIONS

Bedload consists of particles that mainly are in continuous contact 

with the bed. Movement of these particles occurs by rolling, sliding, 

or jumping along the bed.

Suspended-sediment discharge is computed from total water discharge and the concentration of suspended-sediment samples.

Regime of flow includes those flows for which the bed configurations 

are similar.

A sand-bed channel is one in which there is an unlimited supply of 

material in the sand sizes on the bed of the stream, and the median 

diameter of this bed material does not vary appreciably with depth 

to known maximum scour or with change in water discharge.

A sand-gravel channel is one in which the supply of sand-size 

material on the streambed is limited, and median diameter varies 

appreciably with discharge, ranging from sand sizes through coarse 

gravel sizes.

Sediment-transport functions give the rates at which water discharges of any magnitude in a given channel will transport sediment 

particles of sizes which are found in the streambed.

Suspended load is that part of the total sediment load that is in 

equilibrium with a normal fluid stress and for which the grains are 

supported entirely by the fluid stresses. Those particles in colloidal 

suspension are also part of the suspended load.

Total-sediment discharge is the rate of movement or discharge of 

the suspended load plus the bedload.

Unmeasured-sediment discharge is the difference between the totalsediment discharge and the suspended-sediment discharge.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES P9

Fine-material load is that part of the suspended load that consists 

of grain sizes finer than those found in appreciable quantities in the 

bed. Fine-material load is sometimes referred to as wash load.

MEASUREMENT OF HYDRAULIC AND SEDIMENT

VARIABLES

In order to give the reader a better understanding of some of the 

data presented herein, some of the measured variables will be discussed and the methods of field measurement described.

WATER DISCHARGE

The term "water discharge" actually means discharge of the watersediment mixture and includes all dissolved and suspended matter 

being transported by the fluid. However, only mean depth, mean 

velocity, and width are used to compute water discharge.

CONCENTRATION OF SUSPENDED SEDIMENT

Suspended-sediment concentrations were computed from samples 

taken at the same cross section used in the water-discharge measurement. Samples were taken using US DH-48 or US D-49 sediment 

samplers. These samplers are designed to collect a representative 

sample of the water-sediment mixture from the surface to about 0.3 

foot from the streambed. Samplers and sampling techniques are 

described in reports 1 and 6 (Subcommittee on Sedimentation, 

Federal Inter-Agency Kiver Basin Committee 1940, 1952). All 

samples were integrated vertically and were taken at equal intervals 

of width and equal transit rates in the cross section, thus giving discharge-weighted mean concentrations in parts per million by weight. 

Particle-size distributions were determined for all samples by the 

visual accumulation tube-pipette method of analysis.

SUSPENDED-SEDIMENT DISCHARGE

Measured suspended-sediment discharge is the product of total 

water discharge in cubic feet per second, mean sediment concentration in the sampled zone in parts per million, and a conversion factor 

that converts the result to a rate in tons per day. That is, all sediment discharge values, both suspended and total are shown as rate of

transport.

BED ELEVATION

Bed elevations shown in the tables of data for each station are relative to the existing station datum or to a temporary datum established 

at the location. Mean depths are subtracted from the datum or gage 

height to obtain bed elevation. For some stations, a constant was 

added to the gage height in order to obtain positive values.
STUDIES OF FLOW IN ALLUVIAL CHANNELS

SLOPE DETERMINATIONS

Slope is the variable most difficult to measure in the field. Watersurface slopes and energy gradients over short reaches on sandchannel streams vary considerably when measured at different times. 

Use of instantaneous measurements in computing various parameters 

involving slope tends to introduce scatter into any plot that concerns 

those parameters.

Similar fluctuations of instantaneous slope measurement are experienced in laboratory flumes with sand beds. Over a period of 

several hours, a flume considered as flowing in equilibrium may have 

instantaneous slope values varying by 50 percent. A U.S. Geological Survey research team at Colorado State University has used 

a recorder attached to a differential bubbler gage to measure slope 

continuously (Simons and others, 1961). Although fluctuations are 

sizable, the time average has been found to be consistent if a sufficiently long time base is used.

Although the reaches used on the Kio Grande were on the order of 

1,000 feet long, it was hypothesized that instantaneous measurements 

of water surface slope were not significant, but could be used to determine an average slope for the reach.

Three methods were used for testing this hypothesis. First, at 

Bernalillo for the 1952 data, a plot of energy gradients was used to 

determine whether an average slope could be fitted to various longer 

reaches through several sections for all six runs. (See fig. 4.) It was 

found that a slope of about 0.00095 ft per ft could be fitted through 

sections A-2 to A-l and E to G, and often through longer reaches. 

This seemed to indicate that the average slope value might be used 

to compute variables for several sections and perhaps be more accurate than using the instantaneous measured values. Second, the 

average of the instantaneous values of slope for each station and 

reach was compared with the slope as picked from a topographic map. 

These slopes agreed quite well, which indicated that the variations 

were about a mean value for a much longer reach than that normally 

used between sections. Third, for several stations, the variation in 

plots involving slope, such as those of shear and Chezy G, was compared when computed for instantaneous values and for average 

values. The average values gave much less scatter to the plots, indicating that the average values were more meaningful than the 

instantaneous values in describing effects of the slope acting upon the 

system.

In addition a comparison was made of energy gradients and water 

surface slopes for the 1952 Bernalillo runs between reaches A-2 to 

A, a distance of 2,840 feet and F to H, a distance of 2,160 feet. The 

reach from A-2 to A is narrow and that from F to H is wide. The
FLTJVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES

A-2

I I I I I

EXPLANATION

Mean elevation of energy head

O 

More than one channel

5=0.00095

®

®

4 5 6 7 8 9 10 11 

STATIONING, IN THOUSANDS OF FEET

12 13 14

FIGURE 4. Rio Qrande near Bernalillo reach, showing energy gradients.

energy gradient was computed by correcting the water-surface fall 

for the change in velocity head as computed by the formula, he= V2/2g. 

Using the readings observed at these cross sections only, and giving 

no weight to other sections, it was found that the average water-surface slopes and energy gradients for the two reaches were in close 

agreement. The results are given in figure 4 and table 1.

690-231 O 63 3
P12 STUDIES OF FLOW IN ALLUVIAL CHANNELS

TABLE 1. Energy gradients and water-surface slopes for the Rio Grande near

Bemalillo reach, 1952

Date

April 25-.-_--_ --_------.___._

April 12_. ____________________

June 17__ __-__.____ _____ ___

June 20 ___ -___-____._ _ .___

June 26 ___ _ _______ _ _____

July 24_---_-_---_-___-.______

Average slope. _____ ________ _

Sections A-2 to A

Energy drop

2. 67 

2.73 

2. 73 

2. 53 

2.60 

2.37

2. 605 

. 00092

Water-surface 

fall

2. 60 

2.63 

2. 67 

2. 66 

2. 63 

2. 46

2. 608 

. 00092

Sections FtoH

Energy drop

2. 15 

1.74 

1.97 

1. 96 

2. 31 

2. 06

2. 032 

. 00094

Water-surface 

fall

2. 09 

1.80 

1.69 

1.78 

2.34 

2. 07

1. 962 

. 00091

Similar computations were made at the Casa Colorada reach. 

The results were as follows:

Average energy gradients and water-surface slopes agree surprisingly well, both at a reach and between reaches. This should 

be somewhat expected, however, because channel-control conditions 

should prevail at all times in a sand-channel stream, and fluctuations 

of both water-surface slopes and energy gradients should be about the 

same stationary mean value. As a result of these studies, average 

measured water-surface slopes for the range of discharge observed 

for each station were determined and used for computations of all 

parameters in this report.

TABLE 2. Energy gradients and water-surface slopes for Casa Colorada reach

Reacb

116.87-116.47-. _______________________ ___ ____

116.67-116.47_______________ ____ ____-___._-__

117.62-117.43- _______ __ __ _ __ ____________

117.81-117.43____________ _ __________ ___ _.__

Energy gradient

0. 00085

. 00081

Water-surface 

slope

0. 00082

. 00078

. 00087

.00085

BED MATERIAL

It will be shown in this report that particle size of bed material 

at a given cross section is a very important variable in determining 

sediment-transport rate, form of bed roughness, and resistance to flow. 

The median diameter, d, is used in this report as the primary variable 

representing bed material.

This report deals mainly with the sand-bed channels of the Rio 

Grande. Sand is that material larger than 0.062 mm and finer than 

2.00 mm in diameter. It is the authors' belief that the median 

diameter of bed material for a sand-bed channel, as defined in this 

report, usually does not exceed 0.60 mm. For such a channel samples
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES P13

of bed material taken throughout a wide range in discharge show no 

large variation of median diameter.

Most of the stations in this report can be considered as having 

sand-bed channels, the exceptions being the sand-gravel channels of 

the Rio Grande at Otowi Bridge, Cochiti, and San Felipe stations. 

The Rio Grande near Bernalillo station is an excellent example of 

a sand-bed channel. A great number of bed-material samples have 

been collected and analyzed at this station and show very little 

deviation from a median diameter of 0.30 mm. For instance, of 

56 individual bed-material samples collected near Bernalillo in 1958, 

the median diameters for 48 samples range only from 0.20 to 0.40 

mm, whereas for 53 samples the range is 0.20 to 0.48 mm. The 

largest d of the 56 observations was 1.15 mm, whereas the only one 

below 0.20 mm was 0.075 mm.

The stations downstream from Bernalillo are similar in that the 

medians of bed-material samples vary conservatively. Upstream 

tributary flows often will leave a thin film of finer material in the bed. 

This fine-grained sediment apparently produces little or no pro- 

. longed changes in median diameter, because it usually is picked up 

by a subsequent increase in dischage in the main channel.

The Rio Grande at Cochiti station is a good example of a nonsandbed channel, or a sand-gravel channel. During two high-water 

periods of May and June 1957 and 1958, samples of bed material 

show the median diameter to range from 0.13 to 33.0 mm, and size 

distributions of the material show bimodal characteristics.

DEPTH-DISCHARGE RELATIONS

A discontinuity occurs in the depth-discharge relation of many 

sand-bed stations in the middle Rio Grande. For a given depth, there 

may be no unique relation with velocity. This is due to the fact 

that the form of bed roughness and, hence, resistance to flow are a 

function of fluid, sediment, and flow characteristics.

Laboratory studies (Simons and others, 1961) have been used to 

define the various regimes of flow in terms of configuration of the 

sand-bed channel as follows:

Regime of flow Description 

Plane bed.__________ for flow prior to movement.

Lower Ripples_ ___---_______ small uniform sand waves, with little sediment

movement. 

Dunes_______________ much larger more irregular sand waves, with a

great deal of turbulence. 

'Plane bed___________ dunes are smoothed out. Both the water

surface and the bed are plane, -with little 

turbulence.

Upper Standing waves._____ both the water surface and the bed are characterized by standing waves, often termed "sand waves." 

Antidunes.__________ the sand waves move upstream, until at some

critical point they break, then reform.
P14 STUDIES OF FLOW IN ALLUVIAL CHANNELS

The discontinuity occurs between the dune regime and the plane bed 

regime. The roughness of the channel in the lower regimes is about 

twice the roughness for upper regimes. For upper regimes roughness 

is principally a grain roughness, whereas for lower regimes there is 

both grain and form roughness.

The general approach to the determination of roughness is through 

the Chezy formula

which means that the velocity at a cross section varies as the square 

root of the hydraulic radius, if slope and roughness are constant. For 

the wide shallow channels of the Rio Grande, depth and hydraulic 

radius are almost identical; therefore mean depth could be substituted 

for hydraulic radius in the Chezy formula. However, both theory and 

experience on relatively deeper channels indicate that hydraulic radius 

is preferable to depth as a parameter to define the mean velocity of a 

stream. The usual adaptation to rigid channels of this relation is the 

well known Manning's formula, where

C=

n

In this relation, velocity varies as the two-thirds power of hydraulic 

radius, if slope and Manning's n are constant. Because, as stated earlier, slope can be considered as a constant with only statistical variation, a comparison of the variation of velocity with hydraulic radius 

can be used to study the variation of roughness, and, if roughness is 

constant, to determine whether Chezy O of Manning's n is the better 

parameter for representation of roughness. Once the roughness parameter at a station is defined, then its variation among stations can be 

related to physical properties.

Assuming all sands are of about the same specific weight, and that 

temperature variations are averaged out in the relation at each 

station, the parameters most likely to explain the variation between 

stations would be the characteristics of the bed material.

DEPTH-DISCHARGE RELATIONS AT INDIVIDUAL STATIONS

If the Chezy Cis used as the roughness factor, the roughness appears 

to be approximately constant at each main stem station from Bernalillo to San Antonio for all measurements of flows above the discontinuity that were studied for this report. Figures 5 to 8 show plots 

of hydraulic radius and velocity for Rio Grande near Bernalillo, 

N. Mex., the Casa Colorado and Socorro reaches, and the San Fran-
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES P15

EXPLANATION

® 

Standing waves or antidunes

248 

VELOCITY, IN FEET PER SECOND 

FIGUEE 5. Relation of velocity to hydraulic radius for Rio Grande near Bernalillo. .

cisco riverside drain near Bernardo, N. Mex. For each station plot, a 

line has been drawn representing the relation

V=kr1 '2

Thus, since 

then 

The stations from Bernalillo downstream are quite similar in that 

the depth-discharge relations have a discontinuity, an average Chezy C 

can be assumed for the upper regime, and the standing waves and 

antidunes plot among the other upper regime flows. The San Antonio
F16 STUDIES OF FLOW IN ALLUVIAL CHANNELS

EXPLANATION

® 

Standing waves or antidunes

~f=0.63 

C=126

248

VELOCITY, IN FEET PER SECOND 

FIGUBE 6. Relation of velocity to hydraulic radius for Casa Colorada reach near Belen.

station is different, however, in that there seem to be definite shifts in 

the relation, after the discontinuity, of velocity to hydraulic radius. 

It has shown evidence of three separate relations during the period 

studied (figs. 9-11). These major shifts have occurred when the 

stream has been completely dry.

Because the upper regime measurements shown in figures 10 and 11 

plot about an average of 25 percent greater than the RV curve shown 

in figure 9, either the slope must increase or the bed-material size decrease, if Chezy C is assumed constant for a given bed material. 

Whether the shifts in depth-discharge relation are the result of changes 

in energy slope is not known, but the bed material has remained 

practically constant.

Simons (oral communication) stated that in flume studies there is 

a consolidation of the bed whenever the flume is dry. This may be 

a partial explanation of the shifts in the hydraulic radius-velocity 

relation at San Antonio, but there is no explanation as to why this 

effect is selectively applicable at this one reach. In addition, San 

Antonio is downstream from the Kio Puerco and thus receives large 

quantities of fine material in suspension. This also may have some 

effect on the bed consolidation and thus on the shifts at San Antonio.

For the station at San Marcial, only those measurements with 

flows noted as being in standing waves or antidunes were used to 

define the Chezy C for upper regime flows. The station is immediately upstream from a bridge, and local scour at times extends to the
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F17

measuring section, changing the apparent characteristics of the 

depth-discharge relation.

Similar plots for the two tributary stations, Galisteo Creek at 

Domingo and Rio Puerco near Bernardo, are shown in figures 12 and 

13. For Galisteo Creek all measurements for which the average 

velocity was greater than 4 fps (feet per second) were used to define 

the curve after the discontinuity. This included all measurements 

above 400 cfs. For Rio Puerco it was found that the change in 

regime often did not occur until after the peak gage height. This 

may be due to the large concentration of clay which is deposited 

upon the bed during the recession and later hardens into an armoring

6.0 

5.0-

4.0 

3.0-

V)

2 2.0 Q

<

cc 

o

_J

< 

cc

Q

1.0

F=OA9 

C=135

248 

VELOCITY, IN FEET PER SECOND 

FIGURE 7. Belation of velocity to hydraulic radius for San Francisco riverside drain near Bernardo.
F18 STUDIES OF FLOW IN ALLUVIAL CHANNELS

6.0 

5.0

4.0 

3.0

LJ 

LiJ 

Ll_

z

</>

i 2.0

1.0

248 

VELOCITY, IN FEET PER SECOND

FIGURE 8. Relation of velocity to hydraulic radius for Rio Grande at Socorro reach.

layer which must be broken before the stream once again becomes a 

sand-channel stream. The very rapid rises at this station also delay 

the change from lower to upper regime because the depth and velocity 

increase relatively more rapidly than accompanying changes in bed 

configuration. Measurements made during a rising stage were not 

used in defining the roughness factor for Rio Puerco because of the 

dubious accuracy of such measurements. All measurements over 

750 cfs other than those made on a rising stage were used.

CRITERIA FOR ESTIMATING REGIME OF FLOW

The determination of a criterion for estimating the regime of flow 

that will prevail in a sand-bed stream is necessary for many problems. 

In canal design the maximum capacity of discharge and sediment 

transport are functions of the regime of flow at the design depth.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F19

In channel rectification, the regime of flow determines the capacitance 

of the reach. In stream gaging, it determines the velocity of flow, 

as was shown in an earlier section. In problems concerning sediment 

transport, regime has an important bearing on the amount of sediment 

transported.

There have been several attempts at establishing a criterion for 

determination of regime of flow. Garde (1959) proposed an empirical 

relation involving a shear-Froude number relation. Field data do 

not verify the relation. In particular, part of the Rio Grande data 

for upper-regime flows would be estimated as lower regime (fig. 14). 

Disregarding the parameters used, the shape of the relation is believed 

to be in error. Because the Froude number virtually remains constant for upper-regime flows, any relation employing Froude number 

should not present the paradoxical situation, as Garde's does, that 

with a constant Froude number increasing depth can cause a transition 

from upper-regime to lower-regime flows. In addition, it is not believed that the Froude number is an adequate parameter for such a 

relation, because for a given Froude number flow may be in any 

regime depending upon the size of the bed material.

? 2

^=0.62 

C=149

2 3456 

VELOCITY, IN FEET PER SECOND

FIGURE 9. Relation of velocity to hydraulic radius for the Rio Grande at San Antonio, January 1952-June

1953; October 1954-June 1955.

690-231
F20 STUDIES OF FLOW IN ALLUVIAL CHANNELS

Simons and others (1961) proposed a plot of V*d/a> and V*/v, with 

an empirical family of curves based on flume data which would 

delineate the various regimes. The Rio Grande data do not verify 

this plot (fig. 15). Because for a given stream, with a fixed slope and 

bed material, all data will plot on a 45° line depending upon R, this 

family of curves is not believed to be adequate. For any situation 

without a unique relation of R to V, regimes of flow would overlap on 

the Simons' plot, and it has been shown that there is no unique relation 

between R and V for true sand-bed streams. As an example, by 

referring to figure 5, it becomes obvious that at an R of 2.1 at the Rio 

Grande near Bernalillo, lower, transition, and upper regimes of flow 

can occur at V* =^2.1gS.

-Relation from figure 9

248 

I______________L_____________L

VELOCITY, IN FEET PER SECOND

FIGUBE 10. Relation of velocity to hydraulic radius for the Rio Grande at San Antonio, July 1953-May 1954.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F21

i

-Relation from figure 9

248 

VELOCITY, IN FEET PER SECOND

FIGUEE 11. Relation of velocity to hydraulic radius for the Rio Grande at San Antonio, May-September

1954; July-September 1955.

RELATION OF CHEZY C TO BED MATERIAL

Figure 16 shows the variation of average Chezy C for upper-regime 

flows with the median diameter of the bed material for stations covered 

in this report. Average values for all available upper-regime observations are plotted for the sand-bed stations. Individual observations 

are plotted for the sand-gravel stations, Otowi, Cochiti, and San 

Felipe. Also included are average values for several stations distributed throughout the country. These data are abstracted from 

Dawdy (1960) and show that the Rio Grande data are in agreement 

with data from other streams.

In general the reach above the Angostura diversion dam is a gravel 

alluvium over which a veneer of sand is transported. At higher discharges and correspondingly large sediment transport, the bed 

generally has areas bare of sand, with gravel exposed to the flow. At 

times an entire cross section may have a gravel bed. The variable
F22 STUDIES OF FLOW IN ALLUVIAL CHANNELS

± 2

0.5

Note: Only measurements 

for which velocity exceeds 

4 fps are plotted

-^=0.99 

C=75

4 68 

VELOCITY, IN FEET PER SECOND

12 16

FIGUEE 12. Relation of velocity to hydraulic radius for Galisteo Creek at Domingo, N. Mex.

condition of the bed is indicated by samples of the highly variable bed 

material obtained at Otowi, Cochiti, and San Felipe. The variation 

in bed material causes a large amount of scatter in the relation of 

velocity to hydraulic radius and of shear to sediment transport.

Although of the three main-stem stations above Bernalillo, Cochiti 

most nearly approximates a sand-bed channel; it presents a good 

example of a sand-gravel channel, that is, one without a limitless 

supply of sand. As such, any relation developed for it may be used to 

interpret data for the reach from Otowi to San Felipe. The bedmaterial samples for Cochiti showed a large amount of variation in 

median diameter as compared with those of the sand-bed channel
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F23

stations. In addition, although the station seems to experience upperregime conditions, the shifts in the velocity-hydraulic radius plot are 

extensive, as shown in figure 17, and often seemingly are without 

reason. It was hypothesized that part of this shifting may be due to 

the changing bed material, with resultant changes in roughness.

A composite of the bed-material samples for each measurement made 

at Cochiti during May and June of 1957 and 1958 was taken to obtain 

an average median diameter for each measurement. (See table 3.) 

For this compositing, one sample of 0.13 mm median diameter was 

considered to have been taken near the bank in too slow a velocity, so 

that normally suspended fine-grained sediment was included in the 

sample. All samples of more than 1 mm were disregarded, because 

they were not considered to influence the roughness to a major extent. 

All except one measurement of more than 1 mm was taken in what 

appeared to be a local deposit of gravel near the left bank.

EXPLANATION

Sand waves noted

A 

Absence of sand waves noted

248 

I________________I

VELOCITY, IN FEET PER SECOND 

FIGUBE 13. Relation of velocity to hydraulic radius for Rio Puerco near Bernardo, N. Mex.
F24

10

STUDIES OF FLOW IN ALLUVIAL CHANNELS

EXPLANATION

Range of T* for upper 

regime flows for Rio 

Grande stations

Ripples and 

dunes

1.0 Antidunes

Transition: 

Plane bedstanding wave

J.

0.2 0.5 

FROUDE NUMBER

1.0 2.0

FIGURE 14. Garde's criteria for regimes of flow in alluvial channels.

Chezy C was computed for each measurement separately, using a 

constant slope of 0.0012. The results are listed in table 4, along with 

the average median diameter. The variation in Chezy C agreed 

generally with .the variation in median diameter, and the trend for 

Cochiti agrees with that for the mean values at other stations in the 

basin.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES P25

TABLE 3. Median diameter of bed material, in millimeters, for the Rio Grande at

Cochiti

Date

1967 

April 16..... ....... ....

April 29... -.. . 

19S8

TV/Fat7 19

May 20.. ... .. .. .

May 26.-- - - 

Stationing

50-75

0.13

80-110

0.28

.30

.27

.30

.325

.34

.38

.36

120-125

0.275

.31

150-180

0.16

.29

.30

.39

.30

190-220

0.35

FA

33.0 

.295

.39

.60

.62

.70

.65

235-250

6.44

.36

.34

270-85

0.38

4.5

4.2 

6.4

1.5

.80

310-80

1.75

3.9

Average

0.26 

.34 

.43 

.33

.285 

.32 

.37 

.30 

.455 

.48 

.63 

.505

.Median size of bed material

EXPLANATION

Rfo Grande data

 

Upper regime

X

Transition

100 200

v+dlv 

FIGUBE 15. Simons' criteria for regimes of flow in alluvial channels.
F26 STUDIES OF FLOW IN ALLUVIAL CHANNELS

200

k

100

50

1 1

EXPLANATION

Sand-bed stations in the Rio Grande basin

x

Sand-gravel stations Otowi and San Felipe

a 

Sand-gravel stations at Cochiti

Dawdy data for sand-bed stations

D a 

 D

D )P 

X

0.10 0.20 0.30 0.40 0.60 0.80

MEDIAN DIAMETER, IN MILLIMETERS 

FIGURE 16. Variation of Chezy Cwith median diameter of bed material for upper regime flows.

1.0

of 4

2 4 

VELOCITY, IN FEET PER SECOND

FIGURE 17. Relation of velocity to hydraulic radius for Rio Grande at Cochiti.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F27 

TABLE 4. Median diameter and Chezy C for the Rio Grande at Cochiti

Date

1957 

May 16__-_ _ __ _ ___ _-. .

May29-__ _ ___ ___ __ _ ___ -

June 12, _-_____-____--- _ _ ___ _

June26_ ___ _________ ___ ___ __

1958 

May 7_-_ _ _ _ _ _ __ _ --_-_--_

May 12 __ _ ___ ___ ______

May 20. _ ____ _ ______ __ ____-.

May 26._ _____ _ _ -___ __

June3---_-_. _ _ _ _ -__ __ __ __

June 9_ ________________ _

June 12____ ____ ___ _______ ___ _

Junel7______ _______ ___.

Median diameter (mm)

0.26

.34

.43

.33

.285

.32

.37

.30

.455

.48

. 63

.505

k

3.05

2.95

3. 12

3.02

3.38

3.35

3. 18

3.22

2.80

2.45

2. 15

2. 15

Chezy C =fcS-H

88

85

90

87

98

97

92

93

81

71

62

62

OTHER FACTORS INFLUENCING ROUGHNESS

Factors other than bed-material size that have been offered as 

influencing roughness in alluvial streams are relative roughness 

(Leopold and Wolman, 1957), channel-shape factor (Brooks, 1958), 

standard deviation of the bed material (Einstein and Chien, 1958), 

and concentration of suspended sediment (Leopold and Maddock, 

1953, Brooks, 1958).

RELATIVE ROUGHNESS

In analyzing bed roughness, Einstein (1950) divided the total shear 

force into two parts, the shear force owing to form roughness, and the 

shear force owing to grain roughness. For upper-regime flows in 

sand-bed channels, form roughness due to bed configuration is negligible. Using Nikuradse's relative roughness parameter, ±Rjd (Rouse, 

1949, p. 209-212), to describe a grain roughness for our data, it is 

apparent that the effect of relative roughness on total roughness is 

small. The range in relative roughness for upper-regime flow data 

presented in this report is about 1,800 to 57,000, with the greatest 

range at a station being 1,800 to 14,000 at Galisteo Creek. According 

to the Nikuradse curves, a relative roughness of 1,800 gives a friction 

factor, /, of about 0.017, and a relative roughness of 14,000 gives a 

friction factor of about 0.0115. Over this range of relative roughness 

for the Galisteo Creek station, the grain roughness should vary only 

about one-third. All our upper-regime data have high Reynolds 

numbers, so that there is no Reynolds number effect on total roughness. 

These data indicate that, although variations in depth at a station do

690-231 O 63 5
F28 STUDIES OF FLOW IN ALLUVIAL CHANNELS

occur during upper-regime flows, the total roughness expressed as 

Chezy C does not vary appreciably over this range of relative roughness.

CHANNEL SHAPE

The channel shape as expressed in the width-depth ratio does not 

appear to affect the roughness, at least in channels of the width of 

those studied in this report. A good illustration of this is the two 

Bernalillo sections A-2 and F. Section A-2 is in a contracting reach. 

It is a comparatively narrow section of fixed width, ranging only from 

265 to 275 feet in width for flows exceeding 1,000 cfs. Section F is 

in an expanding reach, and the width ranges from 300 to 600 feet for 

the same flows.

The energy gradients through the two sections were shown earlier 

to be mainly the same (fig. 4). The relations of velocity to hydraulic 

radius for the two are quite similar, both for the upper and lower 

regimes. Both change from lower to upper regime at a depth of 

about 2 to 2.5 feet. The only major difference between the two is 

that section A-2 is narrower and, therefore, attains greater depths.

Figure 18 shows the relation of velocity to hydraulic radius for the 

two sections. The average trend drawn for the two plots is the same. 

Figure 5 shows a composite plot of the measurements at both stations, 

with the same trend line drawn. This indication that the width-depth 

relation is not a factor in the determination of roughness is borne out 

by the Casa Colorada reach, where data, for sections having different 

width-depth ratios but similar slopes plot together on one velocity 

relation (fig. 6).

STANDARD DEVIATION OF BED MATERIAL

The variability of the bed-material size as measured by the standard 

deviation and the suspended-sediment concentration have been shown 

by Dawdy (1960) not to affect roughness appreciably. The inaccuracy of the measure of standard deviation was given as the probable 

reason for lack of noticeable effect for that variable. Standard 

deviations determined for stations in the Rio Grande basin are more 

accurately defined than most of those used by Dawdy, but they are 

insufficient in number and too highly correlated with median diameter 

to define any effect of standard deviation on roughness. Values of 

standard deviation and median diameter for the Rio Grande stations 

are given in the following table:
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F29

Rio Orande station

At CochitL- - _ _____ _____ _______________ __

At San Felipe. ______ _______ ___ -_-__-________

Near Bernalillo _ _ _ _______ . ___ _ ___ _ ___

Near Belen. __-_-_ _______ _ ___ _ ___ _ __

Near Bernardo (SFRD)____ _______ ________

Near Socorro. ____ ___ _ ___ __ __ _ ___ - __

At San Antonio_ _ _ _ _ _ _____ _. _ _________ _

At San Marcial __ _ _____ ___ _____ ___ _ ___

Median diameter 

of bed material

0 62

44

67

30

24

26

18

20

14

Standard deviation of bed 

material

2. 61

2. 11

2. 04

1. 68

1.55

1.42

1. 52

1.48

1.43

SUSPENDED-SEDIMENT CONCENTRATION

As to suspend-sediment concentration, there is a large variation 

at each individual station, and a variation between stations that bears 

out the point made by Dawdy that suspended loads do not have an 

effect on roughness for the upper-regime flows. This is verified by 

laboratory studies conducted by the U.S. Geological Survey at 

Colorado State University (Haushild, 1960).

SUMMARY OF OTHER FACTORS INFLUENCING ROUGHNESS

In conclusion, it appears that for the sand-bed streams of the 

middle Rio Grande, roughness for a given reach, as expressed by 

Chezy C, is approximately constant for upper-regime flows. Also, 

roughness for lower-regime flows appears to be approximately constant for a given reach, however, insufficient data are available at 

this time for definite conclusions. Chezy (7, for upper-regime flows 

at a station, mainly is a function of the size of the bed material. 

The variability of the bed material, as measured by the standard 

deviation, also may be a factor, but there is no positive evidence at 

this time. The effect of the depth-roughness ratio, width-depth ratio, 

and suspended-sediment concentration do not appear to be significant variables in determining roughness for upper-regime flows in 

sand-bed streams. Further research is needed, both in the field and 

laboratory, to define lower and transition regime relations for sandbed streams.

CHANGES IN BED ELEVATION

It is a commonly held belief that beds of sand-channel streams scour 

during periods of high flow. This belief is based on evidence of two 

types. First, stage-discharge ratings for sand-channel streams often 

are discontinuous. Thus, for a given water stage, two widely different discharges can be accommodated. Many field personnel explain
F30 STUDIES OF FLOW IN ALLUVIAL CHANNELS

EXPLANATION

® 

Standing waves or antidunes

Section A-2

^=0.29

Section F

^=0.29

^=0.62 

C=114

I I l l

.2 3 4 6 8

VELOCITY, IN FEET PER SECOND 

FIGCBE 18, Relation of velocity to hydraulic radius for Bemalillo sections A-2 and F.

10
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F31

the higher discharge of the two as being due to scour of the bed, 

whereas it is actually due to a change in bed roughness that increases 

the velocity of flow for a given depth of water. Second, gaging stations often are situated at constrictions in the channel. At these 

points, it is possible that great local scour and fill does occur. However, they may not be typical of a representative reach of the channel.

There is a strong possibility that over a reach of several miles 

there may be sections that scour at high flows and fill at low 

flows, which are counterbalanced by sections that fill at high flows and 

scour at low flows (Lane and Borland, 1954). Thus, over a time 

period the reach would approach the condition of a graded stream.

Sediment-discharge records would seem to be an obvious method of 

determining net aggradation or degradation of long reaches of channel. 

However, there are few reaches, if any, in the country where sediment 

discharge is determined accurately enough to estimate the degree of 

deposition of sediment in the channel. Generally, suspended sediment 

only is measured that omits an unmeasured part near the stream 

bed.

In the middle Rio Grande basin, described in this study, many unmeasured tributaries and major diversions greatly complicate any attempt 

at estimating total sediment movement, other than at a section, 

with no accurate relation to other measuring sections possible. Any 

estimate of total sediment movement must be obtained by an indirect 

method. Using the reach from Otowi to Bernalillo as an example, 

it can be shown that the \% feet of scour or drop in bed elevation, 

which occurred at section A-2 at Bernalillo during the period from 

April 15 to June 20, 1952, cannot be a general condition through the 

reach. The distance from Otowi to Bernalillo is about 56 miles. Assume an average channel width of 250 feet during the 2-month period, 

and assume the deposited sediments have a specific weight of 64 Ib. 

per cu. ft. The amount of sediment necessary to be moved in order 

for this reach to scour this amount is :

56X5,280X250X1.5X64 _ nn 

 =3,600,000 tons.

The measured suspended-sediment discharge passing the Bernalillo 

section A-2 station during this period was only about 2,900,000 tons 

plus an estimated 250,000 tons through Albuquerque main canal. 

Inflow of sediment at Otowi was 2,100,000 tons and from the Jemez 

River about 170,000 tons.
F32 STUDIES OF FLOW IN ALLUVIAL CHANNELS

Using these figures of suspended discharge as an index to totalsediment discharge, less than one-fourth of the \% feet of scour possibly 

could be a general condition throughout this 56 mile reach. Considering that the result is arrived at by subtracting two very large 

numbers, each of which is subject to considerable error, no exact 

estimate of scour can be made, but section A-2, at Bernalillo is definitely not a typical cross section of this reach in regard to degree of 

scour and fill. Lane and Borland (1954) used reasoning of this sort 

in arriving at a similar conclusion as to the nonrepresentativeness of 

the normal river gaging station.

Periodic measurements of bed elevation over a period of time would 

be an even more direct method of determining changes in bed elevation. To study changes over a reach, however, readings must be 

obtained at several sections to draw any general conclusions. The 

only data available for which several cross sections in a reach were 

measured over a period of tune are the observations in 1952 near 

Bernalillo and in 1957 and 1958 at Casa Colorada.

Near Bernalillo, 13 cross sections were measured 6 times during the 

spring runoff of 1952. The patterns of scour and fill were not similar 

at the different cross sections. (See fig. 19.) Although all sections 

had a net scour between the first and the last observation, at least 3 

sections filled and at least 4 scoured between each sequent pair of 

measurements. The average range in bed elevation was about a foot, 

with a maximum of about 1.5 feet at the lower end of the reach and a 

minimum of about 0.3 foot at sections .4-1 and D. Section A-2 had 

a range of about 1.25 feet and section F, a range of about 1 foot.

At the Casa Colorada reach, near Belen, 5 measurements were made 

in 1957 and 4 in 1958 at 6 different sections. The 1957 flow was the 

first high water to pass the reach after channel rectification. Two of 

the sections, 117.43 and 116.47, were unstable the first year (fig. 20). 

In general, however, the entire reach filled between 1957 and 1958. 

The major exception was section 117.05, the narrowest section in the 

reach, which scoured more than a foot between August 1957 and April 

1958, creating a negative bed slope from 117.05 to the next downstream section 116.67.

The 1958 observations at Casa Colorada gave results similar to those 

at Bernalillo in 1952. The slopes in the upstream and downstream 

parts of the reach were approximately equal (table 2). In each place 

one of the middle sections was narrow in relation to the other sections, 

section E at Bernalillo and section 117.05 at Casa Colorada. The 

slope in the vicinity of these narrow sections was substantially flatter 

than in the rest of the reach. The scour and fill pattern, as discussed 

earlier, well may be an adjustment of area in order to maintain the 

fixed-energy slope.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F33

i i i i i i i i

Rio Grande near Bernalillo, N. Mex., reach

32

31

30

29

28

27

26

25

24

23

22

21

20

19

Q

Z Q

<? 8h

cob3 2 -

- D

Discharge hydrograph

15 . 25 

April

15 25 4 14 24 

May June 

TIME, IN DAYS

14 24 

July

FIGURE 19. Changes in bed elevation during 1952 spring runoff at Bernalillo reach.
F34 STUDIES OF FLOW IN ALLUVIAL CHANNELS

S

"66 - 

65- 

64 

63

16

53

|o

Rio Grande near Belen, N. Mex., Casa Colorada reach 

117.81

10 20 30

May

9 19 29 

June

19 29 8 18

July Aug.

TliyiE, IN DAYS

20 30 10 20 30 

April May

FIGUBE 20. Changes In bed elevation during 1957 and 1958 spring runoff at Casa Colorada reach.

This same conclusion follows from a consideration of the mechanics 

of the system. It was shown earlier that for a given regime of flow, 

roughness is constant throughout the Bernalillo and Casa Colorada 

reaches. Also, it was indicated that energy slope is principally constant over the same reaches. Therefore, for a given regime prevailing 

throughout a reach, both Chezy C and energy slope may be assumed 

constant. From figure 21, the friction head loss, hf is:

A,= (Z, -Z2)

= (Zi-Z2) + R,(l - RtlRJ + TV/2? (1 - V, 

Since Q=AV~bRV and V=CRl '2Sl '\ 

Then hf= (Z1 -Z2)+Rl (l + C2S/2g) (1 - (&:/&2)2/3).
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F35

FIGURE 21. Schematic diagram showing friction bead loss in open-channel flow.

For a contracting reach 6i>62 , and the second term on the right side 

of the equation is negative. If the ratio of 61 to 62 is constant, then as 

discharge increases, R increases. Therefore, for hf and thus energy 

slope to remain constant, Zt Z2 must increase either through fill at 

the upper section or scour at the lower section, or both. In the usual 

field case for a contracting reach, the ratio of bi to 62 increases with 

discharge, so that the reasoning is even more compelling. Similar 

reasoning applied to the case of an expanding reach shows the same 

pattern of scour and fill at alternate sections. Also, it follows that 

those stations which fill on the rise should scour on the recession and 

vice versa. Thus, if energy gradient is to remain constant, any 

changes in width along a reach will be compensated for by scour and 

fill, so that the change in the ratio of the widths at any two sections 

is related inversely to the change in the ratio of the hydraulic radii. 

The changes in area through such a reach are very conservative. The 

discharge is altering the depth constantly through alternate scour and 

fill in order to maintain an approximately constant energy gradient 

and cross-sectional area.

690-231 O 83 6
F36 STUDIES OP FLOW IN ALLUVIAL CHANNELS

Therefore, it seems that the scour and fill that occurs during high 

water often may be local in extent. In narrow or contracting sections, 

the bottom scours during periods of increasing flow and fills during 

periods of diminishing flow. In wide or expanding sections the opposite seems to be true. For instance, sections A-2 to E at Bernalillo 

are relatively narrow, whereas sections F to L are wider sections. 

(See fig. 2.) A comparison of the mean bed elevations (fig. 18) for the 

two measurements made on April 25 and May 12 during the rising 

stage show all sections from A-2 to I? scoured, whereas all sections from 

F to L filled. Similarly, during the falling stage the 2 measurements 

made June 26 and July 24 show a general tendency toward filling for 

the narrow section (3 filled, 1 scoured, 3 had no change), and a general 

tendency toward scouring for the wider sections (2 filled, 3 scoured, 

1 had no change). Because most gaging stations are maintained at 

narrow, contracting sections, much of the evidence concerning scour 

and fill patterns based on gaging station records is biased toward a 

belief in scouring on the rise and filling on the recession.

SEDIMENT TRANSPORT FUNCTIONS

The measure of the total quantity of sediment transported by 

streams is desired for many problems concerning reservoir design and 

channel stability. Methods have been devised and standardized to 

measure that part of the sediment transported in suspension by water. 

That part of the sediment transported as bedload, however, cannot be 

measured at this time except indirectly.

Many theories have been proposed to determine total sediment 

transport. Most theories, however, merely derive the form of the 

variables to 'be considered. Generally, sediment transport is related 

to boundary shear. Two theories attempt to predict the functional 

relation a priori. They are those proposed by Einstein (1950) and 

by Bagnold (1956). On the basis of field data, Colby and Hembree 

(1955) modified the Einstein theory for computing total sediment 

loads. The Bangold theory as yet has not been subjected to the test 

of applicability in the field.

The relation of sediment transport to shear and a study of both the 

modified Einstein method and the Bagnold theory for computing total 

sediment loads are presented in the following sections.

RELATION OF SEDIMENT TRANSPORT TO SHEAR

Mean velocity approximately doubles with a change from lower to 

upper regime, if mean depth or hydraulic radius remains constant. 

On the other hand the increase in suspended-sediment transport that 

accompanies this change in regime is approximately 8 to 10 times. 

Data for the Bernalillo and Casa Colorada reaches are plotted in 

figures 22-24 to illustrate this increase in transport with the change
PLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F37 

1000

100

10

A-2 . . .1 . A-2 and F _

v ./ :/

'

1.0 1.0 1.0 

HYDRAULIC RADIUS, IN FEET

FIGUBE 22. Relation of suspended sands to hydraulic radius for Bemalillo sections A-2 and F.

from lower- to upper-regime flows. Suspended-sand load varies as the 

three-halves power of hydraulic radius. In a previous section, velocity 

was related to the square root of the hydraulic radius for upper-regime 

flows. This is equivalent to Colby's relation (1957) of sediment load 

varying as the cube of the velocity.

Figure 22 shows the two sections, A-2 and F, for the Bernalillo 

reach. Figure 23 is a combined plot of sections A-2 through F for 

the reach. It is apparent that the same relation holds for any 

individual cross section in the reach regardless of width. By comparing figure 22 with the velocity-hydraulic-radius-relation curve in 

figure 5, it can be seen that the break occurs for both velocity and 

sediment transport at depths slightly over 2.0 feet.

Figure 24 shows a plot of hydraulic radius and suspended sands for 

all sections in the Casa Colorada reach. The well-defined break 

from lower to upper regime occurs at a depth of about 1.80 feet.
F38 STUDIES OF FLOW IN ALLXJVIAL CHANNELS

o:

LU

a.

2 100 

O

CM 

ID

q

o 10

o

LU

Q

UJ 

0.

CO

I I I I I I I I I I I

/

/ ' 

 /

: '/

. 7

/ '

i i i i i i i i_____i i i i i i i i

0.2 1.0 10 

HYDRAULIC RADIUS, IN FEET

FIGUBE 23. Relation of suspended sands to hydraulic radius for Bernalillo reach sections A-2 through F.
SUSPENDED SANDS (> 0.062 MM) PER FOOT OF 

o_________________

T i i i i i m | | | 

t

o

p. O

O. O

5 £ 3 >

i* 2

I c

I? (/>

\
F40 STUDIES OP FLOW IN ALLUVIAL CHANNELS

This is the same point at which the break in the velocity-hydraulicradius relation occurs in figure 6.

For both Bernalillo and Casa Colorada reaches, the suspended 

sands per foot of width varies with the three-halves power of the 

hydraulic radius when the flow is either in the lower regime or in fully 

developed upper regime.

Similar data for Rio Grande at San Antonio is shown in figure 25. 

The break at this station seems to occur at depths between 1.0 and 

2.0 feet; however, there are insufficient data to define either the 

lower or upper-regime curves at this station.

Relation of suspended sands to hydraulic radius for the stations 

presented in these figures, as well as for other stations, have similar 

trends. Since, for constant slope at a station, shear has a constant 

ratio to hydraulic radius, the shear-transport relation would be 

similar to the hydraulic radius-transport relation. The Einstein 

and Bagnold theories attempt, a priori, to explain the differences 

which remain among the relations of shear to transport at the individual 

stations.

MODIFIED EINSTEIN METHOD

The bedload function for sediment transportation by Einstein (1950) 

is based on the integration of the product of the theoretical velocity 

and suspended-sediment concentration along a representative vertical 

in a cross section. The rate of movement and the concentration in 

the bedload layer are based on the probability that a given particle 

will move from its position in the streambed. The discharge of the 

various size ranges of the sediment are computed separately.

The Einstein transport function has been tested by field data and 

found considerably in error. Colby and Hembree (1955) found that 

the original Einstein method gave neither the correct quantity nor 

distribution of sizes of the transported sediment when applied to 

single cross sections. When applied to reaches, for which it originally 

was designed, it gave approximately correct totals but incorrect 

distribution of sizes. On the basis of measurements of suspended 

and total load on the Niobrara River near Cody, Nebr., a modified 

Einstein procedure was developed that gave fairly consistent answers 

at a cross section, both for total-sediment transport and for size 

distribution of the total sediment transported. This modified procedure was designed to use the data obtained by standard measuring 

and sediment-sampling equipment.

The modified Einstein method was used to compute total-sediment 

discharges for several stations in the middle Rio Grande. Because 

actual total loads were not measured at any point, the modified 

Einstein computaLions can be tested only for consistency. Both
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F41 

600, , 

CC 

LU

§100

cr LU a.

LU

O

a.

CO 

CO

10

T I I I I I I I I I I I I I I I

I I I I I LJ . I I _II I I l I I I

0.2 1.0 10 

HYDRAULIC RADIUS, IN FEET

FIGUEE 25. Relation of suspended sands to hydraulic radius for Rio Qrande at San Antonio.
F42 STUDIES OP FLOW IN ALLUVIAL CHANNELS 

100

uj O

V)

-

-1 V)

«£. fci- F;O 10

I-O

of

V

/f

y

I _____ ' I I I I I I I _________ L

10 50 

COMPUTED TOTAL SEDIMENT LOAD-SECTION A-2, 

IN THOUSANDS OF TONS PER DAY

FIGUBE 26. Comparison between computed total sediment loads at Bernalillo sections A-2 and F.

suspended-sediment and computed total-sediment discharges per foot 

of width are listed in the tables of data for several stations.

The consistency of the modified Einstein method for computing 

total loads in the sand-bed channels of the Rio Grande basin is indicated in figure 26. Computed total loads for two stations, Bernalillo 

section A-2 and Bernalillo section F, are compared. Section F is 

8,240 feet downstream from section A-2. Section A-2 is deeper and 

maintains a constant width, whereas section F is more shallow with 

variable widths through the range of discharges observed. Actual 

total loads are assumed to be equal at the two sections during the 

period of observation for each run. The difference between the com-
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES P43

puted total load and the measured suspended load varies from 13 to 

60 percent of the computed total load. Although there is considerable 

scatter of the points, there is a reasonable agreement between the two 

sections. This indicates that for sand-bed streams in the Rio Grande 

basin the modified Einstein method may be expected to give reasonably consistent results regardless of width to depth relations.

The modified Einstein computations indicate that the percentage 

difference between suspended and computed total discharges for all 

stations covered in this report varies from 3 to 60 percent. The 

lower percentages are associated with high concentrations of fine sediment. Unmeasured load computed by the modified Einstein method 

is closely related to both velocity and suspended-sediment concentration, because these are the two principal variables in the Einstein

transport function.

BAGNOLD THEORY

Bagnold (1956) has developed a theory that not only predicts a 

relation of transport function to shear function for materials of uniform grain size, but which also predicts the relation quantitatively. 

Although uniform sands do not exist in the field, many of the ideas 

presented may be helpful in understanding field conditions. This 

section will explore some of the ideas presented by Bagnold, attempt 

to consider their applicability in the field, and, within the limits imposed by the data, test his transport-shear relation with the Rio 

Grande data.

Bagnold tested the transport function by synthesizing data using 

very light water driven particles, natural river sands, windblown 

sands, and experimentally derived shear variables into a single transport equation. Bagnold's effective characteristic applied tangential 

stress contains the usual fluid shear minus critical shear, but this is 

modified by adding an intergranular stress, based upon experiment 

(Bagnold, 1955). The transport function is composed of two parts, 

a bedload transport function, <f> b , and a suspended-load transport 

function, <j> s.

By assuming the energy distribution is such that the work rate 

represented by </> s is equal to that represented by <j> b , Bagnold derives 

</>«=</>& (BS/BI,}

where </> 6 = bedload transport function

</> s = suspended transport function 

<j) t = total transport function 

J5s =dimensionless part of </>, 

J56 =dimensionless part of </> 6 .
P44 STUDIES OF FLOW IN ALLUVIAL CHANNELS

0.03-

0.05 0.1 4.0

MEDIAN DIAMETER, IN MILLIMETERS 

FIGURE 27. Relation between median diameters, B, and Bt.

The dimensionless part of <£ 6, Bj,, is constant for a given grain size, 

or median diameter of bed material. Values of B^ experimentally 

determined by Bagnold are shown in figure 27. The dimensionless 

part of <f>s, Bs, is a function of the velocity of the sediment in suspension. 

Where the product of velocity of flow and slope is much smaller than 

the fall velocity of the median bed-material particle, Bs becomes 

constant (fig. 27). If Bg and B& are constant for a given bed material, 

then 4>s is proportional to <£ 6 , and Qs is proportional to $& In

Bs

similarly-

__ s 

 "»

ft *&<

Thus, for sufficiently large sediment, flat slopes, and relatively 

slow velocities, the suspended-sediment transport, Qs, could be adjusted by a constant factor to obtain total sediment transport, Qt.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES P45

These conditions are approached in the field, because the slopes 

generally are flat in relation to those used in laboratory flume studies. 

Therefore, by logical inference from the Bagnold theory, when these 

conditions exist it is sufficient to measure the suspended-sediment 

load in order to obtain the total sediment load.

THE BAGNOLD PLOT

The Bagnold transport and shear functions were computed for each 

station and are shown in the tables of data. The total-transport 

function was computed from the Bagnold equation

Since only suspended load was measured, for the purpose of this 

report, this equation reduces to the form

where <7r=measured ppm >0.062 mm by weight in suspension. Thus, 

all values of 0 computed for this report differ from the total <£ in the 

same degree that measured suspended load differs from total load.

The characteristic applied tangential stress values were computed 

as 

which reduces to 6= (0.606 +0.378 <7W) DS/d

where C = measured ppm by volume in suspension 

and Cm = measured ppm by weight in suspension.

A combined plot of all the Rio Grande data is shown in figure 28. 

Some data from USGS flume experiments also are included on the 

figure. .The dashed lines show what Bagnold has predicted to be 

the transport-shear relation. The three sets of solid lines show what 

appear to be trends for the field data presented. Although the points 

do not follow Bagnold's predicted relation, the $ for individual stations 

does vary with & /2. To illustrate this, the data for the Casa Colorada 

reach is plotted separately in figure 29. The data for this reach 

covers both lower and upper regimes of flow and the relation is well 

defined.

The fact that field data on natural streams do not follow closely 

relations derived from theory and laboratory experiments is not too 

disturbing. Determination of basic principles governing natural 

phenomena must be derived from theory or from the laboratory, 

where sufficient control and accuracy of measurement can be accomplished. Ultimately, however, theoretical relations between
P46 STUDIES OF FLOW IN ALLUVIAL CHANNELS

10,000

1000

100

10

1.0

0.1

I I

0.01

EXPLANATION

Symbol _d_ 

v 0.62 

n V 

A V 

© 0.40

V 

. 0.30

O

Station 

Otowi Bridge

Cochiti

San Felipe

Galisteo Creek

Angostura heading

Bernalillo reach 

0.24 Casa Colorada reach 

0.24 Rio Puerco-Bernardo 

0.18 Socorro reach 

0.20 San Antonio 

0.14 San Marcial

USGS Flume data

Note: "V" indicates variable size

i i i i i 1111

0.10 1.0

SHEAR FUNCTION, 00 

FIGUEE 28. Bag nold plot of Rio Orande data.

10.0 40.0

variables must be tested and proven by application of field data. 

Several theories and assumptions incorporated in the Bagnold theory 

theory can now be examined more closely in vi&w of the field data 

presented.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F47

lO.OOOr

-9- 

(/)

1000

100 -

10

I I I I 1 TTI I I T

Total load for 

upper regime, <t> u

^Bagnold total load using 

upper regime C/ V g

= 200J

-Bagnold bed load using 

lower regime C/xTg"

Total load lower 

regime,

0.5 1.0 10 50

SHEAR FUNCTION, 9

FIGURE 29. Bagnold relation for Casa Colorada reach. 

CRITTCAIj STRESS 0sw0.4

Bagnold hypothesized that, at the theoretical tangential fluid stress 

0«0.4, the boundary conditions of the fluid changes from a fixed 

boundary of granular roughness to a zone of moving bed-material
F48 STUDIES OF FLOW IN ALLUVIAL CHANNELS

particles. He assumes that the transition from bedload movement 

only is complete at the critical stress of 0«0.4, and therefore, that 

the suspended load is fully developed at this stress. In other words, 

Bagnold explained this transition as entirely due to the development 

of a suspended load. Analysis of field data seems to indicate that 

this transition may be explained more accurately as due to a change 

from lower- to upper-regime flow.

Bagnold's data included only flume data in which total load was 

measured at the outfall. There was no direct measurement of suspended load or bedload. Any such subdivision of the measured total 

load is hypothetical for these data.

Further, it appears that the tangential stress at which the change 

from lower to upper regime occurs is variable. This is verified by 

field data (fig. 28) and laboratory studies at Ft. Collins (Richardson, 

1960). As an example, data for the Rio Grande near Bernalillo reach 

indicate the change from lower to upper regimes to be complete at a 

tangential stress of approximately 0«2.0, whereas the Casa Colorada 

reach data show the change completed at 0« 1.5. Because Bagnold's 

data was for more nearly uniform grain sizes than are found in the 

field, the dominant size from which to compute 6 is debatable. Both 

the difference from the predicted value of 0.4 and the variation among 

stations may be the result of using the median diameter as the dominant diameter.

However, the plotting of the data for each individual station indicates a relatively stable dominant diameter should be used. The 

difficulty of the determination of the dominant diameter of the material 

available for transport may be one of the causes for the variation of 

the station plots from the predicted relation but cannot be the sole 

cause. Because the dominant diameter appears both in the shear and 

the transport terms, any change in the dominant diameter would be 

minimized in the resulting plot. The main effect would be in determination of the tangential stress at which the change in regime takes 

place.

CHARACTERISTIC APPLIED TANGENTIAL STRESS

It becomes evident that, 'as Bagnold intimated, the additive term 

DSC Id in the shear function

becomes negligible in the stream case. Run No. 15 for Bernalillo 

section A-2 shows a concentration by weight of 5,980 ppm, a depth
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F49

of 2.96 feet, a slope of 0.00095 ft per ft and a median bed-material 

diameter of 0.00098 feet. Therefore,

.= (62.4/103+0.00598/2.65)

= 1.74+0.0065 

or 0=1.75

Without this additive term, the tangential stress becomes mainly

or

The bedload equation of Meyer-Peter, Kalinske, and Einstein can be 

expressed as a function of this same tangential stress parameter. 

Thus, for actual streams the additive parameter for effect of concentration in the stress function proposed by Bagnold is not sufficient 

to bring field data to a single relation.

TOTAT, TRANSPORT FUNCTION, <f

According to the a priori relation hypothesized by Bagnold, at 

0=0 .4 both the suspended-load function and the bedload function 

become proportional to 0s /2, and the total-load equation

6=9 P* (1+B.IBj

becomes applicable. Thus, the total-load function, 6, becomes 

proportional to 0s72.

The 'coefficient, 9, was an experimental estimate of the velocity 

term in the Keulegan velocity equation, derived theoretically as 8.5. 

It represented the ratio of the velocity of flow at a distance of one 

grain layer above the bed to the shear velocity. In place of this 

coefficient can be substituted V/V* which equals C/i/g (Bagnold 1960). 

This converts the shear parameter to the equivalent of a stream power. 

Thus, the a priori relation can be written 

and 

Because the Chezy C varies with median diameter of bed material 

for upper regime flows, there should be no unique relation between 

0 and 0s72. Not only does C/-Jg vary from station to station, depending upon bed material, but even more important, Cj-Jg varies 

at a station depending on regime of flow. Because this is so, the 

ratio (l+.B8 /.Bj), is not a sufficient correction for Bagnold's relation. 

An additional correction must be made for the changing C/-\fg with 

change in regime.
F50 STUDIES OF FLOW IN ALLUVIAL CHANNELS

The relation computed from average C/i/g values for lower and 

upper regimes are shown for the Casa Colorada reach in figure 29. 

Data for suspended load for lower regime seems to equal the Bagnold 

relation for bedload. If Bagnold's bedload is correct, this would 

indicate that total load for the data included in this report is about 

twice the suspended load for lower-regime flows. The curve computed from C/V0 values for upper-regime flows (fig. 29) does not 

equal the plot of the suspended-load field data, but rather, gives 

values of </> approximately half the measured suspended load. D. B. 

Simons (oral communication) indicates, on the basis of flume studies, 

that current sediment-sampling techniques tend to measure larger 

percentages of total load than is realized. In fact, for upper-regime 

flows, measured suspended load approaches, and for antidune conditions equals, total load. This may be the case for the Casa Colorada 

reach.

Assuming this is the case, then it seems that Bagnold's ratio 

(l+Bs/Bb), is approximately correct for difference between total 

load for lower and upper regimes if a correction for the changing 

Cl-Jg is included. This seems to indicate, once again, that Bagnold's 

explanation of the two curves as a bedload-total load relation is 

truly a phenomenon of a lower-regime, upper-regime relation. His 

critical 6, the shear at which he predicts a fully developed suspended 

load, probably is the 6 at which upper-regime flow becomes fully 

developed.

Since C/i/g for upper regimes does vary between stations depending 

upon size of bed material, there should be no unique relation for 

total load as indicated by Bagnold. However, if measured suspended 

load for the upper regimes does approximate total load as hypothesized 

by Simons, Bagnold's relation might be used to predict total load in 

the lower regimes. Figure 29 shows that this relation might apply. 

If Bagnold's relation is in error by a scale factor, /3 (see fig. 29), then 

total load for the upper regime equals

The lower-regime total load is found by multiplying the upper-regime 

load by the adjustment ratio

thus, the lower regime total load, as expected, would be
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F51

Both upper- and lower-regime total loads should be in error by 

the same scale factor if our interpretation of Bagnold is correct.

For the Casa Color ad a reach, this scale factor, ft, is equal 

approximately to two.

Colby (1957) and others stated that total load is related to the cube 

of the mean velocity. If this is so the adjustment ratio for lower- to 

upper-regime loads (l+J5s/56 )(C2 /Ci), should be predictable from the 

depth-velocity relation. For a given depth in the Casa Colorada 

reach, the velocity approximately doubles during the change from 

lower- to upper-regime flows. Therefore,

For the Casa Colorada reach, the actual values indicate 

(l+BJBj (Ci/t70 = (3.41) (22.2/10.0) = 7.6.

In conclusion, it appears that field data do not follow the single 

functional relation proposed by Bagnold. The major discrepancies 

stem partly from experimentally determined variables relative to 

effects of concentration on the shear function. The unknown relations 

between model and prototype in sediment-transport studies also add 

considerably to the discrepancies. Also, shear stresses obtained in the 

laboratory flume with small depths and large slopes do not produce 

the same sediment-transport shear relation as do shear stresses resulting from greater depths and lesser slopes that occur in the field.

COMPARISON BETWEEN MODIFIED EINSTEIN 

AND BAGNOLD

The Bagnold computations of total sediment load are based on 

sand sizes only, as shown in a previous section. Modified Einstein 

computations may be compared with Bagnold computations for consistency by plotting modified Einstein computed total sand loads 

against the Bagnold Q t. This has been done in figure 30 using the 

Rio Grande data presented in this report. There is considerable 

scatter in the plot in the range of values less than about 300 tons per 

day per foot of width. In this range the plot indicates, generally, 

greater computed sand loads by the Einstein method. For more 

than 300 tons there seems to be reasonable agreement between values 

computed by the two methods.

A more practical plot is shown in figure 3 1 . The load of fine material 

(finer than 0.062 mm) is simply added to both modified Einstein and 

Bagnold computed total-sand loads. This plot thus represents a comparison of total-sediment transport between the two methods. A 

single line of perfect agreement can be drawn for values more than
F52 STUDIES OF FLOW IN ALLUVIAL CHANNELS

1000

100

Perfect agreement

EXPLANATION

 

Bernalillo section A-2 and F

® 

Casa Colorada reach

V 

Socorro reach

G 

San Antonio

x 

San Marcial

Indicates lower regime

100

BAGNOLD Of - ( Qs> 0.062 MM j ( ^6 + % ) TONS PER DAY PER FOOT 

FIGURE 30. Comparison of Bagnold and modified Einstein computed total sands.

about 300 tons per day per foot of width. Below this point the modified Einstein values are greater by about 15 percent, and the deviation 

from this relation is indicated on the plot by lines at plus and minus 

10 percent.

The 300-ton point at which the two methods predict equal total 

loads cannot be explained on the basis of flow regime. That is, the 

300-ton point is not that point separating lower and upper flows. 

Lower-regime flows seem to break to upper-regime flows at about 100 

tons per day per foot of width for the data presented. It seems reasonable to believe that with more than 300 tons the entire cross section 

of flow may be in fully developed upper regime, whereas in the range 

between 100 and 300 even though average values of velocity and depth 

indicate upper regime, some part of the cross section remains in transition or lower regime.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F53

10,000

1000

100

10

EXPLANATION

A 

Angostura Motion*

 

Bemalillo reach

» 

Casa Colorada reach

V 

Socorro reach

C 

San Antonio

x 

San Marcial

10 100 1000 7000

BAGNOLD TOTAL TRANSPORT, 0,/j 

FIGURE 31. Comparison between modified Einstein and Bagnold total transport.

CONCLUSIONS AND SUMMARY

That part of the middle Rio Grande from the Angostura diversion 

dam to San Marcial can be defined principally as a sand-bed channel. 

In this reach, change from lower regimes of flow to upper regimes of 

flow is accompanied by a change in stream velocity and sedimenttransport characteristics. When transition from lower regime to upper 

regime is complete, velocity is approximately doubled and sedimenttransport capacity for material available in the channel is increased 

about 8 to 10 times.

For this sand-bed channel reach, the plane bed before movement, 

ripple, and dune regimes of flow seem to produce similar relations 

between velocity and hydraulic radius and between suspended sands 

and hydraulic radius and, therefore, can be considered as a single lower 

regime. The plane bed, or flat bed, standing wave, and antidune 

regimes of flow similarly can be considered as a single upper regime.
F54 STUDIES OF FLOW IN ALLUVIAL CHANNELS

The discontinuity, or break, occurs in the transition regime between 

the lower and upper regimes.

Energy slopes at stations remained virtually constant with change in 

discharge for the range in discharge studied. The average of all observed water-surface slopes through the range in discharge studied 

equaled the energy gradient through the Bernalillo and Casa Colorada 

reaches. The average of observed water-surface slopes for each station can be used as energy slope in computations of all flow and transport parameters.

Analysis of bed-material samples taken upstream from the Angostura diversion dam indicates bimodal size distribution and wide variation in median diameter with discharge. Channels with these bedmaterial characteristics are defined in this report as sand-gravel 

channels. Analysis of bed-material samples taken at locations downstream from Angostura heading in the middle Rio Grande generally 

indicate that the median diameter does not vary appreciably with 

discharge. These locations are defined in this report as sand-bed 

channels.

Roughness in a given reach, as expressed by the Chezy C, is approximately constant for upper-regime flows in sand-bed channels. Chezy 

C at a station mainly is a function of the size of bed material. The 

effect of the depth-roughness ratio, width-depth ratio, and suspendedsediment concentration do not appear to be significant variables in 

determining roughness in sand-bed channels.

In sand-bed channels, scour that occurs during high-water periods 

often may be local in extent. In narrow sections, the streambed 

scours during periods of rising flow and fills during periods of diminishing flow. In wide or expanding sections, the opposite seems to be 

true. This seems to be an adjustment of the stream to maintain a 

constant energy gradient and an approximately constant area. Because most stream-gaging stations are maintained at narrow, contracting sections, much of the evidence concerning scour and fill patterns based on gaging-station records is biased toward a belief in 

scouring on the rise and filling on the recession.

Computations of total sediment loads using the modified Einstein 

method give consistent results for the sand-bed channels of the middle 

Rio Grande, regardless of width-depth ratios.

Based on the rio Grande data, the new stress function proposed by 

Bagnold, which included the additive parameter for effect of concentration, is not sufficient to bring field data to a single relation.

For more than about 300 tons per day per foot of width, the same 

total sediment loads can be obtained by using either the modified 

Einstein or the Bagnold method of computation. For less than 300 

tons, modified Einstein values are approximately 15 percent greater 

than Bagnold values.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F55

TABLES OF BASIC DATA AND COMPUTED PARAMETERS

TABLE 5. Basic data and computed parameters for the Rio Grande at Otowi Bridge

near San Ildefonso 

I"This is not a true sand-bed channel. S=0.0021 ft per ft; d=0.00203 ft, 0.62mm; (1+ip) -1.471

Run Date

0/6 Bed 

elevation

9'. 6-24-58 

6-17-58 

6-12-58 

6- 9-58

5 -6-58

6 -3-58 

5-12-58 

5-19-58 

5-26-58

1,130

2,240

5,000

5,210

7,320

8,590

9,340

9,490

10,100

4.8

19.8

40.0

40.4

55.5

63.6

71.8

65.4

72.1

9.14

8.58

7.79

8.72

8.15

1.44

4.69

7.19

6.27

8.11

8.96

10.23

9.38

10.21

234

113

125

129

132

135

130

145

140

1.42

4.33

6.45

5.72

7.22

7.91

8.84

8.30

8.72

3.35

4.23

5.56

6.44

6.84

7.10

7.02

6.98

7.08

316

1,860

1,110

3,180

7,440

1,720

5,020

2,390

2,990

Run

CT

10

Q,>0.062 mm

12

Einstein 

Qr/b

13

Bagnold 

Qrlb

14 15

Regime

16

262

1,770

944

2,800

4,980

1,240

2,910

836

2,150

11,200

15,000

44,700

147,000

39,900

127,000

61,200

81,500

3.4

94

102

305

746

213

567

148

419

15

149

201

584

1,170

376

1,170

539

5.7

143

168

489

1,460

396

1,240

492

779

Upper. 

_do.. 

...do.. 

...do.. 

...do.. 

...do- 

.-do..

--.do..

 do..

1.63

1.10

1.17

1.21

1.23

1.17

1.25

1.17

1.21

Run

17 18 19 20 21 22 23 24

91- 0.321

.308

.305

.298

.295

.305

.294

.305

.298

0.49 

.34 

.38 

.45 

.42 

.42 

.39 

.40 

.39

10.8

7.82

8.41

10.4

9.77

9.70

9.06

9.31

9.22

0.0261

.0452

.0458

.0361

.0405

.0416

.0460

.0435

.0456

0.189

.616

.944

.823

1.06

1.18

1.34

1.23

1.34

0.310

.541

.661

.622

.700

.732

.775

.750

.768

0.92

2.99

4.57

3.99

5.18

5.71

6.53

5.98

6.50

1.7

47

50

151

368

105

278

73

206

i Run 9 not at cableway.
F56 STUDIES OF FLOW IN ALLUVIAL CHANNELS

TABLE 6. Basic data and computed parameters for the Rio Grande at Cochiti 

[This is not a true sand-bed channel. S= 0.0012 ft per ft; d, see column 25]

Run

9 ---------

8 -----------

6 ---------

7 ----------

1__ -------

5 -----------

2 ____.. -__

3 ----------

4 --------

b... ----------

d---- .

Run

9 ----------

8 ---------

6 ---------

7 ----------

1 ----------

5

2 

3... ..-. -

4

a

b-. ----------

d

Run

9 ---------

8 ----------

6 ----------

7 ----.___--

1 --__--_

5 ---------

2 ---------

3

4 .____ __

a

b.. . ---------

d... -----

Date

1 2

Q Q/b

6-24-^8 1,000 3.8 

6-17-58 2,040 7.2 

6-9-58 4,990 16.8 

6-12-58 5,060 12.0 

5- 7-58 7,960 25.8 

6-3-58 8,680 29.4 

5-12-58 8,900 27.1 

5-20-58 8,920 28.2 

5-26-58 9,810 29.3 

3-23-54 309 1 .7 

4-20-54 709 2.4 

6-14-54 667 3.3 

11-17-54 347 3.0

9

CV

141 

5,030 

7,210 

8,750 

3,350 

2,580 

2,680 

1,990 

2,110 

11 

116 

179 

283

18

P

0.30 

.38 

.43 

.37 

.59 

.49 

.58 

.55 

.56 

.30 

.31 

.25 

.29

10

Q.

667 

28,900 

103, 000 

121,000 

131,000 

72,900 

109, 000 

74,900 

82,400 

48 

1,110 

537 

597

19

a*

8.7 

10.9 

12.5 

10.8 

17.0 

14.2 

16.9 

16.1 

16.3 

8.8 

8.9 

7.3 

8.5

11

Q,>0.062 mn

b

1.4 

97 

326 

403 

234 

205 

196 

152 

167 

0.05 

.74 

1.6 

3.1

20

'

0.0331 

.0276 

.0265 

.0311 

.0197 

.0245 

.0199 

.0212 

.0208 

.0300 

.0306 

.0396 

.0334

3

Bed 

slevation

2.68 

2.97 

3.04 

2.58 

3.25 

2.85 

3.55 

3.64 

3.81 

2.21 

2.49 

1.95 

1.73

12

I Einstein

Qr/b

143

508 

527 

487 

292 

442 

290 

276

21

TO

0.128 

.167 

.268 

.296 

.290 

.355 

.302 

.319 

.324 

.076 

.092 

.130 

.112

4

D

1.71 

2.24 

3.64 

4.03 

3.93 

4.85 

4.09 

4.34 

4.39 

1.01 

1.22 

1.73 

1.49

5

6

263 

285 

297 

298 

308 

295 

328 

316 

335 

177 

300 

204 

115

6

R

1.69 

2.22 

3.55 

3.92 

3.83 

4.70 

3.99 

4.22 

4.28 

1.00 

1.21 

1.70 

1.45

13 14

Bagnold Regime 

QT/b

"Lm

149 T.

506 Up 

599 d 

133 d

347 --d .

wer_-

pe

0. 

On

r ...

122 do . 

308 do.

323 --do

IM\

. _ ___-_ _-d-wer.. o

__________ -_do.

. -..-_-- do.

22

V*

0.256 

.293 

.371 

.390 

.386 

.427 

.393 

.405 

.408 

.196 

.217 

.259 

.239

23

e

0.58 

.98 

1.69 

1.42 

3.08 

2.37 

2.83 

2.60 

3.24 

.36 

.33 

1.31 

.94

7

V

2.23 

3.20 

4.62 

4.22 

6.58 

6.07 

6.64 

6.51 

6.67 

1.74 

1.94 

1.89 

2.03

15

T

24 

21 

17 

17 

13 

17 

14 

14 

16 

11 

14 

18 

9

24

,

0.6 

68 

250 

131 

599 

173 

378 

207 

368 

.02 

.24 

3.8 

4.8

8

cm

247 

5,240 

7,670 

8,840 

6,090 

3,110 

4,550 

3,110 

3,110 

57 

581 

298 

637

16 17

*» .

0 .99 0 .338 

1 .06 .256 

1.17 .230 

1.16 .309 

1.31 .116 

1.17 .216 

1.25 .134 

1.25 .161 

1.20 .127 

1 .38 .289 

1 .25 .387 

1.13 .121 

1.47 .143

25

d

0.00213 

.00166 

.00157 

.00207 

.00093 

.00149 

.00105 

.00121 

.00098 

.00203 

.00266 

.00095 

.00115

26

1+f

1.49 

1.49 

1.48 

1.46 

1.49 

1.46 

1.47 

1.46
TABLE 7. Basic data and computed parameters for Galist

[-8=0.004 ft per ft; d=0.00131 ft, 0.40 mm]

Run

5 -------

7 -----

8 -----

2 --------

17... ..-.- ...

1 ----------

15- -------

16 .-- 

11.... .

10 ---- 

12....---------

1ft

14 ----------

g

13 ----------

6 -----------

4 ----------

3

Date

1- 6-54

5-18-54

7-22-54

6-18-53

4-16-58

7- 4-52

8- 6-57

11- 5-27

7-12-55

 do -

7-20-56

7-25-57

8-10-54

7-25-57

K_T7 KA

7-18-53

7-17-53

1

Q

5.9

20.4

20.5

24

30.8

41

75

102

119

129

168

448

1,020

1,730

2,540

4,380

11,700

2

Q/b

0.51

ftQ

.84

1.48-

.88

1.44

3.47

2.17

2.98

3.07

3.05

2.99

5.31

17.1

12.7

31.1

41.3

54.7

3

D

0.32

.36

.40

.47

.35'

.45

.55

.62

.71

.79

.82

.71

1.08

2.14

1.70

2.99

3.96

4.91

4 5

b

11.5

29.5

24.5

16.2

35

28.5

37

47

40

42

55

150

192

101

200

117

106

214

6

n

0.32

.36

4O

.47

.35

.45

.55

.62

.71

.78

.81

.71

1.07

2.05

.1.67

2.85

3.69

4.69

7

V

1.60

1.92

2.09

3.13

2.46

3.23

3.70

3.52

2.98

3.90

3.74

4.23

4 on

8.01

7.49

10.4

10.4

11.14

8

2,140

54,700

46,900

68,400

24,400

59,700

22,700

18,100

82.400

99,000

129,000

110,000

87,800

126,000

104,000

111,000

109,000

99,700

9

<?.

34

3,120

2 fion

4,600

2,030

8,650

4,600

4

QCA

27,500

37,000

62,800

141 nfift

260,000

632,000

766,000

1, 172, 000

1,385,000

3,380,000

Q

1 Information not known.
F58 STUDIES OF FLOW IN ALLUVIAL CHANNELS

TABLE 8. Basic data and computed parameters for the Rio Grande at San Felipe 

[This is not a true sand-bed channel. 5=0.0015 ft per ft; d, see column 25]

Run Date

Q/b

Bed elevation

CT

6-24-58 

6-17-58 

6-12-58 

6- 9-58 

5- 7-58

5-12-58

6- 3-58 

5-21-58 

5-26-58

3-23-54

4-20-54 

6-14-54 

11-17-54

1,020

2,200

5,010

5,120

7,520

8,200

8,590

9,140

9,720

414

762

755

360

5.6

12.1

26.8

27.2

37.4

40.0

43.0

43.5

46.5

2.7

3.6

3.4

2.1

10.80

10.88

10.41

10.46

10.41

10.68

10.13

10.53

10.38

10.64

11.18

11.22

11.17

2.17

2.73

4.47

4.49

5.57

5.56

6.00

5.86

6.17

1.35

1.62

1.51

1.15

181

182

187

188

201

205

200

210

209

153

212

223

172

2.12

2.65

4.28

4.28

5.28

5.27

5.66

5.55

5.83

1.33

1.60

1.49

1.13

2.60

4.44

5.99

6.06

6.71

7.19

7.16

7.43

7.53

2.00

2.22

2.25

1.82

577

1,100

2,740

6,300

4,620

4,410

2,430

2,790

2,580

308

790

339

1,280

415

902

2,410

5,800

2,490

2,780

1,600

1,670

1,550

166

245

197

Run

10

Q, >0.062mm

12

Einstein 

Qr/b

Bagnold 

Qr/6 Regime

15 17 18 19

1,590

6,530

37,100

87,100

93,800

97,600

56,400

68,900

67,700

344

1,630

691

1,240

6.3

29.4

174

426

252

300

186

197

194

2.2

7.7

3.1

7.2

21

59

326

612

12

51

273

672

LowerUpper..

-.do 

-do....

576

363

370

438

493

371

407

405

Upper. 

-.do 

...do , 

.-.do . 

Lower.

-do .

-.do .

-.do .

0.93

.99

1.11

1.11

1.20

1.23

1.11

1.13

1.11

1.33

1.13

1.09

1.55

0.205

.280

.128

.280

".500 

.200 

.086 

.460 

.182 

.177 

.183 

.121

0.31 

.47 

.50 

.50 

.50 

.54 

.52 

.54 

.54 

.30 

.31 

.32 

.30

8.1 

12.4

13.2

13.3

13.3

14.2

13.7

14.3

14.2

7.9

8.0 

8.4 

7.8

Run

20

0.0375

.0257

.0254

.0261

.0272

.0254

.0268

.0254

.0259

.0354

.0360

.0339

.0350

0.200

.250

.404

.404

.498

.497

.534

.524

.550

.127

.152

.142

.108

22

0.320

.358

.455

.455

.505

.505

.523

.518

.531

.254

.278

.269

.234

23

1.50

1.39

4.28

2.23

1.54

3.95

7.39

1.90

.92

1.20

1.09

24

7.1

18.0

428

244

72

187

969

54

1.3

3.0

2.3

9.4

25 26

0.00131

.00177

.00095

.00184

1.48

1.49

1.43

1.49

.00328

.00138

.00072

.00295

.00134

.00126

.00126

.00105

1.39

1.48

1.40

1.42
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F59

TABLE 9. Basic data and computed parameters for the Rio Grande at Angostura

heading near Algodones

[S, see column 26; d, see column 25.]

Run Date

1

Q

2

Q/b

3

Bed 

elevation

4

D

5

6

6

R

7

V

8

Cm

Rio Grande above Angostura heading

1 _ --------

2. --------

3... ------

*> 1 *i4

5-6-54

5-8-54

1,200 (; d

4.2

4.0

2.00

1.84

1.77

222

224

223

1.96

1.81

1.74

2.70

2.29

2.28

l,8tt

97(

78!

Settling basin at Angostura heading

1

2 _ ..- 

3. ---------

4

5

e A KA

g ft KA

5-8-54

1-11-56

1-12-56

588

KRA

KJ.1

510

fi97

10.8

10.1

9

fi

9 7

9

Q

3

AK

3.77

3.62

2.13

9 nd.

54.5

 U 7

54.0

3.06

3.32

2.30

1.97

2.00

3.13

2.69

2.72

4.55

4.77

1,960

1,130

874

2,540

2,550

Albuquerque main canal at Angostura heading

1 . ..- -

2... . ._.____ _

3 ------------

fr4-54

5-6-54

5-8-54

391

457

OQ4

7.8

9.1

7 9

3.48

9 QA

50

50

en

3.05

3.12

2.65

2.25

2.57

2.66

1,94

1,121

92

Waste way at Angostura heading

1

2 --.-..

3

fr4-54

5-6-54

5-8-54

197

97

147

3.4

1 H

9 7

2.32

1 IS

1 IS

58

55

KA

2.15

1 40

1.49

1.46

1.12

1.72

1,521

751

66.
F60 STUDIES OF FLOW IN ALLUVIAL CHANNELS

TABLE 9. Basic data and computed parameters for the Rio Grande at Angostura 

heading near Algodones Continued

Run

9

CT

10

<?.

11

Q,>0.062 mm

6

12

Einstein 

Qifb

13

Bagnold 

Qi/b

14

Regime

15

T

16

J-XIO'

17

0,

Rio Grande above Angostura heading Continued

1 _---.- --

2 . -.-. 

3

504

340

260

5,830

2,480

1,920

7 o

3 Q

2

Q

34

16

12

30

13

10

--do 

--.do -

17

18

18

1.16

1.13

1.13

0.18

.18,

.18,

Settling basin at Angostura heading Continued

i .-.--.--

2

3 ----------

4

5 _-. 

588

497

411

9 IfiA

9 run

3,120

1,690

1,280

S

CArt

3,630

17

14

11

57

KA

68

44

40

107

110

66

37

00

QO

92

 do 

 do 

18

19

19

6

1.13

1.10

1.10

1.81

1.63

0.170

.171

.171

.131

.141

Albuquerque main canal at Angostura heading Continued

1. ..... -___-

2 _-.-- 

3 _-. -

582

378

1,380

981

12

1Q

8

0

AQ

34

26

46

34

24

 do 

 do .

17

18

18

1.16

1.13

1.13

0.121

.12

.12

Waste way at Angostura heading Continued

I.... -------

2 .-_-.__-.-__-

3.. ....

380

225

OOK

808

iQfi

3

e

1.1

1.7

17

4.2

7.4

16

4.1

5.7

 do 

_-.do .-

18

17

16

1.13

1.16

0.17

.17 .IT1
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F61

TABLE 9. Basic data and computed parameters for the Rio Grande at Angostura 

heading near Algodones Continued

Eun

18

F

19

^

20

n

21

TO

22

V*

23

e

24

*

25

d

26

3

27

<

Rio Grande above Angostura heading Continued

I...... .-..--.-..

2....----.-.-..

3....- ..---..

0.34

.30

.30

9.5

8.4

8.5

0.0295

.0329

.0322

0.160

.147

.142

0.284

.273

.268

1.06

.98

.94

8.9

4.6

3.4

0 .00128

.00128

.00128

0.00112

.00112

.00112

1.

1.'

1.'

Settling basin at Angostura heading Continued

I......... .......

2-..----..-..-.

3....----..--..

4................

5....-- .......

A OA

.24

OK

.55

f.Q

9 2

7.6

8.0

17.3

0 .0178

.0221

n9i9

0089

.0083

0 129

.141

-100

ADA

.077

0.341

.355

O4Q

.274

.276

1 06

1.16

1.11

.66

.63

2

K

2

fl

1.6

8.2

7.8

0 0006

.0006

.0006

.0006

0.00118

.00118

.00118

.00118

.00118

1.46

1.46

1.46

1.46

1.46

Albuquerque main canal at Angostura heading Continued

i.. __..-....-__

2.....-....:....

0 91

f)A

.27

7.5,

8 A

9

K

O nORn

0,999

.0190

0.131

.134

.111

0.300

304

.280

1

OQ

1.41

1.17

3

0

3 A

2 9

0.0006

.0006

.0006

O nnAQO

.00092

.00092

I A

I A

1.4

Waste way at Angostura heading Continued

0.17 

.16 

.24

4.9 

4.6 

7.0

0.0294

.0296

.0193

0.087

.059

.059

0.295

.245

.245

0.68 

.46 

.46

4.5 

1.4 

2.1

0.0006

.0006

.0006

0 .00125

.00125

.00125

1.47

1.47

1.47
F62 STUDIES OF FLOW IN ALLUVIAL CHANNELS

TABLE 10. Basic data and computed parameters for the Rio Grande near Bernalillo,

section A-#

j~S=0.00095 ft per ft; <i=0.00098 ft, 0.30 mm; (1+^) =1.46~j

Run Date Q/b Bed

elevation

D

7-24-52 

6-2-53 

4-25-52 

6-26-52 

6-18-58 

6-13-58 

6-20-52 

6-10-58 

6-25-58 

6-17-52 

5-12-52

5-8-58

6-4-58 

5-13-58 

5-21-58 

5-27-58 

4-29-53

5-5-53

6-1-53 

6-4-53 

6-17-53

2,060

2,150

2,730

2,760

4,000

4,340

4,830

5,800

6,040

6,140

6,490

6,860

8,160

8,320

8,680

10,100

1,540

550

2,570

2,090

1,340

7.6

8.0

10.0

10.3

15.0

16.3

17.8

21.5

22.1

22.6

23.9

25.4

30.0

30.7

32.1

37.0

5.7

2.1

9.5

7.7

5.0

2.49

2.89

3.07

2.22

1.96

2.31

1.81

1.86

2.12

2.12

2.22

2.27

1.64

1.78

2.21

1.73

2.19

3.07

2.74

2.74

2.75

2.69

2 56

2. 47

2.76

2.96

2.67

3.49

3.43

3.40

3.79

3.63

3.68

4.34

4.46

4.11

4.80

2.15

1.25

2.66

2.48

2.14

270

270

272

269

267

266

272

270

273

272

272

270

272

271

270

273

270

265

270

270

2.64

2.51

2.43

2.70

2.90

2.62

3.40

3.35

3.32

3.69

3.54

3.58

4.21

4.32

3.98

4.64

2.12

1.24

2.61

2.44

2.11

2.84

3.11

4.06

3.71

5.06

6.10

5.09

6.27

6.50

5.96

6.57

6.91

6.92

6.88

7.82

7.71

2.65

1.66

3.58

3.12

2.34

2,490

2,010

3,320

1,040

5,980

2,080

1,690

3,480

5,410

1,990

3,160

4,420

2,580

4,740

3,400

3,040

2,450

545

2,530

1,600

1,050

Eun

CT

10

Q8>0.062 mm

12

Einstein 

QT/b

13

Bagnold 

Qr/b

14

Eegime

16

13. 

16. 

3..

2..

870

720

1,860

850

2,930

1,710

1,320

2,850

3,950

1,550

2,120

2,480

1,860

3,180

2,240

2,070

735

283

835

672

620

13,800

11,700

24, 500

7,750

64,600

24,400

22,000

54,500

88,200

33,000

55,400

81,900

56,800

106,000

79, 700

82,900

10,200

809

17,600

9,030

3,840

18

16

50

24

119

75

63

166

236

94

136

170

150

262

194

206

11

1.6

21

14

8.3

59

56

126

47

302

176

130

265

432

158

350

404

284

502

541

392

46

4.1

88

47

20

59

51

113

40

296

126

109

277

429

163

264

380

276

509

382

396

44

3.7

75

39

18

Lower. 

.. do...

Lower. 

Upper - 

.do...

T.

Upper.

.do...

-do. 

.do- 

_do.

-do. 

.do. 

_do-

.doLower. 

do.-.

T.

Lower. 

... do-..

0.99

1.06

1.25

1.06

1.10

1.16

1.03

1.13

1.02

1.06

1.16

1.25

1.10

1.21

1.10

1.02

1.25

1.16

1.14

1.16

1.06

Run

18 19 20

TO

21 22 23

e

24

12.

0.146

.141

.128

.141

.134

.133

.143

.133

.144

.141

.133

.128

.134

.131

.134

.144

.128

.133

.133

.133

.141

0.34 

.31 

.39 

.46 

.52 

.66 

.48 

.60 

.62 

.54 

.61 

.63 

.59 

.56 

.68 

.62 

.32 

.26 

.39 

.35 

.28

10.0

11.2

14.9

12.9

17.0

21.6

15.8

19.6

20.4

17.7

20.0

20.9

19.3

18.9

22.4

20.6

10.4

8.5

12.5

11.3

9.2

0.0314

.0277

.0206

.0244

.0188

.0146

.0208

.0167

.0160

.0188

.0166

.0158

.0177

.0181

.0151

.0170

.0291

.0323

.0248

.0271

.0328

0.157

.149

.144

.160

.172

.156

.202

.199

.197

.219

.210

.213

.250

.256

.236

.276

.128

.074

.158

.147

.127

0.284

.277

.273

.288

.298

.283

.323

.320

.319

.336

.329

.331

.359

.364

.349

.374

.254

.195

.286

.276

.256

1.58

1.51

1.45

1.63

1.75

1.58

2.06

2.03

2.02

2.24

2.15

2.17

2.56

2.64

2.44

2.84

1.26

.74

1.56

1.46

1.26

39

34

111

52

262

166

140

365

520

208

301

375

332

581

428

456

25

3.5

47

31

18
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F63

TABLE 11. Basic data and computed parameters for the Rio Grande near Bernalillo,

sections A, B, C, D, E

f" [S, see column 25; d =0.00098,0.30mm; (1+^p) = 1.461

Section

A,. ............

A.... ...........

B... ............

B.. .............

CL--. ----------

C... .......... ..

CL 

C... ......... ... D....... ........

D

E-. ............

E... ......... ..

E... ............

E... ............

Section

A...............

A.. ............

B... ............

B... ...... ......

C.... ...........

C.. .............

C... ............

C...............

D... .........

D

E...............

E.......... ....

E....... ........

E...............

Date

6- 4-53 

6-17-53 

4-13-54 

5-19-54 

6- 4-53 

6-17-53 

4-13-54 

5-19-54 

4-13-54 

5-19-54 

6- 4-53 

6-17-53 

4-13-54 

5-19-54

9

CT

892 

682 

442 

834 

444 

203 

520 

711 

389 

620 

692 

370 

544 

559

1

Q

1,970 

1,320 

1,200 

1,450 

2,070 

1,570 

1,160 

1,430 

1,160 

1,410 

1,780 

1,270 

1,200 

1,430

10

Q,

9,290 

3,740 

11,020 

14,800 

7,100 

2,610 

10,200 

12,500 

10, 100 

11,800 

6,410 

3,030 

11,000 

12, 700

2

Qb

5.0 

4.6 

2.8 

3.3 

5.5 

4.4 

3.1 

3.1 

2.9 

3.5 

6.6 

4.8 

4.5 

5.4

11

Q.>0.062 mm

b

11.9 

8.5 

3.3 

7.5 

6.6 

2.4 

4.4 

7.2 

3.0 

5.9 

12.4 

4.8 

6.7 

8.1

3

Bed

elevation

12

Einstein 

Qr/b

35 

19 

28 

42 

25 

13 

32 

35 

28 

35 

33 

18 

47 

56

4

D

1.69 

1.68 

1.42 

1.33 

2.36 

1.76 

1.45 

1.96 

1.53 

1.50 

2.47 

1.78 

1.98 

1.95

13

Bagnold 

Qr/b

28 

17 

28 

36 

22 

8.5 

30 

36 

26 

32 

30 

14 

45 

52

5

6

397 

286 

432 

434 

376 

353 

370 

383 

399 

401 

268 

267 

265 

266

14

Regime

r--- 

r.... 

Lower.. 

T.......

Lower., 

 do.... 

 do-...

--.do-... 

 do. ..

-.do....

 do-...

 do-...

 do....

 do....

6

R

1.68 

1.67 

1.41 

1.32 

2.33 

1.74 

1.44 

1.94 

1.52 

1.49 

2.44 

1.76 

1.96 

1.93

15

T

19 

24 

17 

20 

22 

24 

17 

23 

17 

23 

21 

23 

17 

21

7

V

2.94 

2.74 

1.96 

2.51 

2.33 

2.52 

2.17 

1.90 

1.89 

2.35 

2.69 

2.68 

2.30 

2.75

16

*X105

1.10 

.99 

1.16 

1.09 

1.03 

.99 

1.16 

1.02 

1.16 

1.02 

1.06 

1.02 

1.16 

1.06

8

cm

1,750 

1,050 

3,400 

3,790 

1,270 

616 

3,250 

3,230 

3,240 

3,100 

1,330 

880 

3,400 

3,290

17

ta

0.134 

.146 

.133 

.134 

.143 

.146 

.133 

.144 

.133 

.144 

.141 

.144 

.133 

.141

Section

A...................

A...................

B...................

B. ..................

C..... ...............

C....... .............

C.. ..................

C.... ...............

D. ....... ...........

D.. .................

E.... ..............

E. ..................

E. ..................

E.......... .........

18

F

0 40

07

.29

.38

.27

00

OO

97

34

.30

OK

90

OK

19

c/Vif

 to f\

19 1

9 A

19 fl

10.1

12.7

19 (\

Q n

1{\ 9

1 9 ft

11.4

 to q

10 9

10 1

20

n

O ftOOO

.0238

.0297

.0223

.0305

rtOQO

.0237

0331

rtOSJO

0970

.0220

.0276

H99R

21

To

0.100

100

084

H7Q

.106 n7Q

.065

088 nfiQ

.068

.111

080

non

088

22

V*

0.227

.226

.208

.201

OO-t

1QQ

1Q1

91 rt

.186

1Q4

9Ofi

.201

91 1

91 (\

23

e

1.00

99

.84

.78

1.39

1.03

.86

1.15

90

.88 i i**

1.05

1.17

1.15

24

<t>

26.5

18.7

7.4

16.4

14.5

5.3

10.0

15.7

6.7

12.9

27.2

10.6

14.6

18.0

25

S

0.00095

0. 00095

0. 00095

0. 00095

.00072

. 00072

.00072

. 00072

. 00072

. 00072

. 00072

. 00072

. 00072

. 00072
F64 STUDIES OF FLOW IN ALLUVIAL CHANNELS

TABLE 12. Basic data and computed parameters for the Rio Grande near Bernalillo,

section F

I"8=0.00095 ft per ft; d=0.00098ft, 0.30 m;( 1+Tr) =1 -46 1

Run Date

0/6 Bed 

elevation

7-24-52 

6- 2-53 

6-26-52 

4-25-52 

6-13-58 

6-20-52 

6-18-58 

6-10-58 

6-25-58 

6-17-52 

5-12-52

5- 8-58

6- 4-58 

5-13-58 

5-21-58 

5-27-58

2,030

2,400

2,850

2,910

4,380

4,720

4,730

5,440

5,960

6,100

6,390

6,730

7,790

8,310

8,700

9,970

3.5

3.7

7.7

4.5

8.8

13.5

9.1

10.5

11.2

12.5

11.2

12.1

15.3

15.4

13.5

15.7

3.59

3.12

3.87

3.61

4.05

3.28

3.85

4.51

4.26

1.58

1.37

2.41

1.18

1.91

2.45

2.28

2.13

2.09

2.18

2.07

2.15

2.72

2.55

2.19

2.64

580

643

370

640

498

350

518

520

532

489

570

557

508

541

645

637

1.58 

1.36 

2.38 

1-.18 

1.90 

2.42 

2.26 

2.11 

2.07 

2.16 

2.06 

2.13 

2.69 

2.53 

2.18 

2.62

2.20

2.71

3.20

3.86

4.60

5.50

4.01

4.91

5.36

5.73

5.42

5.61

5.64

6.02

6.17

5.93

1,740

1,900

852

2,820

1,990

1,460

5,420

2,070

2,800

1,500

2,690

4,700

2,500

4,220

3,350

3,060

Run

10 11

Q,>0.062 mm

12

Einstein

13

Bagnold 

Qr/b

14 15

Regime

16

14. 

4.. 

15. 

13- 

16. 

3-.

12-

574

494

630

1,550

1,670

1,140

3,250

1,450

1,260

1,120

1,530

2,680

1,750

2,570

2,140

2,020

9,540

12,300

6,560

22,200

23,500

18,600

69,200

30,500

45,100

24, 700

46,400

85,400

52,600

94, 700

78, 700

82,400

5

5

13

19

40

41

80

41

38

38

46

87

72

107

78

85

21

26

28

51

117

95

171

102

130

101

134

214

149

246

198

212

17

21

24

44

66

72

170

78

102

68

102

193

136

223

158

168

Lower.. 

T......

Lower.. 

Upper.. 

...do....

...do....

...do 

 ._. 

..do. 

..do.... 

... do..__ 

...do..._

 do....

 do 

...do.... 

... do....

0.93

1.06

1.06

1.14

1.11

1.02

1.04

1.06

.96

1.02

1.14

1.20

1.04

1.16

1.09

1.09

Run

17 19 20 22

Vt

23 24

12.

0.149

.141

.141

.133

.134

.144

.143

.141

.148

.144

.133

.131

.143

.133

.134

.134

0.31 

.41 

.36 

.63 

.59 

.62 

.47 

.59 

.66 

.68 

.66 

.67 

.60 

.66 

.73 

.64

10.0 

13.3 

11.8 

17.6 

19.0 

20.2 

15.2 

19.3 

21.3 

22.2 

21.5 

22. C 

19.7 

21.6 

23.8 

21.0

0.0284

.0210

.0260

.0134

.0154

.0153

.0199

.0155

.0141

.0135

.0138

.0137

.0159

.0143

.0126

.0148

0.094

.081

.143

.070

.113

.145

.135

.126

.124

.129

.123

.128

.162

.151

.130

.157

0.220

.204

.270

.191

.241

.272

.263

.254

.252

.258

.252

.255

.287

.279

.259

.283

0.93

.81

1.42

.70

1.12

1.44

1.35

1.25

1.23

1.28

1.22

1.27

1.60

1.50

1.29

1.55

21

25

25

50

73

82

246

77

84

29

59

250

177

289

153

157
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F65

TABLE 13. Baste data and computed parameters for the Rio Grande near Bernalillo, 

section A # runoff from tributary inflow

\S= 0.00095 ft per ft; d=0.00098 ft, 0.30mm; 1+ = 1

Run Date Source

Bed elevation

7-18-53 

7-30-53

7-15-52

8-27-55 

8-30-57 

8-27-55

7-18-53

8-12-52

9-25-55 

12-17-59 

12-21-59

Jemez----- 

Galisteo_ JemezGalisteo

-.do 

Chama... 

Galisteo...

-..do. . 

JemezGalisteo

- -do - 

Main.....

-.do 

1,370

1,430

4,280

4,300

5,000

7,360

8,020

8,200

13,000

425

505

5.1

5.3

15.9

15.9

18.5

27.2

29.5

30.1

47.6 

1.6 

3.5

2.77

3.21

3.41

3.25

3.04

2.96

2.47

2.59

1.75

1.60

1.60

2.60

2.75

2.86

3.70

3.95

4.01

5.60

1.00

1.72

269

270

270

270

270

271

272

272

273

260

143

1.60

1.60

2.55

2.65

2.80

3.60

3.85

3.85

5.40

1.00

1.68

Run

10

Q.>0.062 mm

12

Einstein 

Qr/6

13

nold 

Qr/6

14

Regime

15

3.18

3.31

6.11

5.80

6.48

7.34

7.46

7.52

8.50

1.63

2.05

42,400

29,200

10,700

59,500

20,400

48,100

74,700

63,400

71,600

724

1,190

1,460

2,030

4,160

2,860

1,440

5,230

5,710

10,700

210

416

163,000

113,000

124,000

716,000

275,000

991,000

1,680,000

1,460,000

2, 610,000

831

1,620

12

21

87

185

143

110

430

482

1,250

.93

4.0

433

567

2,750

1,100

3,760

6,380

5,400

612

429

499

2,740

1,090

3,710

6,380

5,590

10,100

4.1

13

T- - 

Upper. 

...do .

-do 

-do 

.do.

_.do . 

...doLower..

... do 

23

19

17

17

21

17

21

18

16

7

4

Run

16 18 19

cyV?

22 23 24

1.02

1.10

1.16

1.16

1.06

1.16

1.06

1.13

1.21

1.58

1.69

0.144

.134

.133

.133

.141

.133

.141

.133

.131

.112

.107

0.43 

.46 

.67 

.61 

.67 

.67

.63 

.29 

.28

14.4

15.0

21.8

20.4

22.1

22.1

21.7

21.9

20.9

9.3

9.0

0.0197

.0190

.0142

.0155

.0143

.0150

.0154

.0154

.0170

.0284

.0323

0.095

.095

.151

.217

.166

.214

.229

.230

.321

.059

.102

0.221

.221

.280

.285

.293

.332

.344

.344

.407

.176

.227

0.97

.96

1.54

2.29

1.70

2.24

2.43

2.45

3.44

.59

1.01

28

46

190

391

313

232

920

1,020

3,110

2.0

8.7
TABLE 14. Basic data and computed parameters for the Rio Grande ne

I" 5=0.00082 ft per ft; d=0.00079 ft, 0.24 mm; (i+jf) -1

Bun

118.15............

117.81 

117.62... .

117.43..... .......

Date

4-25-57

5-11-57

6- 6-57 

6-18-57 

6-27-57 

8-15-57

4-22-58 

4-30-58 

5-19-58 

5-27-58 

5-13-57

6- 6-57

6-19-57 

6-28-57 

8-16-57

4-24-58 

5- 1-58 

5-20-58 

5-28-58 

4-25-57

5-13-57

6- 6-57 

6-19-57

6-27-57

8-15-57

4-23-58 

4-30-58 

5-19-58

5-28-58

1

0

1,200

3,580

3,730 

4,150 

3,600 

2,760

5,800 

6,150 

7,310 

7,160 

4,440

3,600

3,690 

3,410 

2,610

6,580 

5,760 

7,370 

7,440 

953

4,160

3,800 

3,060

3,230 

833

1,830

6,510 

6,020 

7,310

8,270

2

Qlb

3.4

11.8

12.2 

12.6 

9.8 

6.7

13.0 

13.5 

16.3 

15.7 

12.2

9.2

9.5 

8.9 

6.8

15.3 

14.0 

18.2 

18.2 

6.0

25.4

12.1 

9.7

9.8 

6.2

10.3

19.7 

18.4 

24.0

25.8

3

Bed

elevation

2.03

2.03 

1.93 

1.97 

1.92

2.27 

2.41 

2.21 

2.74 

1.77

2.00

1.63 

1.63 

1.14

1.35 

1.46 

1.62 

2.03

8.62

10.29 

10.52

10.54 

10.08

9.62

9.72 

10.03 

9.99

10.21

4

D

1.67

2.29

2.34 

2.47 

2.15 

1.84

2.29 

2.37 

2.81 

2.74 

2.30

1.78

1.99 

1.85 

1.83

2.67 

2.52 

3.06 

2.90

9 fiS

4.62

2.36 

2.23

2.05 

1.83

2.29

3.30 

2.89 

3.51

3.79

5

6

347

304

306 

330 

366 

410

445 

455 

448 

455 

364

390

387 

384 

382

430 

411 

405 

408 

160

164

315 

315

331 

134

177

330 

327 

305

320

6

R

1.65

2.24

2.30 

2.43 

2.13 

1.82

2.27 

2.34 

2.78 

2.71 

2.27

1.77

1.97 

1.83 

1.82

2.64 

2.49 

3.01 

2.86 

2.76

4.38

2.32 

2.20

2.02 

1.78

2.24

3.24 

2.84 

3.43

3.70

7

V

2.07

5.14

5.21 

5.10 

4.57 

3.66

5.69 

5.70 

5.81 

5.74

5.18

4.80 

4.80 

3.73

5.72 

5.56 

5.95 

6.29 

9 no

5.50

5.12 

4.37

4.76 

3.40

4.51

5.97 

63.7 

6.82

6.82

8

1,200

6,090

4,900 

3,890 

3,170 

6,080

8,440 

4,950 

3,630 

3,510 

6,490

4,550

3,730 

3,380 

13, 300

8,620 

4,990 

3,210 

3,060 

3,710

7,210

5,180 

3,480

3,220

5,780

8,390 

4,810 

3,680

3,620

9

CT

336

1,400

1,810 

1,710 

1,590 

1,280

2,030 

2,230 

2,030 

2,530

1,680

1,680 

1,760 

931

3,190 

2,250 

1,890 

1,990

AQf)

2,380

2,120 

1,770

1,510

1,270

2,430 

2,'160 

2,130

2,530

10

Q«>0.06

6
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F67

CO^*^ OOQ Q O OOiQ tO^OO fr~ OOC<I ** U5CSOS OS tO i I lOO ** i-H CD t 

i I O »-- OS W3O O i-H CO i I tO COO OS i-H CD to OOQ i I O * N to OS CO r-H 00 * 

CO CO i-< 001~ O O <N IM i-< <N i-H IM CO IM IM 1~- 00 t- CO 1-1 IM CO <N IM

t*- CO Q p i-H Cfl O O * to OS OO OO CO r-H to CO tO «* »-- OO CO CO t*» tO i-H ** -* OS OS OS 

i-l£toet^NOlKS,-HtotON<NCOOO-*-*i5totolMOse«5i-H<NCo3lO O5>

CO tO 00 tO tO tP 2} (M OS to * IN IM * CO CO tO U5 « OS U5 OS OO CM O OO OO « iH t~ OO 

t^- O (M tO S OS O i-H 00 >> t-- 00 *< * 00 CO "5 CO CO tO JJ 00 00 * 5i N CO CO 00 * 00

OOOOOOOOOOOOOOOOOOOOOOOOOOOOO OO

doocccocoo^g _5_o 

6 c 6 c 6 6 6 c 6 ^ a S, 1- 'O'O'cl'c T t "OT 'O'O ^

lt> 

.......... .^. .................

l-H-H (Ml-HIMIM *" (M8-H1-H"

IMNi-Hr-TrH'-^riN'lM'lM' i-n'i^TrH'lM'i^i'lM'lM'i-H'i-reQC^'i-ri-ri-H'N"^^!^

i-H CO O 00 t~ i-l * tO tO i-l IM Q «O >* r~ >* (M tO tO "5 CO "3 t~ * Q "5 00 CO O OS to **! t^. u5 os ^*i ob »51^ co to 25 oo to I-* to I-* »o t^. * o t^. co o to I-H I-H u5 c^i ^

J-*CO
TABLE 15. Basic data and computed parameters for the Rio P

[S=0.001 ft per ft; d=0.00079 ft, 0.24 mm]

Run

I ...

7 -----

2. -------

13. -----

16 ------

6 ..- --

10 .----

9

17....- -

15 .- -

1Q

19

20 ------

4_ ------

3 --------

11

18 .-- -

Date

10- 3-50

7-30-52

7-28-51

9- 2-53

8-25-54

7- 7-52

8-23-52

8-14-52

8-23-52

8-29-51

9-13-54

8-12-54

8-10-59

8-12-53

8-26-59

8-25-51

8- 2-51

7-19-53

9-27-54

1

Q

159

197

259

283

301

313

343

595

603

775

7Qft

1,410

1,470

1,600

1,900

2,010

3,440

4,340

5,440

6,620

2

Q/b

3.0

3.9

4.5

5.0

5.6

4.9

5.7

11.2

9.4

13.1

12.2

17.4

19.9

17.2

25.0

19.3

24.0

19.7

22.8

52.5

3

D

0.98

1.24

1.41

1.35

1.24

1.31

1.50

1.87

2.02

2.20

2.00

2.64

2.88

2.63

3.25

2.64

3.21

3.47

3.90

6.97

4

Regime

--.do 

--_-.do .

-.--.doUpper -

----doUpper 

r.-------

-.-.do 

...-do 

.....do 

-- do 

.-.-do 

...-.doLower .....

..-.do 

-.-..do 

5

6

53

50

57

57

54

64

60

53

64

59

65

81

74

93

76

104

143

220

239

126

6

R

0.98

1.24

1.34

1.31

1.19

1.26

1.43

1.75

1.90

2.05

1.88

2.48

2.67

2.48

2.96

2.52

3.07

3.37

3.77

6.27

7

V

3.07

3.18

3.23

3.69

4.48

3.74

3.81

6.00

4.67

5.96

6.07

6.59

6.90

6.55

7.69

7.31

7.49

5.68

5.84

7.54

8

Cm

112,000

87,400

152,000

202,000

110,000

69,700

193,000

199, 000

273,000

273,000

115,000

115, 000

86,600

141, 000

209,000

165,000

123, 000

123,000

90,500

72,900

9

<?.

51,600

49,900

118,000

177,000

96,000

61,000

205,000

367,000

527,000

677,000

263,000

470,000

356.000

677, 000

1, 230, 000

995,000

1, 230, 000

1, 550, 000

1, 430, 000

1, 350, 000

Q»>
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F69

TABLE 16. Basic data and computed parameters for the Rio Grande near Socorro

reach

["s=0.00075 ft per ft; d=0.00059 ft, 0.18 mm;f l+^)=1.38~j

Section

A-l..... .............

A-2..... ..........

B....... .............

A-l. . .

g

B-l..................

A-l........ ..........

A-2- ...

Section

A-l.... __ ______

A-2- .._____ _____

B-l ____________

A-2... __ .....

B-l........ ..........

A-l .... .........

A-2 

Date

4-16-54

... do 

 do 

 do 

.-do 5-21-54 

 do .

do

28-1 

do

MW

8

cm

6,330 

6,210 

6,440 

6,670 

14,900 

15,700 

14,200 

14,000 

125,000 

116,000

16 

Section

J-X105

A-l 

A-2 

B _ ____

B-l. .

A-l .. ..

A-2 

B__ ...

B-l .

A-l 

A-2 

1.32 

1.25 

1.06 

1.04 

1.06 

1.10 

1.02 

.98 

1.04 

.98

1 2

0 0/b

697 4. 0 

. ... . 2.9

. .__. 1.6

3.4

3, 

3,

9

CT

1,540 

1,110 

753 

627 

1,060 

1,070 

923 

994 

15, 800 

16,900

17

w

0.058 

.059 

.067 

.069 

.067 

.066 

.070 

.071 

.069 

.071

891 4. 0 

900 3.9 

874 2. 7 

840 2.3 

600 14. 0 

550 15.2

10

Q, (

11,910 

11,700 

12, 100 

12,600 

35, 800 

38,200 

33,500 

31,750 

1,305,000 

1, 193, 000

18

3

Bed

elevation 1

11

? s>0.062 ma

6

16.5 

8.6 

3.2 

5.8 

11.4 

11.2 

6.7 

6.1 

651 

744

19

F C/V0

0.36 

.51 

.51 

.35 

.55 

.52 

.43 

.61 

.70 

.72

13.6

18.7 

18.6 

12.8 

20.5 

18.9 

15.5 

17.0 

25.7 

26.5

4

D

1.53 

1.00 

.66 

1.44 

1.16 

1.20 

1.07 

.91 

2.30 

2.38

12

1 Einstein

Qrlb

78 

62 

33 

65 

177 

178 

112 

93 

5,320 

5,440

20

n

0. 0210 

.0142 

.0132 

.0218 

.0179 

.0144 

.0172 

.0097 

.0118 

.0114

5

6

175 

241 

447 

202 

222 

233 

327 

368 

258 

234

13

Bagnold

74 

51 

28 

64 

166 

169 

104 

88 

5,310 

5,390

6

R

1.50 

.99 

.66 

1.42 

1.15 

1.19 

1.06 

.91 

2.26 

2.33

14

Regime

Lower.. 

 do .

... do _

 do .

 do 

... do 

...do 

 do 

Upper... 

_ do .....

21 22 23

TO v» e

0.070 0.191 1.18 

. 046 . 155 . 77 

. 031 . 127 . 51 

.067 .187 1.12 

.054 .168 .90 

. 056 . 170 . 93 

. 050 .161 .83 

. 043 . 148 . 71 

.106 .236 1.91 

.109 .240 1.96

7

V

2.60 

2.90 

2.36 

2.40 

3.45 

3.21 

2.50 

2.51 

6.07 

6.37

15

T

12 

14 

21 

22 

21 

19 

23 

24 

22 

24

24

*

142 

74 

27 

50 

99 

96 

57 

53 

5,120 

5,970

1 Not available.

> Buns on Aug. 17,1954, are Rio Puerco flow.
F70 STUDIES OF FLOW IN ALLUVIAL CHANISTELS

TABLE 17. Basic data and computed parameters for the Rio Grande at San Antonio 

f 5=0.00055 ft per ft; d=0.00066 ft, 0.20 mm; (l+|r ) =1.39"1

Bun Date

0/6 Bed 

elevation

6-26-58

6-19-58

6-9-58

6-11-58

5-8-58

6-5-58 

5-13-58 

5-22-58

5-29-58

6-19-52

5-1-53

6-10-53

1 8-19-54

378

3,080

4,090

4,260

6,180

6,570

6,940

7,740

8,500

4,850

1,420

717

739

1.9

13.6

17.8

18.4

26.3

28.0

29.2

32.7

36.2

7.1

5.4

18.7

5.6

1.92

2.32

1.61

1.90

2.07

1.54

2.00

1.52

1.40

.69

2.02

1.70

1.31

1.21

2.59

3.28

3.26

3.87

4.23

4.29

4.64

4.98

3.17

1.57

1.37

1.65

198

227

229

231

235

235

238

237

235

260

199

132

133

1.20

2.54

3.19

3.17

3.75

4.08

4.14

4.47

4.78

3.09

1.54

1.34

1.61

1.58

5.24

5.44

5.66

6.79

6.61

6.81

7.04

7.26

5.89

4.54

3.96

3.37

Run

10

<?,>0.062 mm

12

Einstein 

Qr/b

13

Bagnold

Qr/b

14

Regime

904

5,380

4,620

4,560

12, 600

6,070

11,500

9,280

7,610

3,800

4,980

2,410

85,600

235

1,670

2,730

2,640

5,670

4,130

5,520

5,750

4,640

1,920

723

2,200

3,420

92?.

44, 700

51,000

52, 500

210,000

108,000

215,000

194,000

175,000

49, 800

19,100

4,670

177,000

1

61

131

132

402

312

433

506

455

111

23

11

53

242

287

295

1,040

570

1,030

945

889

271

125

51

1,370

4.8

221

273

279

1,050

581

1,070

1,020

921

235

105

39

1,350

Lower... 

Upper...

-do_. 

..do..... 

..do..... 

..do . 

...do..... 

...do . 

... do -. 

Upper... 

...do.....

-do..... 

T.......

25

27

24

24

18

26

17

24

21

16

26

27

20

Run

16 18 19 20 22 23 24

0.97 

.93

1.15

.96

1.17

.98

1.06

1.19

.96

.93

1.09

0.085

.087

.085

.085

.076

.086

.075

.077

.087

.079

0.25 

.57 

.53 

.55 

.61 

.57 

.58 

.58 

.57 

.58 

.65 

.60 

.46

10.8

24.7

22.9

23.9

26.3

24.6

25.1

25.1

24.9

25.1

27.3

25.5

19.9

0.0254

.0127

.0143

.0137

.0130

.0140

.0137

.0140

.0142

.0130

.0105

.0110

.0146

0.041

.087

.110

.109

.129

.140

.142

.154

.164

.109

.054

.047

.057

0.146

.212

.238

.237

.258

.269

.271

.281

.291

.235

.166

.155

.169

0.61

1.31

1.65

1.64

1.95

2.13

2.17

2.34

2.51

1.60

.79

.69

.87

7.6

387

827

827

2,540

1,970

2,740

3,200

2,860

700

232

66

326

Run on Aug. 19,1954, is Rio Puerco flow.
FLUVIAL CHARACTERISTICS AND HYDRAULIC VARIABLES F71

TABLE 18. Basic data and computed parameters for the Rio Grande Floodway at

San Marcial

Run Date

0/b Bed 

elevation

6-27-58 

6-20-58 

6-10-58 

6-12-58 

5- 8-58

5-12-58

6- 6-58 

5-22-58 

5-28-58

1,990

3,810

4,230

4,570

6,170

6,420

6,870

7,710

10.9

20.3

22.7

24.2

32.0

33.3

35.6

40.4

44.1

9.69

10.29

9.18

9,59

10.00

10.40

9.24

9.29

9.04

2.73

3.62

4.07

4.06

4.97

5.03

5.39

6.23

6.75

183

188

186

189

193

193

193

191

197

2.65

3.48

3.90

3.89

4.73

4.78

5.10

5.85

6.32

3.99

5.60

5.59

5.95

6.43

6.62

6.61

6.48

6.53

Run

10 11

Q,>0.062 mm

12

Einstein 

Qilb

13

Bagnold 

Qi/b

Regime 1

15

3,730

4,210

4,370

4,080

9,630

7,830

5,950

6,080

5,450

1,380

1.520

2,450

2,080

3,270

2,740

3,270

2,310

2,180

20,000

43,300

49,900

50,300

160,000

136,000

110,000

127,000

128,000

44

85

150

136

282

239

313

253

260

136

278

339

322

943

793

668

749

741

125

261

322

315

931

791

683

756

744

22

24

22

21

19

18

23

21

25

Run

16 17 18 19 20 22 23 24

1.03 

.99

1.04

1.05

1.10

1.13

1.02

1.95

.97

0.048

.049

.048

.047

.045

.044

.048

.047

.050

0.43 

.52 

.49 

.52 

.51 

.52 

.50 

.46 

.44

21.3

26.0

24.6

26.2

25.7

26.3

25.4

23.3

22.6

0.0153

.0128

.0139

.0130

.0138

.0134

.0142

.0159

.0167

0.070

.093

.104

.104

.127

.129

.138

.160

.173

0.187

.215

.227

.227

.250

.252

.260

.278

.289

1.47

1.95

2.20

2.19

2.69

2.73

2.92

3.37

3.65

692

1,420

2,560

2,320

4,820

4,200

5,360

4,300

4,430

1 Not known.
F72 STUDIES OF FLOW IN ALLUVIAL CHANNELS

LITERATURE CITED

Bagnold, R. A., 1955, Some flume experiments on large grains but little denser 

than the transporting fluid, and their implications: Proc. Inst. Civil Engineers, excerpt pt. 3, p. 174-205.

> 1956, The flow of cohesionless grains in fluids: Royal Soc. London Philos. 

Trans. ser. A, v. 249, p. 235-297.

 ; 1960, Sediment discharge and stream power a preliminary announcement: U.S. Geol. Survey Circ. 421, 23 p.

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

Am. Soc. Civil Engineers Trans., v. 123, p. 526-594.

Colby, B. R., 1957, Relationship of unmeasured sediment discharge to mean 

velocity: Am. Geophys. Union Trans., v. 38, no. 5, p. 708-717.

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1498-A.
INDEX

[Where several page numbers appear, major references are in italic]

Page

Antidune bed configuration.... .. F3 

Bagnold equation... 45 

Bagnold method_..____.___ ___ 3,54 

Bagnold plot... 46 

Bagnold theory__._____.__-----_ 36,40,43 

Bagnold's total-transport and shear functions. 3 

Basic data tables... 65 

Bed elevations for each station.... 9 

Bed elevation, changes.. _ __. 20 

Bed material... .. 12

particle size - 12,27,28,29

standard deviation.. 27,28 

Bedload._._...-._.. . . 8,36,50 

BedJoad function..... . . .... 40,49 

Bedload transport function..... .- .. 43 

Boundary shear.. . 36 

Channel shape__... 28 

Channel-shape factor. 27 

Chezy C......... 3,14,28,29,34,49,54

relation to bed material 21 

Chezy formula______ . 14 

Computed parameters 66 

Computed total load... 43 

Conclusions and summary 53 

Critical shear_ _ ...- 43 

Critical stress.... 47 

Data observed for stations..... _ 3 

Definition of terms_____.________ 8 

Depth-discharge relations.... IS 

Depth-discharge relations at individual

stations__ 14 

Depth-roughness ratio.. . . 29,54 

Description of reaches.. . __ 4 

Dune regime.. ----_-. . . __ 14 

Einstein method___ . __ 51 

Einstein theory .. .. . . 36,40 

Einstein transport function...___ ___. 40 

Energy gradients for Casa Colorada reach,

average___ .______ 12,35,54 

Energy slope... ___ ____.___. 34 

Fine-material load_____-________ 9 

Flow regime____ ____-________ 3 

Fluid shear____.___ ____.___ 43 

Froude number...__... ___...__.. 19 

Geographic location. _____________ 4 

Hydraulic characteristics at each station___ 3 

Hydraulic measurements, other.______. 6 

Hydraulic radius.... ... ...- 22,28,36,37,40,53 

Hydraulic radius-velocity relation. _____ 16 

Hydraulic variables_________.___ 3

measurement...______________ 9 

Keulegan velocity equation__________ 49 

Laboratory studies ______________ 13 

Manning's formula______________ 14

Page 

Manning's n.................................. F3,14

Mean depth_____.. ____________ 36 

Mean velocity..__..__._________ 36 

Median diameter, d........................... 12

Median diameter of bed material______ 3 

Modified Einstein and Bagnold, comparison

between...._____.______ 51

Modified Einstein method-...______ 3,40,54 

Nikuradse's relative roughness parameter._ 27 

Nonsand-bed channel...___________ 13 

Particle size of bed material.___- ._..___ 12 

Personnel and acknowledgments... _____ 3 

Plane bed._____.____________ 3 

Plane bed regime_______________ 14 

Purpose and scope of report.... .. 1

Regime of flow..___.___________ 8,19 

antidune_ . ........ 53

criteria for estimating_.. . . 18 

flat bed.... ..___.____.___.. 53

lower. 13,19,28,29,36,50,52,53

plane bed_..._ . 53

standing wave_________-___._ 53

upper- ___.- 13,16,19,21,27,28,29,36,37,50,52

Resistance to flow_______.____.__ 12

Reynolds number effect..-- ---.----_-__ 27

Roughness parameters_-. . . . __ 3

Roughness, other factors influencing- 27

relative______-__ . .__ 27

summary of other factors influencing.. _ 29

Sand-bed channel- - 8,13,22,27,42,53,54

reach____________________ 53

Sand-bed channels, upper-regime flow_.__ 54

Sand-bed stations.. 21

Sand-bed stream.. __.__......... 4,18,29,43

Sand-channel stream.... .... 12,18,29

Sand-gravel channel.. ______-__ 8,13,22,54 

Sand-gravel stations... _ 21

Scour and fill- ... . 36

Sediment concentrations.-- 7

Sediment-discharge records. 31

Sediment variables, measurement .. 9

Sediment transport... . 22,37

characteristics..-..-.. 3,53

functions - -... 8

rate. _ .. 12

relation to shear.. 36

studies... . 51

Shear .. . 22,40

Shear function_. ... .. - 3,43 

Shear-transport relation 40 

Slope determinations 10 

Slope value, average.. 10 

Stage-discharge relation 3 

Standard deviation of bed material 28

F73
F74 INDEX

Page

Standing wave..____ _________ F3 

Stream velocity-- - __ 53 

Suspended load.________________ 8,40,48 

Suspended-load function.-- ...____... 49 

Suspended-load transport function.. __.... 43

Suspended-sand load.... ______... 36

Suspended-sediment concentration.._____ 5, 

9,27,28,29,40,54

Suspended-sediment discharge________ 8,9,31 

Suspended-sediment load__._________ 45 

Suspended-sediment transport________ 36,44 

Tangential stress, characteristic applied... 48 

Total load....._.__... ..._.___. 40

computations____ - ________ 3 

data..__-._._. ----. -___.. 6

equation......___....________.. 49

function____________________ 49

Page

Total-sediment discharge . _ _ F8,32,40,42 

Total-sediment loads. _________ 3,36,45,51,54 

Total-sediment movement_..____..__ 31 

Total-sediment transport__________ 36,40,44 

size distribution.-,---.-__________ 40 

Total shear force___ ___________ 27 

Total transport function____________ 49 

Transport function_ ___ ._ 43 

Transport-shear relation,-.. __ 45 

Unmeasured-sediment discharge_______ 8 

Upper-flow regimes_ _. .. 3 

Upper-regime curves-..-- - ___ 40 

Upper-regime flow data - _ 27 

Velocityofflow.... - . 22,28,31,37,53 

Water-surface slopes for Casa Colorada

reach.__- .__...._. .. 12, 54 

Width-depth ratio.. . . 29,54

o