Fluvial Sediment of the 

Mississippi River at 

St. Louis, Missouri

By PAUL R. JORDAN

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1802

Prepared in cooperation with the 

U.S. Army Corps of Engineers

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1965
FLUVIAL SEDIMENT 

MISSISSIPPI RIVER 

ST. LOUIS, MISSOURI
The Mississippi River, part of St. Louis, and East St. Louis. Fluvial sediment 

and streamflow were measured at the bridge nearest the bottom of the photograph. Photograph by Surdex Corp., St. Louis, Mo.
UNITED STATES DEPARTMENT OF THE INTERIOE 

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 - Price 35 cents (paper cover)
CONTENTS

Page

Definitions. _____ ________________--_____-_-__-__-_---_-----__----_- vi

Symbols_ _______________________________________________________ vn

Abstract__ _ _ ____________________________________________________ 1

Introduction-__-______-__________--__________-___---_------_------ 2

General features of the river reach.___-____-____-___-____--_-__--_--- 3

Discharge characteristics-____________________-____-_-_---____------ 7

Suspended-sediment discharge and particle size________________________ 11

Bed material____________________________________________________ 23

Aggradation and degradation.____________________-_---__-------_-_-_ 26

Flow resistance and sediment transportation._________________________ 27

Resistance to flow.______________--______-____---_------_----_- 27

Vertical distributions of velocity and sediment concentration, by

B. R. Colby.-- - __ -_. -- - 42

Velocity________________________________________________ 42

Sediment concentration____________________-__-___-_-_--_- 56

Bedload discharge and bed-material discharge.____________________ 67

Summary_ ______________________________________________________ 86

Literature cited-____-__-__-______________________--___----__--_--- 88

ILLUSTRATIONS

Page 

FIGURE 1. Confluence of Missouri and Mississippi Rivers_______--___- 5

2. Relation of width, depth, and velocity to discharge________- 6

3. Duration curves of daily flows, Missouri River and Mississippi

River_____________________________________________ 8

4. Mean monthly discharges, 1.934-58_______________-_----_- 9

5. Recurrence intervals of annual peak discharges, 1861-1958 10

6. Occurrence of peak discharges, 1861-1958-_____--_-_----_- 11

7. Minimum discharges, 1861-1958________________________ 12

8. Suspended-sediment concentration and discharge, 1940-58___ 14

9. Monthly trend of suspended-sediment concentrations and

discharges.__________________________________________ 19

10. Factors affecting mean concentration._____________---___- 20

11. Relations of suspended-sediment discharge to water discharge- 22

12. Average and extreme particle-size distributions of suspended

sediment ____________________________________________ 23

13. Variation of bed-material size with time.__________________ 24

14. Relation of bed-material size to discharge________________ 25

15. Relation between bed elevation and particle size__-___-----.- 27

16. Relation of monthly mean bed elevation to the discharge for

3-month periods_____-_-___-______-__________--__-_-_- 28
VI CONTENTS

Page 

FIGUBE 17. Relation of Manning's n to discharge, mean velocity, and

shear velocity___________._______________-_______-____ 36

18. Relation of W/M*" to *'_--____________________._- 37

19. Relation of gage height, bed elevation, and velocity to discharge during major rises in 1951_____________________ 38

20. Effect of sediment on the turbulence constant computed from

the vertical distribution of velocity _____________________ 57

21. 2t as a function of w/(ku*)-------~----------------------- 66

22. Relation of measured bed-material discharge to mean velocity

and water temperature._______________________________ 69

23. Bedload discharges computed by various methods._-_-_-___ 73

24. Bed-material discharges computed by various methods._____ 79

25. Comparison of results from different methods of computing

bedload discharge_____-__-__----__---_-------_----__. 84

26. Comparison of results from different methods of computing

bed-material discharge.________--__.__-_______-_-_-___ 85

TABLES

Page

TABLE 1. Monthly and annual summary of streamflow and suspendedsediment discharge, April 1948-September 1958_-_------_ 15

2. Summary of hydraulic and sediment data from concurrent

measurements_ _____________________________________ 30

3. Ratios of shear velocity with respect to the grain to shear

velocity__________________________________________ 44

4. Vertical distributions of velocity________________________ 45

5. Turbulence constants based on vertical distributions of

velocity__________________________________________ 55

6. Values of 21 from point samples_______________________ 58

7. Particle-size analyses of suspended sediment, point-integrated

samples_________________________-___----_--------_--- 60

8. Computed bedload and bed-material discharges ______ 70

DEFINITIONS

Bedload discharge. Discharge of sediment that moves in essentially continuous 

contact with the streambed.

Bed-material discharge. That part of the total sediment discharge consisting of 

particles whose sizes are the same as those present in significant quantities 

in the bed.

Discharge (or streamflow). Rate of flow of a stream, expressed as r volume or 

weight per unit time, or the quantity of flow that passes in a given time. 

It includes the sediment and dissolved solids that are in the water. "Discharge" is the term generally used in this report; streamflow is used where 

necessary to avoid confusion with various types of sediment discharge.
DEFINITIONS VH

Measured bed-material concentration. Ratio of the measured bed-material 

discharge to the streamflow when both are expressed in weight per unit time.

Measured bed-material discharge. That part of the measured suspendedsediment discharge consisting of particles whose sizes are the same as those 

present in significant quantities in the bed.

Measured suspended-sediment discharge. Computed as the product of the 

concentration of depth-integrated samples, the total discharge, and a constant 

for converting the units to a weight per unit time, generally tons per day.

Station. A particular location in the cross section at which sediment samples 

are obtained or hydraulic measurements are made; it is designated by the 

distance, in feet, from an initial point on the west bank at the MacArthur 

Bridge. The initial point has remained the same throughout the 

investigation.

Streamflow. See Discharge.

Total sediment discharge. Weight of all the sediment passing a section in a 

unit time.

Unmeasured sediment discharge. Difference between the total sediment discharge and the measured suspended-sediment discharge.

SYMBOLS

a A specified distance above the streambed.

B Mathematical abbreviation for a group of parameters that depend on the

particle size. 

b Width of flow. 

C A constant relating the rate of change of stage to its equivalent effect in

the reach.

c Concentration of sediment particles in a size range. 

ca Sediment concentration at a distance a above the stre^mbed. 

cv Sediment concentration at a distance y above the streambed. 

d Grain size of bed material. 

de Effective diameter of bed material, equal to 2 rft-«'& where rfj is the average

size of particles in a size range and n is the fraction of material by weight

in that size range.

dt Geometric mean size of a bed-material size range. 

dh/dt Rate of change of gage height. 

dz&, d3&, da, rf65, dn, d90 Particle size at which 25, 35, 50, 65, 73, or 90 percent of

the bed material by weight is finer. 

g Acceleration due to gravity.

Sb "Bed load" according to the definition of Bagnold (1956). 

hb Mean bed elevation between stations 275 and 1,800. 

j Coefficient in b=jQm.

k Von Karman coefficient for turbulent exchange. 

kr Metric coefficient of flow resistance of particles, equal to 26/cfoo1/6 where

dao is in meters.

k, A linear measure of the bed roughness. 

k t Metric coefficient of total flow resistance, equal to u/y02/3S1/2 where u is

in meters per second and t/o is in meters.

L Length between sections at which Qm and Q t are determined, 

log Logarithm to the base 10.
VIII SYMBOLS

m Exponent in b=jQm.

n Manning resistance factor, equal to 1.49 R?/3 Se1/2fu where R is in feet 

	and u is in feet per second.

rid Manning resistance factor during decreasing discharge.

Hi Manning resistance factor during increasing discharge.

p Coefficient in y0 pQr.

Pi Fraction of bed area occupied by the particles in a size rang3, equal to 

	0.35 (ibldi)l'2(ii,ldi) where ib is the fraction of bed material in a size 

	range and di is the geometric mean of the size range.

Q Discharge (volumetric streamflow rate).

Qc Discharge under conditions of constant discharge.

Q e Discharge at the gage.

Qm Measured changing discharge.

q Discharge (volumetric streamflow rate) per unit width.

qani Bed-material discharge per unit width.

qt Bedload discharge per unit width.

R Hydraulic radius.

r Exponent in yo=pQr.

S Slope of the water surface for a 6.5-mile reach.

Se Slope of the water surface under conditions of constant discharge.

Se Energy gradient.

s Coefficient in u=sQl .

t Exponent in u = sQ'.

U Velocity of flood wave.

~UtfU Ratio of the mean speed of movement of grains to mean fluid velocity at 

	the grain level.

u Mean velocity of flow in cross section.

ue Mean velocity under conditions of constant discharge.

um Measured mean velocity under conditions of changing discharge.

« g Mean velocity at a station.

uy Time-averaged velocity of flow at a point a distance y above the stream- 

	bed. ___

w* Shear velocity, equal to -\gRSe .

w*' Shear velocity with respect to the grain.

w-c" Shear velocity for channel irregularities such as ripples and dunes.

w Average fall velocity of sediment particles in a size range.

x A parameter to cover the transition from hydraulically smooth to 

	hydraulically rough boundaries.

y Distance above the streambed.

j/o Depth of flow at a station.

j/o Mean depth of flow in cross section.

z Theoretical exponent for vertical distribution of suspended sediment.

zi Exponent for the actual vertical distribution of suspended secernent.

 y Specific weight of water.

y, Specific weight of sediment particles.

9 Sediment characteristic equivalent to Straub's SF

r e The particular transporting force required to start movement of the bed 

	material.

*' Shear function (intensity of shear on representative particle).

P Density of water.

p a Density of sediment particles.
FLUVIAL SEDIMENT OF THE MISSISSIPPI RIVER AT 

ST. LOUIS, MISSOURI

By PAUL R. JORDAN

ABSTRACT

An investigation of the fluvial sediment of the Mississippi River at St. Louis, 

Mo., was begun in 1948. Most data have been obtained only to determine the 

daily suspended-sediment discharge and the particle-size distribution of suspended sediment and bed material, but a few data have been obtained to study 

the flow resistance, the vertical distribution of sediment and velocity, and the 

bed-material discharge.

The flow of the Mississippi River at St. Louis is made up of the flows from the 

Missouri River, which had an average flow of 79,860 cubic feet per second for 

1897-1958 at Hermann, Mo., and from the upper Mississippi River, which had 

an average flow of 91,890 cubic feet per second for 1928-58 at Alton, 111. The 

Missouri River is partly controlled by reservoirs that had a total capacity of 

90,300,000 acre-feet in 1956, and the upper Mississippi River is prHly controlled 

by lakes and reservoirs that had a total capacity of 4,890,000 acre-feet in 1956.

The flows of the Missouri and upper Mississippi Rivers have not become mixed 

at St. Louis; so the river has a lateral gradient of suspended-sediment concentration. The concentration near the west bank has been as much as 2,400 parts 

per million greater than the concentration near the east bank.

Suspended-sediment discharges from April 1948 to September 1958 ranged 

from 4,250 to 7,010,000 tons per day and averaged 496,000 tons p?r day. Mean 

concentrations for water years decreased steadily from 1,690 parts per million in 

1949 to 403 parts per million in 1956, but they increased to 756 parts per million 

in 1958. Effects of new reservoirs in the Missouri River basin on the concentration have been obscured by the close relation of concentration to streamflow.

Measured suspended-sediment discharge through September 19*8 averaged 47 

percent clay, 38 percent silt, and 15 percent sand. Variations of particle size 

were due mainly to differences in the source areas of the sediment.

Most of the bed material in the main flow was between 0.125 and 1.000 

millimeter in diameter. The average of median diameters was related to the 

discharge for periods of 1 year and longer. Geometric quartile deviations of the 

bed material ranged from 1.1 to 2.5 and averaged 1.5.

The mean elevation of the bed had a range of almost 10 feet end was related 

to the median diameter of bed material by the regression equation h b = 363.0 

 7.8 dso for which the standard error of estimate was 0.91 foot.

The resistance to flow as measured by Manning's n ranged from 0.024 to 0.041 

and was related to the discharge and mean velocity but not to the shear velocity. 

Normal dune height is 2-8 feet, and average dune length is about 2 rO feet. When 

the resistance to flow was low, much of the bed was fairly flat; a few dunes were

1
2 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

present, but they were much longer than the average. For a giver discharge 

during individual rises in stage, the gage height was lower for increasing discharge 

than for decreasing discharge even though the bed elevation was higher. The 

changes in gage height were not caused by changes in energy gradient due to 

changing discharge, by channel storage between the gage and the measuring 

section, nor by return of overbank flow; but they were probably caused by 

a combination of changes in roughness due to changing bed configuration and of 

changes in turbulence constant due to changing sediment concentration.

Turbulence constants (Von Karman's k) computed from velocity measurements 

at 5-10 points in the vertical and from routine velocity measurements at 2 points 

in the vertical averaged 0.35 and 0.33, respectively.

The exponent zi of the vertical distribution of concentration for different size 

ranges varied with about the 0.77 power of the fall velocity. Except for the 

difference between the theoretical variation and the actual variation of z\ with 

changing fall velocity, the theoretical equation for the vertical dist-ibution of 

sediment concentration seems to apply reasonably well for the Mississippi River 

at St. Louis.

The accuracy of methods for computing bedload discharge and bed-material 

discharge could not be evaluated directly but was evaluated from tie relations 

of computed bedload discharge or bed-material discharge to the measured part 

of the bed-material discharge and to mean velocity. These relations indicated 

that bedload discharges can be computed most accurately by using the modified 

Einstein, Schoklitsch, and Meyer-Peter and Muller methods as comoared with 

the Kalinske and Bagnold methods. The relations indicated that bed-material 

discharges can be computed most accurately by adding the unmeasured sediment 

discharge from Colby's procedure to the measured part of the bed-material discharge when data on velocity, concentration, and particle-size distribution are 

available, or by using Straub's equation when such data are not available. Measured suspended-sediment discharge averaged about 95 percent of the total sediment discharge, and bed-material discharge averaged about 14 percent.

INTRODUCTION

The Mississippi River is constantly changing its channel t y cutting 

into its banks, building bars, and aggrading or degrading its bed. 

Any major changes, either natural or artificial, in the shape or alinement of the channel involve the transportation and redistribution of 

billions of tons of sediment. The greatest part of the sediment that 

is being transported by the river will be carried to the deltr.s beyond 

the mouth; but a large amount of sediment will be deposited in bars, 

some of which will eventually become part of the flood plfin as the 

course of the river shifts. Knowledge of the amount and behavior 

of the sediment is necessary for the planning, construction, and 

maintenance of works for control and use of the river or its flood 

plain such as for navigation, waste disposal, water supplies, and flood 

control.

The investigation to provide the necessary knowledge of fluvial 

sediment at St. Louis began in April 1948 with the collection of data 

on suspended-sediment concentration and discharge. Data on 

particle size of suspended sediment and bed material have been
INTRODUCTION 3

collected since 1950 and 1951, respectively. Data on water temperature have been obtained since 1951. Although most of the data were 

obtained only to determine the daily suspended-sediment discharge 

and the particle-size distribution of suspended sediment and bed 

material rather than to study the mechanics of sediment transportation, a few data were obtained to study the vertical distribution of 

sediment and velocity, the bed-material discharge, and the flow 

resistance caused by bed-material grains and by dunes and other 

irregularities on the bed. The data on sediment concentrations and 

discharges, particle size, and water temperature are published in the 

annual series of U.S. Geological Survey water-supply papers entitled, 

"Quality of Surface Waters of the United States."

The purposes of this report are to evaluate and interpret the sediment data, to show the effect of upstream developments on sediment 

concentration and discharge, and to present some theoretical aspects 

of sediment transportation as applied to the river. This report includes evaluation of the data obtained through September 1958 and 

the results of some special studies in 1959 and 1960.

This investigation was made by the U.S. Geological Survey under 

the successive supervision of P. C. Benedict, regional engineer, and 

D. M. Culbertson, district engineer. It was made in cooperation 

with the U.S. Army Corps of Engineers, St. Louis District, who did 

much of the laboratory analysis of concentration and particle size, 

provided gage readings for determination of water-surface slopes, and 

provided results of sonic-fathometer measurements of the configuration of the bed.

The only previously published report that includes information on 

the fluvial sediment of the Mississippi River in the vic:nity of St. 

Louis is a study of the water resources of the St. Louis area (Searcy, 

Baker, and Durum, 1952), which gives results of turbidity measurements and of some sediment analyses.

The symbols used in this report conform, where practicable, to 

those established by the American Standards Association (1958).

GENERAL. FEATURES OF THE RIVER RE> CH

The flow of the Mississippi River at St. Louis is a composite of the 

flows from many tributaries in a drainage area of about 701,000 

square miles. An average of about 45 percent of the flow at St. 

Louis is from the Missouri River, which is confluent with the 

Mississippi River about 15 miles upstream from St. Louis.

The sediment is sampled and streamflow is measured at the MacArthur Bridge, 178.9 miles upstream from the mouth of the Ohio 

River and 1.1 miles downstream from the water-stage recorder. 

Because the flow is confined between artificially stabilized banks and
4 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

levees, the channel in the vicinity of MacArthur Bridge is not typical 

of the channel between the Missouri and Ohio Rivers. At normal 

river stages, the channel from about 4% miles upstream to about 

4 miles downstream from the bridge is slightly curved and is nearly 

uniform in width. (See frontispiece.) The width of flow at the 

bridge varies from about 1,500 feet at low stage to about 1,800 feet 

at the highest stage that is confined within the banks. When the 

flow is over the banks, the width increases, sometimes to more than 

2,800 feet. The mean depth of the flow ranges from about 15 to 

50 feet.

In the vicinity of the sampling section, the west bank is riprapped, 

the east bank is subject to scour, and the flow is affected by two 

bridge piers, each 27 feet wide. The distribution of sediment and the 

elevation of the streambed are locally affected by barges that move 

through the section and that are sometimes moored just upstream 

from the bridge near either bank.

At St. Louis, the flows of the Missouri and upper Mississippi 

Rivers are not homogeneously mixed, and, because the Missouri 

River usually has a higher concentration of suspended sediment than 

does the upper Mississippi, each flow can generally be identified by 

the appearance of the water. The difference in concentration has 

evoked the comments of many observers. Chambers (1910, p. 189) 

wrote that he "saw the coffee-coloured flood of the Missouri add 

itself to the clear water of the Mississippi. As far as Saint Louis, the 

western third of the broad river remained caje au lait in hue." Figure 

1 shows the appearance of the Missouri River water as it enters the 

Mississippi.

The discharge and the sediment concentration and particle size 

are major determinants of the shape of the cross section of a channel. 

According to Leopold and Maddock (1953), up to the bank-full 

stage in a natural river section, the relations of width, depth, and 

velocity to discharge are in the mathematical form of simple power 

functions. The relative rates of increase of width, depth, and velocity 

are determined by the shape of the channel, the slope of the water 

surface, and the roughness of the wetted perimeter. The relations 

shown by Leopold and Maddock for natural river cross sections are, 

in the notation of this report,

b=jQm 

yo=pQT

where

b is width of flow

Q is discharge

yo is mean depth of flow in the cross section

u is mean velocity of flow in the cross section

j, m, p, r, s, and t are constants for a particular cross section
GENERAL FEATURES OF THE RIVER REACH

FIGURE 1. Confluence of Missouri and Mississippi Rivers. Photograph by 

Massie-Missouri Resources Division.

Widths, mean depths, and mean velocities of the Mississippi River 

at St. Louis were plotted against the corresponding discharges on 

logarithmic graph paper (fig. 2). Straight lines were drawn to fit 

the plotted points; and slopes ra=0.07, r=0.43, and <=0.50 were 

measured directly from the graphs. The value of ra (0.07) is much 

less than the average (0.26) given by Leopold and Maddock (1953), 

because the banks of the Mississippi at St. Louis are artificially 

stabilized to a rather steep slope.

Leopold and Maddock asserted that because of the identity

then

Q=jQm pQr sQf 

and it follows that

m+r+t=l.O 

and

j p s=1.0

For the average lines that were drawn to fit the Mississippi River data,

and

m+r+i=0.07+0.43+0.50 

= 1.00

j p s= (680) (0.16) (0.0092) 

= 1.00
6 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

fcUl 

U.

Z

O

innn

 j »« »V tr- *-

6=680 Q007

 r-?---tfrt- f100

y0 =0.16

10

1

30,

^

X

>

r^

w=0.0092 Q°

^^

50 % Js^"^

^^ 

^x^

.

 ^

-^

000 100,000 1,000

DISCHARGE, IN CUBIC FEET PER SECOND

FIGTJKE 2. Relation of width, depth, and velocity to discharge.
DISCHARGE CHARACTERISTICS 7

DISCHARGE CHARACTERISTICS

The discharge of the Missouri River near its mouth, at Hermann, 

Mo., averaged 79,860 cfs (cubic feet per second) for 181:7-1958. As 

of 1956, the Missouri River was partly controlled by reservoirs having 

capacities totaling about 90,300,000 acre-feet, of v^hich about 

51,300,000 acre-feet was on the main stem of the Missouri River 

upstream from Yankton, S. Dak. (Storage-capacity figures were 

computed from Thomas and Harbeck, 1956.) Thus, th°- major part 

of the control of the river is in the upper half of the basin, where floods 

are caused mainly by mountain and plains snowmelt.

Mississippi River at Alton, 111., 7.7 miles upstream from the Missouri River, had a mean discharge of 91,890 cfs for 1928-58. The 

river is partly regulated by a series of 26 dams that provide slackwater navigation to St. Paul, Minn., and by several reservoirs and 

lakes on the main stem and the tributaries. Total capacity of the 

reservoirs and lakes in 1956 was about 4,890,000 acre-feet.

Comparison of the flow-duration curves for Mississippi River at 

Alton and for Missouri River at Hermann (fig. 3) indicates that the 

flow of the Missouri River is more variable than the flow of the 

Mississippi and that the low flow, particularly in 1929-58, was not 

well sustained. The low flow of the Missouri River wrs better sustained in 1949-58 than in 1929-58 partly because the 1953-56 drought 

was not so severe as the 1931-35 drought and mainly because a large 

volume of stored water was released in 1953-56 (Paiford, 1959), 

particularly from Fort Peck Reservoir, which began storage in 1938. 

Comparison of all the curves shows the effects of the flows of the 

Missouri River and upper Mississippi River on the flow at St. Louis. 

The similarity of the two curves for each station indicates that the 

flow for the period of sediment record is representative of the flow 

for the past 25-30 years. However, although the mean discharge 

at St. Louis may be about the same in the future as in the past (174,800 

cfs for 1861-1958), the high and low flows will probaWy be less extreme because of the reservoir storage that has been added in recent 

years.

The discharge at St. Louis follows a definite monthly pattern. 

(See fig. 4.) Discharges are usually high during March-July because 

of runoff from snowmelt in the mountains and plains and from spring 

and early summer rains.

Extremely high flows carry the most sediment, both in suspension 

and along the bed, and they cause the greatest changes in channel 

patterns by cutting the banks, depositing sediment in b*,rs and overflow areas, and scouring the bed, particularly around bridge piers. 

Because high sediment concentrations are associated with high flows,
FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

:^N

\

EXPLANATION

 (1934-58)

 (1949-58) 

Mississippi River at Alton, III.

 (1929-58)

 (1949-58) 

Missouri River at Hermann, Mo.

 - (1934-58)

 (1949-58) 

Mississippi River at St. Louis, Mo.

0.1 0.5 1 2 5 10 20 30 50 70 80 90 95 98 99.5 

PERCENTAGE OF TIME FLOW EQUALED OR EXCEEDED GIVEN DISCHARGE

99.9

FIGURE 3. Duration curves of daily flows, Missouri River and Mississippi River.

the proportion of sediment discharge during a given period of high 

flow to sediment discharge for the year is larger than the proportion 

of streamflow during the period to streamflow for the year. In some 

small rivers, as much as 60 percent of the water and 90 pei-cent of 

the sediment for the year have been discharged during a few days 

of high flow; and in the Mississippi River, as much as 17 percent of
DISCHARGE CHARACTERISTICS

280

240

200

O 160

120

80

40

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FIGURE 4. Mean monthly discharges, 1934-58.

the water and 41 percent of the sediment for the year have been discharged during a 30-day period.

Because of the significance of high flows in transporting sediment, 

a graph that shows the average recurrence interval of annual peak 

discharges is presented (fig. 5). The points that are plotted in figure 

5 represent the annual peak discharges from 1861 to 1958, and the 

curve of figure 5 was derived from graphs of peak discharges presented 

by Searcy (1955, figs. 11, 12). The curve of figure 5 shows that the 

peak discharge in July 1951 of 782,000 cfs would have an average 

recurrence interval of about 9 years and that the peak discharge in 

April 1952 of 684,000 cfs would have an average recurrence interval of 

about 5 years. According to the curve, a discharge of 990,000 cfs or 

more would occur once in 100 years; actually, discharges of more

764-692 O 6
10 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

1000 

900 

800 

700 

600 

500 

400 

300 

200 

100

0

1

./

/

^

y

i

/ 

4

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01 1.1 12 1.3 1.5 2 3 456789 10 20 30 40 50 10

RECURRENCE INTERVAL, IN YEARS

FIGURE 5. Recurrence intervals of annual peak discharges, 1861-1958.

than 990,000 cfs have occurred twice in 184 years (in 1844 and in 

1903).

Because of the increased storage capacity that has been added in 

recent years, particularly in the Missouri River basin, the floodfrequency curve that has been developed from past records probably 

does not represent accurately the frequencies of future flood71 . Most 

of the floods from the upper Missouri River drainage, such as the one 

that resulted from snowmelt in April 1952, will be greatly reduced 

by the reservoirs on the main stem of the Missouri River. Some floods 

from the lower Missouri River drainage, such as the one that resulted 

from heavy rains in July 1951, will be reduced by storage behind 

dams that have been recently completed or are under construction on 

many of the tributaries. Also, peak sediment discharges will be 

reduced by the reservoirs. Most of the annual peak water discharges 

have occurred in April, May, and June; and many have occurred in 

July. (See fig. 6.)
DISCHARGE CHARACTERISTICS 11

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20

18

16

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July

B3 ^ 03 B3

Aug. Sept. Oc*. Nov. Dec.

FIGUKE 6. Occurrence of peak discharges, 1861-195$.

The Mississippi River is subject to periods of low flow, particularly 

in November-January. Bars built up from the large amounts of 

sediment that were transported during high flows become obstructions to river traffic during extremely low flows; a 9-foot channel 

cannot be maintained at all places, and barges cannot be loaded as 

heavily as usual. Figure 7 shows the magnitude and duration of low 

flows for the period 1861-1958. Low flows are likely to be less extreme 

in the future than in the past because of the storage that has recently 

become available in the Missouri River basin and that can be used 

to sustain the flow.

SUSPENDED-SEDIMENT DISCHARGE AND PARTICLE SIZE

Samples of suspended sediment were collected by standard procedures of the Geological Survey. All point-integrated samples and 

most depth-integrated samples were obtained with a U.S. P-46 

sampler suspended from a power-operated reel. At times of high
12 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

60 

50 

40 

30 

20 

10

/

/

I_c ngest period during which discharge was less

tha n i 

amount

^^^- ~

ndi c

-^

/

ated

Lo we 

for

r~~

st 

ir

/

av 

id

/

 '

e 

c

/

ag 

ate

/

;e dischar 

;d period

ge

10 100 1000

CONSECUTIVE DAYS

FIGURE 7. Minimum discharges, 1861-1958.

flow, a 100- or 200-pound weight was attached below the sampler to 

stabilize it. When heavy floating ice prevented the use of the P-46 

sampler, the upper 10 percent of the flow was sampled with a U.S. 

D-43 sampler. Depth-integrated samples were obtained at 2, 8, or 

10 stations in the cross section to define stream concentrations. Usually, stations were chosen at centroids of equal portions of flow as 

defined by streamflow measurements. On a few occasions the stations 

were chosen at points of equal spacing relative to stream w; dth, and 

at these times equal transit rates of the sampler were used.

All suspended-sediment samples were analyzed for concentration, 

and the results are expressed in parts per million by weight. All the 

point-integrated samples and some of the depth-integrated samples 

were analyzed for particle size. Particle-size analyses of depthintegrated samples generally were for composites of samples taken at 

8-10 stations. Before October 1952, the bottom-withdra,wal-tube 

method was used for all particle-size analyses of suspended sediment. 

From October 1952 to May 1955, for most analyses, a bottom-withdrawal tube was used for particles smaller than 0.062 mm and sieves 

were used for particles larger than 0.062 mm; for a few analyses, a 

bottom-withdrawal tube was used alone. Subsequent to May 1955, 

either a bottom-withdrawal tube or a pipet was used for particles 

smaller than 0.062 mm, and either sieves or a visual-accumulation 

tube was used for particles larger than 0.062 mm. Results from the 

bottom-withdrawal-tube, pipet, and visual-accumulation-tube methods are expressed in terms of fall diameter, which is defined (InterAgency Committee on Water Resources, 1958) as the diameter of a
SUSPENDED-SEDIMENT DISCHARGE AND PARTICLE SIZE 13

sphere that has a specific gravity of 2.65 and has the same standard 

fall velocity as the particle. Results from the sieve analyses are expressed in terms of sieve diameter, which is the length of the side of 

the smallest square opening through which the given particle will 

pass.

Suspended-sediment samplers currently available cannot obtain 

samples that are representative of the total sediment discharge. 

The P-46 sampler can obtain samples from the water surface to about 

0.5 foot above the bed or, when the 100- or 200-pound weight is 

attached, from the water surface to about 1.8 feet above the bed. 

Therefore, the part of the total sediment discharge that is suspended 

within 0.5 foot (sometimes 1.8 ft) of the bed or that is slic'ing or rolling 

in almost continuous contact with the bed is not sampled.

The sediment concentration obtained from depth-integrated samples 

for a cross section is the discharge-weighted mean concentration in 

the sampled zone. This concentration is multiplied by the discharge 

for the entire depth and by a units-conversion factor, and the result 

is called the measured suspended-sediment discharge. If the concentration in the sampled zone is equal to the suspended-sediment concentration for the entire depth, the measured suspended-sediment 

discharge is equal to the total suspended-sediment discharge; but 

because the concentration, especially of sand, increase^ toward the 

bed, the measured suspended-sediment discharge normally is less 

than the total suspended-sediment discharge.

In the Mississippi River, the unsampled zone is only 1-5 percent 

of the total depth; and even though the concentration of t?and increases 

substantially toward the bed, most of the material in suspension is 

finer than sand and is nearly uniformly distributed ir the vertical 

direction. Therefore, the measured suspended-sediment discharge is 

nearly equal to the total suspended-sediment discharge, and the 

particle-size distribution of the depth-integrated samples is nearly 

the same as that for the entire depth. In the following discussion, 

the term "suspended-sediment discharge" is used to refer to the 

measured suspended-sediment discharge, which is a close approximation of the total suspended-sediment discharge; and the term 

"mean concentration" is used to refer to the discharge-weighted mean 

concentration, either for an individual sample, for the cross section, 

or for a time period.

Because the flows of the Missouri and Mississippi Rivers have 

not become mixed at the sampling section, the river has a lateral 

gradient of suspended-sediment concentration. The concentration 

near the east bank is usually fairly low, and the concentration increases 

progressively toward the west bank. Differences between concentrations at stations near the west bank and near the ep-st bank have
14 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

been as much as 2,400 ppm (parts per million), and at many times 

the difference has been greater than the mean concentration for the 

cross section. As the discharge and mean concentration increase, 

the lateral concentration gradient increases slightly but the percentage 

change in concentration decreases. The concentration gradient has 

no apparent relation to the proportion of the flow that is from the 

Missouri River or from the upper Mississippi River. Oaly very 

infrequently have concentrations near the east bank beer greater 

than those near the west bank.

Suspended-sediment discharges at St. Louis from April 1948 to 

September 1958 (see table 1) ranged from 4,250 to 7,010,000 tons per 

day and averaged 496,000 tons per day. The annual sediment discharges and concentrations are shown in figure 8. Mean concentrations for water years decreased steadily from 1,690 ppm in 1949 to 

403 ppm in 1956, but they increased to 756 ppm in 1958. The 

monthly trend of suspended-sediment discharges and concentrations 

(fig. 9) is similar to that of streamflow (fig. 4). The highest su^pendedsediment discharges and concentrations are generally in ADril-July 

(frequently in June), and the lowest are in November-February.

400

O 350 - -: 1400

250

200

150

50

1800

- i= 800

400

\

X\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ N

7\

^\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\v

^x\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ 

^,

^

\\\\\\\\\\\\\\\\\\\\\\\\\\\\x

EXPLANATION

I 0 Concentration Discharge

X\\\\\\\\\\\\\\\V I

\\\\\\\\\\\\

I

\ ^

y 

y

y 

y

y

1

L\\\\\\\\\\\\\\\\\

51 56

WATER YEAR

FIGURE 8. Suspended-sediment concentration and discharge, 1949-58.
TABLE 1. Monthly and annual summary of streamflow and suspended-sedim

Month

1948 

Apr. 14-30....... ___ _ -- 

July.................... .. __ 

September. __ .. 

Apr. 14-Sept. 30, 1948.-... .........

1949

\pril.. .............................. ......

July. ......................................

September. _____ .. ___ .. .......

Water year 1948-49- _______ . ...

October..... ..............................

1950

April.. ....................................

July.. .....................................

August ________________ __ .

September- __ . ________ 

Water year 1949-50.. ___ . ......

Streamflow

Cfs-days

4,000,000 

6, 265, 000 

5, 388, 200 

7, 270, 000 

4,422,000 

2, 371, 900

29, 717, 100

2, 240, 800 

2, 641, 100 

1, 975, 100

4, 590, 900 

6, 492, 000 

9, 933, 000 

9, 309, 000 

5, 077, 000 

7, 309, 000 

6,024,000 

3, 106, 100 

3, 263, 500

61, 961, 500

3, 795, 100 

2, 358, 100 

3, 049, 600

5,769,000 

4, 4C8, COO 

6, 840, 000 

9, 877, 000 

11, 422, 000 

8, 950, 000 

7, 088, 000 

5, 338, 000 

3, 654, 800

72, 557, 600

Acre-feet

7, 934, 000 

12, 430, 000 

10, 690, 000 

14, 420, 000 

8, 771, 000 

4,705,000

58, 950, 000

4, 445, 000 

5, 239, 000 

3, 918, 000

9, 106, 000 

12, 880, 000 

19, 700, 000 

18, 460, 000 

10, 070, 000 

14, 500, 000 

11, 950, 000 

6, 161, 000 

6, 473, 000

122, 900, 000

7, 527, 000 

4, 677; 000 

6, 049, 000

11, 440, 000 

3, 333, 000 

13, 570, 000 

19, 590, 000 

22, 660, 000 

17, 750, 000 

14, 060, 000 

10, 590, 000 

7, 249, 000

144,000,000

Discharge 

(tons)

9, 449, 000 

19, 060, 000 

34, 820 000 

51, 640, 000 

30, 040, 000 

5, 631, 000

150, 600, 000

4, 064, 000 

6, 549, 000 

1, 872, 000

12, 770, 000 

18, 330, 000 

44, 480, 000 

52, 970, 000 

16, 820, 000 

65, 990, 000 

36, 540, 000 

5, 662, 000 

16, 220, 000

282, 300, 000

12, 740, 000 

3,999,000 

5, 508, 000

12, 100, 000 

7, 733, 000 

18, 700, 000 

59, 540, 000 

71, 730, 000 

48, 930, 000 

50, 740, 000 

29, 570, 000 

8, 742, 000

330, 000, 000

Dai

Mean

556,000 

615,000 

1, 160, 000 

1, 670, 000 

969,000 

188,000

886,000

131,000 

218,000 

60,400

412,000 

655,000 

1, 430, 000 

1, 770, 000 

543,000 

2, 200, 000 

1, 180, 000 

183,000 

541,000

773,000

411,000 

133,000 

178,000

390,000 

 276,000 

603,000 

1, 980, 000 

2, 310, 000 

1, 630, 000 

1,640,000 

954,000 

291,000

904,000

See footnotes at end of table.
TABLE 1. Monthly and annual summary of streamflow and suspended-sediment disc

Month

1950

1951

April. 

July--. - 

1952

April 

July 

September _ 

December.....------ ----- -----

Streamflow

Cfs-days

3, 337, 400 

2, 544, 900 

1, 870, 400

2, 278, 100 

4, 431, 200 

7, 760, 000 

13, 299, 000 

13, 054, 000 

11, 171, 000 

20, 252, 000 

7, 449, 000 

9, 186, 000

96, 633, 000

6, 199, 000 

7, 024, 000 

4, 355, 400

4, 754, 000 

5, 827, 000 

9, 764, 000 

14, 627, 000 

11, 969, 000 

6, 538, 000 

6, 186, 000 

5, 038, 000 

3, 084, 800

85, 370, 000

2,224,000 

2, 425, 200 

2.295.400

Acre-feet

6, 620, 000 

5, 048, 000 

3, 710, 000

4, 519, 000 

8, 789, 000 

15, 390, 000 

26, 380, 000 

25, 890, 000 

22, 160, 000 

40, 170, 000 

14, 770, 000 

18, 220, 000

191, 700, 000

12, 300, 000 

13, 930, 000 

8, 639, 000

9, 429, 000 

11, 560, 000 

19, 370, 000 

29, 010, 000 

23, 740, 000 

12, 970, 000 

12, 270, 000 

9, 993, 000 

6, 119, 000

169, 300, 000

4,411,000 

4,810,000 

4. 553. 000

Discharge 

(tons)

17, 439, 000 

4, 652, 000 

1, 281, 300

1, 675, 000 

15, 393, 470 

25, 050, 000 

69, 039, 000 

61, 116, 000 

95, 871, 000 

56, 840, 000 

29, 642, 000 

39, 249, 000

417, 247, 770

12, 327, 000 

15, 560, 000 

4, 513, 400

6, 681, 900 

9, 469, 000 

40, 173, 000 

69, 890, 000 

27, 526, 000 

26, 625, 000 

25, 705, 000 

7, 474, 000 

4, 247, 600

250, 191, 900

2, 020, 500 

2,835,300 

1. 172. 800

Dail

Mean

563,000 

155, 000 

41,300

54,000 

550, 000 

808,000 

2, 300, 000 

1, 970, 000 

3,200,000 

1, 830, 000 

956,000 

1, 310, 000

1, 140, 000

398, 000 

519,000 

146, 000

216, 000 

327, 000 

1, 300, 000 

2, 330, 000 

888,000 

888,000 

829, 000 

241,000 

142,000

684,000

65,200 

94,500 

37. 800
1953

April.... 

July..-. 

1954

April...-.. 

July

1965

March

April.-. 

July

Water year 1954-55...-- _ ... ...

December. .. ___ . ___ _ .. __ _ .._

2, 135, 800

3,310,900

5,808,000

7, 768, 000

6, 769, 000

5, 897, 000

5, 712, 000

4, 544, 000

2,625,800

51, 515, 100

2, 162, 000

2, 014, 800

2, 092, 500

1, 700, 700

1, 674, 100

2, 749, 000

4,360,000

6, 538, 000

6, 532, 000

5, 147, 900

3,420,000

3,042,300

41,433,300

5,337,400

2, 961, 900

2, 404, 100

3,469,300

3, 565, 500

5, 890, 000

5,807,000

4, 712, 700

4, 847, 000

3,810,900

2, 537, 800

2,213,500

47,557,100

3,229,400

2,003,400

1, 649, 000

4,236,000

6, 567, 000

11, 520, 000

15,410,000

13,430,000

11, 700, 000

11, 330, 000

9, 013, 000

5,208,000

102,200,000

4,288,000

3, 996, 000

4, 150, 000

3, 373, 000

3, 321, 000

5, 453, 000

8, 648, 000

12, 970, 000

12, 960, 000

10,210,000

6, 783, 000

6, 034, 000

82, 190, 000

10, 590, 000

5, 875, 000

4, 768, 000

6, 881, 000

7,072,000

11, 680, 000

11, 520, 000

9, 348, 000

9, 614, 000

7, 559, 000

5, 034, 000

4, 390, 000

94,300,000

6, 405, 000

3, 974, 000

3,271,000

577,200

3, 708, 500

11, 610, 000

22, 351, 000

18, 809, 000

17, 754, 000

14, 174, 700

3,201,200

1, 390, GOO

99, 605, 100

1, 176, 500

1, 056, 000

837,300

351, 750

6SO, 980

3, 155, 100

5,371,000

13, 929, 000

26, 403, 000

7,742,200

6, 056, 400

3,877,500

70, 646, 730

9,985,900

1,382,100

733, 000

3, 693, 900

10, 169, 600

10, 483, 000

9, 633, 000

7,118,200

8, 744, 500

9, 188, 000

1, 616, 400

1, 782, 900

74, 530, 500

5,002,400

927, 800

343, 090

18,600

132, 000

375,000

745, 000

607, 000

592, 000

457, 000

103,000

46,400

273, 000

38, 000

35,200

27,000

11,300

24,700

102,000

179,000

449, 000

880,000

250,000

195, 000

129, 000

194,000

322,000

46, 100

23,600

119,000

363,000

338, 000

321,000

230, 000

291, 000

296,000

52,100

59,400

204,000

161, 000

30,900

11,100
TABLE 1. Monthly and annual summary of streamflow and suspended-sediment disc

Month

1966

April

September. _ . ..

Water year 1955-56. . _ ...... _ ..

1957 

January _ ____ ____ ______ .

March .....................................

April 

July... .--..... .... . . 

September.. ... _. _ ...... _ .

Water year 1956-57 

1958 

January. ..

Aiarch_---_. __ ......... _ _____

April.... .............................

June ___________________

July . .. .. .... ..

September _________________

Water year 1957-58 

Streamflow

Cfs-days

1, 587, 100 

1, 716, 600 

2, 557, 100 

4, 481, 000 

4, 508, 000 

3, 400, 500 

3, 700, 600 

3, 341, 600 

2, 224, 700

34, 399, 000

1, 822, 500 

1,750,200 

1, 723, 100

1, 751, 000 

1, 931, 400 

2,830,200 

5, 652, 000 

7,245,000 

7,095,000 

6, 856, 000 

3,403,700 

2,874,800

44, 934, 900

2, 752, 800 

2, 702, 000 

2, 903, 600

2, 358, 100 

9( 099, 3"0 

5, 917, 000 

4, 757, 000 

4,147,200 

5,194,200 

9, 709, 000 

6, 838, 400 

3, 647, 600

52,956,200

Acre-feet

3, 148, 000 

3,405,000 

5, 072, 000 

8,888,000 

8, 941, 000 

6, 745, 000 

7, 340, 000 

6, 628, 000 

4,413,000

68,230,000

3, 615, 000 

3, 471, 000 

3,418,000

3,473,000 

3, 831, 000 

5, 614, 000 

11,210,000 

14, 370, 000 

14, 070, 000 

13, 600, 000 

6, 751, 000 

5, 702, 000

89, 120, 000

5, 460, 000 

5, 359, 000 

5, 759, 000

4, 677, 000 

4, 025, 000 

11, 740, 000 

9, 435, 000 

8,226,000 

10, 300, 000 

19,260,000 

13, 560, 000 

7,235,000

105, 000, 000

Discharge 

(tons)

258, 130 

390, 670 

1, 489, 300 

4, 626, 500 

5, 767, 000 

3, 997, 200 

8, 430, 900 

4,439,200 

1, 749, 900

37, 422, 090

1,251,600 

796,900 

565, 110

596, 380 

1, 072, 800 

2, 446-, 500 

9,712,200 

13, 776, 000 

22, 378, 000 

15,456,000 

3,304,000 

3,429,200

74, 784, 690

3, 735, 000 

2,350,500 

3, 154, 000

1,366,400 

1, -235, ICO 

16,222,000 

6,293,000 

8,463,500 

12,627,000 

30,482,000 

13, 950, 800 

8,246,200

108, 125, 500

Daily 

Mean

8,330 

13,500 

48,000 

154, 000 

186,000 

133,000 

272,000 

143,000 

58,300

102,000

40,400 

26,600 

18,200

19,200 

38,300 

78,900 

324,000 

444,000 

746,000 

499,000 

107,000 

114,000

205,000

120,000 

78,400 

102,000

44,100 

ii, 100 

523,000 

210,000 

273,000 

421,000 

983,000 

450,000 

275,000

296,000

1 Maximum measured.
SUSPENDED-SEDIMENT DISCHARGE AND PARTICLE SIZE 19

1200 i 2400

1000

800

Q </> w Z

</) o

-

600

) ? 400

o 

o

z 

< 

200 - £

2000

1600

1200

800

400

EXPLANATION

Concentration Discharge

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June J fly Aug. Sept.

FIGURE 9. Monthly trend of suspended-sediment concentrations and discharges.

Because of the pronounced decrease in mean concentration from 

1949 to 1956, a study was made to determine whethe~ or not the 

decrease was the result of retention of sediment behind dams that 

have recently been completed, particularly in the upper Missouri 

River basin.

The yearly mean concentration is not closely related to the reservoir 

storage capacity. (See fig. 10.) The storage capacity was fairly 

constant from 1948 to the beginning of 1952; howeve^*, the mean 

concentration decreased appreciably. Also, the storage capacity was 

much greater in 1954 and 1955 than in previous years, 1 nt the mean 

concentrations were only slightly less.

One reason why the concentration has no apparent close relation 

to the storage capacity is that any capacity added upstream from 

existing storage would have little effect on the concentration at St. 

Louis. The concentration is expected to be more closely related to 

the amount of uncontrolled drainage area than to the storage capacity. 

Figure 10 shows, however, that the concentration is no more closely 

related to the amount of uncontrolled drainage area than it is to the 

storage capacity. The only major change in the uncontrolled drainage 

area was near the beginning of the 1953 water year, when storage
20 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUT?

400 -

Mean oncentratio

V

I nconl rolled drainage ar

ity/

;5i5

o: cc

WATER YEAR

FIGURE 10. Factors affecting mean concentration.

began at Fort Randall; however, a pronounced decrease in mean 

concentration took place before 1953.

Except for the first 3 years of sediment record, the mean concentration followed closely the trend of streamflow. (See fig. 10.) Even 

though the mean concentration is probably affected by the reservoir 

storage capacity and by the amount of uncontrolled drainp.^e area, 

the effects are obscured by the close relation of concentration to 

streamflow. Because the river can pick up material from its bed and 

banks, the effects of storage on the sediment concentration may not
SUSPENDED-SEDIMENT DISCHARGE AND PARTICLE SIZE 21

be apparent as far downstream as St. Louis until many years after 

the beginning of storage.

A study was made to determine whether or not the relation of 

suspended-sediment discharge to streamflow had been changed by 

the upstream storage reservoirs. Measured suspended-sediment discharges were plotted against the corresponding water discharges, and 

a line was drawn to represent the relation for each year of record. 

(See fig. 11.) The lines were not intended to be rating curves but 

were intended to be only lines of general trend.

From 1949 to 1952 the sediment discharge varied with the 2.0-2.4 

power of the water discharge. However, from 1953 to 1956 the 

sediment discharge varied with the 2.9-3.6 power of the water 

discharge. In 1957 and 1958 the relations were close to those of 

1949-52; the sediment discharge varied with the 2.5 and 2.3 powers 

of the water discharge. The sediment discharges at any given water 

discharge, however, were generally lower in 1957-58 thai in 1949-52. 

Low water discharges carried less sediment in 1953-56 than in other 

years, but high water discharges carried more sediment. The results 

of this study are inconclusive, but they seem to indicate that the 

trend is toward lower sediment discharges for a given water discharge 

and, therefore, toward lower yearly mean concentrations.

Suspended sediment from depth-integrated samples representing 

the entire cross section at St. Louis averaged 47 percent clay, 38 

percent silt, and 15 percent sand when analyzed, chemically and 

mechanically dispersed, in distilled water. The average size distribution of suspended sediment and the smallest and largest percent-finer 

values that were determined for each size are shown in figure 12.

Logically, particle-size distribution of suspended sed;ment would 

be related to discharge, season, temperature, and concentration. The 

amount of sand Would increase as discharge increases because the 

capacity of the flow to transport sand would increase. The amount 

of silt and clay would increase when surface runoff laden with silt 

and clay causes the discharge to increase. Normally, tbe percentage 

of silt and clay would be less in the winter than in other seasons 

because surface runoff would be less. The percentage of sand generally would increase as temperature decreases because the high fluid 

viscosity at low temperature favors high transport capacities for 

sand. The percentage of silt and clay generally would increase as 

concentration increases because the amount of silt and clay is not 

governed by flow conditions and can increase at a faster rate than 

the amount of sand. The particle-size distribution must also be 

governed by the widely different sources of sediment in the large 

drainage area; however, information for determining the source of the 

sediment was not available.
22 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

10

10 

3X104

WATER DISCHARGE, IN CUBIC FEET PER SECOND

FIGURE 11. Relations of suspended-sediment discharge to wrter

discharge.
SUSPENDED-SEDIMENT DISCHARGE AND PARTICLE SIZE 23

99.8 

99.5 

99.0 

98

95 

90

80 

70 

60 

50 

40 

30 

20

10 

0.(

_^.^

- 

-"*

~-~-

-^"

 "^

^,

.--

_

^-

."

*~

^

"

~*

-"''&

£0£^

^^^ ..-^^"

s

^

^ » *'

-

**^

.-^'

"'

-^^

,-

,-

^

^

-

.*-

"

^ -

 "

-

/

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/

/

/

)

/

/

/'

/

/

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^7

f

)01 0.01 0.1 1

DIAMETER, IN MILLIMETERS

FIGURE 12. Average and extreme particle-size distributions of suspended

sediment.

No consistent relationships were found from graphs in which 

various particle-size parameters were plotted with discharge, season, 

temperature, and concentration as independent variables. The expected relationships of particle size to discharge, season, and temperature probably exist but were obscured by the variatior of particle 

size with source area. The expected relationship of particle size to 

concentration was obscured by the variation of partic1 *, size with 

source area and by the narrow range of variation of concentration.

Because of the lateral change of concentration in the cross section, 

a lateral change in particle size would be expected. Su^h a change 

can be determined only from analyses of samples from individual 

stations; however, most of the particle-size analyses were for composites rather than for individual samples. From the few analyses 

of individual samples, no consistent variation in partic1oi size from 

one side of the river to the other could be detected.

BED MATERIAL

Samples of bed material were obtained with a U.S. BM-48 sampler 

from May 1951 to March 1958 and with a U.S. BM-54 sampler from 

April 1958 to July 1959. Both samplers obtain material from the 

upper 1-1 % inches of the bed. Because of improved design, the BM54 sampler is less likely than the BM-48 to permit fine material to 

be washed out as the sample is taken and raised to the bridge. 

Samples were obtained at 4 points in the cross section from May 

1951 to April 1955 and at 10-21 points from May 1955 to July 1959.
24 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

Before April 1956, the sieve method was used to analyze all bedmaterial samples. Since that time, sieve and visual-accumulationtube methods have been used. Samples were analyzed individually, 

and the results were averaged to give the particle-size distribution for 

the entire cross section.

The size distribution of bed material is highly variable with location 

in the cross section. Near the banks, the material is mostly fine 

sand and some silt. Near the piers, the material is very coarse; 

some of the particles are large enough to be retained on a 32-mm 

sieve. In the main flow, most of the material is between 0.125 and 

1.000 mm in diameter.

The size distribution of bed material is also highly varable with 

time. (See fig. 13.) The data for four sampling points are shown for 

1955-59 in figure 13 to indicate the probable reliability of the 1951-55 

data. The data for 4 sampling points have more variation than those 

for 10-21 sampling points and are not completely reliable for individual days; however, they show the trend of bed-material sizes 

rather well. Figure 13 indicates that the median diameters were

2 0.4

Q 0.2

0.1

EXPLANATION 

Average of 4 sampling points

Average for 10 to 21 sampling points

9 samp'tng points

1951 1952 1953 1954 1955 1956 1957 195F 1959

CALENDAR YEAR

FIGURE 13. Variation of bed-material size with time.
BED MATERIAL 25

larger in 1951 and 1952 than in 1953-56 and were generally increasing 

in 1957-59.

A general relation between median diameter and discharge is 

suggested by the fact that the discharge was higher in 1951 and 

1952 than in 1953-56 and was intermediate in 1957-59. A study 

was made to determine whether or not the particle size is related to 

the discharge for short periods. Average median dir.meters were 

plotted against mean discharge for 1-day to 2-year periods, and 1 

year was the shortest period for which a good relation was found. 

The relation for 2-year periods is slightly better than the relation 

for 1-year periods (fig. 14). The absence of short-term relations of 

median diameter to discharge suggests that the bed-material size is 

influenced more by the depth of scour than by the selective removal 

or deposition of fine and medium sands from the upper few millimeters of the bed during short periods of high or lov^ flow. The 

relations between bed-material size and bed elevation are discussed 

in the section, "Aggradation and degradation."

For many sets of bed-material samples, a measure of tl ^ uniformity 

of the material was computed. This measure is called the geometric 

quartile deviation and is computed as T/d75/d25 , where d7<5 and d25 are 

the particle sizes at which either 75 or 25 percent of the bed material 

by weight is finer. Material that is perfectly uniform in size has a 

geometric quartile deviation of 1.00, and material that has a wide 

range of size has a large geometric quartile deviation. Because 

only the middle 50 percent of the material is considered in computing

FOR 1-YEAR PERIODS FOR 2-YEAR PERIODS

SIZE, MEDIAN PARTICLE INMILLIMETERS

opppppoc

Ko bti*!- cu ui>j 

ooooooooc

/

 

/ /.

/

/

7

/

) 100 200 3C 0 100 200 

MEAN DISCHARGE, IN 1000 CUBIC FEET PER SECOND

FIGURE 14. Relation of bed-material size to discharge. 

764-692 O 65 3

300
26 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

this measure, however, values of 1.00 do not necessarily indicate that 

all the material is of uniform size. Also, two particle-size distributions that have the same geometric quartile deviation do not necessarily have the same extreme range of sizes. Because this measure 

is computed from the ratio of two sizes rather than from the difference, 

the geometric quartile deviations for different samples can be compared without making corrections for different average particle sizes. 

The geometric quartile deviations for the bed material in the Mississippi River at St. Louis ranged from 1.1 to 2.5 and averaged 1.5. 

These values are intermediate in relation to those for some other 

streams for which bed material has been measured. Bed material of 

the Colorado River near Blythe, Calif., (median diameter about 0.33 

mm) and of the Rio Grande near Bernallilo, N. Mex., (median diameter about 0.30 mm) has geometric quartile deviations of about 1.3 

and 1.4, respectively. Bed material of the Kansas River at Wamego, 

Kans., (median diameter about 0.61 mm) has a geometric quartile 

deviation of about 2.1.

AGGRADATION AND DEGRADATION

Discharge measurements made about once each week, and sometimes more often, include data on depth and water-surface elevation 

that provide information on aggradation and degradation at the 

MacArthur Bridge. A study was made of the factors that affect 

the streambed elevation. Mean bed elevations were computed for 

the part of the section between stations 275 and 1,800, so that a constant width could be used and so that the bed elevation would not be 

affected by the sloping banks. The range of mean bed elevations 

was from 355.1 to 364.4 feet above mean sea level during the period of 

sediment record.

The mean bed elevation is not significantly related to the instantaneous discharge, mean velocity, shear velocity, mean depth, nor suspended-sand concentration. The bed elevation and the median 

diameter of the bed material are fairly closely related (fig. 15). The 

relation indicates that the particle size is partly dependent on the 

depth of scour or that the depth of scour and the particle size are mutually dependent on the same causes. If the bed elevation k regarded 

as the dependent variable, it can be computed from the regression

equation

h h = 363.0-7.8 dm 

where

ht, is mean bed elevation, in feet above mean sea level 

d50 is median diameter of bed material, in millimeters

The standard error of estimate for this equation is 0.91 foot. Multiple
AGGRADATION AND DEGRADATION 27

regressions with discharge, mean velocity, shear velocity, water-surface slope, and suspended-sand concentration did not result in significantly better relationships than d^ alone.

Failure of the bed elevation to show a significant relation to instantaneous values except for d50 suggests that the effect of such variables 

as discharge, mean velocity, water-surface slope, and surr>ended-sand 

concentration is cumulative over periods such as a week or a month. 

The cumulative effect of discharge on the bed elevation was studied 

by plotting the mean bed elevations for various period?1 against the 

discharges for various other periods that preceded or included the 

periods for which the mean bed elevations were determined. A 

relation was found between monthly mean bed elevation and the 

discharge for a 3-month period (fig. 16), but it changed from year to 

year.

FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 

RESISTANCE TO FLOW

Resistance to flow in sand-bed streams is governed mostly by the 

size and shape of the irregularities on the bed rather than by the

_i 362

LU

LU

_l

2i 361

V)

 z. 

<

Ld

^ 360

LU

0 

00

< 359

ti

LU 

Lu

^. 358 £ 

o

> 357

LU

_l 

LU

Q

£ 356 

 9t;t;

X

V-

 

 X* 

 *-

4

 

-.

 N.

 \

.*

 

<

\-»

>< 

>. 

 

V

N. 

 v

i 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 

MEDIAN DIAMETER OF BED MATERIAL, IN MILLIMETERS

FIGURE 15. Relation between bed elevation and particle size.

0.9
28 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

LJ 

§

< 363

(/}

z

LJ 

^ "3C O

LJ

O

CO

< 361

LJ

LL.

E 360

O 

hLJ 

LJ

Q 

LU m OCQ 358

2 

LJ

8

/v

A A 

(

X&

X

XX

^

 . '

 

0

) A A

X

X y

K

t

9

o

" ;

o

0

.

;\

0 c

o

.

.

EXPLANATION

1944-45

o

1950

A 

1951

X

( 1958

A

A

,

A ^

^LA

356 

0 10 20 30 40 50 60 70 80 9

DISCHARGE, IN MILLIONS OF ACRE-FEET

FIGURE 16. Relation of monthly mean bed elevation to the discharge for 3-month 

periods. The mean bed elevation for each month has been plotted against 

the sum of the discharges for that month and the two preceding months.

grain size of the particles in the bed. Small rivers typically have 

dimes on the bed at low flow, but the dunes are washed out and the 

bed is fairly flat and regular at high flow. Measured by Manning's n, 

the resistance when dunes are on the bed is as much as twice the 

resistance when the bed is flat and regular. In shallow rivers the 

height of dunes is as much as half the depth of flow. The resistance 

to flow, however, is governed by the spacing of the dunes as well as 

by their height. One difficulty in the field study of resistance to 

flow in nonuniform cross sections is that the bed may be flat and 

regular in one part of the section but may have dunes in another 

part; thus, a resistance coefficient for the whole section will represent 

neither dunes nor a flat bed. Several methods of predicting the 

resistance to flow in alluvial channels have been proposed. Most of 

these methods have been based on experiments in laboratcry flumes 

and on a small amount of data from canals and natural streams, most 

of them small.
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 29

Among the few observations of bed configuration in large rivers 

are those of the lower Mississippi River in Louisiana (Carey and 

Keller, 1957). Carey and Keller concluded that the large-scale 

irregularities of the bed vary systematically with changes in discharge 

and constitute a major element of resistance to flow.

Although the data for the Mississippi River at St. Louis were not 

obtained primarily for the purpose of research, they can be used to 

supplement the data for flumes, small rivers, and the lower Mississippi 

River in the study of resistance to flow. Particularly useful are the 

data that permit comparison of resistance coefficients and the height 

and spacing of dunes with data for flumes and small rivers.

Pertinent measured and computed data from nearly concurrent 

measurements of discharge and sediment are shown in table 2. 

Hydraulic and sediment characteristics generally remain fairly 

constant for periods of a few days; therefore, data were considered 

to be concurrent if the time between the discharge measurement and 

the bed-material or suspended-sediment measurement was not more 

than 2 days.

The water-surface slopes in table 2 were determined from gage 

readings made at 8:00 a.m. each day at gages 4.4 miles upstream and 

2.1 miles downstream from MacArthur Bridge. Readings at a gage 

near MacArthur Bridge were also used in determining the uniformity 

of slopes in the reaches upstream and downstream from the bridge. 

Gage readings were furnished by the U.S. Army Corps of Engineers, 

St. Louis District. During 1950-53, the slopes changed widely from 

time to time, but the slopes upstream and downstream from the 

bridge were generally about the same at any given time. The slopes 

in the upstream reach tended to be slightly steeper th&n the slopes 

in the downstream reach. During 1954-59, the sloper were fairly 

constant, but those in the upstream reach were consistently steeper 

than those in the downstream reach; in 1956-57, the slopes upstream 

were about twice as steep as those downstream.

The widths shown in table 2 are the widths of the water surface 

excluding the two piers, each 27 feet wide. The hydrauPc radius was 

computed by dividing the cross-sectional area, which excluded the 

area of the piers, by a wetted perimeter computed as the width plus 

twice the mean depth. The shear velocity was computed as -\fgRS, 

where g is the acceleration due to gravity, R is the hydraulic radius, 

and S is the slope of the water surface for the 6.5-mile reach and is 

assumed to be equal to the energy gradient, for most conditions.

In July 1951 the flow was over the banks, and the width increased 

from about 1,780 to 2,800 feet. Inclusion of 1,000 feet of shallow, 

slow-moving, overbank flow in the computations would have produced highly nontypical values of mean depth and hydraulic radius.
30 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

TABLE 2. Summary of hydraulic and

Date

I960

May 22... 

Aug. 7. 

Sept. 25 

1951 

Apr. 17 

May 21 __

June 18 _____

July 16. __

July 22.- __

July 30. _ 

Sept. 17 -

Sept. 24.. ___

Oct. 8 . __ -

Oct. 15 

Nov. 13 

Nov. 26 __ .

195S 

Feb. IS. 

Apr. 28.. _ .

Apr. 30 __ . ...

July 7 _ 

Antr 1Q

Sept. 29 .

Oct. 20 

196S 

Jan. 13 

Feb. 11 

Feb. 16.. ..

Feb. 24... ......

Mar. 16 

Apr. 27 

July 13... __ -

July 20.... 

Aug. 10 

Sept. 14 

Sept. 28 

Oct. 19 . 

Dec. 28...- 

1964 

Jan. 28 

Feb. 8 

Mar. 22.- 

Apr. 19..... 

Apr. 27--. 

July 12.... 

July 26 

Sept. 21... 

Oct. 18. 

Dec. 1 _____

Hydraulic data

Watersurface 

slope

0.0000997 

.0000924 

.0000909 

.0000428 

.0000399 

.0000399

.000106 

.0000982 

.0000822 

.000126 

.000139

.0000851 

.0000632 

.0000530 

.0000341 

.0000355

.0000312 

.0000400 

.0000370

.0000544 

.000116 

.000110 

.0000545 

.0000502

.0000428 

.0000428 

.0000355 

.0000487 

.0000516

.0000574 

.0000530 

.0000603 

.0000545 

.0000487

.0000603 

.0000589 

.0000603 

.0000632 

.0000632

.0000603 

.0000661 

.0000559 

.0000516 

.0000516 

.0000661

.0000749 

.0000807 

.0000720 

.0000720 

.0000720

.0000691 

.0000720 

.0000603 

.0000647 

.0000734 

.0000720

Discharge 

(efs)

330,000 

348,000 

327,000 

147,000 

149,000 

128,000

521,000 

362,000 

322,000 

704,000 

763,000

468,000 

388,000 

285,000 

208,000 

182,000

219,000 

233,000 

190,000

195,000 

670,000 

681,000 

198,000 

204,000

167,000 

74,700 

78,700 

67,500 

67,500

62,000 

129,000 

117,000 

204,000 

210,000

321,000 

241,000 

179,000 

172,000 

197,000

157,000 

159,000 

80,700 

67,700 

66,600 

61,800

45,900 

51,000 

80,500 

138,000 

163,000

283,000 

173,000 

115,000 

100,000 

214,000 

75.800

Width 

(ft)

1,681 

1,690 

1,692 

1,606 

1,606 

1,594

1,711 

1,692 

1,683 

1 1, 770 

'1,780

1,746 

1,716 

1,671 

1,647 

1,641

1,646 

1,651 

1,631

1,648 

1,834 

1,888 

1,648 

1,664

1,633 

1,558 

1,552 

1,546 

1,549

1,544 

1,596 

1,588 

1,646 

1,642

1,700 

1,654 

1,617 

1,608 

1,635

1,594 

1,595 

1,546 

1,530 

1,524 

1,523

1,487 

1,491 

1,545 

1,581 

1,595

1,668 

1,597 

1,551 

1,567 

1,622 

1.527

Mean 

depth 

(ft)

37.3 

37.2 

37.3 

28.0 

28.4 

24.7

41.3 

40.4 

39.1

154.8 

'56.7

49.9 

45.0 

39.4 

34.5 

33.0

33.5 

34.6 

31.0

27.9 

46.5 

46.9 

33.1 

33.5

30.3 

21.4 

21.6 

20.4 

20.3

19.7 

27.1 

25.4 

31.8 

32.3

40.2 

33.0 

28.1 

27.4 

30.1

27.9 

27.6 

20.2 

18.4 

18.2 

17.7

15.3 

16.1 

19.8 

25.5 

27.5

34.2 

28.9 

24.1 

22.8 

31.3 

19.7

Hydraulic 

radius 

(ft)

35.7 

35.6 

35.7 

27.1 

27.4 

23.9

39.4 

38.6 

37.4 

'51.6 

'53.4

47.2 

42.7 

37.6 

33.2 

31.8

32.1 

33.2 

29.9

27.0 

44.2 

44.7 

31.8 

32.2

29.2 

20.8 

21.0 

19.9 

19.7

19.2 

26.2 

24.6 

30.5 

31.1

38.4 

31.7 

27.1 

26.5 

29.0

26.9 

26.6 

19.7 

18.0 

17.8 

17.3

15.0 

15.8 

19.3 

24.7 

26.6

32.9 

27.9 

23.3 

22.1 

30.1 

19.2

Mean 

velocity 

(fps)

5.26 

5.54 

5.18 

3.27 

3.27 

3.26

7.37 

5.29 

4.89 

17.26 

17.63

5.37 

5.03 

4.33 

3.66 

3.36

3.97 

4.08 

3.75

4.24 

7.86 

7.69 

3.63 

3.66

3.37 

2.24 

2.35 

2.14 

2.15

2.04 

2.98 

2.90 

3.90 

3.96

4.69 

4.42 

3.94 

3.90 

4.00

3.54 

3.61 

2.59 

2.40 

2.40 

2.30

2.01 

2.12 

2.63 

3.42 

3.72

4.96 

3.74 

3.07 

2.80 

4.22 

2.52

Sheavelocity 

(fps)

0.338 

.3% 

.313

.316 

.3'9 

.315

l .4"i8 

l .4W

.3"0 

.295

.41Q 

.318

.219

.273

.229 

.232 

.243

.229 

.238

.r>? 

.i*")

.2^ 

.2.11 

.239 

.248

.271 

.254 

.213 

.214 

.267 

.211

n

0.030 

.028 

.030

.024 

.032 

.031 

i .032 

1.033

.033 

.029

.026 

.026

.034

.028

.026 

.027 

.028

.029 

.030

.035

.039 

.040 

.035 

.031 

.030

.025 

.031 

.031 

.034 

.029 

.036

See footnotes at end of table.
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 

sediment data from concurrent measurements

31

Date

1950

1951

May23__ .....

June 19. _____

July 16.. .......

Sept. 19... _ . _ .

Sept. 26.... .......

Oct. 17... .........

Nov. 13.. ........ .

Nov. 28.. . ........

1958 

Feb. 20. ........

Apr. 26 ....

May 2 ..........

June 16.- .........

July 9 ...

Aug. 19- ..........

Dec. 9--......- ....

Dec. 31 .........

195S 

Jan. 14............

Feb. 12............

Feb. 18 .........

Feb. 26 ... ......

Mar. 18-- 

Apr. 27 

July 14..-. .-.-

July22 .. ....

Aug. 10...-- _

Sept. 16-... __ -

Sept. 30 _ -... -

Oct. 20 .... .....

Dec. 30. 

1964 

Jan. 29... ... .

Feb. 8-. 

Mar. 22 __ . ___

Apr. 19.. _ .......

July 12... ......

July 26.... 

Sept. 21...- _-_ __

Oct. 19 __ __ __

Nov. 29.... ....

Bed material

dso 

(mm)

0.65 

.55 

.71

.78 

.75

.72

.33 

.18

.19 

.54 

.48 

.61 

.69

.63 

.67

.68 

.57

.58 

.50 

.28 

.64

.48

.55 

.19

.19

.24

.23 

.22 

.27 

.29 

.29 

.25

.24 

.24 

.21 

.23

.23 

.30 

.29 

.29 

.33 

.29

V<frs/d25

1.58 

1.52 

1.36

1.59 

1.48

1.86

2.12 

1.18

1.17 

1.82 

1.58 

1.51

1.85

1.41 

2.50

1.93 

2.09

1.84 

1.86 

1.84 

1.75 

2.04

2.16 

1.12

1.70 

1.76

1.43 

1.23 

1.51 

1.78 

1.68 

1.91

1.60 

1.55 

1.70 

1.30

1.57 

1.92 

1.73 

1.81 

1.90 

1.61

Date

1950

May23__._ _ ....

Aug. 8_ ...........

Sept. 7 ..........

Sept. 26 __ ......

1951 

Apr. 18 .........

May 23_-... ...

July 16 

July 22...... ......

July 30 ......

Sept. 17... .. ......

Oct. 10 .. __ ...

Oct. 17 

Nov. 13...........

1952 

Feb. 20 .........

Tnl 17 Q

Aug. 19 . 

Sept. 29 

Oct. 22 

196S

7an 14

Feb. 26 -

Mar. 18.... ...

July 14.. 

July 22.. 

Sept. 15 __ _ 

Oct. 20 

1954

Feb. 10. -

Mar. 22 

Apr. 27 

July 26.. 

Sept. 21 

Oct. 18 

Nov. 29... 

Suspended sediment

Sand concentration 

(ppm)

185 

205 

234 

80 

111 

89

342 

206

175 

181

102 

214

78 

120 

84

155

182 

221

304

43

26 

6 

12

20 

13

81 

100

123

82 

90 

64

61 

51 

13 

8 

11

11 

32 

73 

101

148

17 

26 

102 

26

Sand discharge (tons 

per day)

137,000 

186,000 

176,000 

26,300 

37,000 

23,900

469,000 

199,000

332,000 

375, 000

133,000 

224,000 

50,500 

75,800 

38,600

91,200

99,300 

131,000

553,000

24,300

11,700 

1,240 

2,360

3,600 

2,240

40,700 

59,700

92,300

39,400 

42,800 

32,500

26,400 

21,900 

3,080 

1,530 

1,980

1,590 

6,960 

27,000 

44,700

115,000

5,280 

6,870 

58,400 

5,480

Water 

temperature (°F)

58 

69 

71 

76 

71 

67

47 

71 

74 

77 

81

82 

70 

68 262 

63

47 

40 

43

39 

58 

65 

81 

80

79 

70 

52 

43 

35

41 

39 

38 

39

48

50 

54 

73 

80 

80

84 

79 

71 

70 

65 

33

34 

38

42 

61 

65

67 

81

80 

70 

57 

42
32 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

TABLE 2. Summary of hydraulic and

Date

1966 

Feb. 24.. 

Mar. 30 

May 24..... .

Dec. 27..-- __ .

1966 

Feb. 21... 

Mar. 27 

Apr. 24... 

July 9.... 

Oct. 2 

Nov. 5. 

1967 

Jan. 21... .......

Mar. 20 

Mar. 26 

Apr. 9 ..........

May 20 .....

June 25 .........

Oct. 7 ....

1968 

Apr. 14.. __ . .

Apr. 29.. ....

July 8 ........

July 25 .

Sept. 8... .... ...

Sept 29

Nov. 18 

1969 

Mar. 23 

May 13 

July 1...........

Hydraulic data

Watersurface 

slope

.0000720 

. 0000793 

.0000691 

.0000822

.0000822 

.0000763 

.0000836 

.0000836 

.0000749

.0000822 

.0000938 

.0000938

.0000982 

.0000932 

.0000874 

.0000903 

.0000903

.0000845 

.0000991 

.0000962 

.0000932 

.0000816

.0000845 

.0000816 

.0000787 

.0000932 

.0000991

.000105 

.0000728 

.0000583 

.0000787

.0000991 

.000111 

.0000874 

.0000903 

.0000699 

.0000612

Discharge 

(cfs)

291,000 

163,000 

98,500 

59,800

56,100 

82, 400 

172, 000 

149, 000 

155, 000

105,000 

59,400 

55,200

49,200 

69,600 

136,000 

259,000 

193,000

172, 000 

308,000 

219, 000 

220,000 

74,100

172,000 

135,000 

109, 000 

310,000 

235,000

496,000 

106,000 

126,000 

104,000

228,000 

301,000 

180,000 

241,000 

141,000 

124,000

Width 

(ft)

1,672 

1,592 

1,540 

1,508

1,510 

1,548 

1,630 

1,612 

1,616

1,566 

1,504 

1,510

1,488 

1,520 

1,588 

1,692 

1,638

1,632 

1,658 

1,678 

1,644 

1,524

1,622 

1,596 

1,568 

1,676 

1,638

1,714 

1,562 

1,576 

1,550

1,656 

1,710 

1,606 

1,668 

1,576 

1,570

Mean 

depth 

(ft)

34.0 

26.8 

22.8 

17.0

16.9 

19.8 

28.6 

27.7 

27.5

22.5 

17.2 

15.8

15.2 

17.6 

24.5 

32.2 

28.9

28.1 

36.9 

32.2 

33.0 

18.5

27.9 

24.8 

22.1 

35.0 

31.1

44.4 

22.6 

23.4 

21.1

30.6 

35.8 

29.5 

32.4 

26.3 

24.5

Hydraulic 

radius 

(ft)

32.7 

25.9 

22.1 

16.7

16.5 

19.3

27.6 

26.8 

26.6

21.8 

16.8 

15.5

14.9 

17.2 

23.8 

31.0 

27.9

27.1 

35.3 

31.0 

31.7 

18.1

26.9 

24.1 

21.5 

33.6 

29.9

42.2 

22.0 

22.7 

20.5

29.5 

34.3 

28.5 

31.2 

25.5 

23.7

Mean 

velocity 

(fps)

5.11 

3.82 

2.81 

2.33

2.20 

2.68 

3.69 

3.34 

3.49

2.98 

2.30 

2.31

2.18 

2.61 

3.50 

4.76 

4.08

3.76 

5.03 

4.05 

4.06 

2.63

3.81 

3.41 

3.15 

5.29 

4.62

6.48 

3.00 

3.41 

3.18

4.51 

4.92 

3.80 

4.45 

3.40 

3.23

Sheavelocity 

(fps)

.275 

.2o' 

.222 .2")

.219 

.218 

.272 

.2^8 

. 2J3

.240 

.225 

.216

.2^7 

.227 

.2'9 .3"") 

.285

.272 

.336 

.310 

.378 

.218

.270 

.252 

.233 

.317 

.309

.378 

.227

.228

.307 

.350

.vw

.301 

.240 

.216

«

.025 

.030 

.035 

.038

.040 

.035 

.034 

.036 

.033

.035 

.041 

.039

.041 

.037 

.033 

.029 

.032

.033 

.032 

.036 

.035 

.035

.032 

.033 

.032 

.028 

.031

.028 

.033

.031

.031 

.034 

.034 

.031 

.032 

.030

i Excluding overbank flow. 2 Estimated.

Therefore, these values were computed for only the part of the flow 

that was between the banks.

The variation of water-surface slope with river stage and with time 

indicates that the water-surface slope sometimes diverged radically 

from the energy gradient. The divergence between energy gradient 

and water-surface slope may have been caused by the peculiar conditions of the cross section about 3-4 miles downstream from MacArthur 

Bridge. During medium discharge, a narrow part of this section
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 

sediment data from concurrent measurements Continued

33

Date

1965 

Feb. 25 _ -. .---

Apr. 1 _____ .

May 24..... ...

Dec. 28 .

1956 

Feb. 22 

Apr. 25 

MaylO__.__ 

July 10.. .

Aug. 6_____. 

Oct. 2 

Nov. 6 . ..... 

1967 

Jan. 21. .. ...

Mar. 20.. ....

Mar. 26.. _

Apr. 9_ -. . . 

Apr. 23.........1..

May8.... ....

May 21.. .........

June 27.. _____

Oct. 7 ......

1958 

Apr. 14... ... ... ...

Apr. 29 

May 19... ________

June 17 _.________

July 10. _ .. __ ._

Sept. 9... ___

Oct. 1 ________

Nov. 20. .

1959 

Mar. 24...........

Apr. 8__. ___ ....

May 6 _ . ________

May 13__... __ _.

July 2_ ......

Bed material

d^ 

(mm)

.25 

.23 

.30 

.31

.31

.30 

.29 

.33

.31 

.26

.28

.32 

.24 

.23 

.22 

.24

.29 

.27 

.31 

.34 

.37

.29 

.35 

.37 

.34 

.40

.44 

.44 

.36

.34 

.42 

.46 

.44 

.50 

.54

V-W<*-6

1.57 

1.24 

1.54 

1.46

1.44

1.40 

1.32 

1.35

1.36 

1.36 

1.46

1.60 

1.42 

1.34 

1.37 

1.30

1.40 

1.41 

1.35 

1.40 

1.55

1.39 

1.41 

1.51 

1.62 

1.49

1.57 

1.53 

1.72

1.43 

1.48 

1.40 

1.48 

1.43 

1.39

Date

1955 

Feb. 25 

Mar. 31.. 

May24._.._ 

Dec. 27 

1966 

Feb. 21 

Mar. 28..... ...

Apr 24

May 9... __.._ .

July 9 ... ... ...

Aug. 6_____ .

Oct. 2. ... .

1967

Mar. 26 ___________

Apr. 9 _______

May 21.. ...__..__

Oct. T. ............

1968 

Apr. 14............

Apr. 29 .... _ ..

May 19 _ ___ _____

July 8 ._.______

July 25 ......

Oct. 1 ......

Nov. 20.. ___......

1959 

Max. 25.. .........

May 13...........

July 2 ......

Suspended sediment

Sand concentration 

(ppm)

220 

124 

15 

22

14

79 

99

72 

64

37 

19 

18

176 

307

63 

159 

110

40

102 

96 

56 

198 

116

134 

54 

42 

65

212 

86 

63 

94 

58 

37

Sand disc-urge (tons 

per day)

163,000 

51,900 

4,130 

3,410

2,120 

18,900 

45,400 

30,900 

27,000

10,500 

3,050 

2,720

64,400 

215,000

29,300 

128,000 

63,800

7,950

47,300 

34,800 

16,400 

166,000 

74,200

180,000 

18,800 

11.800 

21,000

139,000 

67,000 

24,600 

60,600 

22,100 

13,100

Water 

temperature (°F)

35 

43 

73 

36

36 

49 

49 

61

77

84 

69 

58

38 

48 

47 

49 

60

66 

65 

72 

2 78 

62

47 

56 

72 

73 

78

78 

78 

65 

55

47 

51 

70 

67 

76 

80

near the west bank is fairly deep and the rest of the section is wide 

and shallow. During very low discharge, the entire flow is near the 

west bank and a sand bar is exposed in the eastern part of the section. 

At high discharges, the flow can spread out over the wide section; 

and, as the discharge increases, the stage does not increase as much as 

it does at the narrower sections upstream. Therefore, the watersurface slope is greater at high discharges than at medium discharges. 

The water-surface slope was extremely low at some times of low and
34 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

medium discharges, such as in August-November 1951. Normally, the 

relation of the elevations of the bed at this section and at sections upstream is such that the low and medium discharges pass without any 

noticeable effect on the water-surface slope. But the upstream sections, such as at MacArthur Bridge, were scoured out during the 

high flows of 1951 and 1952; and the deep part of the downstream 

section may have been partly filled in by sediment. After the high 

flows had passed, the elevation of the bed at the downstream section 

probably was higher than the elevation of the bed upstream; thus, 

the water-surface slope was less than normal. Water-surface slopes 

are normally high when discharges are high, regardless of scour or 

fill; however, water-surface slopes were extremely low only after upstream sections had been scoured and sediment probably 1 ad been 

deposited in the deep part of tire downstream section.

Data for computation of backwater curves had not been obtained 

when the water-surface slopes were extremely low, so sample computations were made to determine if the low water-surface slop es could 

reasonably have been caused by unusual nonuniformity of the channel. 

On November 13, 1951, the average slope in the 6.5-mile reach was 

0.0000312, and the mean depth and mean velocity at MscArthur 

Bridge were 33.5 feet and 3.97 feet per second, respectively. A backwater computation was made for the reach between Mf.cArthur 

Bridge and the gage 2.1 miles downstream; gradually varied flow was 

assumed. Solution of the Bernoulli energy equation and the I fanning 

velocity equation by trial showed that a water-surface slope of 

0.0000312 could have resulted if the mean velocity 2.1 mile^ downstream was 2.9 feet per second and if the average n was 0.035. Inspection of the water-surface slopes indicates that the normal slope 

is about 0.00009. Because shear velocity and n vary with the square 

root of the energy gradient, errors in the energy gradient will not 

cause very large errors in shear velocity nor in n. Therefore, the 

water-surface slope was assumed to be about equal to the energy 

gradient when it was not greatly different from 0.00009; but shear 

velocity and n are not shown in table 2 unless the water-surface slope 

is greater than 0.00006.

Data obtained with a sonic fathometer by the Corps of Engineers, 

St. Louis District, show that the normal dune height in the vicinity 

of MacArthur Bridge is from 2 to 8 feet and that the average dune 

length is about 250 feet. On April 30, 1952, when the resistance to 

flow as measured by Manning's n was relatively low (0.026), dunes in 

the east side of the channel were from 2 to 7 feet high but r.veraged 

about 900 feet in length; in the central and western parts of the channel, although the depths were not uniform, the changes were very 

gradual, and only a few isolated dunes were located.
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 35

The range of variation of n from 0.024 to 0.041 indicates that the 

bed at some times becomes fairly flat and regular. The fact that the 

minimum values of n exceed the minimum for shallow streams, however, may indicate that the bed never becomes flat across the entire 

section but that dunes remain in parts of the section even when the 

discharge and mean velocity are very high.

The relations of n to discharge, mean velocity, and shear velocity 

are shown in figure 17. The absence of a discontinuity in the relations 

of n to discharge and mean velocity indicates that the f ow resistance 

of dunes is variable and that, at high flows, part of tl e section has 

dunes and part has a relatively flat bed. The facts that n is not 

closely related to the shear velocity and that the range of shear velocities is not as great as the range of mean velocities are to be expected 

if the bed sometimes has dunes and sometimes is flat. If dunes are 

on the bed, the resistance to flow will be great and the velocity will 

be fairly low; thus, the flow will be fairly deep. If the discharge increases and the bed becomes flat, the resistance will decrease and the 

velocity will increase. Because of the increased velocity, the increased 

discharge can be carried at the same depth as before; and if the slopes 

are about the same, the shear velocities will be about the same. 

Therefore, the range of shear velocities will be small, and roughness 

coefficients will vary widely for a given shear velocity.

A method for computing mean velocity from Keulegr-n's equations 

was presented by Einstein (1950). In this method the shear velocity 

is divided into two parts: one part pertains to the shear- transmitted to 

the boundary along the roughness of the grainy sand surface (u*'), 

and the other part pertains to the shear transmitted to the boundary 

in the form of normal pressures at the different sides of the bed irregularities such as ripples and dunes (u*"). The accuracy of the method 

depends on the accuracy of the relation of the ratio uju*" to the shear 

function ^' (Einstein, 1950, fig. 5).

For proper application of Einstein's method, the computations 

should be made for the average of several cross sections in a reach; 

however, data were available only for the section at MacArthur 

Bridge. Because the 6.5-mile reach for which the slopes vere measured 

is rather uniform, the bridge section probably represents the reach 

about as well as the average of several cross sections would. Therefore, 

the functions ufu*" and *%' were computed from representative data 

at MacArthur Bridge, and their relation is shown in figure 18. The 

Mississippi River data confirm Einstein's relation very yell except for 

low values of ^''. The lack of agreement at low values of V can be 

attributed partly to the fact that at high flows the water-surface 

slope used in the computations for the Mississippi River is greater 

than the energy slope and partly to the fact that dunes exist in parts
36 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

0.038 

0.034 

0.030 

0.026 

0.022

0.018 

1

0.042 

0.038 

0.034 

0.030 

0.026 

0.022

, .

, t » 9 ^

'. ". * .' .

a

M

 

"

 

4

M 

*

O 4 10 5 

DISCHARGE, IN CUBIC FEET PER SECOND

-]

 i

" 

.

 

 

*

1

1234567 

MEAN VELOCITY, IN FEET PER SECOND

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 

SHEAR VELOCITY, IN FEET PER SECOND

FIGUBE 17. Relation of Manning's n to discharge, mean veloc-'ty, 

and shear velocity.
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 37

i.o 10

FIGURE 18. Relation of u/w*" to *'. Curve from Einstein (1950, fig. 5).

of the cross section even though much of the bed is fairly flat and 

regular.

When gage height is plotted against discharge of more than about 

300,000 cfs and consecutive measurements are connected, a loop generally appears in the curve; the gage height for a given discharge is 

generally lower when the discharge is increasing than when it is decreasing. The largest difference in gage heights for the same discharge 

for individual rises during the period of sediment record was in April 

and May 1951; the gage height was 23.8 feet for a dischr.rge of 420,000 

cfs when the discharge was increasing and 26.6 feet for the same discharge when the discharge was decreasing (fig. 19). During the same 

rise, at a gage height of 25.0 feet the increasing discharge was about 

450,000 cfs and the decreasing discharge was about 380,000 cfs. 

Possible conditions that could cause this kind of loop in the relation 

of gage height to discharge are (1) scour during increasing discharge 

and fill during decreasing discharge, (2) lower turbulence constant 

due to higher sediment concentrations during increasing discharge 

than during decreasing discharge, (3) less channel roughness during 

increasing discharge than during decreasing discharge, and (4) higher 

energy gradient during increasing discharge than durng decreasing 

discharge.

Figure 19 shows that, for a given discharge, the mear bed elevation 

is consistently higher when the discharge is increasing' than when it 

is decreasing. Therefore, scour and fill could not cause the loop in 

the relation of gage height to discharge.
38 PLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

MEAN VELOCITY, IN FEETSEA FROMSTATIONS LEVEL, 

PER SECOND 275 TO1800GAGE HEIHT, IN FEET

CO 00 

UlOl-JUl3lOt-0000 O-P-00? 4* N> 01M

/

;M

//

/ Jur

ay 28

May 28 /"

.

^

une 18/"

*MA

ay 28

/'

'7

e 18

Apr

^^

ne 18

Apr

^

July :

/

' /

 ^Af

OX

X

tyx

ril 3

/

t? x7

7

X

y

/

1 3

^

July C

^

\

 

"----.

Q- '

I3 /T

^

X

x

7^

/'

Jul\

>

^

\

^^

^-

/

 -^

X

/ > 'X"

A

\

x^'

_ _

__^_.

/*

+

\__

lx

^ v

/

/

^

30

-^

x*v-

,^

x

-^

 ^. 

^"

-r

' j

0 300 400 500 600 700 800 90

DISCHARGE, IN 1000 CUBIC FEET PER SECOND

FIGURE 19. Relation of gage height, bed elevation, and velocity 

to discharge during major rises in 1951.
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 39

Graphs of mean velocity plotted aga: nst discharge (fig. 19) show 

that, for a given discharge, the mean velocity is generally much 

higher for increasing discharge than it is for decreasing discharge. 

The velocity for decreasing discharge is low enough not only to 

counterbalance the scour of the bed but to cause a higher gage height. 

The lower velocity could be caused by higher turbulence constant, 

by greater channel roughness, by lower energy gradient due to changing discharge, by channel storage between the gage and the measuring 

section, or by return of overbank flow.

Sample computations were made to determine the change in turbulence constant that would be necessary to cause the observed 

change in mean velocity. Keulegan's equation for mean velocity in 

rough channels can be written as

^-=625+ lo 

"l/sje K KS

where

u# is shear velocity and equals *\/gRSe, in which Se is the energy gradient

k is the Von Karman coefficient for turbulent exchange

k, is a linear measure of the bed roughness

Turbulence constants were computed for increasing and decreasing 

discharges of 420,000 cfs in April and May 1951. Because the purpose was to determine the change in turbulence constant alone that 

would cause the observed change in mean velocity, the energy gradient 

Se was assumed to be constant at 0.00011, the bed roughness ks was 

assumed to be constant at 1.6, and the constant 6.25 for clear water 

was assumed to be applicable for sediment-laden flow. For increasing discharge of 420,000 cfs in April 1951, the mean ve'ocity was 6.5 

feet per second and the hydraulic radius was 37 feet. Solution of 

Keulegan's equation gave the result &=0.27. For decreasing discharge of 420,000 cfs in May 1951, the mean velocity was 5.8 feet 

per second and the hydraulic radius was 40 feet. Solution of the 

equation gave the result &=0.35. Vanoni (1946) reported that 

k decreased as suspended-sediment concentration increased when the 

discharge and boundary conditions remained constant. The decrease 

in k was larger when the suspended sediment was of small particle 

size than when the suspended sediment was sand. Einstein and 

Chien (1955) showed a relation of k to a parameter of suspendedsediment concentration and fall velocity. According to this relation, 

the sediment having high fall velocity (large size) would have a greater 

effect on k than the sediment having low fall velocity (small size). 

The suspended-sediment concentration of all particle sizes at an 

increasing discharge of 420,000 cfs in April 1951 was about twice as 

great as the concentration at a decreasing discharge of 420,000 cfs in
40 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

May 1951. The difference in concentration was mostly in the finer 

sizes. According to the relation of Einstein and Chien, the observed 

decrease in concentration would not be enough to increase k from 

0.27 to 0.35. Further information on the change in k is given 

in the section, "Vertical distributions of velocity and rediment 

concentration."

A sample computation was made to determine what changes in 

roughness with constant energy gradient would be necessary to 

cause the observed change in mean velocity. For simplicity, the 

Manning equation was used instead of the Keulegan equation. For 

a constant energy gradient, let nt be the Manning resistance factor 

during increasing discharge of 420,000 cfs in April 1951, and let 

nd be the Manning resistance factor during decreasing discharge of 

420,000 cfs in May 1951. 

Then

1 4.Q 6.5 = 

Hi

and

1 4.Q 5.8= 

Solving for nf,

Changes in resistance factor of 15 percent or more are common at 

St. Louis; therefore, change in roughness alone could account for the 

loop in the relation of gage height to discharge.

Corbett and others (1943) stated that when the discharge is changing 

with respect to time, the relation of gage height to discharge may 

be affected by an increase or a decrease of water-surface slope from 

that corresponding to steady-flow conditions, conversion of discharge 

into or out of channel storage, or return of overbank flow. If any of 

these factors were to account for the loops, the effects would have to 

be large enough to balance the changes in cross-sectional are."1, due to 

the changes in bed elevation.

The effect of changes in slope due to changes in discharge was 

computed from an approximate equation given by Corhstt and 

others (1943, p. 153, eq. 10):

Qc ^ V& 

Qm T/Sc+(l/U)dh/dt 

in which

Qe is the discharge for a given gage height under conditions of constant

discharge

Qm is the measured changing discharge for the same gage height 

Se is the slope of the water surface under constant discharge conditions 

U is the velocity of the flood wave 

dh/dt is the rate of change of stage
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 41

When the formula is written in terms of discharge Qc/Qm, the crosssectional area must be assumed to be constant for a given gage height. 

The cross section at MacArthur Bridge is subject to scour and fill; 

so the formula was rewritten in terms of mean velocity:

in which

u c is mean velocity under conditions of constant discharge

um is measured mean velocity under conditions of changing discharge

To compute the maximum effect of changing discharge, the velocity 

of the flood wave U was computed from the empirical forirula (Corbett 

and others, 1943, p. 155, eq. 14) U=l.3u.

During most discharge measurements, the rate of change in gage 

height was very low. The effect of change in discharge was computed 

for two discharge measurements having relatively high rates of change 

in gage height; for the discharge measurements of June 29 and July 

30, 1951, the rates of change in gage height were +0.036 and 0.127 

foot per hour, respectively. For these computations, the watersurface slope for constant high discharge was assumed to be 0.00010. 

The computed ratios uefum were 0.994 and 1.029 for June 29 and 

July 30, respectively. These results show that the effect of change in 

discharge was too small to account for the loop in the relation of 

gage height to discharge.

Because the discharge measurements were made 1.1 miles downstream from the recording gage, channel storage could have some 

effect on the stage-discharge relationship. The effect was computed 

by using the equation (Corbett and others, 1943, p. 156, eq. 16):

in which

Qm is the measured discharge 

Qg is the discharge at the gage

L is the length between the sections at which Qm and Qg are determined 

C is a constant relating the rate of change of stage dh/dt to its equivalent 

effect in the reach

Because the reach is nearly uniform, the constant C was taken as 

1.00. The computed differences Qm Qg were +100 and 350 cfs 

for June 29 and July 30, respectively. The results indicate that 

channel storage does not affect the stage-discharge relationship 

significantly.
42 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIF

The return of overbank flow could not a'"--Hint for the loops, 

because the loops have been observed for ^lages for which the flow 

was within the banks at the gage and at least 4 miles upstream and 

downstream.

The conclusions from the study of the loops in the relation of gage 

height to discharge are:

1. For a given discharge during an individual rise, the gage height 

is lower for increasing discharge than for decreasing discharge 

even though the bed elevation is higher.

2. Change in turbulence constant due to changing sediment concentration could not in itself account for the loops.

3. Change in roughness could in itself account for the loops.

4. Change in energy gradient due to changing discharge, channel 

storage between the gage and the measuring section, or return 

of overbank flow could not account for the loops.

5. A combination of changes in roughness due to changing configuration of the bed and changes in turbulence constant due to 

changing sediment concentration probably account for the loops.

VERTICAL DISTRIBUTIONS OF VELOCITY AND SEDIMENT 

CONCENTRATION

By B. R. COLBY

The Mississippi River at St. Louis provides ample depths for 

studies of vertical distributions of velocity and sediment concentration. Because the depth effect is not thoroughly understood for 

some aspects of sediment transportation, relationships defined for 

shallow flows should not be arbitrarily assumed to apply to deep 

flows. Therefore, the available information for the Mississippi River 

at St. Louis, even though incomplete and perhaps in part inexact 

(such as for water-surface slopes), may define vertical distributions of 

velocity and sediment concentration sufficiently well to aid in understanding theoretical and empirical relations for the Mississippi River 

and other streams.

VELOCITY

A convenient measure of the vertical distribution of velocity at 

constant shear velocity is the turbulence constant k in equations that 

were given by Keulegan (1938) and used by Einstein (1950) for 

point and mean velocities in about the forms

MV =2.30 ^ log (30.2 xy/k.) 

M 8=2.30 log (12.27
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 43

In these equations, » *

uu and u s are, respectively, the time-averaged velocity at a point and the

mean velocity at a station 

y is the distance above the streambed 

x is a parameter to cover the transition from hydraulically smooth

to hydraulically rough boundaries 

y0 is the depth of flow

The equations were derived by Keulegan for clear-water flow and 

rigid channel boundaries. According to Einstein (1950, p. 8), the 

d65 size of a sediment mixture is the representative size to use as a 

measure of the roughness of a bed of sediment of mixed particle 

sizes. If no bed nor bank roughness exists except that due to the 

stationary grains, Einstein reasoned that d^ could be used in place of 

ks in the equations and, for no significant sediment movement, that 

k should about equal 0.40.

These velocity equations may require some modifications for flows 

over beds of shifting sediment. Vanoni (1946) and Einstein and Chien 

(1954) reported that k became less than 0.40 for sediment-laden 

flows over relatively smooth beds. The apparent reason for the reduction of k is a dampening of turbulence because of the Pediment in the 

flows. Another modification is in the roughness ks . If the streambed 

has ripples, bars, or dunes, ks is far greater than d65 and presumably 

depends both on the heights of the dunes, or other major roughness, 

and on the spacing of the dunes. A large ks can seldom be evaluated 

directly from the bed configuration, partly because the bed configuration is usually not known completely and partly because the spacing 

of the major elements of bed roughness has an uncertain effect on ks.

Einstein (1950, p. 10) adjusted the shear velocity for flows over 

beds of shifting sediment and used an equation for mean velocity in 

about the form

w s=2.30 ~ log (12.27

in which u^ ' is the shear velocity with respect to the grr.in (the shear 

velocity that will give the correct mean velocity) and 0.40 is substituted for k. The ratio u^ '/u^. is equivalent to the ratio of the actual 

mean velocity to the mean velocity for a clear-water flow over a 

stationary bed whose only roughness is due to the unshifting grains 

and can be represented, at least roughly, by d65 . Ratios of u^'/u^. as 

low as those for the Mississippi River at St. Louis (table 3) indicate, 

as did the other measure of roughness n, that the bed of the river 

generally has the major roughness that might be carded by bars, 

ripples, or dunes.
44 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

TABLE 3. Ratios of shear velocity with respect to the grain to shea" velocity

Date u*'/u* Discharge (cfs)

Apr. 18, 1951------------------------------ 0.64 510,000

July 16 -------------------------------- .53 704,000

June?, 1954.---------------.-----._..----- .55 283,000

Mar. 30, 1955 --------------------------- .45 163,000

Dec. 27__-----------__-_.__-.____ .36 59,800

Feb. 21, 1956----------------------------- .34 56,100

Apr. 24 -------------------------------- .42 172,000

May 9-------------_--------_----_------- .42 149,000

July 9 _--------------------------------- .43 155,000

May 13, 1959----------------------------- .47 241,000

Even though ks cannot be evaluated for the flows over the rough 

streambed at St. Louis, the vertical distribution should still depend 

on the ratio of shear velocity to k if the equations of the Keulegan 

type apply for both point and mean velocities. That ip if these 

equations apply, the difference in point velocities at a distance IQy 

above the streambed and at a distance y above the bed equals 2.30 

u^/k, no matter what ks may be. For major roughness spaced as 

widely as bars or dunes may be, the vertical distribution cf velocity 

may be, however, a function of the location of a vertical with respect 

to a dune or bar as well as of u^/k. In other words, as P^yre and 

Albertson (1959, p. 57-62) found for widely spaced baffles and clearwater flow, the k determined from the vertical distribution cf velocity 

may not be the same as the k for the mean-velocity equation.

Some variation of k with change of the observation station can be 

shown by information at crest and trough of dunes in tfre Middle 

Loup River at Dunning, Nebr. Two k's from vertical distributions 

of velocity at the crest of a dune were 0.32 and 0.62 as compared with 

k's of 0.11 and 0.19 for stations in a trough downstream from the 

crest.

Basic data are shown in table 4 for current-meter observations of 

the vertical distributions of velocity at St. Louis. The k's in table 5 

were computed from the data in table 4 and from the velocities of 

routine discharge measurements.
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 45

TABLE 4. Vertical distributions of velocity 

[Velocities are averages for about 40-60 sec. unless otherwise noted]

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps)

MAR. 2, 1948 

Station 400; total depth, 38.2 ft

1.5 

2.3 

3.8 

5.7 

7.6 

11.5 

15.3 

19.1 

22.9 

26.7 

30.6 

344 

37.2

3.08 

3.45 

3.67 

419 

4.19 

4.99 

5.10 

5.23 

5.77 

6.09 

6.20 

6.45 

6.45

Station 625; total depth, 41.0 ft

1.5 

2.5 

41 

6.2 

8.2 

12.3 

16.4 

20.5 

24.6 

28.7 

32.8 

36.9 

40.0

3.01 

3.22 

3.15 

3.83 

3.91 

4.19 

5.10 

5.10 

5.10 

5.58 

5.87 

5.98 

5.87

Station 850; total depth, 41.2 ft

1.5 

2.5 

41 

6.2 

8.2 

12.4 

16.5 

20.6 

24.7 

28.8 

33.0 

37.1 

40.2

3.45 

3.26 

409 

4.19 

4.88 

5.31 

5.67 

5.98 

5.98 

6.45 

6.57 

6.85 

6.71

Station 1,200; total depth, 46.4 ft

1.5 

2.8 

46 

7.0 

9.3 

13.9 

18.6 

23.2 

27.8 

32.5 

37.2 

41.8 

45.4

2.51 

3.15 

3.15 

3.67 

439 

499 

5.10 

5.49 

5.98 

5.87 

6.57 

6.85 

6.85

Time

Measuring point

Distanc» 

from bed (ft)

Velocity 

(fps)

MAY 21, 194F 

Station 400; total depth, 31.6 ft

12:23 p.m ___ . ......

1.6 

2.6 

3.6 

46 

5.6 

6.6 

7.6 

9.6 

11.6 

13.6 

15.6 

17.6 

19.6 

21.6 

23.6 

25.6 

27.6 

29.6

2.44 

2.29 

2.61 

2.80 

2.80 

3.06 

3.21 

3.06 

3.21 

3.43 

3.43 

3.50 

3.98 

3.72 

3.80 

416 

4.16 

4.07

Station 625; total depf h, 33.0 ft

12:46 p.m... . 

1.5 

2.0 

3.0 

4.0 

5.0 

7.0 

9.0 

11.0 

13.0 

15.0 

17.0 

19.0 

21.0 

23.0 

25.0 

27.0 

29.0 

31.0

2.50 

2.55 

2.74 

3.06 

2.50 

2.74 

2.34 

2.86 

3.65 

3.65 

3.57 

4.07 

416 

4.16 

426 

4.75 

455 

4.55

Station 850; total dep'h, 35.7 ft

12:55 p.m...-.--- - 1.5 

2.7 

3.7 

4.7 

5.7 

7.7 

9.7 

11.7 

13.7 

15.7 

17.7 

19.7 

21.7 

23.7 

25.7 

27.7 

29.7 

31.7 

33.7

2.39 

2.92 

3.06 

3.21 

3.13 

3.37 

3.80 

3.65 

4.16 

3.72 

3.84 

4.07 

4.16 

4.37 

4.16 

446 

437 

4.55 

4.65
46 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS 

TABLE 4. Vertical distributions of velocity Continued

Time

Measuring point

Distance Velocity 

from bed (ft) (fps)

MAY 21, 1948 Continued 

Station 1,050; total depth, 34.3 ft

1:23 p.m .. ...... . .

1:42 p.m... ..........

0.5 

1.3 

2.3 

3.3 

4.3 

6.3 

8.3 

10.3 

12.3 

14.3 

16.3 

18.3 

20.3 

22.3 

24.3 

26.3 

28.3 

30.3 

32.3

2.05 

2.92 

2.63 

3.21 

3.50 

3.37 

3.65 

3.89 

4.37 

4.26 

4.26 

4.07 

4.16 

4.37 

4.37 

4.37 

4.55 

4.46 

4.55

Station 1,200; total depth, 38.3 ft

2:07 p.m_. ...........

1.5 

2.3 

3.3 

4.3 

5.3 

6.3 

8.3 

10.3 

12.3 

14.3 

16.3 

18.3 

20.3 

22.3 

24.3 

26.3 

28.3 

30.3 

32.3 

34.3 

36.3

2.55 

2.61 

2.58 

2.92 

3.50 

3.21 

3.72 

3.98 

4.20 

4.07 

4.26 

4.07 

4.16 

4.07 

3.98 

4.65 

4.55 

4.16 

4.85 

4.75 

4.85

Station 1,400; total depth, 42.0 ft

2:15 p.m.... .........

2:35 p.m ___ . _ . ...

1.5 

2.0 

3.0 

4.0 

5.0 

6.0 

8.0 

10.0 

12.0 

14.0 

16.0 

18.0 

20.0 

22.0 

24.0 

26.0 

28.0 

30.0 

32.0 

34.0 

36.0 

38.0 

40.0

2.55 

3.29 

2.92 

2.86 

2.99 

3.06 

2.86 

2.92 

3.21 

3.21 

4.16 

4.85 

4.96 

4.96 

4.55 

4.37 

4.96 

5.32 

5.32 

5.45 

5.55 

5.45 

5.45

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps)

MAY 21, 1948 Continued 

Station 1,500; total depth, 3«.2 ft

1.5 

2.2 

3.2 

4.2 

5.2 

6.2 

8.2 

10.2 

12.2 

14.2 

16.2 

18.2 

20.2 

22.2 

24.2 

26.2 

28.2 

30.2 

32.2 

34.2 

36.2

2.99 

3.65 

4.16 

3.31 

3.80 

4.07 

4.37 

4.37 

5.08 

4.75 

4.85 

4.65 

4.85 

4.96 

5.32 

5.08 

5.20 

5.20 

5.45 

5.32 

5.55

Station 1,650; total depth, 40.5 ft

1.5 

2.5 

3.5 

4.5 

6.5 

8.5 

10.5 

12.5 

14.5 

16.5 

18.5 

20.5 

22.5 

24.5 

26.5 

28.5 

30.5 

32.5 

34.5 

36.5 

38.5

3.72 

3.80 

3.57 

3.98 

4.37 

4.37 

4.46 

4.20 

4.37 

4.46 

4.28 

4.37 

4.55 

4.96 

4.75 

4.75 

4.55 

5.08 

5.45 

5.08 

4.96

MAR. 17, 1952 

Station 500; total depth, 40.1 ft

Q.on o m 1.5 

4.0 

8.0 

11.9 

15.7 

19.5 

23.3 

27.0 

30.9 

34.8

4.86 

5.71 

6.62 

7.19 

7.35 

7.35 

7.69 

8.07 

8.07 

8.27

Station 900; total depth, 33.8 ft

1.5 

3.5 

6.6 

9.8 

13.0 

16.1

6.37 

6.90 

7.35

7.88 

7.88 

8.32
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 47

TABLE 4. Vertical distributions of velocity Continued

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps)

MARCH 17, 1952 Continued 

Station 900; total depth, 32.8 Continued

11:05 a.m.. ..........

19.4 

22.1 

25.6 

28.6

8.65 

8.82 

9.19 

9.19

Station 1,275; total depth, 48.1 ft

1:30 p.m. _____ .... 1.5 

3.4 

8.3 

13.3 

18.3 

23.1 

28.0 

32.8 

37.7 

42.3

4.31

5.14 

5.52 

6.37 

6.97 

7.S5 

7.60 

7.78 

7.88 

8.17

Station 1,600; total depth, 44.1 ft

2:00 p.m ___ .--_--.

2:15 p.m _ ____ ..

1.5 

4.7 

9.1 

13.4 

17.7 

21.8 

26.1 

30.4 

34.5 

38.7

5.52 

6.13 

6.75 

7.19 

7.44 

7.69 

8.07 

7.78 

7.78 

7.88

APR. 30, 1952 

Station 750; total depth, 52.1 ft

5.1 

10.3 

15.6 

20.8 

26.0 

31.2 

36.4 

41.7 

46.9

5.42 

6.55 

7.48 

7.80 

8.34 

8.70 

8.73 

9.12 

9.35

JUNE 7, 1954 

Station 475; total depth, 37.5 ft

11:42 a.m___. ......... 1.5 

3.7 

7.5 

15.0 

22.5 

33.7

3.16 

3.76 

3.93 

4.41 

4.70 

5.51

Station SOO; total depth, 34.3 ft

10:46 a.m.. _.____._._ 1.5 

3.4 

6.8 

13.7 

20.5 

30.9

4.41 

5.13 

4.90 

6.01 

6.24 

6.36

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps;

JUNE 7, 1954 Continued 

Station 1,300; total depth, 44.6 ft

10:11 a.m._. ..........

10:15 a.m.. _ . _ ...

1.5 

4.5 

8.9 

17.8 

26.7 

40.1

3.40 

4.31 

4.41 

6.01 

6.01 

6.36

Station 1,600; total deith, 42.6 ft

1.5 

4.3

8.4 

17.0 

25.5 

3S.3

3.68 

4.01 

4.60 

4.70 

5.13 

5.70

AUG. 10, 1954 

Station 1,000; total de-»th, 23.1 ft

-_--. .--. .

9:40a.m.2_ _ __ .....

9:45 a.m..-.. - -

1.5 

3.1 

5.1 

7.1 

9.1 

11.1 

13.1 

15.1 

17.1 

19.1 

21.1 

1.5 

3.1 

5.1 

7.1 

9.1 

11.1 

13.1 

15.1 

17.1 

19.1 

21.1 

1.5 

3.1 

5.1 

7.1 

9.1 

11.1 

13.1 

15.1 

17.1 

19.1 

21.1 

1.5 

3.1 

5.1 

7.1 

9.1 

11.1 

13.1 

15.1 

17.1 

19.1 

21.1 

1.5 

3.1 

5.1 

7.1

12.72 

12.45 

12.99 

13.40 

13.05 

13.71 

13.45 

13.48 

14.04 

13.74 

14.12 

12.48 

12.96 

12.99 

13.18 

13.50 

13.65 

13.53 

13.07 

13.90 

13.77 

13.93 

12.33 

12.46 

13.01 

13.18 

13.42 

13.25 

13.62 

13.50 

13.90 

13.97 

14,04 

12.81 

12.15 

13.09 

!3.32 

13.65 

13.42 

13.59 

13.48 

13.65 

!3.81 

13.90 

12.91 

13.28 

13.05 

13.01

See footnotes at end of table, p. 54.
48 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS 

TABLE 4. Vertical distributions of velocity Continued

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps)

AUG. 10, 1954 Continued 

Station 1,000; total depth, 23.1 ft Continued

12:39 p.m.2. _ .. ..

12:43 p.m.2._ .... ...

12:47 p.m.*..... .......

12:50 p.m.. ..-. . 

9.1 

11.1 

13.1 

15.1 

17.1 

19.1 

21.1 

1.5 

3.1 

5.1 

7.1 

9.1 

11.1 

13.1 

15.1 

17.1 

19.1 

21.1 

1.5 

3.1 

5.1 

7.1 

9.1 

11.1 

13.1 

15.1 

17.1 

19.1 

21.1 

1.5 

3.1 

5.1 

7.1 

9.1 

11.1 

13.1 

15.1 

17.1 

19.1 

21.1

13.50 

13.30 

13.42 

13.87 

13.74 

14.12 

14.12 

12.61 

12.65 

13.45 

12.95 

13.32 

13.45 

13.18 

13.8! 

13.81 

13.71 

14.08 

12.68 

13.01 

13.07 

13.05 

13.40 

13.53 

13.77 

13.68 

13.62 

13.77 

13.87 

12.50 

13.05 

13.12 

13.20 

!3.39 

13.05 

13.71 

13.59 

13.81 

14.04 

13.90

AUG. 27, 1954 

Station 1,000; total depth, 24.0 ft

8:40 a.m.. . ..........

--- - 

9:15 a.m.z.-. ......

9:50 a.m. ______ .

11:30 a.m...... .......

11:45 a.m.2... ......

12:00 m.. .............

1.5 

4.0 

6.0 

10.0 

14.0 

18.0 

22.0 

1.5 

4.0 

6.0 

10.0 

14.0 

18.0 

22.0 

1.5 

4.0 

6.0 

10.0 

14.0 

18.0 

22.0 

1.5 

4.0 

6.0 

10.0 

14.0 

18.0 

22.0

32.43 

32.78 

33.25 

33.45 

33.41 

33.82 

33.78 

32.54 

32.89 

32.98 

33.23 

33.58 

33.54 

33.82 

2.52 

3.38 

3.50 

3.83 

3.80 

3.82 

4.30 

3.07 

3.30 

3.33 

3.57 

3.96 

3.82 

4.32

Time

Measumg point

Distance 

from bed (ft)

Velocity 

(fps)

MAR. 31, 1955 

Station 500; total depth, 24.7 ft

1.5 

3.5 

4.5 

6.5 

8.5 

10.6 

13.6 

16.6 

19.6 

22.7 

1.5 

3.5 

4.5 

6.5 

8.5 

10.6 

13.6 

16.6 

19.6 

22.7

2.90 

3.29 

3.42 

3.70 

3.95 

3.95 

3.74 

4.08 

4.33 

4.44 

2.78 

3.26 

3.49 

3.63 

3.86 

3.63 

4.18 

4.18 

4.33 

4.50

Station 925; total depth, 2J.1 ft

12:40 p.m... _ 1.5 

5.5 

8.5 

11.4 

14.4 

18.3 

21.1 

1.5 

5.5 

8.5 

11.4 

14.4 

18.3 

21.1

3.46 

3.86 

3.95 

4.33 

4.28 

462 

4.58 

3.06 

3.38 

3.78 

3.95 

4.13 

4.23 

4.62

DEC. 27, 1955 

Station 550; total depth, 11- 8 ft

12:50 p.m.. ...... ..

12:55 p.m... ... 

1:45 p.m . .... 

1:50 p.m... .... ....

2.4 

4.7 

7.1 

10.6 

2.4 

4.7 

7.1 

10.6

2.35 

2.40 

2.45 

2.76 

2.35 

2.45 

2.51 

2.69

Station 925; total depth, 15 2 ft

2:00 p.m ____ -._ 

2:05~p.m ____ .

2:50 p.m. . ...

2:55 p.m ...

1.5 

3.0 

6.1 

9.1 

13.7 

1.5 

3.0 

6.1 

9.1 

13.7

1.51 

2.16 

2.25 

2.63 

2.76 

1.55 

2.21 

2.45 

2.57 

2.76

See footnotes at end of table, p. 54.
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 

TABLE 4. Vertical distributions of velocity Continued

49

Time

Measuring point

Distance Velocity 

from bed (ft) (fps)

DEC. 28, 1955 

Station 1,275; total depth, 23.7 ft

10:00 a.m. ............

10:45 a.m.... ._ .....

10:50 a.m. ___ ...

2.4 

4.7 

9.5 

14.2 

21.3 

2.4 

4.7 

9.5 

14.2 

21.3

1.36 

1.39 

2.30 

2.63 

3.01 

1.42 

1.58 

2.01 

2.94 

2.94

Station 1,525; total depth, 19.5 ft

11:00 a.m.. ____ ...

11:05 a.m. __ _ .....

1.9 

3.9 

7.8 

11.7 

18.3

1.88 

2.25 

2.69 

2.82 

3.01

FEB. 21, 1956 

Station 550; total depth, 12.0 ft

11:30 a.m.. ........... 1.5 

2.4 

4.8 

7.2 

10.8 

1.5 

2.4 

4.8 

7.2 

10.8

1.53 

2.24 

2.03 

2.33 

2.59 

1.68 

1.91 

2.24 

2.43 

2.54

Station 925; total depth, 14.4 ft

1:10 p.m _ __ . ....

2:25 p.m ____ . ...

1.5 

2.9 

5.8 

8.6 

13.0 

1.5 

2.9 

5.8 

8.6 

13.0

1.79 

1.99 

2.08 

2.33 

2.85 

1.76 

1.95 

2.48 

2.54 

2.59

Station 1,275; total depth, 20.5 ft

2:40 p.m _ . .........

3:35 p.m.... ..........

2.1 

4.1

8.2 

12.3 

18.5 

2.1 

4.1 

8.2 

12.3 

18.5

1.79 

1.76 

2.38 

2.85 

2.97 

1.79 

1.87 

2.48 

2.85 

3.11

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps)

FEB. 21, 195ft Continued 

Station 1,525; total depth, 18.5 ft

1.9 

3.7 

7.4 

11.1

16.7 

1.9 

3.7 

7.4 

11.1 

16.7

1.87 

2.24 

2.59 

2.66 

2.72 

1.95 

2.28 

2.33 

2.54 

2.85

APR. 24, 1956 

Station 475; total depth, 29.0 ft

12:35 p.mA. .......... 2.9 

5.8 

11.6 

17.4 

26.1

3.04 

3.34 

3.56 

4.04 

4.13

Station 900; total depth, 26.8 ft

2:16p.m.».. - 

2.7 

5.4 

10.7 

16.1 

24.1 

2.7 

5.4 

10.7 

16.1 

24.1

3.04 

3.26 

4.23 

4.33 

4.72 

3.18 

3.26 

3.87 

3.95 

4.62

Station 1,300; total depth, 43.0 ft

4.3

8.6 

17.2 

25.8 

39.0 

4.3 

8.6 

17.2 

25.8 

39.0

2.48 

2.09 

3.78 

4.33 

4.44 

1.76 

2.97 

3.26 

4.33 

4.53

Station 1,575; total depth, 32.0 ft

4:15 p.m.2__ __.__.- 

3.2 

6.4 

12.8 

19.2 

28.8 

3.2 

6.4 

12.8 

19.2 

28.8

2.91 

3.71 

3.87 

4.23 

4.72 

3.26 

3.63 

4.35 

4.35 

5.04

See footnotes at end of table, p. 54.
50 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS 

TABLE 4. Vertical distributions of velocity Continued

Time

Measuriag point

Distance 

from bed (ft)

Velocity 

(fps;

MAY 9, 1956 

Station 475; total depth, 27.6 ft

10:45 a.m.2 __ ... __

11:25 a.rnA. _ ......

2.8 

5.5 

10.0 

16.6 

24.8 

2.8 

5.5 

10.0 

16.6 

24.8

2.65 

3.03 

3.18 

3.86 

4.23 

2.78 

3.10 

3.34 

3.95 

4.13

Station 900; total depth, 25.9 ft

12:25 p.m.'...... 

2.1 

5.2 

10.4 

15.5 

23.3 

2.1 

5.2 

10.4 

15.5 

23.3

2.72 

3.18 

3.95 

4.13 

4.53 

2.23 

2.84 

3.49 

4.04 

4.44

Station 1,300; total depth, 41.5 ft

1:00 p.m.'.. ....... .

l:35p.m.s _______

4.1 

6.3 

16.6 

24.9 

37.3 

4.1 

6.3 

16.6 

24.9 

37.3

2.03 

2.59 

3.78 

3.95 

4.62 

1.98 

2.18 

2.65 

3.86 

4.44

Station 1,577; total depth, 31.5 ft

1:45 p.mA..... .__....

2:25p.m.2 _ . _____

3.1 

6.3 

12.6 

18.7 

28.3 

3.1 

6.3 

12.6 

18.7 

28.3

3.34 

3.95 

4.13 

4.33 

4.44 

3.18 

4.04 

4.23 

4.33 

4.72

JULY 9, 1956 

Station 500; total depth, 25.8 ft

11:30 a.m... _ ......

12:00 m.___. ........._

2.6 

5.2 

10.3 

15.5 

23.2 

2.6 

5.2 

10.3 

15.5 

23.2

2.85 

3.34 

3.42 

3.71 

4.13 

2.79 

2.91 

3.42 

3.63 

4.23

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps)

JULY 9, 1956 Continued 

Station 925; total depth, 25.7 ft

12:05p.m __ . _ . __

12:35 p.m. .. ____

2.6 

5.1 

10.3 

15.4 

23.1 

2.6 

5.1 

10.3 

15.4 

23.1

2.79 

3.63 

3.95 

3.95 

4.44 

3.04 

2.97 

3.95 

4.23 

4.33

Station 1,275; total depth, 38.8 ft

12:40 p.m..... ........ 3.9 

7.8 

15.5 

23.3 

34.9 

3.9 

7.8 

15.5 

23.3 

34.9

1.99 

2.20 

3.11 

4.13 

4.82 

2.48 

2.04 

3.26 

4.23 

4.72

Station 1,575; total depth, 27.0 ft

1:45 p.m. 

3.0 

6.0 

12.0 

18.0 

27.0 

3.0 

6.0 

12.0 

18.0 

27.0

2.43 

3.49 

3.56 

4.23 

4.62 

2.66 

3.26 

3.71 

4.23 

4.62

NOV. 5, 1956 

Station 600; total depth, 10.5 ft

1.5 

2.1 

4.2 

6.3 

9.5 

1.5 

2.1 

4.2 

6.3 

9.5

1.80 

1.91 

2.38 

2.33 

2.33 

1.69 

1.95 

2.24 

2.28 

2.43

Station 1,000; total depth, 15.5 ft

1.5 

3.1 

6.2 

9.3 

13.9 

1.5 

3.1 

6.2 

9.2 

13.9

1.69 

1.80 

2.43 

2.54 

2.48 

1.69 

1.91 

2.19 

2.66 

2.43

See footnotes at end of table, p. 54.
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 51

TABLE 4. Vertical distributions of velocity Continued

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps)

NOV. 5, 1956 Continued 

Station 1,375; total depth, 39.3 ft

1.5 

3.9 

7.9 

15.7 

23.6 

35.4 

1.5 

3.9 

7.9 

15.7 

23.6 

35.4

1.61 

1.47 

1.69 

2.43 

2.72 

3.34 

1.21 

1.15 

1.65 

2.24 

2.91 

3.26

Station 1,600; total depth, 18.0 ft

1.5 

1.8 

3.6 

7.2 

10.8 

16.2 

1.5 

1.8 

3.6 

7.2 

10.8 

16.2

1.54 

2.24 

2.24 

2.43 

2.97 

2.91 

1.67 

1.87 

2.33 

2.60 

2.97 

2.97

APR. 17, 1958 

Station 500; total depth, 25.1 ft

11:45 a.m. ___________

11:51 a.m... _ _______

12:10 p.m .__. _ . _

12:16 p.m__-_________.

1.5 

2.6 

5.0 

10.0 

15.1 

22.6 

1.5 

2.6 

5.0 

10.0 

15.1 

22.6

2.26 

2.36 

3.08 

4.00 

3.91 

4.39 

1.71 

2.22 

3.31 

3.52 

3.82 

409

Station 950; total depth, 28.0 ft

11:13 a.m....... ___ __

11:18 a.m-_.______- ...

11:32 a.m _ _____ ....

11:40 a.m ___ _ .._..._

1.5 

2.8 

5.6 

11.2 

16.8 

25.2 

1.5 

2.8 

5.6 

11.2 

16.8 

25.2

2.31 

2.82 

3.15 

3.52 

3.74 

4.18 

2.11 

3.01 

2.94 

3.45 

4.28 

4.57

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps)

APR. 17, 1958 Continued 

Station 1,250; total de-rth, 32.0 ft

10:40 a.m... _ ____.__. 

11:00 a.m... ..........

11:07 a.m..___.._____-

1.5 

2.2 

6.4 

12.8 

19.2 

28.8 

1.5 

2.2 

6.4 

12.8 

19.2 

28.8

3.08 

3.21 

3.23 

4.48 

4.57 

4.87 

3.08 

3.31 

3.59 

457 

467 

5.10

Station 1,550; total depth, 27.3 ft

10:05 a.m ____ ... 

10:25 a.m __ . __ _ _

10:20 a.m __ ... . ._

1.5 

2.7 

5.5 

10.9 

16.4 

24.6 

1.5 

2.7 

5.5 

10.9 

16.4 

24.6

3.45 

4.08 

400 

418 

487 

5.22 

3.59 

3.39 

4.28 

4.39 

4.98 

5.10

MAY 13, 19F9 

Station 375; total depth, 28.2 ft

9:20a.m.> _ . __ _ 2.8 

5.6 

11.3 

16.9 

22.6 

25.4

2.69 

3.59 

4.57 

4.41 

438 

429

Station 575; total depith, 30.0 ft

9*40 a m ^

9'30 a m ^

3.0 

12.0 

18.0 

24.0 

27.0

3.30

4.47 

466 

447 

5.09

Station 774; total detth, 32.3 ft

9:55a.m.> ____ __ 3.2 

12.9 

19.4 

25.8 

29.1

3.32 

4.29 

5.09 

5.21 

5.21

Station 924; total de-"th, 32.8 ft

10:05 a.m.2____________ 3.3 

13.1 

19.7 

26.2 

29.5

466 

5.09 

4.98 

5.47 

5.34

See footnotes at end of table, p. 54.
52 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS 

TABLE 4. Vertical distributions of velocity Continued

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps)

MAY 13, 1959 Continued 

Station 1,074; total depth, 35.0 ft

10:20 a.m.*... ......

10:10 a.m.2 . ____

3.5 

14.0 

21.0 

28.0 

31.5

3.99 

5.34 

5.66 

5.66 

5.96

Station 1,200; total depth, 35.5 ft

10:40 a.m.*._..____ ....

10:30 a.m.*..- .....

3.6 

14.2 

21.3 

28.4 

31.9

3.52 

5.34 

5.34 

5.76 

6.07

Station 1,300; total depth, 44.3 ft

10:50 a.m.*.. ......

4.5 

17.7 

26.6 

35.4 

39.9

3.59 

5.34 

5.66 

5.86 

6.19

Station 1,425; total depth, 43.2 ft

ll:20a.m.«_.__-_.._ 

11:10 a.m.2-. ..........

4.3 

17.3 

25.9 

34.6 

38.9

3.52 

5.09 

5.76 

5.86 

6.19

Station 1,551; total depth, 36.2 ft

11 :35 a.mA. .......... 3.6 

14.5 

21.7 

29.0 

32.6

3.82 

5.09 

5.66 

6.43 

6.43

Station 1,675; total depth, 39.4 ft

11:60 a.m.*..... .......

11'40 a Tn 2

3.9 

15.8 

23.6 

31.5 

35.5

3.26 

4.18 

4.76 

4.98 

4.57

JULY 10, 1959 

Station 710; total depth, 32.7 ft

9:20 a.m.. ______

Q-QQ o IYI

1.5 

3.3 

6.5 

9.8 

13.1 

16.3 

19.6 

22.9 

26.2 

29.4

1.82 

1.63 

1.93 

2.89 

2.70 

3.23 

3.40 

3.76 

3.61 

3.84

Time

Measurirg point

Distance 

from bed (ft)

Velocity 

(fps)

JULY 10, 1959 Continued 

Station 750; total depth, 26.3 ft

9:05 a.m. .............

9:15 a.m. .............

1.5 

2.6 

5.3 

7.9 

10.5 

13.1 

15.8 

18.4 

21.0 

23.7

2.41 

2.64 

3.02 

3.34 

3.47 

3.47 

3.76 

4.30 

4.10 

3.92

Station 800; total depth, 25.3 ft

8:40 a.m...--.--- -..- 1.5 

2.5 

5.1 

7.6 

10.1 

12.7 

15.2 

17.7 

20.2 

22.8

2.70 

2.64 

3.16 

3.16 

2.95 

3.53 

4.10 

3.84 

4.20 

3.84

Station 1,000; total depth, 29 5 ft

8:20 a.m.. ___ __ .

8:30 a.m ___ ...

1.5 

2.9 

5.9 

8.9 

11.8 

14.7 

17.7 

20.7 

23.6 

26.5

2.77 

2.64 

3.09 

3.92 

3.47 

4.10 

4.20 

4.01 

4.20 

4.41

APR. 14, 1960 

Station 351; total depth, 42.7 ft

9:00 a.m.2 

9:08a.m.*_ 

4.4 

8.5 

17.1 

25.7 

34.2 

38.4

6.47 

6.35 

7.02 

7.50 

7.85 

7.85

Station 525; total depth, 46.6 ft

9:18 a.m.*. 4.7 

9.3 

18.7 

28.0 

37.3 

41.9

4.69 

5.51 

7.50 

7.50 

7.50 

7.67

See footnotes at end of table, p. 54.
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 53

TABLE 4. Vertical distributions of velocity Continued

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps;

APR. 14, 1960 Continued 

Station 750; total depth, 48.4 ft

9:45a.m.2_.._ ....... 4.8 

9.7 

19.4 

29.0 

38.7 

43.6

5.37 

6.60 

7.17 

7.50 

8.24 

8.04

Station 924; total depth, 51.2 ft

10:05 a.m." _____ .

10:10 a.m.«._ . 

5.1 

10.2 

20.5 

30.7 

41.0 

46.1

5.37 

5.37 

7.17

7.85 

8.24 

8.04

Station 1,074; total depth, 50.0 ft

10:25 a.m."..... .......

10:30 a.mA ........

5.0 

10.0 

20.0 

30.0 

40.0 

45.0

6.11 

6.23 

7.17 

7.85 

7.85 

8.97

Station 1,200; total depth, 54.7 ft

10:40 a.m.'..... ....

5.4 

10.9 

22.1 

32.8 

43.8 

49.2

6.11 

6.11 

7.85 

8.04 

9.35 

9.55

Station 1,320; total depth, 58.2 ft

10:50 a.m.2___.____ ....

10:55 a.rnA.. .........

5.8 

11.6 

23.3 

34.9 

46.6 

52.4

7.17 

8.24 

8.79 

9.55 

9.98 

9.98

Station 1,451; total depth, 61.6 ft

11:15 a.m.*.... -.

11:20 a.m.2____ _.

6.1 

12.3 

24.7 

37.0 

49.3 

55.4

7.33 

8.62 

8.79 

9.55 

10.71 

10.46

Station 1,551; total depth, 61.1 ft

11:30 a.m.» ...

11:36 a.m.'..... .......

6.1 

12.2 

24.4 

36.7 

48.9 

55.0

8.14 

8.45 

9.55 

10.71 

9.35 

9.76

Time

Measuring point

Distarce 

from bee (ft)

Velocity 

(fps)

APR. 14, 1960 Corfinued 

Station 1,701; total de-»th, 52.6 ft

11:55 a.m.'.. .....

12:00 m. __.. ..

5.3 

10.5 

21.1 

31.6 

42.1 

47.3

6.11 

6.35 

6.60 

6.73 

7.50 

7.02

JUNE 21, 1»V) 

Station 375; total depth, 23.3 ft

9:25 a.m.a... ....... ...

9:15 a.m.8 .... 

2.3 

4.7 

9.3 

14.0 

18.6 

21.0

3.07 

3.07 

3.21 

3.99 

4.18 

4.76

Station 575; total dei «h, 22.7 ft

9:40a.mA_ .....

2.3 

4.5 

9.1 

13.6

18.2 

20.4

3.38 

3.99 

3.99 

4.47 

4.87 

4.76

Station 750; total depth, 31.0 ft

10:05 a.m.2 _ . ........

3.1 

6.2 

12.4 

18.6 

24.8 

27.9

3.58 

3.42 

3.74 

4.28 

4.57 

4.38

Station 950; total de^th, 31.7 ft

10:30 a.m.2 _ . . _

10:20 a.m."..... ....

3.2 

6.3 

12.7 

19.0 

25.4 

28.5

3.66

4.08 

3.99 

4.98 

4.87 

5.22

Station 1,100; total d^pth, 36.8 ft

10:35 a.m.2__ ..........

3.7 

7.4 

14.7 

22.1 

29.4 

33.1

2.87 

3.82 

4.18 

4.66 

4.87 

5.22

See footnotes at end of table, p. 54.
54 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

TABLE 4. Vertical distributions of velocity Continued

Time

Measuring point

Distance 

from bed (ft)

Velocity 

(fps)

JUNE 21, 1960 Continued 

Station 1,200; total depth, 38.0 ft

10:55 a.m.*... . ,-__ 3.8 

7.6 

15.2 

22.8 

30.4 

34.2

3.07 

4.08 

5.09 

4.57 

5.48 

5.22

Station 1,320; total depth, 51.4 ft

11:10 a.m.2... ......... 5.2 

10.3 

20.6 

30.8 

41.1 

46.3

2.50 

4.38 

4.57 

5.48 

5.48 

5.48

Time.

Measuring point

Distance 

from bed (ft)

Velocity 

(fps)

JUNE 21, 1960 Continued 

Station 1,601; total depth, 41.5 ft

11:30 a.m.*.. _ . 

11:20 a.mA.... ....

4.0 

8.1 

16.2 

24.3 

32.4 

36.5

3.82 

3.90 

4.57 

4.66 

5.09 

5.34

Station 1,701; total depth, 44.0 ft

11:45 a.m.»._ ... ... .. 4.4 

8.8 

17.6 

26.4 

35.2 

39.6

2.62 

2.56 

3.38 

3.58 

3.74 

3.58

1 Average for about 11-15 seconds. 2 Estimated. »Average for about 115-130 seconds.

Velocity distributions at each of four or more stations in the cross 

section defined the average k's that are shown in columns 4 and 5 of 

table 5. The k's in column 4 were obtained by averaging the computed k's for the individual stations; the k's in column 5 were computed 

from the averages of the differences hi velocity for a 10 to 1 change in 

distance above the streambed for the individual stations. T e difference between the two types of average k's is a rough measure of the 

uniformity of the k's for the individual stations and is small unless, 

as on May 13, 1959, k for one of the stations is large. The averages 

of the k's in columns 5 and 6 are 0.35 and 0.33, respectively.

As relatively few vertical distributions of velocity were defined by 

current-meter observations, k was also computed from the velocities 

of routine discharge measurements. Differences between the velocities 

at 0.2 and at 0.8 of the depth for all stations except those ne.^r banks 

and piers were added, and the total was divided by the number 

of stations to obtain the average velocity difference per station. 

The Keulegan type of equation for point velocity indicates that the 

velocity difference equals 2.30 (u#/fc) log 4 or 1.39 u*/k for 0. relative 

change of 4 to 1 (0.8 to 0.2) in the distance above the streambed. 

Hence, k for the cross section was computed by dividing 1.39 u# by 

the average velocity difference per station.
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 55

TABLE 5. Turbulence constants based on vertical distributions of velocity

Date 

(1)

1948 

Mar. 2 ...... . ... ...

May 21.. 

1950 

May 8... .... ................

May 22 _ _

.Time 5

1951 

Apr. 17 __ . _____ __

Apr. 19... ...... . __ ..

July 16. 

July 22 .

JulySO. 

Sept. 17. __ _ _________

195S 

Mar. 17............... .......

Apr. 30 .

1954 

June 7 -__

Aug. 9 

Aug. 27 _ _

1955 

Mar. 30, 31 __

Dec. 27, 28... . .

1956 

Feb. 21 

Apr. 24 

July 9 -.

1958 

Apr. 17 

1959 

May 13. ...

July 10. . . 

1960 

Apr. 14... --. .

.Tune 31

Daily mean 

discharge 

(1,000 cfs)

(2)

327 

214

330 

347 

326

527 

4% 

704 

765 

472 

387

411 

682

281 

115 

111 

118

163

57.4

56.1 

169 

159 

154

164

240 

150

2581

2211

Watersurface slope

(3)

0.0000551 

. 0000589

. 0000997 

. 0000924 

. 0000909

.000106 

.000107 

. 000126 

.000139 

.0000851 

.0000632

.0000661 

.000110

.0000691 

.0000647 

.0000633 

.0000720

.0000793 

.0000822

.0000822 

.0000836 

.0000836 

.0000749

.0000962

.0000903 

.0000670

.000131 

.0000728

Average fe for cross section from 

Average of 

fc's for 

stations

(4)

0.21 

.36

.30 

i .24

.40

1.35 

1.44

.41 

.37

.40 

.39 

.37 

.34

.40

.40 

.32

.40 

.34

Average 

velocity 

difference at 

stations

(5)

0.21 

.36

.28

.40

.40 

.36

.40 

.37 

.35 

.32

.39

.34 

.32

.35 

.34

Discharge 

measurements

(6)

0.21

.33 

.32 

.31

.37 

.31 

.38 

.34

.27 

.22

.35

.34 

.33

.37 

.39

.58 

.32 

.32 

.32

.25

.37 

.33

1 One station only.

2 Measured discharge.

The 11 fc's computed from discharge measurements averaged 

almost the same 0.345 as compared with 0.349 (table 5, cols. 6, 5), 

as the 11 fc's determined on the same days from several velocity observations at each of a few stations. Theoretically, the fc's in column 5, 

which are based on measured velocities at only a few stations, should 

represent the average vertical distribution of velocity more closely 

for the measuring stations and less closely for the whole cross section
56 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

than the k's in column 6, which are based on velocities at about 20-30 

stations. Actually, the differences in the two types of k's may be 

due mainly to experimental errors.

The method for computing k from discharge measurements is 

simple and rapid and usually requires no additional fieldwork except 

determining a reasonably accurate energy gradient. Although the 

velocity differences may be much less consistent from one station to 

another in shallow flows over dune beds than in the deep flews of the 

Mississippi River, the vertical distributions defined by many observations at only a few stations are also likely to be less consistent. 

For such shallow flows, the velocity differences for the large number 

of stations that are included in a discharge measurement, especially 

if the stations are spaced randomly with respect to the dunes, may 

provide a more representative vertical distribution of ve] ocity for 

the cross section than the vertical distribution that can be obtained 

from detailed information for only a few stations.

The turbulence constants, mostly computed from discharge measurements, are fairly consistent (fig. 20) with those reported by Einstein and Chien (1955, fig. 15). Individual k's scatter considerably 

from the curve perhaps partly because of the rough streambed of the 

Mississippi River at St. Louis. Also, the data for flume studies and 

for the Missouri River, collected primarily for research studies, probably were more accurate than some of the routinely determired watersurface slopes at St. Louis and some velocity differences computed 

from discharge measurements. The k's based on 22 discharge measurements for the Mississippi River at St. Louis (table 5) average 0.33, 

which is considerably less than 0.40 but somewhat greater tl an would 

be indicated by the curve (fig. 20) that was defined by Eirstein and 

Chien.

SEDIMENT CONCENTRATION

The usual equation for the vertical distribution of suspended sediment of a particular fall velocity is

a V

o a/

in which

cu and c0 are concentrations of sediment of a particular fall velccity at distances y and a, respectively, above the streambed

z theoretically equals the fall velocity w divided by ku*
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 57

S co

0.1 

0.01 

0.001 

0.0001

0.00001 

0.

\

X

 .

0

o 

o

K °

U V o nn

<rx.

0 ,0 0^

o

O «

* . A 

 

0 °

A °

\

A ^\ 

 \.

 '. ' \

 

 

 

* « .

EXPLANATION

 

Flume studies

0

Missouri River

y

Atchafalaya River

A 

Mississippi River 

at St. Louis

>

 -j

k:.--

> \"

0 \

 \ *. ' -'A

 \

 \

'. "\

. .

. 

 

A

0 

A

 

U ' .

 

 

 1 y *

\

<

 

 

 

5 0 20 0.25. 0.30 0.35 0.

FIGURE 20. Effect of sediment on the turbulence constant computed 

from the vertical distribution of velocity. Data for the Mississippi 

River added to figure 15 of Einstein and Chien (1955).

764-692 O 65
58 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS 

TABLE 6. Values of z^from point samples

Date

1950

Aug. 8.. 

Sept. 7. - ...

Sept. 26.. 

1951 

Apr. 18.... __

July 16 - 

July 22 

July 30 

Sept. 26 

Oct. 17 - 

Nov. 13 -

1962

Sampling 

station

400 

1200 

1500 

400 

625 

900 

1100 

1250 

1400 

1500 

1650 

400 

1200 

1500 

400 

1200 

1500 

400 

1200 

1500 

400 

1200 

1500

450 

925 

1250 

1600 

900 

1275 

1600 

450 

875 

1250 

1600 

450 

875 

1250 

475 

900 

1275 

1600 

475 

900 

1275 

1600 

475 

900 

1275 

1600 

475 

900 

1275 

1600

450 

850

zi for indicated 

particle-size range

<0.062 

mm

0.01 

.02 

.06 

.02 

.02 

.01 

.04 

.01 

.01 

0 

.02 

.02 

.02 

.02 

.05 

.05 

.02 

.06 

.04 

.02 

.03 

.01 

.15

.02

.06 

.01 

.02

.01

.02 

.01 

.02 

.02 

.02

.01

.03 

.02 

.03 

.02 

.07 

.05 

.02

.01 

.01

0.062- 

0.125 

mm

0.12

........

.02

.08 

.12 

.38

.07 

.47 

.49 

.37

.05

.27 

.14 

.11 

.09

.21

.10 

.22

.16

.14

.18 

.20

.21 

.23 

.03

.37 

.27

.30

.24

.48

.14

.24 

.09

0.125- 

0.250 

mm

0.38

.28

.14 

.41 

.24 

.21 

.21 

.12

.07

.43

.32 

.35

.47

.36

.23

.32

.27

.20

.25

.38 

.13

.48 

.50

.68 

.51

.28

Date

1952 Con. 

May 1 Con.

1953 

Apr. 24 

1954

1955 

Mar. 31. 

Dec. 27 

1956 

Feb. 21 

Apr. 24. 

July 9 

1959 

May 13. 

July 10... 

Sampling 

station

1275 

1575

500 

900 

1275 

1575 

525 

925 

1275 

1550

475 

900 

1275 

1600

500 

925 

1275 

1575 

550 

925 

1275

550 

925 

1275 

1575 

475 

900 

1300 

1575 

475 

900 

1300 

1575 

500 

925 

1275

375 

575 

775 

925 

1075 

1200 

1300 

1425 

1550 

1675 

710 

750 

800 

1000

zi for indicated 

particle-size range

< 0.062 

mm

0.03 

.04

.03 

.06 

.05 

.01 

.01 

.01 

0 

.03

.01 

.02 

.10 

.04

.01 

.02

.03 

0 

.08

0 

.01 

.02

.02

0 

.02 

.04 

.01 

.05 

.02

.07

.01 

.02 

0 

.02 

.03 

.03 

.04 

.02 

.02 

.03 

.02 

.02 

.02 

.01

0.06?- 

0.125 

mri

0.21

.26 

.27 

.35 

.26 

.30 

.30 

.30 

.40

.22 

.25 

.26 

.27

.13 

.27 

.21 

.14 

.26 

.23 

.10

.41 

.38 

.05 

.. .22

.29 

.39 

.18 

.23 

.26 

.41 

.28

.33

.31

.04 

.03 

.13 

.25 

.33 

.27 

.23 

.23 

.22 

.16 

.21 

.13 

.05 

.15

0.125- 

0.250 

mm

0.29

.56 

.83 

1.32

.77

.73 

.59 

.99

.75 

1.02 

.72

.49 

.42 

.41 

.32 

.82 

.61 

.74

.43

.58 

.67 

.50 

.49 

.48 

.48 

.48 

.76 

.70 

.34 

.95 

.75 

.81 

.67

.62 

.17 

.35 

.49 

.57 

.42 

.59 

.38 

.33 

.53 

.17 

.96 

.35 

.55

This equation is based on the assumption that the water surface and 

streambed are plane and parallel. In general, the form of the equation 

has been found to be correct except that the actual exponent, called 

zi, generally differs materially from wj(ku*) (Anderson, 1942; Vanoni, 

1946; Einstein and Chien, 1954).
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 59

The Zi's for the Mississippi River at St. Louis were computed for 

most times when point-integrated sediment samples from each of several points at a station were analyzed for sediment concentration and 

particle size. Each z\ for a station and a size range is listed in table 6 

and was determined by measuring the slope of the straight line through 

the plotted points of the logarithm of the concentration for a size 

range against the logarithm of (yo y)/y- Some plotted points were 

too irregularly and widely scattered to define a line, and the Zi's based 

on the slopes of other lines were obviously inconsistent from one size 

range to the other. In general, the ZI'B were more consistent and 

seemed to be more dependable after March 31, 1955, vrhen the size 

analyses of the sands were made with the visual-accumulation tube 

(see table 7), than the Zi's on or before March 31, 1955, when the size 

analyses of sands were made with the bottom-withdrawal tube.
TABLE 7. Particle-size analyses of suspended sediment, p

[Method of analysis: C, chemically dispersed; M, mechanically dispersed; P, pipet; V, visu

Date

1955 

Dec . 27. _ .....

1966 

Feb. 21. ________

Time

12: 52 p.m. 

1:02 

l: 1 - 

1 : 22 

1:32 

l.*0

2:02 

2:12 

2:22 

2:32 

2:40 

2:45

9: 56a.m. 

10:08 

10:18 

10:28 

10:32 

10:38 a.m.

11:36 a.m. 

11:50 

12: 03p.m. 

12:14 

12:28 

12:42

1:22 

1:30 

1:44 

1:58 

2:08

Discharge 

(cfs)

58,000 

58,000 

58,000 

58, 000 

58, 000 

58,000

58,000 

58, 000 

58,000 

58,000 

58, 000 

58, 000

58,000 

58, 000 

58, 000 

58, 000 

58,000 

58,000

56,100 

56,100 

56, 100 

56, 100 

56,100 

58, ICO

56,100 

56, 100 

56, 100 

56,100 

56,100

Water 

temperature 

(°F)

36

36 

36

36 

37

36 

36

36

Sampling 

station

550 

550 

550 

550 

550 

550

 925

925 

925 

925 

925 

925

1,275 

1,275 

1,275 

1,275 

1,275 

1,275

550 

550 

550 

550 

550 

550

925 

925 

925 

925 

925

Total 

depth 

(ft)

11.6 

11.6 

11.6 

11.6 

11.6 

11.6

15.2 

15.2 

15.2 

15.2 

15.2 

15.2

23.7 

23.7 

23.7 

23.7 

23.7 

23.7

11.9 

11.9 

11.9 

11.9 

11.9 

11.9

14.3 

14.3 

14.3 

14.3 

14.3

Sus

Sampling point

Depth

(ft)

10.6 

10.4 

9.3 

7.0 

4.6 

1.2

14.2 

13.7 

12.2 

9.1 

6.1 

1.5

22.7 

21.3 

19.0 

14.2 

9.5 

2.4

10.9 

10.7 

9.5 

7.1 

4.8 

1.2

13.3

11.4 

8.6 

5.7 

1.4

Concentration 

(ppm)

218 

293 

188 

202 

163 

166

190 

164 

164 

162 

153 

125

107 

100 

121 

84 

64 

50

138 

115 

121 

103 

102 

102

112 

98 

80

88

78

Percen

0.002 0.004 
Apr. 24.......__

Mav9 _____

2:37

2:52

3:02

3:12

3:22

3:30

3:52

4:02

4:11

4:20

4:28

4:37 p.m.

12:45 p.m.

12:50

12:55

1:00

1:05

1:15

1:40

1:45

1 * 50

1'55

2:00

2:10

2:40

2:45

2:50

3:00

3:05

3:10

3:35

3:40

3:50

4:00

4:05

4: 10 p.m.

10:55 a.m.

11:00

11:05

11:10

11:15

11:20

56,100

56,100

56,100

56,100

56,100

56,100

56,100

56, 100

56,100

56, 100

56,100

56,100

170,000

170,000

170, 000

170, 000

170, 000

170, 000

170, 000

170,000

170, 000

170, 000

170, 000

170, 000

170, 000

170, 000

170, 000

170, 000

170,000

170, 000

170, 000

170, 000

170, 000

170, 000

170, 000

170, 000

159, 000

159, 000

159, 000

159, 000

159, 000

159, 000

1,275

1,275

1,275

1,275

1,275

1,275

1,525

1,525

1,525

1,525

1,525

1,525

475

475

475

475

475

475

900

900

900

900

900

900

1,300

1,300

1,300

1,300

1,300

1,300

1,575

1,575

1,575

1,575

1,575

1,575

475

475

475

475

475

475

22.3

22.3

22.3

22.3

22.3

22.3

18.5

18.5

18.5

18.5

18.5

18.5

27.8

27.8

27.8

27.8

27.8

27.8

27.0

27.0

27.0

27.0

27.0

27.0

43.9

43.9

43.9

43.9

43.9

43.9

30.6

30.6

30.6

30.6

30.6

30.6

27.8

27.8

27.8

27.8

27.8

27.8

21.3

20.1

17.8

13.4

8.9

2.2

17.5

16.7

14.8

11.1

7.4

1.9

26.8

25.0

22.2

16.7

11.1

2.8

26.0

24.3

21.6

16.2

10.8

2.7

42.9

39.5

35.1

26.3

17.6

4.4

29.6

27.5

24.5

18.4

12.2

3.1

26.8

25.0

22.2

16.7

11.1

2.8

67

94

80

60

49

46

90

95

69

60

46

61

696

508

421

415

354

359

878

558

420

434

332

272

587

519

377

317

245

251

455

364

343

309

262

224

1,260

1,030

987

886

887

838

67

94

80

60

49

46

90

95

69

60

46

61

696

508

421

415

354

359

R7R

558

420

4S4

332

979

587

377

317

245

251

455

364

343

309

262

994

1,260

987

887

838

20

23

25

25

28

31

16

16

22

29

30

12

12

23

29

34

43

19

22

26

32

32

38

11

16

17

18

21

24
TABLE 7. Particle-size analyses of suspended sediment, point-integ

Date

1956 Con. 

May 9 Con.

July 9.. .....

Time

11: 50a.m. 

11:55 

12: 00m. 

12: 05p.m. 

12:15 

12:20

1:10 

1:05 

1:00 

1:20 

1:25 

1:30

1:55 

2:00 

2:05 

2:10 

2:13 

2: 20p.m.

ll:32a.m. 

11:32 

11:32 

11:32 

11:32 

11:32

12: 10p.m. 

12:10 

12:10 

12:10 

12:10 

12:10

Discharge 

(cfe)

159, 000 

159, 000 

159, 000 

159, 000 

159, 000 

159,000

159, 000 

159, 000 

159, 000 

159, 000 

159,000 

159,000

160,000 

160,000 

160,000 

160,000 

160,000 

160,000

154,000 

154,000 

154,000 

154,000 

154,000 

154,000

153, 000 

153,000 

153,000 

153,000 

153, 000 

153,000

Water 

temperature 

(°F)

60

60

62

Sampling 

station

900 

900 

900 

900 

900 

900

1,300 

1,300 

1,300 

1,300 

1,300 

1,300

1,575 

1,575 

1,575 

1,575 

1,575 

1,575

500 

500 

500 

500 

500 

500

925 

925 

925 

925 

925 

925

Total 

depth 

(ft)

27.0 

27.0 

27.0 

27.0 

27.0 

27.0

43.8 

43.8 

43.8 

43.8 

43.8 

43.8

32.8 

32.8 

32.8 

32.8 

32.8 

32.8

25.8 

25.8 

25.8 

25.8 

25.8 

25.8

25.7 

25.7 

25.7 

25.7 

25.7 

25.7

Susp

Sampling point

Depth 

(ft)

26.0 

24.3 

21.6 

16.2 

10.8 

2.7

42.8 

39.4 

35.0 

26.3 

17.5 

4.4

31.8 

29.5 

26.2 

19.7 

13.1 

3.3

24.8 

23.2 

20.6 

15.5 

10.3 

2.6

24.7 

23.1 

20.6 

15.4 

10.3 

2.6

Concentration 

(ppm)

1,210 

898 

817 

663 

598 

526

501 

314 

340 

236 

320 

205

821 

377 

293 

190 

165 

159

2,150 

1,930 

1,910 

1,850 

1,720 

1,770

1,590 

1,550 

1,460 

915 

1,480 

1,440

Percen

0.002

12 

14 

17 

17 

19 

22

12 

24 

18 

16 

20 

32

4 

8 

15 

4 

14 

16

53 

52 

52 

53 

59 

56

51 

61 

57 

58 

60 

63

0.004

58 

59 

58 

61 

67 

64

58 

63 

65 

69 

67 

64
1959

12:45

12:45

12:45

12:45

12:45

12:45

1:18

1:18

1:18

1 * 1R

1:18

6:30 a.m.

6:36

6:39

6:42

6:45

6:50 

6:54

6:57

7:00

7:03

7:07 

7:10

7:13

7:16

7:19

7:24

7:27

7:30

7:33

7:36

7:40 

7:44

7:47

7:50

7:53

7:59 

8:02 8

. f\K

8:08

8:00

153,000

153,000

153,000

153,000

153, 000

153,000

153,000

153, 000

153, 000

153,000

153,000

153,000

239,000

239, 000

239, 000

239,000

239,000

239,000 

239, 000

239, 000

240, 000

240, 000

240, 000 

240, 000

240,000

240,000

240,000

240, 000 

240,000

240, 000

240, 000

240, 000

240,000 

240, 000

240, 000

240, 000

240,000

240, 000 

240,000

240, 000

240, 000

240. 000

68

68

68

68

68

67

1,275

1,275

1,275

1,275

1,275

1,275

1,575

1,575

1,575

1,575

1,575

1,575

1,675

1,675

1,675

1,675

1,675

1,550 

1,550

1,550

1,550

1,550

1,425 

1,425

1,425

1,425

1,425

1,300 

1,300

1,300

1,300

1,300

1,200 

1,200

1,200

1,200

1,200

1,075 

1,075

1,075

1,075

1.075

38.8

38.8

38.8

38.8

38.8

38.8

30.0

30.0

30.0

30.0

30.0

30.0

41.7

41.7

41.7

41.7

41.7

39.4 

39.4

39.4

39.4

39.4

44.4 

44.4

44.4

44.4

44.4

45.0 

45.0

45.0

45.0

45.0

36.8 

36.8

36.8

35.3

36.8

38.2 

38.2

38.2

38.2

38.2

37.8

34.9

31.0

23.3

15.5

3.9

29.0

27.0

24.0

18.0

12.0

3.0

37.5

33.4

25.0

16.7

4.2

35.5 

31.5

23.6

15.8

3.9

40.0 

35.5

26.6

17.8

4.4

40.5 

36.0

27.0

18.0

4.5

33.1 

29.4

22 1

117

3.7

34.4 

30.6

22.9

15.3

3.8

1,010

1,120

777

709

638

467

312

231

245

254

165

887

809

870

732

713

1,110

936

1,190

810

826

1,110

1,080

1,040

1,010

942

1,280

1,370

1,150

1,130

1,060

1,510

1,500

1,430

1,230

1,270

2,000

1,660

1,620

1,690

1.430

50

47

44

47

53

53

53

52

53

56

64

71

32

54

51

72

64

82

See footnotes at end of table. 
TABLE 7. Particle-size analyses of suspended sediment, point-inte

Date

1969 Con. 

May 13 Con.

July 102..-. 

Time

8 : 15 a.m. 

8:18 

8:21 

8:24 

8:27

8:32 

8.35 

8:38 

8:41 

8:44

8:48 

8:51 

8:54 

8:57 

9:00

9:05 

9:08 

9:11 

9:14 

9: 17 a.m.

5:26 a.m. 

5:34 

5:40 

5:45 

5:50

5:56 

6:01 

6:06 

6:11 

6:16

Discharge 

(cfs)

240,000 

240,000 

240,000 

240,000 

240,000

240,000 

240,000 

240,000 

240,000 

240,000

240,000 

240,000 

240,000 

240,000 

240,000

240,000 

240,000 

240,000 

240,000 

240,000

154,000 

154,000 

154,000 

154,000 

153,000

153,000 

153.000 

153,000 

153,000 

153.000

Water 

temperature 

(°F)

67

68

67

67

Sampling 

station

925 

925 

925 

925 

925

775 

775 

775 

775 

775

575 

575 

575 

575

575

375 

375 

375 

375 

375

1,000 

1,000 

1,000 

1,000 

1,000

,000 

,000 

,000 

,000 

.000

Total 

depth 

(ft)

34.2 

34.2 

34.2 

34.2 

34.2

32.6 

32.6 

32.6 

32.6 

32.6

30.0 

30.0 

30.0 

30.0 

30.0

28.4 

28.4 

28.4 

28.4 

28.4

31.7 

31.7 

31.7 

31.7 

31.7

31.7 

31.7 

31.7 

31.7 

31.7

Susp

Sampling point

Depth 

(ft)

30.8 

27.4 

20.5 

13.7 

3.4

29.3 

26.1 

19.6 

13.0 

3.3

27.0 

24.0 

18.0 

12.0 

3.0

25.6 

22.7 

17.0 

11.4

2.8

30.2

28.5 

25.4 

22.2 

19.0

15.8 

12.7 

9.5 

6.3 

3.2

Concentration 

(ppm)

2,050 

2,020 

2,010 

1,890 

1,750

2,210 

2,150 

2,100 

2,160 

2,080

2,460 

2,380 

2,350 

2,290 

2,250

2,590 

2,490 

2,410 

2,430 

2,420

2,340 

2,290 

1,970 

2,270 

2,240

2,180 

2,140 

2,200 

2,180 

2.140

Percent 

0.002 0.004 
6:56

7:02

7:08

7 *1Q

7:20

7:24

7 .OQ

7-34

7:40

7 -44

8:16

8 

.HO

8

*97

8

.09

8

.QQ

8 '43

8*48

8

, K9

9

-ni

9 -nfl

9 '12

9 .10

9

-94

9'30

9

.OA

0-41

9 -4ft

9'51

152,000

152,000

152,000

1R9 fifift

152,000

1K9 nnn

152,000

1R9 ftnn

152 000

151,' 000

151, 000

151,000

151,000

151,000

151,000

151,000

151,000

1 HI ftfift

150,000

150,000

150, 000

150 000 i5o!ooo iRft nftft

150,000

150,000

150,000

150,000

150,000

150,000

800

800

800

800

800

800

800

800

800

750

750

750

750

750

750

750

750

7»sn

750

710

710

710

710

710

710

710

710

710

710

26.0

26.0

26.0

26.0

26.0

26.0

26.0

26.0

26.0

26.0

26.2

26.2

26.2

26.2

26.2

26,2

26.2

26 2

35.2

35.2

35.2

35.2

35.2

35.2

35.2

35.2

35.2

35.2

24.5

23.4

20.8

18.2

15.6

13.0

10.4

7.8

5.2

2.6

24.7

23.6

21.0

18.3

15.7

13.1

7.9

5.2

2.6

33.7

31.7

28.2

24.6

21.1

17.6

14.1

10.6

7.0

3.5

2,560

2,540

2,540

2,520

2,540

2,490

2,500

2,500

2,500

2,420

2,570

2,590

2,550

2,580

2,590

2,600

2,490

2,500

2,440

2,500

2,540

2,670

2,630

2,560

2,620

2,570

2,580

2,540

2,540

2,530

iEstimated.

2 Percent-finer values accurate to ±0.2 because large amounts of material were analyzed.
66 FLUVIAL SEDIMENT, MISSISSIPPI RIVEK, ST. LOUIS

The average 2t for a cross section and for a range of sand size was 

plotted against w/(ku*) to define the relationship (fig. 21) between

X

&? 

 VVO^OO

y 2

yfcP o o

&/

x*/ 4 ^

4 <*

A

A A

A

A> /(/ /\*

^

A

A

/

/

/

/

A

EXPLANATION

May 8, 1950 to March 30, 1955

o

0.062 to 0.125 mm

0.125 to 0.250 mm

December 27, 1955,

to July 10 1959

 

0.062 to 0.125 mm

A

0.125 to 0.250 mm

A

FIGURE 21. 0! as a function of w/(ku^).

Zi and s. (A size range including both silt and clay is too wide to 

have a single representative fall velocity; so, the 2t's for the range of 

smallest sizes were not plotted.) The Zi's and z's through March 31, 

1955, were based, respectively, on size analyses of sands that were 

made with the bottom-withdrawal tube and on k's that were computed 

from the discharge measurements; they are less consistent than the 

Si's and z's for later times. Although the points scatter widely in 

figure 21, especially for the earlier determinations, the average of all 

the ZiS in table 6 for the size range from 0.062 to 0.125 mm is 0.20, 

which compares reasonably well with the average z of 0.27. If based 

only on the seven determinations after March 31, 1955, the average 

zl and 2 are 0.24 and 0.21, respectively. Thus, for this size range the 

average 2t is roughly the same as the average z. The ratio of the 

average Zi for the size range from 0.125 to 0.250 mm to th«s average 

2i for the size range from 0.062 to 0.125 mm is 0.41/0.20 (equah 2.0:1.0) 

for all the determinations or 0.59/0.24 (equals 2.5:1.0) for the last 

seven determinations. The ratio of fall velocities of representative
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 67

particles for the two size ranges varies with temperature but averages 

about 3.3:1.0. These fall velocities were based on equations given 

by Rubey (1933). Hence, the average 2/s for all the determinations 

indicate a variation of zl with about the 0.58 power of the fall velocity, and the average Zi's for the last seven determinations indicate a 

variation of 2X with about the 0.77 power of the fall velocity. For 

some shallow streams in Nebraska, Zi for sands varied with about the 

0.7 power of fall velocities computed from Rubey's equations (Colby 

and Hembree, 1955, p. 70; Hubbell and Matejka, 1959, p. 72). Except for the difference between the theoretical variation and the actual 

variation of zl with changing fall velocity, the theoretical equation 

for the vertical distribution of sediment concentration se?ms to apply 

reasonably well for the Mississippi River at St. Louis.

The relationship (fig. 21) of zt to wj(ku*} for the deen flows over 

rough beds at St. Louis seems to be generally similar and about as 

good as the relationship that was reported by Einstein and Chien 

(1954, p. 3 and fig. 1) for flows over a plane bed in the Missouri 

River at Omaha. That is, the Zi's and z's are approximately equal 

for low z's, but the zi's do not increase nearly so fast as the z's. In 

general, Zi seems to be the same function of w/(ku#) icv deep flows 

over dune beds as for flows over plane beds. However, this conclusion is inconsistent with the suggestion by Einstein (1950, p. 28, 

59) that z be computed from the equation s=iy/(0.40 u#'). The 

difference between iy/(0.40w./) and wj(ku^) is large at St>. Louis. As 

k averaged about 0.34 and the ratio of w*' to u* for the 10 determinations in table 3 averaged 0.46, the z's computed according to Einstein's 

equation might be about 0.34/(0.40) (0.46) or roughly 1.8 times as 

large as those that were computed from w/(ku#). Vanoni and 

Brooks (1957, p. 73-75) noted that the observed vertical distributions 

of sediment over dune beds in certain laboratory experiments were 

inconsistent with any decrease in u* such as Einstein suggested. 

A recent reexamination of Einstein's derivation of the equation for 

z indicates that the classical equation z=w/(ku*) probably should 

have been obtained for flow over dune beds as well as for flow over 

plane beds. Although the basic assumptions on which the derivation 

is based do not apply accurately for flow over dune beds, the only 

obvious change in the equation for z for flow over dune beds as compared with flow over plane beds is that the k for widely spaced major 

roughness elements, such as dunes, may not be a tru°s turbulence 

constant.

BEDLOAD DISCHARGE AND BED-MATERIAL DISCHARGE

Samples obtained with samplers currently available for practical 

field use can be used to determine the sediment discharge in the zone
68 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIF

traversed by the sampler or the size distribution of the material in 

the bed, but they cannot be used to determine the discharge of material on the bed or in close proximity to the bed. No samplers are 

as yet available that will measure the bedload discharge or the total 

sediment discharge in a natural stream. In various rivers the measured suspended-sediment discharge probably ranges from about 40 

percent to nearly 100 percent of the total sediment discharge. The 

bed-material discharge affects the stage-discharge relationship and 

builds bars that may obstruct the channel for navigation; so it is 

a significant part of the sediment discharge even though it may be 

a fairly small percentage of the total. Therefore, the relation of 

bed-material discharge to velocity and temperature was studied, and 

several different equations were used to compute bedload discharge 

and bed-material discharge.

Because the bed-material discharge consists of particles of the same 

size as those present in significant quantities in the bed, the size 

distributions of samples from the bed were examined to c'etermine 

the sizes that are part of the bed-material discharge. On the average, 

the bed-material samples had very small amounts of material finer 

than 0.125 mm. Therefore, the bed-material discharge is considered 

in this report to be the rate of transport of all particles larger than 

0.125 mm, regardless of the mode of transport.

The measured bed-material discharge (see "Definitions") is computed from the measured concentration of particles larger ttan 0.125 

mm in the sampled zone and the streamflow for the whole cross 

section. Therefore, it includes all the bed-material discharge in 

the sampled zone and part of the bed-material discharge in the 

unsampled zone. The measured bed-material discharge was closely 

related to the mean velocity and to the water temperature (fig. 22). 

The measured bed-material discharge increased with about the fourth 

power of the mean velocity; and, for a given mean velocity, the high 

discharges were associated with low water temperatures.

Several different equations were used to compute bedload discharges and bed-material discharges, and the results are shown 

in table 8. For most of the computations, the hydraulic data and 

sediment data were obtained from measurements made within a 

3-day period and are considered to be concurrent. For the other 

computations, hydraulic data were obtained from rating curves of 

discharge, depth, and velocity plotted against gage height. The 

results were studied to determine the equations that are best suited 

for application to this river and to similar rivers.

Because an accurate measurement of bedload discharge or total 

bed-material discharge is not possible, an absolute determination of
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 69

1000

100

10

0.1

60 70 80 90 100

WATER TEMPERATURE, IN 

DEGREES FAHRENHEIT

FIGURE 22.-

10 100 

MEAN VELOCITY, IN FEET PER SECOND

-Relation of measured bed-material discharge to 

mean velocity and water temperature.
TABLE 8. Computed bedload and bed-materia

Date

1961 

May 23. 

July 16. 

Tnl IT 99

July 30... .........

Qpnt 1 7

Oct. 10.. ..........

Oct. 17 

1961 

Feb. 20... . 

Mar. 17..... ...

July9_ ...

July 24. 

Aug. 19-- 

Sept. 11..... 

1953

May 25--.-. ......

July 13. 

4.U2. 10.... 

1964 

Mar. 22.-... ......

Apr. 19... - 

July 26. ...... -

Oct. 18--.- __ ...

Streamflow 

(cfs)

359, 000 

704,000 

763,000 

468,000 

387,000

238,000 

234,000 

170,000 

225,000 

202,000

222,000 

411, 000 

674,000 

198,000 

210,000

178, 000 

161,000 

167, 000 

107,000 

74,700 

67,500

62,000 

179, 000 

197, 000 

159, 000

80,500 

138, 000 

115,000 

214.000

Mean 

velocity 

(fps)

5.26 

»7.26 

»7.53 

5.37 

5.03

3.93 

3.91 

3.31 

3.97 

3.88

6.36 

7.96 

3.62 

3.70

3.37 

3.13 

3.37 

2.68 

2.24 

2.15

2.04 

3.94 

4.00 

3.61

2.63 

3.42 

3.07 

4.22

Measured 

bed-material 

discharge ' 

(tons per 

day)

94,000 

250, 000 

300,000 

46,000 

61,000

11,000 

30,000 

11,000 

55,000 

52,000

96.000 

250, 000 

440,000 

5,600 

13,000

4,500 

5,200 

5,600 

2,600 

540 

2,000

750 

26,000 

25,000 

15,000

4,400 

21,000 

3,700 

44.000

Sediment discharge com

Bedload discharge

Schoklitsch

10,000 

33,000 

26,000

1,900

540 

630

3,300 

9,400 

20,000 

1,600 

2,000

1,300 

680 

970 

330 

240 

190

200 

2,800 

2,800 

2,700

1,200 

2,600 

1,100 

3.500

Meyer-Peter 

and M tiller

150

140 

2,200 

2,700 

1, 0,00

710 

1,400 

980 

3.300

Kalinske

2,500

2,000 

3,000 

3,800 

3,400

2,800 

3,500 

3,200 

4.900

Modifie

Einstein

8,40

22,00

24,00

8,60

6,10

1,80

2,30

80

3,80

2,00

6,90

30,00

1,50

1,40

77

6

9

2

2,00

2,90

1,°0

3

1,40

1,10

4.30
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 71

0o

SS8S

§

00 o 

Sc5 c5

10ct

co- -f

8 S3

ofco"

8 8 b» O>

S

ooc OO! 5t-OOC

i-t ooco 

>ococ<i

CD SP CD i-< CD C

 * W* * * (N !N COCOWO^C

SS

OO OOC 0000 

o o o o 188 "S ^

i«

SooS

1^1 

S«jS
72 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS'

the accuracy of an equation cannot be made. Indirect methods of 

evaluating the equations must be used. The measurable quantity that 

is probably most closely related to the bedload discharge and to the 

total bed-material discharge is the measured part of the bed-material 

discharge. This quantity was used as the primary means of evaluating 

the results of the different equations.

Measurements in rivers that have natural contractions or artificial 

turbulence flumes where the total sediment discharge is in suspension 

have shown that the bed-material discharge is closely related to the 

mean velocity in a normal section of the river. The bed-material 

discharge varies with about the third power of the mean velocity. 

Therefore, the mean velocity was used as a secondary means of 

evaluating the results of the equations.

Bedload discharges were computed with the Schoklitsch, the 

Meyer-Peter and Miiller, the Kalinske, the modified Einstein, and 

the Bagnold methods.

Schoklitsch's equation (Shulits, 1935) expresses the bedload discharge as a function of the particle diameter, the slope, the streamflow, 

and a critical discharge that depends on the particle diameter:

where

qt is bedload discharge, in pounds per second per foot of width

d is particle diameter, in feet

Se is "hydraulic slope," presumably the slope of the energy grad; <?nt

q is streamflow, in cubic feet per second per foot of width

The equation can be used to compute the bedload discharges by 

ranges of particle size. Bedload discharges computed for the whole 

width with Schoklitsch's equation and converted to tons per day are 

shown plotted against the measured bed-material discharge in figure 

23-4. The dashed lines in figure 23 are lines of equality and are 

shown, not to imply that the computed bedload discharge should be 

equal to the measured discharge of particles larger than 0.125 mm, 

but to indicate the relative magnitudes of the two discharges. The 

bedload discharges increased with about the 0.8 power of the measured 

bed-material discharge and with about the fourth power of the mean 

velocity.

Meyer-Peter and Miiller's equation (1948) for bedload discharge 

in wide channels with negligible influence from the bankr can be
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 73

105 i I ii I

104

UJ 

O 

K. 

<

o io3

C/3

UJ hD 

0. 

2 

O

" ID2

101

A, Schoklitsch method

103 10* 105

MEASURED BED-MATERIAL DISCHARGE, IN TONS PE7 DAY

FIGURE 23. Bedload discharges computed by various methods. A, Schoklitsch 

method; B, Meyer-Peter and Miiller method; C, Kalinske method; D, modified 

Einstein method; E, Bagnold method. (B-E on following pages.)

written for units of meters, metric tons, and seconds as

 -v\2/3

where

7 is specific weight of water, in metric tons per cubic meter 

k t is equal to n/2/o2/3 St1/2, a discharge coefficient
74 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

105

104

103

102

101

7

B, Meyer-Peter 

and Muller method

103 104 105

MEASURED BED-MATERIAL DISCHARGE, IN TONS PER DAY

k r is equal to 26/(rf90) 1/6 , an approximation of the maximum discharge 

coefficient that would occur with bed material of a giver size and 

a plane bed with no bed-material movement 

dg0 is the particle size, in meters, at which 90 percent of the bed material

by weight is finer

ys is specific weight of the sediment, in metric tons per cubic me^er 

d e is effective diameter of bed material, in meters v 31 is bedload discharge, in metric tons per second per meter of width

The ratio kt/k r depends on the form of the bed; so the equation is 

one of the few that account for the effects of bed forms on the bedload
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 75

105

104

103

102

101

C, Kalinske method

103 104 105 

MEASURED BED-MATERIAL DISCHARGE, IN TONS PER DAY

discharge. The equation can be used to compute bedload discharge 

by ranges of particle size. Bedload discharges computed for the 

whole width from this equation and converted to tons per day are 

shown plotted against measured bed-material discharge in figure 23J3. 

Bedload discharges increased with about the first power of the 

measured bed-material discharge for low and medium discharges and 

with about the one-third power for high discharges. Bedload discharges increased with about the fourth power of the mean velocity.
76 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

105

104

103

102

101

y

D, Modified Einstein method

103 Id4 105

MEASURED BED-MATERIAL DISCHARGE, IN TONS PER DAY

Kalinske's equation (1947) is used for computing bedload discharges 

by ranges of particle size. The equation can be written

where

~ 

U

§i is bedload discharge of a size range, in pounds per second per foot

of width 

«* is shear velocity, in feet per second
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 77

106

105

o </)

Q

Q 

< 

O

Q 

LU 

00 104

Q

103

103 104 105 

MEASURED BED-MATERIAL DISCHARGE, IN TON? PER DAY

ys is specific weight of sediment, in pounds per cubic foot 

d{ is geometric mean diameter of a size fraction of bed material, in feet 

Pi is the fraction of bed area occupied by the particles in a size range 

Ug/U is the ratio of mean speed of movement of the grains to mean fluid 

velocity at the grain level

The factor Ue/U depends on the relative intensity of turbulence and 

on the relative bed-shear stress. Bedload discharges were computed 

for the whole width and converted to tons per day. In figure 23C, 

bedload discharges increased with only the 0.13 power of the measured 

bed-material discharge. The bedload discharges increased with only 

the first power of the mean velocity.

The modified Einstein procedure (Colby and Hembree, 1955) can 

be used to compute bedload discharge, bed-material discharge, and 

total sediment discharge. In the procedure is used a maximum 

amount of measured data, which include suspended-sediment concentration, particle-size distribution, mean velocity, and temperature. 

Bedload discharges increased with about the 0.95 power of the

764-693 O 65-
78 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

measured bed-material discharge (fig. 23.D) and with about the fourth 

power of the mean velocity.

Bagnold (1956, p. 250) defined the material composing "bed load" 

as "that part of the load whose normal immersed weight component 

is in normal equilibrium with the grain stress * * * This stress is 

transmitted downwards via the dispersed grains to the stationary 

grains of the bed upon which it therefore ultimately rests." Thus 

the bedload discharges computed by Bagnold's equations may 

include some material that would be in suspension and that might 

be sampled by suspended-sediment samplers. For the particular 

conditions of the Mississippi River at St. Louis, Bagnold's equations 

can be simplified to

g t = 5,lWB(y0S)W

where

0» is "bed load" discharge, in pounds per second per foot of width

B is a mathematical abbreviation for a group of parameters that depend

on the particle size 

y0 is depth of flow, in feet 

S is slope of the bed surface, assumed to be the same as the slope of the

water surface for a 6.5-mile reach

Bedload discharges were computed for the whole width and converted 

to tons per day. They were nearly constant at low and medium 

discharges and increased with about the first power of the measured 

bed-material discharge at high discharges (fig. 23E). They increased 

with about the third power of the mean velocity.

Bed-material discharges have been computed using Strauh's equation, the modified Einstein procedure, and Bagnold's method, and 

by adding the unmeasured sediment discharge computed witt Colby's 

method to the measured bed-material discharge.

Straub's equation (U.S. Congress, 1935) is intended for computing 

"bed load." However, because re and 6 for the equation we^e determined from data for bed-material discharge and because sediment discharges computed with the equation are about the same in magnitude 

as those computed with other methods for bed-material discharge, 

the results are regarded as bed-material discharges rather than bedload 

discharges. The equation can be written as

qnM = QyoS e (y0Se J 

where

qsM is bed-material discharge, in pounds per second per foot of width

0 is the sediment characteristic

2/0 is the depth of flow, in feet
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 79

106

105

103

102

Straub method

103 104 l(r

MEASURED BED-MATERIAL DISCHARGE, IN TONS PIR DAY

FIGURE 24. Bed-material discharges computed by various methods. A, Straub 

method; B, modified Einstein method; C, Colby method; D, Bagnold method. 

(B-D on following pages.)

T C is the transporting force required to start movement of the bed material, in pounds per square foot 

T is the specific weight of water, in pounds per cubic foot

Bed-material discharges computed for the whole width with Straub's 

equation and converted to tons per day are shown plotted against 

measured bed-material discharge in figure 24 A. The d ashed lines in 

figure 24, as in figure 23, are lines of equality. Computed bed-material
80 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

B, Modified Einstein method

MEASURED BED-MATERIAL DISCHARGE, IN TONS PER DAY

discharge will not be less than the measured bed-material discharge 

unless one or both of the discharges are in error. The discharges from 

Straub's equation increased with only the one-half power of measured 

bed-material discharge at low discharges and with about the first 

power at high discharges. They increased with about the third power 

of the mean velocity.

Bed-material discharges computed with the modified Einstein 

procedure (Colby and Hembree, 1955) increased with the 0.9 power 

of the measured bed-material discharge (fig. 245). The scatter of
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 81

IO6

I io5

tr

10<

IO2

~I I I I I I I I

c, Colby method

____i iii

ioj io4 io5

MEASURED BED-MATERIAL DISCHARGE, IN TONS PER DAY

points is not excessive. The bed-material discharges increased with 

about the fifth power of the mean velocity.

Colby (1957) presented a method for computing unmeasured 

sediment discharge from the relation to mean velocity, depth, and 

concentration of suspended sands. Total bed-material discharges can 

be computed by adding the unmeasured sediment discharge to the 

measured bed-material discharge. The bed-material discharges increased with about the three-fourths power of the measured bed-
82 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

103 10* 105

MEASURED BED-MATERIAL DISCHARGE, IN TONS PER DAY

material discharge (fig. 24(7) and with about the fourth powf of the 

mean velocity.

Bagnold (1956) gave functions for "total transport rate." This 

term was interpreted to be the total transport rate of particle sizes 

that are in the bed, and it should be comparable to the bed-material 

discharge that was computed by other methods. Bed-material 

discharges from Bagnold's functions increased with about the one-half 

power of the measured bed-material discharge for low discharges and 

with the first power for high discharges (fig. 24Z>). For high dis-
FLOW RESISTANCE AND SEDIMENT TRANSPORTATION 83

charges, the bed-material discharges from Bagnold's functions were 

about equal to the measured bed-material discharges, whereas in 

reality the total bed-material discharge must be greater than the 

measured part of the bed-material discharge.

For comparison of the results obtained with the different equations, 

the average curves from figures 23 and 24 were plotted together in 

figures 25 and 26, respectively. The equality lines are also shown.

Figure 25 shows that the Schoklitsch equation and the modified 

Einstein procedure gave about the same results for bedload discharge. The Meyer-Peter and Miiller equation also gave similar 

results except at high discharge, where it gave lower bedload discharges than the other two equations. The Kalinske equation gave 

bedload discharges that are not in agreement with the results of any 

other equation. Kalinske bedload discharges increased very slowly 

with measured bed-material discharge; therefore, this equation is 

probably not suited for application to rivers similar to tte Mississippi. 

Because Bagnold's definition of "bed load" is different from that for 

the other equations, the results are not in agreement with those from 

any of the other equations.

This study indicates that the modified Einstein, the Schoklitsch, 

and the Meyer-Peter and Miiller bedload methods are the most 

suitable for the Mississippi River and similar rivers.

Figure 26 shows that the bed-material discharges computed by the 

modified Einstein method and those determined by adding the unmeasured sediment discharge from Colby's procedure to the measured 

bed-material discharge are in very good agreement. The figure 

indicates that the results are logical and reasonable; the computed 

discharges are greater than the measured discharges, and they increase at a slightly slower rate than the measured discharges. The 

Straub equation gives results that are higher than those for the 

modified Einstein and the Colby methods in the low range and are 

about the same in the high range. Bed-material discharges from 

Bagnold's functions are similar to those computed f-om Straub's 

equation, but on the average they are about equal to the measured 

bed-material discharge in the high range.

This study indicates that, when the required data mch as measured velocities, concentrations, and particle-size distributions are 

available, the most suitable methods of computing bed-material 

discharge for the Mississippi River and similar rivers are the modified 

Einstein method and the addition of the unmeasured sediment discharge from Colby's procedure to the measured bed-material discharge. When such data are not available, the Straub equation is 

the best method to use; but it probably will give results that are 

too high in the low range.
84 FLUVIAL SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

io6

105

m IO3

4(/

io2

io1

io3 10* io5

MEASURED BED-MATERIAL DISCHARGE, IN TONS PER DAY

FIGURE 25. Comparison of results from different methods of computing

bedload discharge.
COMPUTED BED-MATERIAL DISCHARGE, IN 

c

c ftCc

 ccH

g* £

f «

B g

c+- £

E c

&c

* i

P aC

h- ac9C

c 

 cc

cr

h- 

(ft

2 

« C

d

1 1 ? **

' c 

; 33

3 m

J 0

CD > S

s ?

» 1 ' \

2 ? 5

i i & i * §rn

<- * 

5 1

5 Z

? ^

L 33 =3! i 1-

2^

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N

s

\

«

\

\

>

\

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\\\\

x

s

\S\

N,

'vf\

X\

^\

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S,

s
86 FLUVIAI^ SEDIMENT, MISSISSIPPI RIVER, ST. LOUIS

As an example of the relative magnitudes of measured su^pendedsediment discharges and total sediment discharges that could be 

expected over fairly long periods of time, bed-material discharges 

and total sediment discharges were computed for the 1958 water 

year. The year 1958 was chosen both because conditions during that 

year represent those after most of the dams on the Missouri River 

main stem had been closed and because the mean flow of 145,000 cfs 

was fairly close to the long-term mean of 175,000 cfs. Rating curves 

of mean depth, mean velocity, and width were prepared from the 

weekly discharge measurements. For each day on which no discharge 

measurement was made, the depth, velocity, and width we^e determined from these curves. Water temperatures were measured or 

estimated for each day. These depths, velocities, widths, and water 

temperatures were used with figure 22 to compute the bed-material 

discharge in the sampled zone. These bed-material discharges were 

expressed as concentrations by dividing by the streamflow and by the 

units-conversion constant 0.0027. The unmeasured sediment discharge was then computed by Colby's method (1957).

These computations resulted in an unmeasured sediment discharge 

of 5,800,000 tons and a total sediment discharge of 114,000,000 tons 

for the year, compared to a measured suspended-sediment discharge 

of 108,125,500 tons. The suspended-sediment discharge was about 

95 percent of the total sediment discharge, and the bed-material 

discharge, 15,800,000 tons, was about 14 percent of the total sediment 

discharge. These percentages probably are typical for ary years 

except those having extreme conditions.

SUMMARY

An average of about 45 percent of the flow at St. Louis is from the 

Missouri River, which was partly controlled by reservoirs having a 

total capacity of 90,300,000 acre-feet in 1956. The Mississippi 

River at Alton, 111., upstream from the Missouri River, was partly 

controlled by lakes and reservoirs having a total capacity of 4,890,000 

acre-feet in 1956.

The relative rates of increase of width, depth, and velocity with 

discharge at the MacArthur Bridge can be expressed by the simple 

power functions

6=680Q°-07 

jfo=0.16 g»-« 

u = 0.0092 Q°-50

The average recurrence interval of the peak discharge in July 

1951 of 782,000 cfs is 9 years, and the average recurrence interval 

of a discharge of 990,000 cfs or more is 100 years. Peak discharges
SUMMARY 87

and minimum discharges will be less extreme in the future than in the 

past because of the increased storage capacity in the drainage basin.

The flows of the Missouri and upper Mississippi Risers have not 

become mixed at St. Louis; so the river has a lateral gradient of suspended-sediment concentration. The concentration rear the west 

bank has been as much as 2,400 ppm greater than the concentration 

near the east bank.

Suspended-sediment discharges from April 1948 to September 1958 

ranged from 4,250 to 7,010,000 tons per day and averaged 496,000 

tons per day. Mean concentrations for water years decreased steadily 

from 1,690 ppm in 1949 to 403 ppm in 1956, but they increased to 756 

ppm in 1958. Effects of the new reservoirs in the Missouri River basin 

on the concentration were obscured by the close relation of concentration to streamflow.

The measured suspended-sediment discharge averaged 47 percent 

clay, 38 percent silt, and 15 percent sand. Variations c* particle size 

were due mainly to differences in the source areas of th<^ sediment.

Most of the bed material in the main flow is between 0.125 and 1.00 

mm in diameter. The average of median diameters is related to the 

discharge for periods of 1 year and longer. Geometric cuartile deviations of the bed material ranged from 1.1 to 2.5 and averaged 1.5.

The mean bed elevation from stations 275 to 1,800 ranged from 

355.1 to 364.4 feet above mean sea level and was related to the median 

diameter of bed material by the regression equation A, 6 =363.0 7.8 c?50 , 

for which the standard error of estimate was 0.91 foot.

The resistance to flow as measured by Manning's n ranged from 

0.024 to 0.041 and was related to the discharge and mean velocity 

but not to the shear velocity. Normal dune height is 2-8 feet, and 

average length is about 250 feet. When the resistance to flow was 

low, much of bed was fairly flat and the few dunes were much longer 

than the average. Data obtained at St. Louis confirm Einstein's relation of u/u*' to V very well except for low values of V. Loops in 

the relation of gage height to fairly high discharge are caused by a combination of changes in roughness and turbulence constant.

Turbulence constants (Von Karman's k) computed from velocity 

measurements at 5-10 points in the vertical and from routine velocity 

measurements at 2 points in the vertical averaged 0.35 and 0.33, 

respectively. Turbulence constants were fairly consistent with those 

reported by Einstein and Chien (1955).

The exponent Zi of the vertical distribution of concentration for 

different size ranges varied with about the 0.77 power of the fall 

velocity. Except for the difference between the theoretical variation 

and the actual variation of Zi with changing fall velocity, the theoreti-
88 FLUVIAL SEDIMENT, MISSISSIPPI RIVEE, ST. LOUIS

cal equation for the vertical distribution of sediment concentration 

seems to apply reasonably well for the Mississippi Kiver at St. Louis. 

The relations of computed bedload discharge to the measured bedmaterial discharge and to the mean velocity indicated that the most 

suitable methods for computing bedload discharge of the Mississippi 

River and similar rivers are the modified Einstein, Schoklitsch, and 

Meyer-Peter and Miiller methods. The relations of computed bedmaterial discharge to the measured bed-material discharge ard to the 

mean velocity indicated that the most suitable methods for computing 

bed-material discharge are the modified Einstein procedure or the 

addition of the unmeasured sediment discharge from Colby's procedure 

(1957) to the measured bed-material discharge when data on velocity, 

concentration, and particle-size distribution are available; the Straub 

equation is the most suitable method when such data are not available. 

Measured suspended-sediment discharge averaged about 95 percent 

of the total sediment discharge, and the bed-material discharge averaged about 14 percent of the total sediment discharge.

LITERATURE CITED

American Standards Association, 1958, American standard letter symbols for 

hydraulics: ASA Y10.2-1958.

Anderson, A. G., 1942, Distribution of suspended sediment in a natural stream: 

Am. Geophys. Union Trans. 23d ann. mtg., pt. 2, p. 678-683.

Bagnold, R. A., 1956, The flow of cohesionless grains in fluids: Royal Soc. [London] 

Philos. Trans. 964, v. 249, p. 235-297.

Carey, W. C., and Keller, M. D., 1957, Systematic changes in the beds of alluvial 

rivers: Am. Soc. Civil Engineers Proc., Hydraulics Div. Jour., v. 83, Paper 

1331, 24 p.

Chambers, Julius, 1910, The Mississippi River and its wonderful valley: New 

York and London, G. P. Putnam's Sons, 308 p.

Colby, B. R., 1957, Relationship of unmeasured sediment discharge to mean 

velocity: Am. Geophys. Union Trans., v. 38, no. 5, p. 708-717.

Colby, B. R., and Hembree, C. H., 1955, Computations of total sediment discharge, Niobrara River near Cody, Nebraska: U.S. Geol. Survey WaterSupply Paper 1357, 187 p.

Corbett, D. M., and others, 1943, Stream-gaging procedure A manual describing 

methods and practices of the Geological Survey: U.S. Geol. Surve.v WaterSupply Paper 888, p. 152-157.

Einstein, H. A., 1950, The bed-load function for sediment transportation in open 

channel flows: U.S. Dept. Agriculture Tech. Bull. 1026, 71 p.

Einstein, H. A., and Chien, Ning, 1954, Second approximation to the solution of 

the suspended load theory: California Univ. Inst. Eng. Research, Missouri 

River Div. sediment ser. 3, 30 p.

 1955, Effects of heavy sediment concentration near the bed on velocity 

and sediment discharge: California Univ. Inst. Eng. Research, Missouri 

River Div. sediment ser. 8, 75 p.

Hubbell, D. W., and Matejka, D. Q., 1959, Investigations of sediment transportation, Middle Loup River at Dunning, Nebraska: U.S. Geo'- Survey 

Water-Supply Paper 1476, 123 p.
bed

LITERATURE CITED

Inter-Agency Committee on Water Resources, 19,

particle size analysis, in A study of methods used ir

of sediment loads in streams: Rept. 12, 55 p. 

Kalinske, A. A., 1947, Movement of sediment as bedUnion Trans., v. 28, p. 615-620. 

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

Standards, Jour. Research, v. 21, no. 6, p. 707-74 

Leopold, L. B., and Haddock, Thomas, Jr., 1953,

stream channels and some physiographic im]

Prof. Paper 252, 57 p. 

Meyer-Peter, E., and Muller, R., 1948, Formulas for

Assoc. Hydraulic Structures Research, 2d mtg., St 

Pafford, R. J., 1959, Operation of Missouri River

Soc. Civil Engineers Trans., v. 124, no. 2984. 

Rubey, W. W., 1933, Settling velocities of gravel,

Jour. Sci., 5th ser., v. 25, no. 148, p. 332. 

Sayre, W. W., and Albertson, M. L., 1959, The effect o

open channels: Fort Collins, Colo, Colorado State 

Searcy, J. K., 1955, Floods in Missouri, magnitude

Survey Circ. 370, 126 p. 

Searcy, J. K., Baker, R. C., and Durum, W. H., 19

St. Louis area, Missouri and Illinois: U.S. Geol. 

Shulits, Samuel, 1935, The Schoklitsch bed-load

p. 644-646, 687. 

Thomas, N. O., and Harbeck, G. E., Jr., 1956, Reser

U.S. Geol. Survey Water-Supply Paper 1360-A, < 

U.S. Congress, 1935, 73d Gong., 2d sess., H. Doc. 2

River). 

Vanoni, V. A., 1946, Transportation of suspended se<

Civil Engineers Trans., v. Ill, p. 67-133. 

Vanoni, V. A., and Brooks, N. H., 1957, Laboratory s

suspended load of alluvial streams: California ]

River Div. sediment ser. 11.

O

89

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iment by water: Am. Soc.

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