Vertical Distribution of 

Velocity and 

Suspended Sediment 

Middle Rio Grande 

New Mexico

GEOLOGICAL SURVEY PROFESSIONAL PAPER 462-B
Vertical Distribution of 

Velocity and 

Suspended Sediment 

Middle Rio Grande 

New Mexico

By CARL F. NORDIN, JR., and GEORGE R. DEMPSTER, JR. 

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 462-B

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1963
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 

Abstract___________________________________________ Bl

Introduction _________ 

Purpose and scope. 

AcknowledgmentsDescription of reaches,. 

Measured data_____.

.______-__-__._____._.____._ 1

.-_..---__-_-____-_________-_ 1

._-_-________________ 1

____________________________ 1

.------_--__-____.____-_____ 2

General approach______________.______________________ 3

Page

Velocity distribution________________-__-----_-______-_ B4

Mean velocity_-______________---_---_--__-__--__- 6

Suspended-sediment distribution.______..________--__-_-_ 7

Effects of high concentrations on fall velocity._______ 12

Conclusions.___-___-__________-_-____-__--_-__-_----_ 13

Basic data and computed parameters..__________________ 14

References cited______________________________________ 20

ILLUSTRATIONS

FIGURE 1. Location and sketch map____-________________________

2. Definition sketch.__________________________________

3. Variation of velocity with depth_______________________

4. Variation of k with concentration._____________________

5. Variation of k with C/V<7_-_-__-_______-_-___-________

6. Bar-resistance curve, Bernalillo and Socorro_.___________

7. Bar-resistance curve, Bernalillo, 1952_________________

8. Variation of concentration with (D y)/y, Bernalillo._____

9. Variation of concentration with (D y)/y, Socorro.______

10. Variation of Z\ with Z and Zk_________________________

11. Size distribution of bed material-__--__-__--__________.

12. Variation of Z\ and fall velocity.______________________

13. Variation of k and /3_._______________________________

14. Qualitative relation of velocity and sediment distribution.

15. Variation of fall velocity with concentration.___________.

16. Comparison of computed Z values_____________________

Page

B2

2

4

5

5

7

7

8

8

9

10

11

12

12

13

13

TABLES

TABLE 1. Velocity distribution______________________________________________________._______________-___-____--_ B14

2. Suspended-sediment distribution_____-_______-________________-_______-_---_-_-__--__--------_-_--_--- 16

3. Basic data.-_-___________________________________________________-_-__-_________-___------_--_-_-_--- 18

4. Computed parameters__._________________________________-_________-______________-___--_-------------- 19

5. Basic data and computed parameters for the average of 13 cross sections through a 16,000-foot reach, Rio Grande

near Bernalillo, N. Mex________-____-_____--__-___-___-___________________-_-__--__--_------_-----_- 19

in
	SYMBOLS

Symbols Units

a Reference distance above the bed_____________________________________________________________ ft

c Concentration of suspended sediment-_____________________-__________-_--__-_-__-_-____-_------ ppm

C/Vff Dimensionless Chezy coefficient_____-_____________________-__________-_--__--_---__---_-------- 0

Ci A constant__________________________________________________________________________________ 0

Cr A coefficient of discharge.-_---__-__________________________________-______-__-_______-_------ 0

ds& Particle size for which 35 percent of the bed material by weight is finer, as determined by sieve analysis-___ _ mm

dso Particle size for which 50 percent of the bed material by weight is finer_____________________________ mm

des Particle size for which 65 percent of the bed material by weight is finer__________-__-_____-_-_____-- mm

dy Increment of distance above stream bed---__-______-_---__--__--__-__-_-_-_-_-_-----_----_------ ft

Z) Depth of flow at a vertical__-_--_____-____________________-____-__-_______-__-___-___-__-_--_ ft

D Mean depth of flow in a cross section._________________________________________________________ ft

g Acceleration of gravity----_-_-____-_______-______-___-______-_---_--___-___-_-____-_-_-_------ ft per sec2

i An exponent.._______________________________________________________________________________ 0

j An exponent.._______________________________________________________________________________ 0

k The coefficient of turbulent exchange. __________________________________________________________ 0

K, A length parameter.,_________________________________________________________________________ ft

m Slope of semilogarithmic graph of velocity versus depth for a single vertical __________________________ ft per sec

m Average slope of velocity versus depth for all verticals in a cross section.____________________________ ft per sec

q3 Transport rate of suspended sediment______________________-__-___-___--___-____-_-___------_- Ib per sec per ft

Pw Wetted perimeter.____________________________________________________________________________ ft

R Hydraulic radius_____________________________________________________________________________ ft

R' Hydraulic radius with respect to the sand grain___________________________________________-_--_-- ft

R" Hydraulic radius with respect to dunes and bars_-_-_-_____-_-----_---_-_---_-___--__-----__--_-_- ft

S Water surface slope__-____-___-_-_-______________-______-________-_-_-____-__--____-____-__-_- 0

Se Energy slope_______________________________________________________________________________ 0

V Velocity at a point-___ ____________________-___________-___--_____-_-___________-__-__---__-- ft per sec

V Mean velocity.______________________________________________________________________________ ft per sec

V* Shear velocity_______________________________________________________________________________ ft per sec

x A correction factor for transition from smooth to rough boundary___-___-__________-__-___-___--___ 0

y Distance above stream bed-___-_____________________-__--_________---_-________-_-___--_--_--_ ft

Z Computed exponent for vertical distribution of suspended sediment using k = 0.4____---_-_______--__- 0

Zi Exponential measure of the actual distribution of suspended sediment_______________________________ 0

Zk Computed exponent for vertical distribution of suspended sediment using fc = (2.3/m) V* _______________ 0

(8 Factor of proportionality between e s and em ______________________________________________________ 0

7 Specific weight of water_______________________________________________________________________ Ib per ft3

5' Thickness of laminar sublayer.._______________-______________---__-_-__-__--__-_______-_-----_- ft

A An increment of change________________________________________.______________________________ 0

em Momentum transfer coefficient-_________________-___-_____-__--___-_-________---__-__--_------- 0

ea Sediment transfer coefficient____________________________-___-_-_-___-_-___-___-__----____----_- 0

v Kinematic viscosity__________________________________________________________-,_______________ ft2 per sec

pf Density of fluid._____________________________________________________________________________ slugs per ft3

p a Density of sediment__________________________________________________________________________ slugs per ft3

TO Tractive force on the bed_____________________________________-_-________-_-____--__----_--_- Ibs per ft2

$' A flow intensity parameter.__--_________-_________________--_---_-__-___-_---__-----_----__--- 0

w Fall velocity of sediment particles. ___________________-_________-__________-___-_-_-___-_--_---- ft per sec

IV
SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

VERTICAL DISTRIBUTION OF VELOCITY AND SUSPENDED SEDIMENT, MIDDLE RIO GRANDE,

NEW MEXICO

By CARL F. NORDIN, JR. and GEORGE R. DEMPSTER, JR.

ABSTRACT

Samples of suspended sediment and measurements of velocity 

at 3 to 5 points in a vertical are used to define vertical sediment 

concentration and velocity profiles for cross sections in reaches 

of the Rio Grande near Bernalillo and Socorro, and of the Rio 

Puerco near Bernardo, N. Mex.

Velocity profiles show the velocity to vary logarithmically 

with depth. The coefficient of turbulent exchange, k, is found 

to decrease systematically for the transition zone and upper 

regime flow. For lower regime flow, k varies from about 0.4 to 

1.2, indicating three-dimensional flow effects.

Assuming a conventional logarithmic velocity equation to be 

applicable, it is found that the range of values of Ks, the height 

of the representative roughness element, is dependent upon the 

condition of the channel bed. The ratio of maximum to minimum Kf is about 20,000 for lower regime flow, 40 for transition 

and upper regime flow, and 4 for flow over a clay-armored bed. 

However, the relation of the average K, value to the average 

representative bed-material size for each of the reaches is about 

constant, and is approximately 400 times greater than d®, the 

size of bed material for which 65 percent by weight is finer.

The Einstein-Barbarossa bar-resistance curve is shown to describe frictional losses for individual cross sections of the Bernalillo and Socorro reaches with reasonable accuracy. Twenty of 

the 23 computed values of mean velocity are within 25 percent 

of the measured values. When an average cross section is used 

for the Bernalillo reach, the computed mean velocities are within 

15 percent of the measured values.

Suspended sediment is more uniformly distributed through a 

vertical than predicted by conventional theory. The measured 

exponent of the sediment distribution, Z\, varies with about the 

0.55 power of the fall velocity. The fall velocity is reduced 

appreciably by the presence of nigh concentrations of suspended 

fine material.

The ratio of the sediment transfer coefficient to the momentum 

transfer coefficient, /3, appears to be a direct function of particle 

size and bed configuration. For a given particle size the highest 

values of /3 are associated with upper regime flow, while for 

lower regime flow, /3 values are close to unity.

INTRODUCTION 

PURPOSE AND SCOPE

The purpose of this report is to present measured 

values of vertical velocity and suspended-sediment 

concentration distributions, and to compare the measured values with values computed from theoretical

considerations. Some of the variables in the distribution equations are analysed. In addition, one 

method of estimating mean velocity is discussed.

Data are presented for 23 observations in reaches of 

the Kio Grande near Bernalillo and the Bio Grande 

near Socorro, N. Mex. Limited data for the Rio 

Puerco, a tributary to the Rio Grande, also are included 

to indicate some of the effects of high suspendedsediment concentrations. Data for the Rio Grande 

near Bernalillo and near Socorro were collected during 

the period 1953-54 as part of a cooperative program 

between the U.S. Geological Survey and the U.S. 

Bureau of Reclamation to study sediment transport 

in the Middle Rio Grande, N. Mex.

This report is one of several utilizing available data 

for the Middle Rio Grande basin for studies of sedimenttransport parameters in sand-bed streams.

ACKNOWLEDGMENTS

This report was written under the supervision of 

J. M. Stow, district chemist, and J. K. Culbertson, 

hydraulic engineer, Quality of Water Branch, Albuquerque District, N. Mex.

Appreciation is expressed to A. A. Fischback, Jr., 

district engineer, Surface Water Branch, Oklahoma 

City, Okla., and others for their cooperation.

DESCRIPTION OF REACHES

Velocity and suspended-sediment concentration distributions were measured in two reaches of the Rio 

Grande: Rio Grande near Bernalillo, and Rio Grande 

near Socorro, N. Mex. In addition, several observations were obtained for a single cross section on the 

Rio Puerco near Bernardo. A location and sketch 

map of the reaches is shown in figure 1.

The Bernalillo reach is located approximately 3 

miles southwest of Bernalillo and 9 miles downstream 

from the Jemez River. The right bank at the upstream 

portion of the reach is a high bluff composed of calcareous sandstone. The bluff veers away from the

Bl
B2 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Sandstone bluff

B ' f

 -'-.zX

Socorro

Section A-2

N 

A

Bernardo

Bernalillo

FIGURE 1. Location and sketch maps of Eio Grande near Bernalillo, Eio Qrande 

near Socorro, and Eio Puerco near Bernardo, N. Mex.

river about 200 yards downstream from the uppermost 

cross section. Throughout the rest of the reach, both 

banks consist of a mixture of sand, silt, and clay, 

and are partially stabilized by vegetation. The reach 

is laterally unconfined except at section A-2, which is 

the site of a U.S. Geological Survey gaging station. 

The reach is about 7,000 feet in length.

The Socorro reach is approximately 28 miles downstream from the mouth of the Eio Puerco and a quarter 

of a mile northeast of Socorro. Both banks of the 

reach consist of silty clay and are partially stabilized 

by vegetation. The reach diverges somewhat and is 

about 4,000 feet hi length.

The Bernardo reach is located about 1 mile southwest of Bernardo and 3 miles upstream from the mouth 

of the Eio Puerco. This is the site of a U.S. Geological 

Survey gaging station. Both banks consist of silty 

clay and are stabilized by vegetation. The cross 

section is located about midway of a slightly converging 

reach approximately 630 feet in length immediately 

downstream from the gaging station. The reach 

has a sand bed, but for the several observations presented, the bed was armored with a layer of clay and 

silt 0.1-0.6 foot thick.

MEASURED DATA

Basic data for 26 observations of velocities and 

suspended-sediment concentrations are shown in tables 

1 and 2.

Velocities were measured with a Price current meter 

and samples of suspended sediment were collected at 

points in the vertical with a US P-46 sampler or a 

modified DH-48 hand sampler. Suspended-sediment 

samples were analyzed for particle-size distribution 

by the pipette-visual accumulation tube method. Vertical distributions of velocity and suspended sediment 

were defined at approximate equal centroids of flow 

at each cross section. The number of centroids varied 

from 2 to 5, except in one case, where 15 velocity 

profiles were obtained. The number of points in a 

vertical varied from 3 to 5 and were obtained at approximate equal (D y)ly horizons. Concentrations 

shown in table 2 were determined from a composite 

of samples for the indicated horizons. Figure 2 is a

Distance or number 

of vertical from bank

Typical section 

FiGtJEE 2. Definition sketch of equal (D y)/y horizons, any cross section.

definition sketch showing equal (D y)ly horizons in 

any cross section. Verticals were numbered consecutively from the right bank.

Obtained concurrently with velocity and suspendedsediment samples were water discharge, width, mean 

depth, mean velocity, water temperature, water-surface 

slope, and bed-material samples. These data are shown 

in table 3.

Water-surface slopes for the Bernalillo and Socorro 

reaches were determined as the slope of the line fitted 

by method of least squares through the plotted watersurface profile. Particle-size distributions of bedmaterial samples were determined by serving. Values 

of d65) d5o, and c^sj where the subscript denotes the 

percent finer by weight, were read from a logarithmic 

probability plot of size distribution. These data were 

furnished by the United States Bureau of Eeclamation.

Water-surface slopes in the Bernardo reach were 

determined by dividing the difference in water-surface 

elevation between two cross sections by the distance 

between the two sections.

For the data herein, the width-depth ratio is large 

and it is assumed R=D for a cross section. For
DISTRIBUTION OF VELOCITY AND SUSPENDED SEDIMENT, MIDDLE RIO GRANDE B3

practical purposes, the flow is considered uniform and 

Se=S; also bank friction is considered to be negligible.

GENERAL APPROACH

The equation for suspended-sediment discharge per 

unit width for two-dimensional flow is given by

f

*=y\

Ja

(1)

where

g,=the transport rate of suspended sediment between 

the depths a and D

7= the average unit weight of the water-sediment mixture

a=reference depth 

D=flow depth 

FB =flow velocity at depth y 

cy=concentration at depth y

In order to integrate equation 1, Vv and cv must be 

expressed as functions of y.

The velocity distribution for two-dimensional openchannel flow over a rough boundary as presented by 

Keulegan (1938) is

(2)

where

e=shear velocity 

&=von Karman coefficient of turbulent exchange 

y=distance above bed 

Kt=& length parameter 

d=a constant

gr=acceleration due to gravity 

R=hydraulic radius 

St=energy gradient

Equation 2 is not generally applicable for flow over an 

alluvial boundary, but in this report the equation will 

be used throughout as a basis for comparison with 

measured velocity distributions.

The equation for sediment suspension was introduced 

by O'Brien (1933) as

where

dc

w^the fall velocity of the sediment particle. 

c= concentration of suspended sediment.

, os (3)

dc 

e s -p=rate of upward transfer of suspended sediment

from turbulent exchange.

Rouse (1937) showed that equation 3 could be integrated to yield an equation for the distribution of the 

relative concentration of the suspended sediment as

where

cv= (D-y a V 

ca V y D aJ (4)

c»=concentration of a grain size at depth y above bed. 

ca = concentration of a grain size at reference level a 

above bed.

Z=theoretical exponent of the distribution equation 

given by

(5)

where

18=ratio of the transfer coefficient for sediment (e,) 

to the momentum transfer coefficient (e OT).

In the derivation of equations 4 and 5, it was assumed 

that

and

«S= «m

*-T a _^* m -

, _ 1

k=QA

The general forms of equations 2 and 4 are well 

established, but the solution to the suspended-sediment transport rate is not completely formulated. 

Neither k nor Ks is constant and the exponent Z given 

by equation 5 does not agree with Z^ the exponent 

that fits the measured data.

Equation 2 may be integrated over a representative 

vertical to obtain mean velocity. Keulegan (1938) 

has shown that the mean velocity for open-channel 

flow over a wholly rough surface of a rigid boundary 

may be expressed as

where

 =6.25+5.75 log -jV iff J\-g

F=mean velocity.

(6)

The constant 6.25 is a mean value, and varies with 

several factors such as effect of the shape of section, 

the free surface, and nonuniform distribution of the 

tractive forces at the boundary. For sand-grain 

roughness only, such as flow over a flat sand bed, K, 

assumes the value of a representative grain size or an 

equivalent height of the roughness elements. For 

natural river sediments, Einstein (1950) used the value 

of d65 for Ks. In many natural channels with flow over 

an alluvial bed, Ks is greater than d65 owing to the 

presence of dunes and bars on the bed.

The quantitative relation between dune characteristics and the roughness parameter Ks is not known. 

Flume studies with rigid boundaries (Sayre and Albertson, 1961) have shown that roughness conditions are 

dependent upon the relative size and spacing of the 

roughness elements and that the overall boundary 

roughness can be expressed as one parameter in the 

velocity equation. If the relative size and spacing of 

dunes and bars in a natural channel could be measured, 

a more complete evaluation of Kf could be made. 

Sonic-sounding equipment offers possibilities in this 

field. Sonic-sounding equipment has been used in the 

Mississippi River (Carey and Keller, 1957) and in the
B4 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

laboratory (Richardson, Simons, and Posakony, 1961), 

but the information obtained is more qualitative than 

quantitative and thus is not subject to a rigorous 

mathematical analysis.

Several flume and field studies present qualitative 

information on the relations between resistance coefficients and bed configuration. The forms of bed roughness observed in flume studies using 0.28 mm and 0.45 

mm median-diameter sand have been described in 

detail by Simons and Richardson (1961). They indicate that flow may be classified into lower regime and 

upper regime with a transition zone between, and that 

both resistance and sediment transport are intimately 

related to flow regime. The lower and upper flow 

regime classification is based upon magnitude of 

resistance to flow, bed and water surface configuration, 

and mode and magnitude of sediment transport. The 

bed roughness for lower regime flow is ripples or dunes 

or both, the resistance to flow is large, and the bed 

material transport rate is low. For upper regime 

flow, the bed is relatively plane, standing waves or 

antidunes may be present on the water surface, the 

flow resistance is low, and the rate of transport of bed 

material is relatively high. These general regimes of 

flow are applicable to natural streams. Culbertson 

and Dawdy (1963) and Dawdy (1961) have shown that 

these different regimes of flow occur in the Rio Grande 

and in many other sand-bed streams.

VELOCITY DISTRIBUTION

Typical velocity profiles (fig. 3) show that the velocity 

distributions fit a logarithmic law. It is noted that 

lateral variation of velocity distribution and depth 

occur in the cross section. For practical purposes, 

mean values of velocity and depth are used.

Values of the Von Karman coefficient of turbulent 

exchange (k} can be computed from a form of equation

2 as

Vi-Va 2.3 Tr __.

log 3/1 log (7)

where V\ and V% are the velocities at depth yl and y2 , 

respectively, and m is the slope of the velocity profile 

in feet per second change per log cycle of depth; thus

. 2.3 T^

k = F* 

m

(8)

The average k for_a cross section was computed using 

m and I7* where m is the average of the individual m 

values of all the verticals in a cross section and

V# ="\gDS. The values of m and k are shown in 

table 4. Values of k vary widely, ranging from 0.15 

to 1.20. For the Socorro reach and Bernardo cross 

section, the values of k appear to vary systematically

i i

Socorro reach . Section B

April 16, 1954 

iverage'm=1.00

Section D

May 19,1954

Average ni 0.62

Section A-2 

August 17, 1954 

Average m = 4.

246 

VELOCITY, IN FEET PER SECOND

10

FIGURE 3. Variation of velocity with depth, Rio Grande near Bernalillo and 

Socorro.

and are generally less than 0.4. Conversely, the 

Bernalillo values appear to be random and generally 

are greater than 0.4, varying from 0.35 to 1.2.

Flume and river measurements show that the k for 

sediment-laden flow generally varies from the 0.4 that 

was determined by Nikuradse for pipe flow with clear 

water. Vanoni and Brooks (1957) and Ismail (1951) 

suggested that sediment dampens the turbulence and 

reduces the momentum transfer. In effect, this results 

in a reduction of k. Einstein and Chien (1955) measured the reduction of k by the amount of turbulent 

energy spent in supporting the sediment in suspension. 

The rate at which frictional energy is spent per unit 

weight of fluid per unit time in supporting the sediment 

in suspension was expressed as

(9)

where cs=average concentration by weight of a given 

particle size, and S signifies the summation of the concentrations and fall velocities of all the particle sizes 

present. Values of k plotted versus equation 9 in 

figure 4 show wide scatter. Socorro and Bernardo 

data generally follow the predicted trend, while the 

Bernalillo data show no definite trend. Dashed lines 

on the figure indicate the approximate scatter of points 

from which the relation was defined by Einstein and 

Chien. About half of the 26 points fall within or close
DISTRIBUTION OF VELOCITY AND SUSPENDED SEDIMENT, MIDDLE RIO GRANDE B5

0.20

0.10

0.01

0.001

o Bernalillo

 Socorro

9 Bernardo

0.2 0.4 0.6 0.8 1.0 1.2

FIGUEE 4. Variation of fc with concentration, Eio Qrande near Bernalillo, Socorro, 

and Eio Puerco near Bernardo. Dashed lines indicate approximate envelope of 

points used to define the relation. From Einstein and Chien, 1965.

to the envelope. Values of equation 9 for the data 

herein are shown in table 4. That portion of the summation for particle size less than 0.062 mm was obtained by assuming all material was in a size range of 

0.002-0.062 mm and then using a fall velocity based on 

the geometric mean size of this class.

Chien (1954) suggested that k may change with 

roughness if the height of the roughness elements are 

comparable to the mean depth of flow. Field observations in the Bernalillo reach show that the height of 

dunes in fully developed lower regime flow is often equal 

to or greater than one-half the mean depth. Under 

such conditions, extreme lateral variations in a cross 

section may occur and the flow may exhibit three dimensional characteristics. _

Figure 5 shows the variation of k with V/V* Cj-^g. 

In this figure there is no quantitative measure of the 

dune height, but a qualitative measure of bed configuration based on the three regimes of flow may be shown

1

1X

Ul

I1

£3~

u. 

O

1-

z

Ul

o

u.

u.

Ul

O

O

1.2

1.0

0.8

«

0.6

0.4

0.2

0

1 1 1 1 1 1 1 1 1

- o

° o Bernalillo

 Q Socorro 

0 Bernardo

0

0

o

_ 0

O 6

A O

_ ^ __

Q.O a

 * ^

Jb

0

Lower regime Upper regime * 

 (dunes) j*- Transition ~H (plane bed) ^-

8 10 12 14 16 18 20 22 24 26

£= C

FIQUEE 5. Variation of fc with C/-\g. 

689288 68 2

The <7/V<7 values indicated on the figure for the various 

flow regimes are based on field observations where bed 

configuration was verified by probing. These <7/V<7 

values are in close agreement with those reported by 

Simons and Richardson (1961). The figure clearly 

indicates that extreme variations of k occur for flow over 

a dune bed.

Sayre and Albertson (1961) reported k values ranging 

from 0.34 to 2.77 as determined by the velocity-profile 

method (equation 8) for clear-water flow with isolated 

roughness baffles. However, from the slope of the 

average lines drawn through plots of V/V* versus 

relative roughness, they determined that the average or 

"integrated" k was in fact a constant, with a value of 

0.38. They attribute the wide variation in k values 

determined from the velocity-profile method to threedimensional flow effects and large scale vortices, and 

they conclude that equation 8 is not adequate to define 

k where such flow conditions exist. The wide range of 

k values for flow over a dune bed shown in figure 5 

probably reflects the same effects that were reported 

by Sayre and Albertson.

The decreasing value of k with increasing C/^/g for 

transition and upper regime flow may or may not be 

related to changing roughness. Because sediment 

transport generally increases with an increase in Cl-^fg, 

the decrease of k may be attributed, in part, to a concentration effect.

Although k may not be adequately defined for flow 

over a dune bed, the velocity for such flow is still proportional to the logarithm of the depth. If a form of 

equation 2 applies, and if k attains a near-constant 

value of about 0.4, the proportionality factor between 

V and log y does not equal the shear velocity V#, but 

must assume a much smaller value. From equation 7, 

the proportionality factor is approximately equal to 

m/5.75. Einstein (1950) introduced a shear velocity 

with respect to the grain roughness, V*', which is less 

than V*. For the data in table 4, the factor of proportionality between velocity and the logarithm of the 

depth, m/5.75, is considerably less than Einstein's V*'.

Regardless of the value of the proportionality factor 

relating velocity to the logarithm of the depth, if equation 2 applies with d=8.5 as given by Keulegan, the 

value of Ks may be determined from a plot of V versus 

log y by extrapolating the line through the plotted 

point to intercept the ordinate at zero velocity. This 

follows from equation 2, where the velocity must equal 

zero when the logarithm of 3Q.2y/Ks equals zero.

Values of Ks for each cross section were determined 

for the data hi table 4 by two methods: first, as the 

average of the Kt values for the individual verticals 

read from the V versus log y plots extrapolated to 

intercept the ordinate at zero velocity; second, by plot-
B6 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

ting mean velocity V at y=QAD on semilog paper, and 

extending a line with slope m to intercept the ordinate 

at zero velocity. For any given cross section, the 

values of Ks computed by the two methods vary appreciably but are of the same order of magnitude; 

therefore, the two values were averaged to obtain the 

Kt shown in table 4.

The values of m and Ks in table 4 were defined from 

a limited number of verticals, and thus may not describe accurately the average velocity distribution in a 

cross section. Even so, for a given reach, the range of 

values of Ks and the ratio of the average Ks to the 

average d65 should provide an indication of bed-configuration effects on velocity distributions. These 

data are shown in the table below.

For Bernalillo, where flow was in lower regime, Ks 

varies by a factor of about 20,000. Flow in the 

Socorro reach was mostly in transition or upper regime, 

and the ratio of maximum to minimum Ks is 48. At 

Bernardo the bed was armored with clay, the flow was 

comparable to flow over a rigid boundary, and Ks varies 

by a factor of 4. These values indicate clearly the 

extreme influence which bed configuration has on 

velocity distributions.

It is significant that the mean value of K, is much 

greater than d65, even for the clay-armored bed of the 

Rio Puerco, which was relatively free of irregularities. 

The values of the ratio of the mean Ks to d65 are remarkably constant, considering the wide differences hi 

bed conditions for the three reaches. That such 

similarities should be fortuitous seems unlikely. The 

data tabulated below suggest that although the bed condition dictates the range of K, values, it is the size of 

the bedmaterial and not the bed configuration which 

determines the mean Kt. For the range of conditions examined, the mean K3 is about 400 times as 

great as d65 ,

In the foregoing discussion, no consideration was 

given to the correction factor for the transition from 

smooth to rough boundaries (Rouse, 1937). Inclusion 

of the factor could alter the values of Ks by as much as 

20 percent.

MEAN VELOCITY

Where the relative effects of bed configuration on flow 

resistance are minor, mean velocity may be predicted 

with reasonable accuracy by using empirical formulas 

of the Manning or Chezy type with coefficients based 

upon a grain-size roughness.

Two empirical formulas which attempt to predict the 

relation between bed configuration and flow resistance 

have been proposed (Liu and Hwang, 1959; Einstein 

and Barbarossa, 1952).

Summary of Ks values

Reach

Bernalillo. _

Bernardo __

K,, in ft

minimum.

0. 000086 

.020

.03

maximum

1.86 

.95

.11

mean

0.47 

.27

.078

K, max

.Kimin

22,000 

48

4

dtt 

ft

0. 00121 

.00072

.0002

Mean if.

da

388 

375

390

Bed condition

Dunes. 

Transition and 

plane bed. 

Clay-armored.

Liu and Hwang presented a formula of the Chezy type

"W f K=UfZtJ?iQf» ft(Y\ 1o* \*-v)

where CT and the exponents, i and j, are functions of 

bed configuration and particle size of the bed material. 

It has been shown that Liu's criterion for the prediction 

of bed configuration is not applicable to the Rio Grande 

data (Culbertson and Nordin, 1960).

Einstein and Barbarossa (1952) introduced an approach to the determination of flow resistance where 

the total resistance was divided into two parts, one due 

to the sand-grain roughness, and the other due to bars, 

dunes, and the general irregularities of the channel bed. 

The velocity equation given by Einstein and Barbarossa 

was

V-=5.75 log*

where

0-f (11)

K,=the representative grain roughness d®.

Rr the hydraulic radius with respect to the sand

grain.

z=a correction factor for channels which are not 

hydrodynamically rough and is given as a

jr

function of -r/-

S'=the theoretical thickness of the laminar sub-

, , . , . , , 11.6v layer, which is equal to v , 

y=the kinematic viscosity.

That part of the resistance due to bars and dunes was 

expressed as a functional relation between the dimensionless resistance factor, F/F#", and flow intensity, 

^', where V*"=T/gR"S, the shear velocity with 

respect to the dunes and bars, and

R'S, (12)

p, and p/=the densities of the sediment and fluid

respectively, 

and d^=representative grain diameter of bed material.

The functional relation of "F/F*" to $', called the barresistance curve, was defined from average cross sections and representative slopes for reaches in several 

natural channels. For a given mean depth, slope, and 

bed material, the mean velocity may be computed by
DISTRIBUTION OF VELOCITY AND SUSPENDED SEDIMENT, MIDDLE EIO GRANDE B7

trial and error from equations 11 and 12 and several 

graphs presented by Einstein. The accuracy with 

which mean velocity may be predicted depends upon 

the accuracy with which the V/V*" iI/' relation expresses frictional losses due to bars, dunes, and other 

irregularities on the bed for the channel under consideration. Vanoni and Brooks (1957) and Vanoni and 

others (1961) have discussed the applicability of the 

bar-resistance curve for flume data and for some limited 

natural-channel data.

The graphical method presented by Vanoni and 

Brooks was used to compute values of V/V#" and $' 

for the Bernalillo and Socorro data. These values, 

listed in table 4, are plotted in figure 6 and show 

reasonable agreement with the predicted relation. Of 

23 computed values of mean velocity using the EinsteinBarbarossa approach, 20 are within 25 percent of the 

measured values. Some scatter on the plot may be 

attributed to the use of A:=0.4 in the velocity equation 

and to the use of data at individual cross sections.

From the manner in which the bar-resistance curve 

was derived, the curve should describe conditions for 

a reach of a natural unconfined channel. The relations 

do not necessarily apply to an individual cross section. 

Vanoni and Brooks (1957) apply data for several cross 

sections of the Bernalillo reach to the bar-resistance 

curve. On the basis of the scatter of the points for 

these individual cross sections, they conclude that the 

1952 data "do not lend confidence to the bar-resistance 

curve." Figure 7 shows the 1952 Bernalillo data using 

average conditions for 13 cross sections through a 

16,000-foot reach. All computed values of mean 

velocity are within 15 percent of the measured mean

100

10

O Bernalillo reach 

 Socorro reach

0.1 ,.'- p*-pf

10 50

Pf ~'~W~S~e

FIGURE 6. Einstein-Barbarossa bar-resistance curve for Rio Grande near Bernalillo 

and near Socorro. Curve from Einstein and Barbarossa, 1952.

100

1Q

0.1 10 50

R'SK

FIGUBE 7. Einstein-Barbarossa bar-resistance curve for Rio Grande near Bernalillo, 

1952 data. Curve from Einstein and Barbarossa, 1952.

velocities. Basic data for these calculations are given 

in table 5.

From figures 6 and 7, it is concluded that mean 

velocity may be predicted within reasonable limits by 

the Einstein-Barbarossa method for the Rio Grande 

near Bernalillo and near Socorro.

SUSPENDED-SEDIMENT DISTRIBUTION

The vertical distribution of suspended-sediment concentration for several size ranges was determined from 

particle-size analysis of point-integrated samples. Data 

for the Bernalillo, Socorro, and Bernardo reaches are 

shown in table 2. The data show that suspended 

sediment less than 0.062 mm in diameter was almost 

uniformly distributed throughout the depth of flow. 

The vertical distribution of suspended sediment greater 

than 0.062 mm in diameter was defined for three size 

classes: 0.062-0.125 mm, 0.125-0.250 mm, and 0.250- 

0.50 mm. Theoretical distributions for these size 

classes were computed using the fall velocities from 

figure 5 of "Inter-Agency Report No. 4," 1941, for the 

geometric mean of the size class.

Equation 4 plotted logarithmically is a straight line 

with a slope,

= " = measured exponent of suspended-sediment dislog

D-j

y

tribution.

which may be read directly from the logarithmic plot 

of c versus (d y)/y. Figures 8 and 9 are typical 

plots using several sets of data from table 2. The 

plots show that log c varies directly with log (D yY/y, 

thus the distribution function is of the correct form.
B8 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

20

10

1.0

0.1

Section A-2 

June 2, 1953

0.125- 

0.250 mm 

2=0.33

Section D 

May 19, 1954

0.250-0.500 mm 

2=0.61

0.125-0.250 mi 

Z=0.34

0.062-125 mm 

2=0.22 J

100 1000 0 10

SUSPENDED-SEDIMENT CONCENTRATION, IN PARTS PER MILLION

FIGURE 8. Variation of concentration with (D y)fy, Eio Qrande near Bernalillo.

100 1000

20

10

1.0

0.1

0.062-0.125 mm 

2=0.32

- 0.125-250 mm 

2=0.80

Note: Flow in 

upper regime

0.062-125 mm 

2=0.16

100 1000 10,000 100 1000

SUSPENDED-SEDIMENT CONCENTRATION, IN PARTS PER MILLION

FIGTTBE 9. Variation of concentration with (D-y)jy, Eio Qrande near Socorro.

10,000 100,000

Values of Z may be calculated from equation 5, 

using the original assumptions as previously mentioned 

(0=1, k QA). An alternate Z, designated ZK, can 

be calculated assuming /3=1 and using the computed 

k from equation 8. Values of Zb and p=ZK/Z, are 

shown in table 4.

Figure 10 shows the plots of Zl versus Z and Zft for 

the three size classes used herein. For small Z or Zfc 

values, Zi is generally in close agreement with Z or Zfc. 

For large Z or Zk values, Zi is smaller than Z or Zk, 

indicating the suspended sediment is distributed more 

uniformly than the theory would predict. The deviation of the computed exponent from the measured 

exponent becomes greater with increasing particle size. 

This is typical of the results found by Anderson (1942), 

Colby (1955), and others.

Points on the Z\ versus Z plot in figure 10 tend to 

group by reach along the ordinate (Za ) and by particle 

size along the abscissa (Z). Grouping by particle size 

in Z values is indicative of the limited range in shear 

velocity, V*. On the Zl versus Z* plot, the points 

scatter and are more random, but the trend by reach is 

still evident. This apparent difference between Zi's for 

the Bernalillo, Socorro, and Bernardo data may be
DISTRIBUTION OF VELOCITY AND SUSPENDED SEDIMENT, MIDDLE RIO GRANDE B9

CD 

.O

1 D

E LO

§ 2

</) d

</) i

JS CM

o g

N d 

c/5

o

LOCM

in CM

8

o

i

o

LO 

CM

.1

3

01

CM

65

 o§N

i

o

CO II "3

q CM q CM
BIO SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

attributed to the marked difference in average size of 

bed material (fig. 11) and to individual characteristics 

peculiar to each reach.

The curves in figure 11 are the average of the size 

distributions of bed material shown in table 3. The 

median diameter of bed material in the Socorro reach 

was about 0.19 mm compared to 0.30 mm in the 

Bernalillo reach. The median diameter of bed material 

for the Bernardo data was in the clay-size range.

Some of the characteristics that may influence Z\ 

values for the different reaches are flow regime and bed 

conditions. The Bernalillo data have low 

values for a given $' (fig. 6) and high k's for low 

values (fig. 5), thus indicating the persistence of dunes

99.9

F/F*"

o Rio Grande near Bernalillo

 Rio Grande near Socorro

o Rio Puerco near Bernardo

0.1

DIAMETER, IN MILLIMETERS 

FIGURE 11. Average particle-size distribution of bed material.

in this reach. The flow in the Socorro reach is mostly 

in transition and upper regime, while at Bernardo the 

bed was armored with clay. The launching of the 

particles into suspension may be different from a dune 

bed than from a plane bed. The suspended sand in the 

Bernardo reach is probably not from the bed, but is 

supplied from an upstream source. All these factors 

contribute to the apparent difference of the measured suspended-sediment distributions for Bernalillo, 

Socorro, and Bernardo.

Figure 12 shows Zv to vary curvilinearly with the fall 

velocity. For comparison, curves showing the variation of Zi with the 0.55 power of the fall velocity are 

plotted on the figure for the Bernalillo and Socorro 

reaches. When one point is high, the corresponding

points for adjacent size classes are also high. Colby 

and Hembree (1955) found Zi to vary with the 0.7 

power of the fall velocity in the Niobrara River. The 

suspended-sediment distribution is relatively more uniform for the Rio Grande than for the Niobrara River. 

Vanoni (1946) and Ismail (1952) proposed that es is 

not the same as em but is related by the factor of 

proportionality p=es/em where j8 seems to be a function 

of particle size. Also

-= B= 

thus j8 indicates the deviation of Zi from Z*.

Ismail (1952) found em affected only through changes 

in k when sand was present. Values of em could not be 

measured directly but could be evaluated by studying 

es and the relations between em and es. He found that 

j8=1.5 for a 0.10 mm sand and 1.3 for a 0.16 mm sand.

Figure 13 shows the comparison of k and j8 for the 

three size classes used herein. Trend by size class is 

evident. When the value of 0 for one size class is 

large, the corresponding jS's for the other size classes 

are also high. Thus the trend is consistent within itself. 

j8 and k are intimately related. It is noted that at 

k QA, average values of j8 are approximately 0.85, 1.4, 

and 2.2 or greater for the 0.062-0.125 mm, 0.125-0.250 

mm, 0.250-0.500 mm size classes, respectively. The 

value 1.4 compares favorably with Ismail's value of 1.3 

for 0.16 mm sand. Ismail's k values were slightly less 

than 0.4. From Ismail's findings, j8 decreased with increasing particle size. For the data herein, j8 increases 

with increasing particle size and with decreasing roughness. It is of special interest that j8 values are closest 

to 1.0 for lower regime flow, where k values vary upward 

to about 1.2; while for upper regime flow, where k ranges 

from about 0.2 to 0.4, j8 varies upward to about 9. This 

indicates that for flow over a dune bed the predicted 

suspended-sediment distribution follows approximately 

the measured distribution; for flow over a plane bed, 

the predicted suspended-sediment, distribution deviates 

considerably from the measured distribution. On the 

other hand, measured velocity distribution for upper 

regime flow follows a predicted distribution (&«0.4), 

while for lower regime flow the velocity distribution is 

more uniform than predicted (&»0.4). These relations 

are shown qualitatively in figure 14.

Einstein and Chien (1954) presented several approaches to the solution of the suspended load theory 

using various assumptions on the nature of the mixing 

length and turbulence characteristics. All of the approaches are cumbersome and require that experimentally determined constants be selected on the basis 

of measured data. The approach which most closely
DISTRIBUTION OP VELOCITY AND SUSPENDED SEDIMENT, MIDDLE RIO GRANDE Bll

2.0

1.6

Q. 

UJ 

Q

UJ

Q

UJ

o

LU

cc. 

o

O

UJ

cr

O

a:

NI

1.2

0.8

0.4

Size Class (mm) 

0.062-0.125 

0.125-0.250

0.250-0.500

Socorro

Reach 

Bernalillo

a 

A

o

Bernardo

X

i

0.04 0.08 0.12

FALL VELOCITY CnJ), IN FEET PER SECOND

FIQUEE 12. Variation of Z\ and fall velocity.

0.16 0.20

fits the measured suspended-sediment distribution 

herein is given by the following equation:

"I z -

1+NkZ

where

1 ~r 'V

1 1+-WI /

Z)

D^y

D J

V

D

i

IDLV j

^+ATfcZ

J "T-iVK/i

2Z

i\72J'c2 72 1

(13)

=an experimentally determined constant

In deriving this equation, Einstein and Chien assumed 

that the turbulence was unsymmetric. Equation 13 

using a value of Nk=QA is shown on figure 10. The 

equation generally fits the trend of the measured data 

throughout the range of values. It should be noted 

that the distribution function given by equation 13 is 

changed from the functional relation of equation 4, 

but the suspended-sediment distribution can still be 

approximated by a straight line for a plot of c versus 

(D y}ly on a logarithmic plot. For small Z values in 

equation 13.

D-y « V

y d-aj
B12 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Size Class (mm) 

0.062-0.125 

0.125-0.250 

0.250-0.500

Socorro

Reach

Bernardo 

D 

A 

O

Bernalillo 

x

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

k

FIGURE 13. Variation of fc and |3.

Lower regime 

(dune bed)

Upper regime 

(plane bed)

Lower regime 

(dune bed)

Upper regime 

(plane bed)

LogC 

Concentration distribution

Log V 

Velocity distribution

FIGURE 14. Qualitative relation of predicted and measured velocity and suspendedsediment distribution for lower regime flow and upper regime flow. Predicted 

distribution, dashed line; measured distribution, solid line.

Einstein and Chien (1954) favored an approach where 

mixing length and velocity fluctuations of turbulent 

flow lollow certain probability distributions, and the 

higher derivative terms of the concentration gradient 

are included. For low Z values, this approach does 

not fit the data herein as well as that given by equation 13.

Einstein (1950) used the shear velocity with respect 

to the sand grain, V*', in equation 5 to compute the 

distribution exponent Z. Values of Z computed in this 

manner show the same trend as indicated in figure 10. 

Because F*'<V*, the values of Z deviate even further 

from the measured values than those computed using 

V*. Vanoni and Brooks (1957) have questioned the 

use of V*' in computing the distribution exponent Z.

In modifying the suspended-sediment distribution 

theory, Einstein and Chien (1954) used V*=^gDS to 

compute values of Z. Presumably, the flow was over 

a plane bed, and it was implied that for flow over a dune 

bed, V*' should be used. For most field data, V*' is 

less than V*, even for upper regime flow; that is, there 

are always some additional trictional losses beyond 

those due to the grain roughness only. Thus, in using

the approaches suggested by Einstein and Chien, and 

in defining the constants, for example N in equation 13, 

it is important that the shear velocity used in computing 

the values of Z be consistent throughout.

Einstein and Chien (1955) also suggest that k from 

the graphical relation of figure 4 be used in computing 

Z. For the data presented herein, the relation does not 

define the value of k for lower regime flow.

EFFECTS OF HIGH CONCENTRATIONS ON FALL 

VELOCITY

The observations of velocity and concentration distributions for the Rio Puerco near Bernardo and for the 

Rio Grande near Socorro (August 17, 1954) were obtained in flows which carried high concentrations of 

fine material «0.062 mm) in suspension. The 

Socorro flow was inflow from the Rio Puerco.

The Rio Puerco flows intermittently. Concentrations of fine material of 100,000 ppm (parts per million) 

are common, and concentrations up to 400,000 ppm 

are not unusual. Core samples of the bed of the Rio 

Puerco show the bed material to be a fine sand with a 

size distribution similar to that of the Socorro reach 

(d50 «0.20 mm). As flow recedes, clay impregnates 

the bed to a depth of about 0.6 foot. When the bed 

dries, this clay-impregnated layer hardens into an 

armor coating.

When the bed of the Rio Puerco is armored with clay, 

the concentrations of suspended sand are low, probably 

because the material is not readily available for transport. When the clay layer is broken up, and flow is 

over the sand bed, the capacity of the Rio Puerco to 

transport sand is several times greater than the capacity of a stream with comparable flow of clear water or 

flow carrying negligible concentrations of fine material. 

The major factors which contribute to this increased 

capacity for transport are the increase in viscosity and 

mass density of the fluid and the concurrent decrease 

in the fall velocity of the sediment (Simons and others, 

1961).

The general effects of concentration on fall velocity 

in sedimentation chambers have been investigated 

("Inter-Agency Report No. 12, 1957"), but the overall 

effects of high concentrations under natural stream 

conditions are not known. Figure 15 shows the apparent reduction in fall velocity at 24 °C for various 

concentrations of fine material for the geometric mean 

diameters of the three size classes used in this report. 

This figure was developed from visual accumulation 

tube analyses of bed material in clear water and in 

native water of the Rio Puerco with varying concentrations of suspended fine material. The reduction in fall 

velocity thus includes the effects of the dissolved solids 

as well as the effects of the fine material.
DISTRIBUTION OF VELOCITY AND SUSPENDED SEDIMENT, MIDDLE RIO GRANDE B13

1.0

0.1

0.01

o.ooi

0.0001

0 100,000 200,000 

CONCENTRATION OF FINE MATERIAL, IN PARTS PER MILLION

FIGURE 15. Variation of fall velocity with concentration of fine material.

Figure 15 was developed from limited data and should 

be considered tentative. The reduction of fall velocity 

with increased concentration in the visual accumulation 

tube is probably not quantitatively comparable to the 

reduction in fall velocity which actually occurs in the 

stream, but figure 15 shows clearly that the effect of 

concentration on fall velocity is appreciable for the 

range of conditions encountered in the Rio Puerco flow. 

If the fall velocities from figure 15 are assumed applicable in computing Z, values of the computed sediment 

distribution exponent show much closer agreement 

with the measured exponent Zi for the high concentration flows at Bernardo and Socorro (fig. 16). The 

effect of concentration on fall velocity for concentrakV.

Size Class (mm) 

0.062-0.125 

0.125-0.250 

0.250-0.500

Reach

Socorro Bernardo 

 X

0123456

Z = 

B

FIGURE 16. Comparison of measured sediment distribution exponent, Zi, with the 

exponent, Z*, computed (a) using fall velocities in distilled water, and (b) using 

fall velocities from figure 15.

tions less than about 10,000 ppm in the Rio Puerco and 

middle Rio Grande is negligible for practical purposes.

CONCLUSIONS

For the data presented, measured values of vertical 

velocity and suspended-sediment concentration distributions were compared with values predicted from 

theoretical considerations. The data included observations of flow in lower regime, transition zone, several 

in upper regime, and several with high suspendedsedunent concentrations. Results and conclusions, 

some of which may be applicable only for this study, 

are summarized as follows:

1. For flow over a dune bed, the predicted suspendedsediment distribution follows approximately the 

measured distribution, and the velocity distribution 

is more uniform than predicted; while for flow over a 

plane bed, the predicted suspended-sediment distribution deviates considerably from the measured 

distribution, and the velocity distribution follows 

approximately the predicted distribution.

2. Mean velocity for the Rio Grande near Bernalillo 

and near Socorro is adequately described by the 

Einstein-Barbarossa bar-resistance relation.

3. For a given reach the range of values for Ks depends 

on bed configuration. However, the average value 

of Ks for a reach does not appear to be related to bed 

configuration, but depends upon size of bed material. 

For the three reaches, the average value of Ka is 

approximately 400 times as large as d65 .

4. The value of the coefficient of turbulent exchange, 

k, decreases with high concentration for upper regime 

flow; and varies widely for lower regime flow, probably due to a three-dimensional flow effect. There 

is not apparent effect of concentration on k for flow 

over a dune bed. The coefficient k appears to 

decrease with decreasing bed roughness as measured 

indirectly by C/V? for transition and upper regime 

- flow.

5. The suspended sediment is distributed more uniformly than conventional theory predicts. The 

deviation of the measured exponent, Zi} from the 

computed exponent, Z, becomes greater with increasing particle size. Differences between measured 

and computed values of Z are due to flow regime, to 

size of bed material, and to the effects of the concentrations of suspended fine material.

6. The measured exponent, Zi} varies with about the 

0.55 power of the fall velocity.

7. The factor of proportionality j8 increases with 

increasing particle size and with decreasing roughness. 

Values of j8 are closest to 1.0 for flow over a dune bed.

8. Fall velocity is effectively decreased in flows with 

concentrations greater than about 10,000 ppm.
B14 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

BASIC DATA AND COMPUTED PARAMETERS

TABLE 1. Velocity distribution

Date

6- 2-53

4-53 

4-13-54

5-19-54

Beach

Bernalillo__--__

_____do-----__-_

_____do_. _______

__._.do_......._

Section

A-2

A-2 

A 

C 

E 

B

C 

D 

E 

B 

C

No. of 

vertical

1 

2 

3 

4 

5

6 

7 

8 

9 

10

11 

12 

13 

14 

15

1 

2 

3

1 

2 

3

1 

2 

3

1 

2 

3

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

Temp

op

71 

70 

70

70 

70 

71 

71 

71

71 

71 

71

72 

71

62 

62 

63

70 

71 

71

70

61 

61 

61 

62 

63

63 

64 

64 

64 

63

63 

63 

63 

63 

63

62 

62 

62 

62 

61

70 

69 

68 

67 

65

72 

74 

74 

73 

73

D

ft 

3.0 

3.0 

2.6 

3.0 

2.6

2.7 

2.5 

2.5 

2.5 

2.4

2.5 

4.0 

5.0 

5.0 

5.4

2.5 

2.0 

2.5

3.5 

4. 6 

4. 6

1.6

2.7 

3.2

3.8 

1.6 

2. 1

1.5 

1. 1 

1.7 

1. 5 

2. 5

1.5 

.8 

1. 1 

2.5

4.4

2.0 

1.9 

1. 6 

1.8 

2.2

1.7 

2. 7 

2.0 

2. 5 

2. 1

4.7 

4. 6 

2. 6 

1. 8 

1. 9

5.0 

1. 6 

2.0 

2. 1 

2 1

Horizon

A

V

ft 

0.30 

.30 

.30 

.30 

.30

.30 

.30 

.30 

.30 

.30

.30 

.40 

.50 

.50 

.50

.30 

.30 

.30

.30 

.40 

.40

.30 

.30 

.40

.50 

.30 

.30

.20 

.20 

.20 

.20 

.20

.20 

.20 

.20 

.20 

.20

.30 

.30 

.30 

.30 

. 30

. 30 

. 30 

.30 

.30 

.30

.20 

.20 

.20 

.20 

.20

. 15 

. 15 

. 15 

.15 

1ft

V

ft per sec 

2.68 

2.75 

3.74 

1.84 

3.26

3.51 

2.45 

2.87 

1.88 

2.08

1.84 

2.08 

1.48 

2.87 

1.01

3.35

2.87 

3.26

3.72 

4.36

4.74

.75

2.56 

1.21

3.43 

2.61 

3.25

1.38 

1.88 

1. 23 

1.08 

1.84

1.58 

1.88 

2.49 

1.23 

1. 50

.43 

1. 16

2.47 

1.72 

2.65

2. 13 

1. 14 

2. 23 

1. 10 

1.50

3.05 

2.80 

3. 32 

1.51 

1.84

1.32

.84 

1.76 

1. 58 

1. 84

B

V

ft

1.00 

1.00 

.80 

1.00 

.80

.80 

.80 

.80 

.80 

.80

.80 

1.20 

1.40 

1.50 

1.70

.80 

.60 

.80

1.00 

1.20 

1.20

.60 

. 80 

1.00

1.20 

.55 

.70

.38 

.28 

.42 

.38 

.62

.38 

.20 

.28 

.62 

1.10

.50 

. 50 

. 40 

.50 

.60

.50 

.60 

.40 

.60 

.60

1. 18 

1. 15 

. 65

. 45 

. 48

1. 25 

.40 

.50 

.52 

. ft2

V

ft per sec 

3.26 

3. 10 

3.94 

3.30 

3.90

3.82 

3.70 

3.00 

2.36 

2. 18

1.88 

2.20 

2.01 

3.00 

2. 10

4. 18 

3.21 

3.38

4.09 

4.59 

5.00

1.06 

3.07 

3. 10

3.76 

2.67 

3.51

1.88 

2. 15 2. 10* 

1.47 

2.80

1.80 

1.96 

2.49 

1.92 

3.02

.78 

1. 12 

2.42 

1.90

2.77

2. 13 

1.40 

2.20 

1.28 

1.86

3. 57 

3.50 

4.06 

2.00 

2.20

2.67 

1.62 

2.05 

2.25 

2. 2ft

C

V

ft 

1.50 

1.50 

1.20 

1.50 

1.20

1.20 

1.20 

1.20 

1.20 

1.20

1.20 

2.00 

2.30 

2.50 

2.70

1.30 

1.00 

1.30

1.75 

2.30 

2.30

.80 

1.40 

1.60

1.90 

.80 

1.10

.75 

.55 

.85 

.75 

1.25

.75 

.40 

.55 

1.20 

2. 20

1.00 

1.00 

.80 

.90 

1.10

.80 

1.20 

.80 

1. 20 

1. 10

2. 35 

2. 30 

1. 30 

.90 

.95

2. 50 

.80 

1.00 

1.05 

1. Oft

9

ft per sec 

3.58 

3.38 

4.08 

4.28 

4.04

3.74 

3.74 

3.00 

2.75 

2.30

2.36 

2.50 

2.53 

3.00 

2.53

4.38 

2.93 

3.70

4.36 

5.06 

5.44

1.21 

3. 14 

3.51

4.02 

2.86 

3. 38

2.24 

2.20 

2. 15 

1.92 

3.43

1.96 

2.22 

2.61 

2.05 

3.33

2.33 

2.33 

2.80 

2. 15 

2.89

2.30 

1.66 

2.40 

1.82 

1.92

3.97 

3.97 

4.25 

2.49 

2.05

3. 13 

1.54 

1.70 

2. 49 

2.49

D

V

2.00 

2.00 

1.70 

2.00 

1.70

1. 70 

1.70 

1.70 

1.70 

1.60

1.70 

2.80 

3. 10 

3.50 

3.80

1.70 

1.40 

1.70

2.50 

3.20 

3.20

1.00 

1.90 

2.20

2.60 

1.05 

1.50

1.20 

.88 

1.36 

1.20 

2.00

1.20 

.64 

.88 

2.00 

3.52

1.50 

1.40 

1.10 

1.30 

1.70

1.20 

2.20 

1.50 

2.00 

1.60

3.52 

3.45 

1.95 

1.35 

1.42

3.75 

1.20 

1.50 

1.58 

1.58

V

ft per sec 

3.58 

3.51 

4.04 

4.66 

4.28

3.74 

3.90 

2.81 

2.81 

2.25

2.62 

2.75 

2.75 

2.81

2.72

4.38 

2.90 

3. 74

4.36 

5. 18 

5.06

1.50 

3.32 

3.90

4.06

2.77 

3.30

2.34 

1.96 

2.29 

2.00 

3.64

1.94 

1.73 

2.42 

2.00 

3.50

2.28 

2.50 

2.80 

2.33 

2.89

2.50 

1.90

2.47 

2.42 

1.90

4.02 

4.36 

4.36 

2.86 

2.05

3. 20 

1.08 

2. 15 

2.55 

2.44

E

V

2/70 

2.70 

2.20 

2.70 

2.20

2.20 

2.20 

2.20 

2.20 

2. 10

2.20 

3.60 

4.50 

4.50 

4.90

2.20 

1.70 

2.20

3.20 

4.20 

4.20

1.30 

2.40 

2.80

3.30 

1.30 

1.80

V

ft per sec 

3.38 

3.54 

3.99 

4.38 

4.54

3.74 

3.94 

2.75

2.72 

2.28

2.65 

2.81 

2.90 

2.75 

2.65

4. 18 

2.62 

3.74

4.25 

4.84 

4.50

1.61 

3.08 

3.94

4. 15

2.74 

3.07
DISTRIBUTION OF VELOCITY AND SUSPENDED SEDIMENT, MIDDLE BIO GRANDE

TABLE 1. Velocity distribution Continued

B15

Date

5-19-54 

4-16-54

5-21-54 

8-17-54

Reach

Socorro. _ ____

_____do__. ______

Section

D 

E 

A-l 

A-2 

B 

B-l 

A-l 

A-2 

B 

B-l 

A-l 

A-2

No. of 

vertical

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

1 

2 

3 

4 

5

Temp

op

72 

72 

73 

73 

73

71 

71 

70 

69 

67

51 

54 

54 

56 

59

56 

57 

58 

59 

60

71 

70 

69 

68 

68

71 

72 

72 

72 

72

67 

68 

69 

70 

71

65 

67 

66 

67 

68

75 

73 

72 

72 

71

75 

75 

75 

75 

75

70 

71 

72 

72 

73

74

78

D

f.

2.2 

2.0 

1.9 

1.6

2.9 

2.1 

1.5 

2.4 

1.1

2.7 

2.8 

3.5 

3.0 

1.4

1.3 

.7 

1.3 

.9 

1. 1

1.5 

1. 1 

1.1 

1.0 

1.1

2.8 

40 

41 

3.3 

1.0

3.4 

1.8 

1.3 

1.0 

1.2

1.2 

1. 1 

1. 1 

1. 1 

1.5

2.4

.8 

.8 

.7 

.9

.9 

1.3 

.8 

1.7 

2.0

2.2 

2.9 

3.2 

2.0

2.8

1.8 

2. 1 

2.5 

2.6

3. 6

Horizon

A

V

ft 

.30 

.55 

.50

.48 

.40

.72 

.50 

.38 

.60 

.25

.30 

.30 

.30 

.30 

.30

.20 

.20 

.20 

.20 

.20

.30 

.30 

.30 

.30 

.30

.20 

.20 

.20 

.20 

.20

.20 

.20 

.20 

.20 

.20

.20 

.20 

.20 

.20 

.20

.20

.20

.20 

.20

.20 

.20

.20

.20 

.20

.20 

.20 

.30

c

ft per sec 

1.94 

2.37 

2.53 

3.02 

1.31

401 

3.02 

2.96 

1.94 

2.28

1.67 

408 

3.07 

3.30 

.39

2.99 

3.30 

2.99 

1.84 

1.03

2.59 

1.17 

3.07 

3.44 

3.44

1.26 

1.96 

3.05 

3.04 

2.05

2.27 

2.83 

3.34 

3.32

2.77

2. 77 

3.47 

3.32 

2.83 

2.65

1.45

2.96

2.65 

2.96

1.46 

3.09

3.07

3. 74 

2.81

3.66 

3.92 

3.90

B

y

ft 

.60 

1. 10 

1.00 

.95 

.80

1.45 

1.05 

.75 

1.20 

.55

.50 

.50 

.50 

.50 

.50

.32 

. 18 

.32 

.22 

.28

.70 

.50 

.50 

.50 

.50

.70 

1.00 

1.00 

.82 

.25

.85 

.45 

.30 

.25 

.30

.30 

.28 

.28 

.28 

.38

.60 

.20 

.25 

.20 

.22

.30 

.30 

.20 

.42 

.50

.55 

.72 

.80 

.50 

.70

.45 

.52 

.60 

.65 

.90

c

ft per tec 

2. 18 

2.50 

2.47 

3.24 

1.62

436 

3.64 

3.02 

2.28 

2.77

2. 34 

4.57 

3.38 

4.38 

.49

3.43 

3.97 

4.06 

2.53 

1.38

3.07 

1.39 

3.25 

3. 82 

3.51

2. 10 

2.49 

3.88 

4. 45 

2.92

2.65 

3.47 

3.84 

3.68 

3.02

3. 16 

3.76 

3.54 

3.09 

3.02

1.60 

2.71 

3. 24 

3.16 

2.96

3.02 

3. 16 

3. 24 

1.53 

3.48

3.66 

6.56 

5.65 

4. 76

3. 78

4.38 

5.48 

6.44 

6.25 

6. 63

O

V

*«0

1.65 

1. 50 

1.42 

1.20

2. 16 

1. 60 

1. 12 

1.80 

.85

1.40 

1.40 

1.80 

1.50 

.70

.65 

.35 

.65 

.45 

.55

1.00 

. 80 

.80 

.70 

.80

1.40 

2.00 

2.05 

1.65 

.50

1.70 

.90 

.65 

.50 

.60

.60 

.55 

.55 

.55 

.75

1.20 

.40 

.40 

.35 

.45

.45 

.65 

.40 

.85 

1.00

1. 10 

1. 45 

1.60 

1.00 

1.40

.90 

1.05 

1.25 

1.30 

1.80

V

TiS"

2.77 

2.53 

3.32 

1.79

469 

3.76 

2.68 

2.47 

2.53

3.14 

5.48 

498 

430 

.63

3.88 

4 15 

4.45 

2.86 

1.80

3. 14 

1.58 

3.38 

3.90 

3.90

2.05 

2.34 

4 15 

474 

3.72

2.96 

3.93 

430 

420 

3. 54

3.61 

4.01 

3.97 

3.68 

3. 40

1.58 

3. 12 

3.47 

3.58 

3.28

3.40 

3.84 

3.76 

1.38 

3.80

3.90 

8.31 

7.29 

6. 19 

471

5.95 

7. 13 

6.91 

8.10 

7.54

D

V

ft

2.20 

2.30 

3.00 

2.50 

1.10

.90 

.42 

.90 

.60 

.75

1.90 

2.80 

2.90 

2.30 

.73

2.55 

1.35 

1.00 

.75 

.90

.90 

.83 

.83 

.83 

1.12

1. 80 

.60 

.60 

.52 

.68

.70 

1.00 

.60 

1.28 

1.50

1.65 

2. 18 

2. 40 

1.50 

2.10

1.35 

1.58 

1.90 

1.95 

2.70

V

ft per sec

3.58 

5.86 

5.97 

4 38 

.74

406 

4.45 

4. 64 

2.99

1.88

1.96 

2. 15 

450 

5.44 

3.60

3.09 

420 

469 

4.20 

3.61

3.76 

4.36 

4.20 

3.80 

3.68

1. 64 

3. 16 

3.47 

3. 40 

3.20

3.32 

3.93 

3.64 

1.53 

3.97

4.76

8.74 

8.74 

6.44

487

6.63 

7.90 

8.92 

8.49 

8. 10

E

y

ft

V

ftper sec
B16 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 1. Velocity distribution Continued

Date

7-10-61 

8-18-61 

19-61

Reach

_-_-_do __-_-_

.. __ do -----

Section No. of

vertical

1 

2

1 

2

1 

2

Temp

Ojp

75 

75

74

74

D

ft 

2. 6 

2.5

3.6 

2. 6

5.8 

4.8

Horizon

A

y

.*»

.30

.50 

.50

.50 

.50

V

ft per sec 

2. 92 

2.86

3.20 

3.43

3.80 

4. 45

B

y

.'TO

.70

1.00 

1. 10

1.00 

.80

V

ft per sec 

3.28 

3. 43

3.88 

3.97

4. 25

4.48

o

V

ft

1. 10 

1. 20

2.00 

1. 60

2. 20 

1. 80

»

ft per sec 

3. 80 

3.72

4.25 

4. 15

4. 84 

4.69

D

V

ft

1.60 

1.70

3.00 

2. 10

3.40 

2.80

»

ft per sec 

3. 97 

3. 97

4. 54 

4. 15

5. 18

4.88

E

V

ft

2.20 

2. 10

460 

3.80

V

ft per se 

3. 97 

3. 97

5. 18 

5. 12

TABLE 2. Suspended-sediment distribution

Date

6- 2-53

4-53

4-13-54

4-13-54

Reach

Bernalillo _____ __ __ _

_-_-_do---_-_--_________-_

-----do__--_-__-___-__-_._

.... _do.._______._ -_---_-.

Section

A-2

A-2

A

C

E

B

C

D

E

Horizon

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

Average D-v 

y

8. 28

2. 17

1.07

.50

. 13

6.78

2. 19

.95

.46

.15

10.54

2.73

1.00

.43

.09

6.44

2.08

.98

.49

. 16

5.64

2.03

.97

.46

. 18

15.6

2.98

1.00

.25

19.6

2.98

1.00

.25

18.0

2. 81

.98

.36

21.0

3. 11

1. 17

.31

Concentration, ppm of indicated sizes

<0.0625

mm

1,300

1,310

1,240

1,240

1,150

840

1,070

907

861

837

802

796

804

704

719

895

830

775

734

753

774

827

821

763

675

3,090

2,920

2,870

2,720

2,890

2,620

2,670

2,720

2,550

2,810

2,730

2,740

3, 100

2,840

2,770

2,750

0.0625-0.125

mm

726

569

500

398

309

489

381

386

287

291

656

572

451

368

282

355

314

248

248

191

334

222

238

189

156

988

537

361

270

567

344

315

267

769

344

241

230

749

357

304

246

0.125-0.25

mm

637

396

284

239

168

403

156

261

169

169

821

396

270

159

144

334

208

117

124

81

434

291

258

165

120

1,250

431

200

105

859

305

272

191

1, 120

315

178

92

1,300

350

240

135

0.25-0.50

mm

207

85

63

58

23

59

16

27

13

33

80

45

15

9

6

76

18

9

15

5

48

40

34

14

6

188

27

10

44

43

23

10

330

107

29

3

604

61

23

13

Total

2,870

2,360

2,090

1,930

1,650

1,790

1,620

1,580

1,330

1,330

2,360

1,810

1,540

1,240

1, 150

1,660

1,370

1,150

1,120

1,030

1,590

1,380

1,350

1, 130

956

5,520

3,920

3,440

3, 100

4,360

3,310

3,280

3, 180

4,930

3,580

3, 170

3,070

5,810

3,610

3,340

3, 150
DISTRIBUTION OF VELOCITY AND SUSPENDED SEDIMENT, MIDDLE RIO GRANDE

TABLE 2. Suspended-sediment distribution Continued

B17

Date

5-19-54 

4-16-54 

5-21-54

8-17-54

Reach

Socorro

* 

 __do- 

_ __do__ _ . __ . ________

Section

B 

C 

D 

E 

A-l 

A-2 

B 

B-l 

A-l 

A-2 

B 

B-l 

A-l 

A-2

Horizon

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

A 

B 

C 

D

Average D-y

V

30.2 

2.99 

1.00 

. 33

24.6 

3.02 

1.00 

.33

16.8 

2.99 

1.00 

.33

19.0 

3. 12 

1.00 

.32

26.0 

4. 36 

.97 

.22

9. 60 

3.02 

1.00 

.50

10. 6 

2. 87 

1. 15 

. 41

29. 4 

3.02 

1.00 

. 42

7. 70 

3.06 

1.00 

.32

5.00 

2.95 

1.00 

.33

6. 60 

3. 52 

1.00 

.33

5. 70 

2. 88 

1.00 

.32

12. 6 

3.00 

1.00 

.33

10.8 

3.04 

1. 00 

.33

Concentration, ppm of indicated sizes

<0.0625

mm 

2,850 

2,880 

2,880 

2,760

2,490 

2,390 

2,380 

2,300

2,390 

2,370 

2,270 

2,360

2,900 

2,890 

2,760 

2,760

6,490 

5,390 

5,240 

4,840

5,890 

5,660 

5,200 

5, 180

6,390 

6,270 

5,740 

5,400

6,660 

5,720 

5,520 

5,580

14, 300 

13, 900 

13, 600 

13, 600

15, 200 

15, 000 

14, 800 

14, 500

13, 500 

13, 800 

13, 300 

12, 900

13, 000 

13, 300 

12, 900 

12, 600

109, 000 

110,000 

107, 000 

105, 000

100, 000 

100, 000 

98, 900 

99. 100

0.0625-0.125

mm 

710 

454 476' 

403

863 

482 

440 

377

382 

444 

323 

267

715

388 

258 

252

1,620 

1, 120 

641 

313

1,310 

1,050 

512

488

1,290 

755 

399 

405

1,850 

661 

376 

326

2,220 

1,050 

754 

525

2,590 

1,570 

1,060

544

1,000 

1,040 

649 

612

1,620 

1, 120

778 

475

13, 700 

10, 800 

10, 500 

8,380

15, 600 

17, 700 

15, 100 

8. 140

0.125-0.25

mm 

1, 150 

431 

381 

264

1,200 

302 

240 

199

348 

210 

142 

95

1, 120 

237 

170 

96

2,740 

897 

408 

148

1,450 

560 

176 

134

626 

232 

203 

65

2,460 

564 

158 

109

1,660 

431 

160 

43

2,230 

564 

242 

91

465 

444 

169 

109

2,020 

680 

250 

106

18, 100 

11, 200

6,880 

4,010

38, 500 

13, 600 

7,810 

2.750

0.25-0.50

mm 

456 

116 

76 

45

439 

32

18 

6

44 

21 

8 

5

327 

11 

3 

3

154

17

42

316 

14 

6 

12

36

100

67

5,000 

396 

250 

118

4,770 

528 

122

Total

5, 180 

3,880 

3,810 

3,470

4,990 

3,210 

3,080

2,880

3, 160 

3,040 

2,740 

2,720

5, 110 

3,530 

3,260 

3,110

11, 000 

7,410 

6,280 

5,300

8,680 

7,270 

5,880 

5,810

8,350 

7,260 

6,340 

5,870

11, 300 

6,960 

6,060 

6,030

18, 200 

15, 400 

14, 500 

14, 200

20, 100 

17, 100 

16, 100 

15, 100

15, 000 

15, 300 

14, 100 

13, 600

16, 700 

15, 100 

13, 900 

13, 200

147, 000 

132, 000 

125, 000 

118, 000

159, 000 

132, 000 

122, 000 

110.000
B18 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 

TABLE 2. Suspended-sediment distribution Continued

Date

7-10-61

8-18-61 

19-61

Reach

Bernardo. ________________

_._-_do. ___-_-_-__._______

do

Section

,

Horizon

A 

B 

C 

D 

E

A 

B 

C 

D

A 

B 

C 

D 

E

Average D-y

9

7.33 

3.27 

1.08 

.47 

. 19

4.20 

1.36 

.62

.24

9.60 

4.90 

1.66 

.71 

.26

Concentration, ppm of indicated sizes

<0.0626

mm 

66, 400 

65, 600 

65, 700 

64, 900 

65, 200

177, 000 

177, 000 

177, 000 

177, 000

128, 000 

127, 000 

128, 000 

128, 000 

125, 000

0.0625-0.126

mm 

475 

398 

265 

261 

196

410 

357 

391 

268

1,970 

1,870 

1,790 

1,860 

1,850

0.125-0.25

mm 

881 

265 

199 

131 

131

374 

357 

355 

250

1,520 

1,330 

1,320 

1,130 

955

0.25-0.50

mm

Total

67, 800 

66, 300 

66, 200 

65, 300 

65, 500

178, 000 

178, 000 

178, 000 

178, 000

132, 000 

130, 000 

131, 000 

131, 000 

128, 000

TABLE 3. Basic data

Reach

Bernalillo __

Socorro __ ._

Bernardo- ___

Date

6- 2-53

4-53

4-13-54

5-19-54

4-16-54

5-21-54

»> 8-17-54

7-10-61

8-18-61

19-61

Section

A-2

A-2

A

C

E

B

C

D

E

B

C

D

E

A-l

A-2

B

B-l

A-l

A-2

B

B-l

A-l

A-2

Q

eft

2,150

2,090

1,970

2,070

1,780

1,200

1,160

1,160

1,200

1,450

1,430

1,410

1,430

697

697

697

697

891

900

874

840

3,600

3,550

403

636

2,380

w

ft

270

270

397

376

268

432

370

399

265

434

383

401

266

175

241

447

202

222

233

327

368

258

234

82.0

90.0

119

D

ft

2.56

2.48

1.69

2.36

2.47

1.42

1.45

1.53

1.98

1.33

1.96

1.50

1.95

i 1. OOt\\

1.00

.66

1.44

1. 16

1.20

1.07

.91

2.30

2.38

1.71

2.08

4.47

F

ft per sec

3.11

3. 12

2.94

2.33

2.69

1.96

2.17

1.89

2.30

2.51

1.90

2.35

2.75

2.60

2.90

2.36

2.40

3.45

3.21

2.50

2.51

6.07

6.37

2.88

3.40

4.46

Ave. 

temp.

op

71

62

66

71

70

62

63

63

62

68

73

73

70

KK OO

58

69

72

69

67

73

75

72

76

72

75

74

Slope

ft per ft

»0. 000826

. 000826

. 000826

. 000826

. 000826

. 000864

. 000864

. 000864

. 000864

. 000864

. 000864

. 000864

. 000864

. 000758

. 000758

. 000980

. 000980

. 000844

. 000844

. 00100

. 00100

. 000855

. 000855

. 000385

. 00049

. 00024

Composition of bed material

Percent finer than indicated size

0.062

mm

0.7

.5

1.0

.3

.6

.5

.9

1.2

1.0

1.0

.7

.6

1.0

3.6

4.2

5.4

1.7

3.2

4.7

8.8

2.3

5.3

2.6

53.3

84.8

65.6

0.125

mm

4.1

3.7

6.0

1.8

4.5

12.4

6. 1

7.5

5.9

5.6

4.3

3.7

5.2

16. 7

19.9

25. 1

10.0

16.6

21.4

29.0

11.3

12.6

7.7

70.8

88.7

69.3

0.250

mm

27.8

34. 1

32.9

16.9

43.7

45.7

43.0

40.2

35.5

34.8

30.6

34.5

36.9

68. 1

87.4

85. 7

67.2

76.5

88.0

89.8

79.2

53.4

48.3

92.3

96.9

81.1

0.500

mm

86.6

74.3

89.4

57.8

94.8

96.3

90.4

84.9

80.5

82.4

76.2

81.6

90.4

83.2

99.3

98.7

94.5

96.5

99.2

99.2

98.4

94.4

97.7

99.8

99.7

98.2

1.000

mm

97.9

91.0

97.4

87.8

99.0

99.7

97.3

96.3

95. 1

94.5

94.5

94. 1

98. 1

84. (_?^£* 2.u

99.9

99.4

98.2

99. 1

99.8

99.6

99.0

99.4

99.3

100.0

100.0

100.0

du

mm

0.27

.25

.25

.35

.23

.21

.35

.23

.25

.25

.26

.25

.25

. 15

. 15

. 14

. 18

. 16

. 14

.13

.16

.19

.21

.0092

da,

mm

0.32

.33

.30

.42

.26

.26

.37

.29

.31

.31

.27

.31

.30

. 17

. 17

.16

.21

. 19

. 16

. 15

. 19

.24

.25

.048

du

mm

0.37

.42

.35

.60

.31

.30

.56

.35

.38

.38

.41

.38

.35

. 19

.19

.19

.24

.22

. 19

.18

.21

.29

.29

. 10

 Estimated on basis of adjoining values. 

b Flow on this day is from Rio Puerco.
DISTRIBUTION OF VELOCITY AND SUSPENDED SEDIMENT, MIDDLE RIO GRANDE

TABLE 4. Computed parameters

B19

Reach

Bernalillo__

Socorro_ _

Bernardo _ _

Date

6- 2-53 

4-53

4-13-54

5-19-54 

4-16-54

5-21-54

8-17-54 

7-10-61

8-18-61

19-61

Sec.

A-2 

A-2 

A 

C 

E 

B

C

D 

E 

B 

C 

D 

E 

A-l

A-2

B

B-l 

A-l

A-2

B

B-l

A-l 

A-2

m

fPS

1.20 

.55 

.55 

1.84 

.49 

1.32

.47

1.44 

. 81 

.99 

.87 

.62 

.99 

1.66

1.54

1.00

1. 13 

1.44

1. 44

.85

1.06

3.52

458 

1.36

1.46

1.21

k

0.501 

1.08 

.888 

.313 

1.20 

.348

.982

.330 

.666 

.447 

.620 

.758 

.542 

.247

.215

.332

.434 

.283

.289

.504

.372

.165 

. 129 

.238

.285

.354

K.

o. 50"

. 00035 

. 000086 

1. 86 

. 00042 

.50

.0072

1. 36 

.29 

. 11 

1. 32 

.054 

.092 

.69

.22

.079

.098 

.060

.076

.020

.044

.44 

.95 

. 11

.094

.030

v*

fp» 

0.261 

.257 

.212 

.250 

.256 

1QQ

.202

.206 

.234 

. 192 

.233 

.204 

.233 

. 178

.144

. 144

.213 

.177

.181

. 186

.171

.252 

.256 

.141

. 181

. 186

v,"

13. 9 

14.4 

17.4 

10.4 

11.8 

11.1

12. 7

10.2 

11.0 

16. 1 

8.85 

13. 5 

13. 8 

16.5

29.0

23.6

13.0 

32.0

25.9

16.8

1Q 0

61. 8 

90.4

*'

1.59 

2.35 

2.70 

4. 76 

2. 93 

4.25

5.57

5. 00 

3.82 

3.40 

5.47 

3.80 

2.97 

2. 10

1.77

2.28

2.71 

1. 41

1. 46

1.91

2.41

.62 

.59

^r^C.a

v o< 

Pi Pf

Pi

0. 0092 

.0070 

.0107 

.0062 

.0123 

.0070

.0091

.0090 

.0107 

.0198 

.0178 

.0091 

.0061 

.0169

.0102

.0068

.0046 

.0084

.0090

.0072

.0095

.110 

.090 

.0197

.0364

.103

C

Vi

11.9 

12. 1 

13.9 

9.32 

10.5 

9.85

10.7

9. 17 

9.83 

13.1 

8. 12 

11.5 

11.8 

14.6

20. 1

16.4

11.3 

19. 5

17.7

13.4

14 7

24 1 

247 

20.4

18.8

24.0

0.062

-0.125

mm 

0.21 

.21 

.19 

.14 

.22 

34

16

.32 

.26 

. 13 

.18 

.22 

.31 

.29

.32

36

.44 

31

, 51

, 25

44

. 14 

. 16 

.24

17

.05

Zi

0.125

-0.250

mm 

0.33 

.35 

.40 

.38 

.37 

63

.32

.62 

.53 

.32 

.19 

.34 

.32 

.60

80

.69

.73 

.95

.82

,59

,83

.42 

.76 

33

. 18

. 12

0.250

-0.600

mm 

0.51 

.56 

.58 

.66 

.50

1.19 

1.06 

.50 

.98 

.61 

.86

1.08

.89 

1. 52

0.062

-0.125

mm 

0.81 

.34 

.59 

2.00 

.33 

84

63

.92 

.49 

1. 91 

.87 

.66 

.57 

1.42

1 80

1.26

.55 

1.39

.79

.96

82

3.83 

442 

2.96

2.65

6 80

/S=-Zk/Zi

0.125

-0.250

mm 

1.57 

.65 

.87 

2.29 

.59 

1.43

1.00

1.51 

.76 

2.40 

2.53 

1.32 

1.71 

2.20

2.45

2.03

1.02 

1.41

1.52

1.21

1.34

3.93 

3.04 

8.91

7.61

8.83

0.250

-0.600

mm 

2.57 

1.05 

1.53 

3.30 

1.10

1.99 

.98 

3.92 

1.22 

1.84 

1.58

1.73

465 

3.54

TABLE 5. Basic data and computed parameters for the average of 13 cross sections through a 16,000-foot reach,

Rio Grande near Bernalillo, N. Mex.

Date

195S 4-25

5-12

6-17

20

26

7-24

Q

cfs

2,820

6,440

6, 120

4,775

2,800

2,030

Pw

ft

454.0

485.2

477.3

429.5

384.3

4244

R

ft

1.63

2.35

2.41

2.20

2.04

1.95

b

ft

452

477

475

427

382

422

V

ft per sec

3.83

5.65

5.32

5.09

3.57

2.48

T

op

61

64

72

72

70

78

fir

ft per ft

0. 00090

.00086

. 00086

. 00086

. 00085

. 00088

Bed material (mm)

</J5

0. 230

.278

.270

. 290

.260

.283

dw

0.330

.406

.385

.420

.375

.405

*'

1.61

.96

1.04

1.16

1.99

3.94

VfV"

25.7

47.1

36.4

38.9

19.5

11.9
B20 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

REFERENCES CITED

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natural stream: Am. Geophys. Union Trans. 23d Ann. Mtg., 

pt. 2, p. 678-683.

Carey, W. C., and Keller, M. D., 1957, Systematic changes in 

the beds of alluvial rivers: Am. Soc. Civil Engineers Jour., 

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Chien, Ning, 1954, The present status of research on sediment 

transport: Am. Soc. Civil Engineers Proc., separate no. 

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characteristics and hydraulic variables, middle Rio Grande, 

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1498-F.

Culbertson, J. K., and Nordin, C. F., 1960, Discussion of discharge formula for straight alluvial channels: Am. Soc. 

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Einstein, H. A., and Chien, Ning, 1954, Second approximation 

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 1955, Effects of heavy sediment concentration near the 

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sediment ser. 8, 45 p.

Ismail, H. M., 1951, Turbulent transfer mechanism and suspended sediment in closed channels: Am. Soc. Civil Engineers Proc., separate no. 56, 26 p.

Keulegan, G. H., 1938, Laws of turbulent flow in open channels:

U.S. Natl. Bur. Standards, Jour. Research, v. 21, no. 6,

p. 707-741. 

Liu, H. K., and Hwang, S. Y., 1959, Discharge formula for

straight alluvial channels: Am. Soc. Civil Engineers Journ.,

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O'Brien, M. P., 1933, Review of the theory of turbulent flow

and its relation to sediment transportation: Am. Geophys.

Union Trans., v. 14, p. 487-491. 

Richardson, E. V., Simons, D. B., and Posakony, G. J., 1961,

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Geol. Survey Circ. 450, 7 p. 

Rouse, H., 1937, Modern conceptions of the mechanics of fluid

turbulence: Am. Soc. Civil Engineers Trans., paper 1965,

v. 102, p. 463-543. 

Sayre, W. W., and Albertson, M. L., 1961, Roughness spacing

in rigid open channels: Am. Soc. Civil Engineers Jour., v.

87, no. HY 3. 

Simons, D. B., and Richardson, E. V., 1961, Forms of bed

roughness in alluvial channels: Am. Soc. Civil Engineers

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

The effects of fine sediment on the mechanics of flow: U.S.

Geol. Survey Water-Supply Paper 1498-G. 

U.S. Inter-Agency Report No. 4, 1941, Methods of analyzing

sediment samples: St. Paul, Minn., U.S. Dept. Army. 

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

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O