Summary of Alluvial 

Channel Data From Flume 

Experiments, 1956-61

By H. P. GUY, D. B. SIMONS, and E. V. RICHARDSON

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 462-1

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHING TON : 1966
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

Library of Congress catalog-care No. QS 66-219

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

Washington, D.C. 20402 - Price 70 cents (paper cover)
CONTENTS

Glossary of terms__-________-_

Symbols.----. _----__----__--

English-metric conversion table. 

Abstract_____________________

Introduction _________________

Equipment and sands--___--_- 

Equipment __ _ __---__-__

Operation procedure. -__-__---___-____._____-______-

Description of experimental variables and parameters. _ _ 

Water-surface slope. ___-__--___-_____._-________

Depth of flow__------_-_---------__-__-______._

Water discharge-_--_-_-_-_________________.____

Water temperature. __. --_----_-________--_______

Suspended-sediment concentration. _______________

Concent ra tion of total-sediment discha rge_ ___--_-__

Size gradation of sediment- _--________._____.-_._

Bed configuration _ _-___---_______--_____-___-_

Mean velocity of flow. -------__-_-___________--_

Velocity profile. --------_-_--___-_._________-___

Shear velocity. _________________________________

Bed-material discharge. -_-_-_-______________-___

Page

vi

vii

vii

I 1

1

2

2

3

3

6

7

7

7

8

8

8

8

9

9

9

9

Description of experimental variables and parameters 

Continued

Kinematic viscosity._____________________________

Shear stress at bed______________________________

Reynolds number--___________ __________________

Froude number.-__________-_-_--_____----__-___

Resistance factors.____________________________

Description of individual runs.__-___-____.._--________

Runs using 0.19-mm sand in 8-foot-wide flume. 

Runs using 0.27-mm sand in 8-foot-wide flume. 

Runs using 0.28-mm sand in 8-foot-wide flume. 

Runs using 0.45-mm sand in 8-foot-wide flume. 

Runs using 0.93-mm sand in 8-foot-wide flume_ 

Runs using 0.32-mm sand in 2-foot-wide flume_ 

Runs using 0.33-mm (uniform) sand in 2-foot-wide 

flume____________________________ ___________

Runs using 0.33-mm (graded) sand in 2-foot-wide 

flume____________________________________

Runs using 0.47-mm sand in 8-foot-wide flume. 

Runs using 0.54-mm sand in 2-foot-wide flume.

Basic data.______-______-_____---___--__---__---__-

References.____..___-____-______---_-___-_--_-__-_-

I 10 

10 

10 

10 

10

10

11

21

25

31

36

44

47

49

52

57

61

96

ILLUSTRATIONS

	Page 

FIGURE 1. Schematic diagram of 8-foot-wide flume__________________________________________________________ 13

2. Schematic diagram of 2-foot-wide flume. __.,________________________-__________________--------_-- 3

3. Particle-size distribution curves for bed materials having median sizes of 0.19, 0.27, 0.28, 0.45, and 0.93 mm. - 4

4. Particle-size distribution curves for bed materials having median sizes of 0.32, 0.33U, 0.33G, 0.47, and 0.54

mm_ _____________________________________________________________________________________ 4

5. Photographs of representative sand particles of bed materials used in the experiments-________------__- 5

6. Graph showing kinematic viscosity-temperature relation of aqueous dispersions of bentonite_____________ 10

7-30. Photographs showing flow and bed conditions for runs using 0.19-mm sand:

7. Longitudinal upstream view of the flume bed showing ripples, run 2__________-__-_--_------__ 11

8. Transverse view of ripple formation at end of run 2___________________-_--___-_------------ 11

9. Upstream view of ripples formed during run 25_ ___--------_--------_---------------------- 12

10. Transverse view of ripples formed during run 31 __--------_-------------------------------- 13

11. Upstream view of ripple pattern on flume bed at end of run 23 __ ____________________________ 13

12. Upstream view of bed configuration at end of run 32______________________________________ 13

13. Upstream view of ripple-dune pattern at end of run 8_______-------_-_-__^--_-__----------- 14

14. Downstream view of rippled-bed configuration through flow during run 3_-___----------------- 14

15. Upstream view of bed configuration at end of run 11_______-------------------------------- 15

16. Typical bed configuration at end of run 13_______________________________________________ 15

17. Upstream view of bed configurations at end of run 14_______________________-___--_--_------ 15

18. Upstream view of water surface during run 34_ ____-______-_______-___-_---_-_------------- 16

19. Upstream view of water surface during run 12_ ________________________---_---_------------ 16

20. Bed configuration at end of run 12, viewed upstream.-____________..______-------__--_-_--_-- 16

21. Upstream view of ripples on low dunes characteristic of run 6_------------------------------ 16

22. Upstream view of water surface during run 6_____---------_------------------------------- 17

23. Upstream view of bed configuration at the end of run 7________________-_-__-_-__----------- 17

24. Upstream view of water surface showing standing waves during run 16----------------------- 17

in
IV CONTENTS

FIGURE 7-30. Photographs showing flow and bed conditions for runs using 0.19-mm sand Continued Page

25. Upstream view of water surface showing antidunes during run 18___------_-_--_____________ 118

26. Side views of antidune flow during run 19________-----------------------_----------_______ 19

27. Upstream view of antidune wave pattern during run 21______________________________________ 19

28. Side view of breaking antidune during run 21_---_---------------------------------_--______ 20

29. Upstream view of chute-and-pool flow conditions during run 36_______________________________ 20

30. Side views of chute-and-pool flow conditions during run S7----------------------------------- 20

31-41. Photographs showing flow and bed conditions for runs using 0.27-mm sand:

31. Upstream view of ripples on the bed at the end of run 50 D____-_-___-----_-_______-________ 21

32. Upstream view of ripples on the bed at the end of run 51 ____________-------_-______________ 21

33. Upstream view of ripples on the bed at the end of run 52 ________________________________ 22

34. Upstream view of the bed configuration at the end of run 53_______-_---_-__________________ 22

35. Upstream view of bed configuration at the end of run 56.______--__----__-_______-__________ 23

36. Upstream view of bed configuration at the end of run 55____________________________________ 23

37. Side view of the sliding face of a dune during run 43________________________________________ 23

38. Upstream view of water surface during run 58____________-_-_-_-_-----_---_-______________ 24

39. Upstream view of bed configuration at the end of run 58___-_-_---___-------_-______________ 24

40. Downstream view of water-surface conditions during run 48_ --__--_-------_-_--____-________ 25

41. Downstream view of chute-and-pool flow during run 40_ _------_------------_-______________ 25

42-49. Photographs showing flow and bed conditions for runs using 0.28-mm sand:

42. Transverse view of rippled bed pattern at the end of run 9_-_________-_-____-_______________ 26

43. Upstream view of rippled bed form at the end of run 4_____________________________________ 26

44. Upstream view of the dune-bed configuration at the end of run 14__________________________ 27

45. Upstream view of the dune-bed configuration at the end of run 20__________________________ 27

46. Side view of avalanche face of a large dune formed during run 20___________________________ 28

47. Upstream view of bed configuration at the end of run 34__ __________________________________ 29

48. Flow and bed conditions for run 25_____________________________________________________ 30

49. Downstream view of antidune flow conditions during run 31__________-_-____________________ 30

50. Sketch of chute-and-pool phenomenon_______________-___-_-_-_-_---_-_-_-_---_-_-_-______________ 31

51-58. Photographs showing flow and bed conditions for runs using 0.45-mm sand:

51. Transverse view of ripples formed during run 18___________________________________________ 32

52. Upstream view of the dune-bed configuration at the end of run 21 ________________________ 33

53. Upstream view of the dune-bed configuration at the end of run 25__________________________ 33

54. Upstream view of the dune-bed configuration formed during run 23_________________________ 34

55. Flume conditions for run 27...---------------------------------------------------------- 35

56. Upstream views during and after run 36_ ___---_--_---_-----_-----_-----------____________ 35

57. Flow conditions during run ^2,-..-------------------------------------------------------- 37

58. Upstream views of flow conditions for run 45_ ___----------_----_--_-----------_-__________ 38

59-71. Photographs showing flow and bed conditions for runs using 0.93-mm sand:

59. Flume bed at end of run 14____________________________________________________________ 39

60. Upstream view of plane bed at the end of run Z2..----------------------------------------- 39

61. Upstream view of dunes formed during run 16____--____--____-_-_---_--__---______________ 39

62. Upstream view of the dune-bed condition at the end of run 35._______--_-_--____-___________ 40

63. Upstream view of low dunes on the flume bed at the end of run 33___________________________ 40

64. Upstream view of the dune configuration at the end of run 10- ___-------------_-----________ 40

65. Upstream view of dune-bed configuration formed during run 6_______________________________ 40

66. Upstream views of the flow conditions for run 11_________________________________________ 41

67. Erosion of narrow dune trough during run 12_.-_______________-___------___-______________ 42

68. Upstream views of flow and bed conditions for run 13-___-_----____-----____________________ 42

69. Flow conditions for standing waves during run 2__-_-_--__-_-_-___-----_-_____-_---_--_--__ 43

70. Upstream views of flow conditions for run 4___-__-__-__---___-___-------___-__-_---_-_____ 43

71. Upstream views of flow conditions for runs 43 and 39_______________________________________ 44

72-75. Photographs showing flow and bed conditions for runs using 0.32-mm sand:

72. Downstream view of dune-bed configuration formed during run 6__-__-_-------_---__-------- 45

73. Side view of dunes and flow conditions during run 8_---_-_--_____------------_---_--------_ 46

74. Side view of bed and flow during run 9__________________________________________________ 46

75. Side views of antidune flow conditions during run 15_ ___---_------_-------------------_---- 47

76-79. Photographs showing flow and bed conditions for runs using 0.33-mm (uniform) sand:

76. Upstream view of rippled flume bed at the end of run 8------------------------------------- 48

77. Flow and bed conditions for run 6________________________-______--------_---------_---- 48

78. Side view of standing waves during run ^------------------------------------------------- 49

79. Side view of breaking antidune during run 3__ __---_-_----____-__------"----_-----_-__---__- 49
CONTENTS V

FIGURE 80-86. Photographs showing flow and bed conditions for runs using 0.33-mm (graded) sand: Page

80. Upstream view of ripples at the end of run 16___-_-----------___-___-_____________________ 150

81. Upstream view of ripples formed during run 6___--_---__---_-_-___________________________ 50

82. Upstream view of ripples formed during run 5_ __------_------__---_-_-__-_________________ 51

83. Upstream view of the dune-bed configuration at the end of run 1_________________________ ___ 51

84. Upstream view of the dune-bed configuration formed during run 9___------_-_______________ 51

85. Upstream view of the dune-bed configuration at the end of run 2___________________________ 51

86. Upstream view of bed conditions at the end of run 12___-_____---____________._.__..______ 52

87. Particle-size distribution of bentonite used in flume studies.______________________________________ 52

88. Mineralogy of bentonite_____________________________________________________________________ 53

89-100. Photographs showing flow and bed conditions for runs using 0.47-mm sand:

89. Side view of ripples and lenses of fine material during run 88____-____-______________________ 54

90. Upstream view of the bed configuration typical of runs 93, 92, and 91____-___________________ 54

91. Upstream views of water surface during runs 51 and 96_--_--_____-_______-____________.____ 54

92. Upstream views contrasting dune shapes formed during runs 82 and 96___-_----______________ 55

93. Upstream view of water surface during run 95__---_---------___--_---_-_--_-______________ 56

94. Upstream view of water surface during run 78__--------------_-_--_--_____________________ 56

95. Upstream view of water surface during run 59_-_------------____-_--______________________ 56

96. Upstream view of water surface during run 60_ __-_----------____-__-_-_-_____________-____ 56

97. Upstream view of water surface typical of runs 64, 65, and 66_-------_---_--________________ 57

98. View of water surface typical of runs 81, 62, 67, and 79.-_-_--__---_--------_____________-__ 57

99. Upstream views of standing waves and breaking antidunes during run 84______________________ 58

100. Downstream view of antidunes during run 98__------------_-__--___--_--__-_______________ 58

TABLES

TABLE 1. General information about the sands used in the experiments._______________________________________ 14

2-11. Experimental variables and parameters for:

2. 0.19-mm sand in 8-foot-wide flume.______________________________________________________ 62

3. 0.27-mm sand in 8-foot-wide flume.______________________________________________________ 64

4. 0.28-mm sand in 8-foot-wide flume.______________________________________________________ 64

5. 0.45-mm sand in 8-foot-wide flume.______________________________________________________ 66

6. 0.93-mm sand in 8-foot-wide flume.______________________________________________________ 68

7. 0.32-mm sand in 2-foot-wide flume-.-------------------------------------------..-------- 70

8. 0.33-mm (uniform) sand in 2-foot-wide flume______________________________________________ 72

9. 0.33-mm (graded) sand in 2-foot-wide flume____-__-_-_____-_-_-_----__--_-_-_---_--_-_____ 72

10. 0.47-mm sand in 8-foot-wide flume._-_______-_-_-----____---______--_-____-__-----______- 74

11. 0.54-mm sand in 2-foot-wide flume_______________________________________________________ 76

12-21. Velocity-profile data for:

12. 0.19-mm sand in 8-foot-wide flume__----------------------------------------------------- 78

13. 0.27-mm sand in 8-foot-wide flume_______-____-___-_-___--___----_----__----------------- 80

14. 0.28-mm sand in 8-foot-wide flume._____--__-_-__----_______-___-_______---__---__---___- 81

15. 0.45-mm sand in 8-foot-wide flume_-__________-_-_____-______-----_-____--__-----------__ 83

16. 0.93-mm sand in 8-foot-wide flume._ _____-_-_-----_-_-__-_-_-----__----_----------_--___- 86

17. 0.32-mm sand in 2-foot-wide flume.______________________________________________________ 89

18. 0.33-mm (uniform) sand in 2-foot-wide flume.__________________ _ _________________________ 90

19. 0.33-mm (graded) sand in 2-foot-wide flume.______________________________________________ 90

20. 0.47-mm sand in 8-foot-wide flume_---_-----------_---__----------_---------------------- 91

21. 0.54-mm sand in 2-foot-wide flume._ _____________________________________________________ 95
VI CONTENTS

GLOSSARY OF TERMS

Alluvial channel. A channel whose bed is composed of noncohesive material that has been or can be transported by 

the flow.

Antidunes. Bed features that usually form in upstream-moving 

trains and are inphase with and strongly interact with 

gravity water-surface waves. The flow is in the upper flow 

regime; therefore, the water-surface waves have larger 

amplitudes than the antidunes. At higher Froude numbers, 

the surface waves usually grow until they become unstable 

and break in the upstream direction. The agitation accompanying breaking obliterates the antidunes, and the 

process of antidune initiation and growth is then repeated. 

At lower Froude numbers, the antidunes usually diminish 

in amplitude without the surface waves ever breaking.

Bar. A depositional feature whose length is of the same order 

as the channel width or greater, and whose maximum 

height is comparable to the mean depth of the generating 

flow. In longitudinal section, bars are approximately 

triangular, having very long gentle upstream slopes and 

short downstream slopes that are approximately the same 

as the angle of repose of the bed material. Alternate bars 

and point bars have transverse profiles that are triangular 

and taper from the bank to a point in the channel.

Bed material. The material of which a streambed is composed.

Clay. Sediment finer than 0.004 mm (millimeter), regardless of 

mineralogical composition.

Chute-and-pool flow. A flow condition that occurs where slopes 

are relatively steep and water-sediment discharges are 

relatively great, the channel consists of a series of pools, 

in which the flow is subcritical, connected by steep chutes, 

in which the flow is supercritical. A hydraulic jump forms 

at the downstream end of each chute, where the chute 

enters a pool. The chutes and pools may move slowly 

upstream.

Dunes. Bed features smaller than bars but larger than ripples 

that are out of phase with any water-surface gravity waves 

that accompany them. Dunes generally form at larger flow 

and sediment-transport rates than do ripples, but at smaller 

flow and transport rates than do antidunes; however, ripples 

often form on the upstream slopes of dunes at smaller rates 

of flow. In longitudinal profile, 'dunes are approximately 

triangular, having fairly gentle upstream slopes and downstream slopes that are approximately equal to the angle of 

repose of the bed material.

Fall diameter or standard fall diameter. The diameter of a 

sphere that has a specific gravity of 2.65 and the same terminal uniform settling velocity as the particle (any specific 

gravity) when each is allowed to settle alone in quiescent 

distilled water of infinite extent and at a temperature 

of 24°C.

Fine sediment. That part of the sediment discharge that 

consists of sediment so fine that it is about uniformly 

distributed in the vertical and is only an inappreciable 

fraction of the sediment on the streambed (referred to by 

some writers as wash load). Its upper size limit at a 

particular time and cross section is a function of the 

characteristics of the flow as well as of the characteristics 

of the sediment particles.

Flow regime. A range of flow conditions having somewhat 

similar resistance and sediment transport characteristics 

that produce similar bed forms.

Lower flow regime. Flow in sand channels which result in bed 

forms of ripples, ripples on dunes, and dunes.

Median diameter. Midpoint in the size distribution of a sediment, at which half the particles by weight are larger and 

half are smaller.

Plane bed. A bed form that has no irregularities larger in 

amplitude than a few grain diameters of the bed material. 

The plane bed in a sand channel that has movement of bed 

material occurs in the upper flow regime.

Ripples. Small triangular-shaped bed forms that have wave 

lengths of less than about 2 feet and heights of less than 

about 0.2 foot.

Sand. Sediment particles between 0.062 and 2.0 mm in diameter.

Sand waves. Crests and troughs (such as ripples, dunes, or 

symmetrical undulations) formed on the bed of an alluvial 

channel by the movement of the bed material.

Sediment. Fragmental material that originates from the disintegration of rocks and is transported by, suspended in, 

or deposited by water or air, or is accumulated in beds by 

other natural agencies.

Sediment concentration. The ratio of the dry weight of the 

sediment to the total weight of the water-sediment mixture, 

expressed in parts per million.

Sediment discharge. The amount of sediment that is moved 

by water past a section in a given length of time.

Silt. Sediment particles between 0.004 and 0.062 mm in 

diameter.

Suspended sediment. Sediment suspended in the flow by 

turbulent currents and (or) by colloidal suspension.

Standing waves. Virtually stationary waves that generally 

develop as a train. They are sometimes called nonbreaking 

antidunes.

Transition. A category for flows that mold bed forms ranging 

from those typical of the lower flow regime to those typical 

of the upper flow regime.

Upper flow regime. Flow in sand channels which results in 

bed forms of plane bed (with sediment movement), standing 

waves, and antidunes.

Velocity profile. Horizontal components of flow velocity in 

relation co depth at a vertical section over a point on the bed.
CONTENTS

SYMBOLS

VII

A 

B

C

CNg

Cf

Cs

Ct

D

d

R 

R

S

T

V

V*

W

7

Area of flow cross section.

Slope of semilogarithmic plot of velocity versus depth, above the bed.

Velocity at a depth of 1.0 foot above bed.

Chezy coefficient of discharge; equal to V/V*.

Concentration of fine-sediment discharge.

Concentration of suspended-sediment discharge.

Concentration of bed material discharge.

Average depth of flow.

Particle size in terms of fall diameter.

Particle size for which 16 percent of the sediment by weight is finer.

Median particle size of the sediment.

Particle size for which 84 percent of the sediment by weight is finer.

Darcy-Weisbach resistance coefficient; equal to V2 

V Froude number; equal to .

Acceleration of gravity (32.2 ft per sec per sec). 

Manning's resistance coefficient. 

Discharge of water-sediment mixture. 

Discharge of suspended sediment. 

Discharge of bed material. 

Hydraulic radius.

VD Reynolds number; equal to 

Water-surface slope.

Temperature.

Average velocity based on continuity principal.

Shear velocity; equal to -JgDS or

Width of flume.

Specific weight of water or water-sediment mixture.

Dynamic viscosity.

Kinematic viscosity.

Mass density of water.

A measure of sediment particle size gradation; equal to }4 I ^~ + "3~ I'

Shear stress or tractive force on bed; equal to yDS. 

Fall velocity of a particle.

sq ft

fps per log unit

fps

ppm 

ppm 

ppm 

ft

mm or ft 

mm or ft 

mm or ft 

mm or ft

ft per sec per sec

ft1'6

Cu ft per sec

Ib per sec per ft

lb per sec per ft

ft

°C

fps

fps

ft

lb per cu ft

Ib-sec per sq ft

sq ft per sec

slug per cu ft

lb per sq ft 

ft per sec

ENGLISH-METRIC CONVERSION TABLE

ft.

Principal items 

Depth of flow_ ----_-_________________.

Length and width of flume______________

Particle size___________________________

Hydraulic radius. _____________________

Area of cross section___________________

Velocity of flow_ ______________________

Fall velocity of particles...____________.

Velocity of bed configuration_________________ ft per min.

English unit

sq ft_

" > ft per sec.

Water discharge, _____ 

Sediment discharge. _ _ . 

Acceleration of gravity.

Shear stress._________

Kinematic viscosity. 

Dynamic viscosity _.

Specific weight. 

Ma Eass density.

Factor Metric unit

0. 3048_-_------ m

30.48----------- cm

304. 8-_---------- mm

J929. 0_____------- sq cm

\ .09290-------- sq m

/ 0. 3048_ ________ m per sec

\ 30. 48_ _.-------- cm per sec

0. 005080. _----_ m per sec

. 5080. ____---- cm per sec

. 01829___---_- km per hr

,, ,,. / 0. 02832__._--_- cu m per sec

cu ft per sec (cfs)____-_-_- j 2. 832X104 _ . _ __ cu cm per sec

lb per sec per ft__ _.____-- 1.488---------- kg per sec per m

f 0. 3048_ _-_--_-- m per sec per sec ft per sec per sec_ ________ \30.48___________ cm per sec per sec

T478. 8___--------- dynes per sq cm

lb per sqft______________ { 0. 4882____---_- g per sq cm

I 4. 882. _ ________ kgm per sq m

sq ft per sec . __________ 929. 0 sq cm per sec (Stokes

,. ,, / 0.04788.------- g per cm -sec (Poise) lb sec per sq ft__________. j 4482___.-_ - g-sec per sq cm

Ib.per cu ft_____-________ 0. 01602__----_- g per cu cm

slug per cu ft_ ___________ 0. 5154__------_ g per cu cm

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

SUMMARY OF ALLUVIAL CHANNEL DATA 

FROM FLUME EXPERIMENTS, 1956-61

By H. P. GUY, D. B. SIMONS and E. V. RICHARDSON

ABSTRACT

The primary purpose of this report is to summarize and make 

available to other investigators the results of the hydraulic and 

sediment data collected by D. B. Simons and B. V. Richardson 

in a unique series of experiments at Colorado State University 

between 1956 and 1961. The 339 equilibrium runs were made 

in 2- and 8-foot-wide recirculating flumes for 10 sets of conditions to determine the effects of size of the bed material, tempera'tnire of the flow, and fine sediment in the flow on the 

hydraulic and transport variables. The investigations for each 

set cover flow phenomena ranging from a plane bed and no sediment movement to violent antidunes.

INTRODUCTION

As a part of the research program of the Water 

Resources Division of the U.S. Geological Survey, a 

project was organized in September 1956 to study the 

mechanics of water and sediment movement in alluvial 

channels. Answers to questions on resistance to flow 

and sediment transport rates were sought at this time. 

The solutions to resistance and transport problems are 

complicated by the multitude of variables and parameters involved and by the complex interdependence of 

the variables.

The objective of the experiments was to obtain mean 

values of the resistance and transport variables and 

parameters for a large range of conditions most commonly found in natural streams and artificial channels. 

The large quantity of data required for a general solution to the problem was considered best obtained by 

use of recirculating flumes which tend to simulate 

conditions of uniform flow and sediment transport in 

an infinitely long channel. The recirculating-flume 

data are indirectly comparable to those for most 

streams where the water discharge, the imposed sediment discharge, and water temperature change considerably during the period of storm runoff. Such recirculating flume data are very comparable to data

for regulated streams and canals fed by ground water 

or man-made storage facilities and to data for streams 

in which the water discharge changes slowly.

This report is a compilation of the data for 10 sets 

of conditions, or for a total of 339 equilibrium runs in 

recirculating flumes. The investigations for each set 

covered flow phenomena ranging from a plane bed and 

no movement of sediment to the antidunes first described by Gilbert (1914). The general procedure of 

recirculating the water-sediment mixture aided in obtaining the equilibrium conditions, because the roughness elements which resisted the flow were formed by 

the flow and the respective sediment-movement characteristics. In the experiments used for this compilation, the form of the bed was changed from plane 

without sediment movement, to ripples, to dunes, to 

transitional, to plane with sediment movement, and to 

antidunes by altering flow conditions. For a set of 

runs with a specific sand and flume, discharge and 

slope were the principal controllable variants for altering flow conditions. Depth, velocity, fluid resistance, 

sediment discharge, and, to some extent, slope changed 

with time until equilibrium was reached.

The scheme of presentation in the report is to:

1. Describe the equipment and sands.

2. Describe the procedure of operation.

3. Describe the data obtained.

4. Describe the characteristics of the individual runs.

5. Tabulate the mean values of the basic data for each 

run.

6. Tabulate the velocity-profile data for the runs having such data.

The project was under the general supervision of 

L. B. Leopold, Chief Hydrologist, Water Resources 

Division, with technical guidance from P. C. Benedict, 

R. W. Carter, and others from the Geological Survey.

II
12 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

The principal investigators were D. B. Simons, project 

chief, and E. V. Kichardson. Technical guidance was 

also received from faculty members, especially from 

M. L. Albertson, at Colorado State University, where 

the project was located. The principal investigators 

were assisted in various phases of the work by W. L. 

Haushild, D. W. Hubbell, and E. K. Fahnestock, of 

the Geological Survey, and by H. J. Morel-Seytoux, 

E. J. Garde, A. A. Bishop, K. Al-Shaikh Ali, Niwat 

Daranandana, and H. C. Hilbrand, graduate students 

in Civil Engineering. The report was compiled after 

careful review of the original notes assembled during 

the laboratory work.

The data contained in this report have been used in 

several U.S. Geological Survey reports, professional 

societies' publications, and graduate student theses. A 

partial list of these papers, exclusive of those given as 

references, follows:

Bishop, A. A., 1961, Sediment transport in alluvial channels, a 

critical examination of Einstein's theory: Fort Collins, 

Colo., Colorado State Univ., Dept. Civil Eng., Ph.D. 

dissertation.

Chang, F. M., 1962, An investigation of total sediment discharge

in alluvial channels: Fort Collins, Colo., Colorado State

Univ., Dept. Civil Eng., Ph. D. dissertation. 

Chang, F. M., Simons, D. B., and Richardson, E. V., 1965, Total

bed-material discharge in alluvial channels: U.S. Geol.

Survey Water-Supply Paper 1498-1, 23 p. 

Daranandana, N., 1962, A preliminary study of the effect of

graduation of bed material on flow phenomena in alluvial

channels: Fort Collins, Colo., Colorado State Univ., Dept.

Civil Eng., Ph. D. dissertation. 

Garde, R. J., 1959, Total sediment transport in alluvial channels:

Fort Collins, Colo., Colorado State Univ., Dept. Civil Eng.,

Ph. D. dissertation.

Haushild, W. L., 1960, The effect of fine sediment on the 

mechanics of flow in alluvial channels: Fort Collins, Colo., 

Colorado State Univ., Dept. Civil Eng., M.S. thesis.

Haushild, W. L., Simons, D. B., and Richardson, E. V., 1961, 

The significance of the fall velocity and effective fall diameter of bed materials: U.S. Geol. Survey Prof. Paper 424-D, 

p. 17-20.

Hubbell, D. W., and Ali, Al-Shaikh, K., 1961, Qualitative effects 

of temperature on flow phenomena in alluvial channels: 

U.S. Geol. Survey Prof. Paper 424-D, p. 21-23.

Richardson, E. V., 1960, Sediment transport in alluvial channels 

(examination of Bagnold's 1956 hypothesis) : Fort Collins, 

Colo., Colorado State Univ., Dept. Civil Eng., M. S. thesis.

 1965, Resistance to flow in sand channels: Fort Collins, 

Colo., Colorado State Univ., Dept. Civil Eng., Ph. D. 

dissertation.

Richardson, E. V., Simons, D. B., and Haushild, W. L., 1962, 

Boundary form and resistance to flow in alluvial channels: 

Belgium, Internat. Assoc. Sci. Hydrology Bull., 5 p.

Simons, D. B., and Richardson, E. V., 1960, Resistance to flow 

in alluvial channels: Am. Soc. Civil Engineers Proc., v. 86, 

no. HY5, 27 p. Also published with closure in ASCE Trans., 

v. 127, pt. 1, no. 3360,1962, p. 927-1006.

Simons, D. B., and Richardson, E. V., 1961, Forms of bed roughness in alluvial channels: Am. Soc. Civil Engineers Proc., v. 

87, no. HY3, 19 p. Also published with closure in ASCE 

Trans., v. 128, pt. 1, no. 3414, 1963, p. 284-323.

 1963, A study of variables affecting flow characteristics 

in alluvial channels: Federal Inter-Agency Sed. Conf., 2d, 

Proc., ARS, Misc. Pub. 970, p. 193-207.

 1966, Resistance to flow in alluvial channels: U.S. Geol.

Survey Prof. Paper 422-J (in press).

Simons, D. B., Richardson, E. V., and Haushild, W. L., 1961, 

Variable depth-discharge relations in alluvial channels: 

U.S. Geol. Survey Prof. Paper 424-C, p. C45-C47.

 1962, Depth-discharge relations in alluvial channels: 

Am. Soc. Civil Engineers Proc., v. 88, no. HY5, 16 p.

Simons, D. B., Richardson, E. V., and Nordin, C. F., Jr., 1965, 

Sedimentary structures generated by flow in alluvial channels a symposium: Soc. Econ. Paleontologists and Mineralogists Spec. Pub. 12, p. 34-52.

 1965, Bed load equation for ripples and dunes: U.S. 

Geol. Survey Prof. Paper 462-H, 9 p.

EQUIPMENT AND SANDS

The flumes and related equipment used are in the 

hydraulic laboratory adjacent to the Engineering 

building on the main campus at Colorado State University. The bed materials were selected from natural 

river sands found within a few hundred miles of Fort 

Collins.

EQUIPMENT

Most of the data were collected in a recirculating 

flume 8 feet wide, 2 feet deep, and 150 feet long. The 

flow could be varied from 0 to 22 cfs (cubic feet per 

second) by use of two pumps and a valve control on 

the discharge lines. The slope of the plywood channel could be adjusted from 0 to 1.5 percent by screw 

jacks. A schematic diagram of this flume is shown in 

figure 1.

Many data relative to the effect of temperature and 

fine sediment on resistance to flow and sediment transport were collected in a recirculating flume 2 feet wide, 

21/2 feet deep, and 60 feet long that has l/2 -inch clearplastic sidewalls and a 14-inch stainless-steel plate 

floor. The flow could be adjusted from 0 to 8 cfs, and 

the slope, from horizontal to 10 percent. A schematic 

diagram of this flume is shown in figure 2.

Each flume has specific entrance conditions, wall 

roughness, and flow characteristics which may affect the 

flow and transport variables. A given run, therefore, 

cannot be reproduced exactly in another flume. These 

recirculating flumes with constant-head tailboxes most 

nearly duplicate flow conditions in alluvial channels, 

except for highly variable flow of sediment from 

tributaries.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 13

FIGURE 1. The 8-foot-wide flume. After Simons, Richardson, and Albertson (1961, p. 21). a, pumping units; b, orifices; c, headbox and diffuser; d, baffles and screens 

«, flume (8X2X150ft);/, tailgate; g, total-load sampler; h, tailbox; i, jacks supporting flume; j, connection to storage sump; k, transparent viewing window.

SANDS

The sands used for the 10 sets of experiments were 

obtained from 5 sources: a deposit of decomposed sandstone near Denver, Colo.; the Elkhorn Kiver near 

Waterloo, Nebr.; the Cache la Poudre Kiver at Fort 

Collins, Colo.; the North Platte River near Scottsbluff, 

Nebr.; and the Black Hills Silica Sand Corp., Hill 

City, S. Dak. These national sands were modified by 

sieving or washing away components of different sizes 

for some of the experimental sets.

The sands used as bed material in the experiments 

are identified by their median fall diameter. Table 1 

lists each sand, where it was obtained, the kind of

processing used, and the general character of the experiments. A particle-size distribution curve (size in 

millimeter versus percent finer than indicated size) is 

given in figures 3 and 4 for each sand. Figure 5 is 

a composite of photographs of each sand to show 

roundness, gradation, and relative size.

OPERATION PROCEDURE

The general operation procedure was the same for 

both flumes and for the various sand sizes. In a natural stream, depth is dependent on discharge, slope, 

bed roughness, and shape of channel. In a flume, only 

discharge and shape of channel can be controlled 

precisely, and slope only approximately. Slope and

FIGURE 2. The 2-foot-wide flume. After Simons, Richardson, and Haushild (1963, p. 3). a. pumping unit; b, motor; c, center support; d, orifice; «, flexible connection 

/, jacks; g, manifold diffuser; h, headbox; i, baffles and screens; j, rails; k, instrument carriage; I, flume (2X2.5X60 ft); m, tailgate; n, total-load sampler; o, tailbox.
14 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 

TABLE 1. General information about the sands used in the experiments

Median 

size 

(mm)

0.19 

.27

.28 

.45

.93 

.32 

.33TJ

.33G 

.47

.64

Gradation

<r

1.30 

1.56

1.67 

1.60

1.54 

1.57 

1.25

2.07 

1.54

1.52

Source of sample

Decomposed sandstone near 

Denver, Colo. 

Elkhorn River near Waterlou, 

Nebr. 

- do--.- 

Cache la Poudre River at Fort 

Collins, Colo. 

North Platte River near Scottsbluff, Nebr. 

Elkhorn River near Waterloo, 

Nebr. 

Black Hills Silica Sand Corporation, S. Dak. 

. .do--.. .

Cache la Poudre River at Fort 

Collins, Colo.

 do... 

Method of obtaining and processing sand

The sandstone was run through a hammermill to break up the large 

chunks and then washed to remove the clay binder.

From 0.27-mm sand. Coarser sand retained as fines were washed 

away in overflow.

From 0.45-mm sand. Coarser sand retained as fines were washed 

away in overflow.

From 0.45-mm sand. Coarser retained as fines were washed away in 

overflow.

Type of study

 .do-- - . -

 do-- 

 . . .do.-. ... .... 

 -.do.-- -

Effect of viscosity by varying 

temp.

 ..do-.. 

Effect of viscosity by varying 

concentration of fine sediment. 

 ..do.-.- - 

Width of 

flume 

used (ft)

S 

8

8 

8

8 

2 

2

2

8

2

depth reach equilibrium in accordance with the bed 

roughness for specific flow conditions.

The procedure followed for some runs involved 

recirculating a given discharge of water-sediment mixture in the flume at a preselected slope until equilibrium conditions were established. Equilibrium here 

should be defined as a condition of statistically uni99.9

0.080.1 0.2 0.3 0.40.50.6 0.81.0 

DIAMETER, IN MILLIMETERS

2.0 3.0

FIGURE 3. Particle-size distribution curves for bed materials having median sizes 

of 0.19, 0.27, 0.28, 0.45, and 0.93 mm.

form velocity, concentration, and slope with respect to 

both time and space in the flume where the variables 

are observed. Even though discharge can be held 

relatively constant, depth, slope, and sediment discharge in the final equilibrium condition (several hours 

or days after the start of the run) could be consider99.9

0.080.1 0.2 0.3 0.4 0.50.6 0.8 1.0 

DIAMETER, IN MILLIMETERS

2.0 3.0

FIGURE 4. Particle-size distribution curves for bed materials having median sizes 

of 0.32, 0.33TJ, 0.33G, 0.47 and 0.54 mm.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 15

 > « V, ~ * :*- ^".* m?" " - *» s^^k^. '

iiitiinipiio.45

»> **..<* -. " -ov F,.if MH Hi 0.3 2

33

FIGURE 5. Representative sand particles of bed materials used for the 10 sets of experiments. The number in the lower right corner of each 

photograph is the median diameter of the sand, in millimeters. The scale also is in millimeters. See table 1 for further description of 

each sand.
16 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

ably different from those in the initial condition. For 

some runs depth was kept constant either by adjusting 

the tailgate slope or discharge. For some other runs 

slope was kept constant either by adjusting the tailgate 

or the discharge, or both.

For runs having a relatively high rate of sediment 

discharge and requiring a short time to reach equilibrium (slopes greater than 0.006 ft per ft), the slope 

was preset by adjusting the tailgate and allowing the 

bed to adjust itself by scour and fill. For runs with 

Froude numbers greater than 1, the tailgate was often 

completely removed. For runs having a low rate of 

transport (slopes less than 0.006 foot per foot), the 

desired preset slope was established by planing or 

screeding the bed and then adjusting the tailgate to 

make the slope of the water surface parallel to the bed.

The nonequilibrium flow caused by change of bed 

roughness was eliminated by continuing the run until 

the average bed slope and the average slope of the 

water surface became parallel by natural adjustment 

of the sand bed. Equilibrium flow was considered as 

established, and collection of the data started, when 

(1) the bed configuration was consistent in the full 

length of the flume, excluding the sections influenced 

by entrance or exit conditions, and (2) the average 

water- and bed-surface slopes remained constant and 

parallel with respect to time. The time required to 

establish equilibrium conditions varied with the slope 

and the discharge. Some runs on flat slopes required 

3 or 4 days to achieve equilibrium, whereas runs on 

steeper slopes established equilibrium within 2 or 3 

hours. In each run, the flume was operated continuously until equilibrium had been reached and the necessary data collected. To insure the achievement of equilibrium conditions, most runs were continued longer 

than the required time as indicated by observations of 

variables likely to change prior to equilibrium.

The general procedure was different for the 0.47-, 

0.54- and 0.32-mm sands. After equilibrium had been 

established and the data collected for a given run, 

the run was continued and, for the 0.47- and 0.54-mm 

sands, bentonite was either added or extracted from 

the flow, or, for the 0.32-mm sand, the temperature 

was changed. The new run was then continued until 

equilibrium was again established, and the necessary 

data collected. This procedure of adding or extracting bentonite or changing the temperature without 

stopping the flow was continued for a series of runs.

DESCRIPTION OF EXPERIMENTAL 

VARIABLES AND PARAMETERS

Following the operating procedure discussed led to 

the establishment of equilibrium conditions for a 

given run. Two or more measurements of slope made

some time apart were required prior to the data-collection phase to insure that equilibrium had been established. In this investigation, slope observations were 

not started until visual inspection showed that a relatively systematic bed configuration and, consequently, 

a uniform resistance to flow had been established the 

full length of the test section.

When the rough movable boundary occurred in the 

flume, flow and transport values varied considerably 

during a given run. As a result, representative average values for all the basic variables had to be obtained 

by making successive observations during a relatively 

long period of time. The frequency and the time period over which the observations were made depended 

mainly on the bed form. For example, a few slope observations over a short time were sufficient to give a 

reliable average for the rippled condition; but many 

observations over a long time were required for the 

dune condition.

The following kinds of data were collected and are 

reported in tables 2-11 ("Basic Data" section) :

1. Water surface slope.

2. Depth of flow.

3. Water discharge.

4. Water temperature.

5. Suspended-sediment concentration.

6. Concentration of total bed-material discharge.

7. Size graduation of sediment.

8. Bed configuration.

Several of these measured variables cen be used to 

compute other variables and parameters useful for 

evaluating flow and transport characteristics in the 

flume channel. These variables include:

1. Mean velocity.

2. Velocity profile.

3. Shear velocity.

4. Sediment discharge.

5. Kinematic viscosity.

6. Shear at bed.

7. Reynolds number.

8. Froude number.

9. Resistance factors.

The inherent errors of each computation are proportional to the errors in the observation data. More 

specifically, the composite error (&X) of the computed 

variable or parameter will be

. . . -\-mnXn

where Xi to Xn is the error of specific observation 

data, mi to mn is the exponent of the respective X's, and 

Ti is the number of X's.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 17

WATEB-SUBFACE SLOPE

The water-surface slope (col. 2, tables 2-11) was 

determined by observing the water-surface elevation 

with a level and a mechanical point gage, and also 

with a differential bubbler gage (Barren, 1963). The 

slopes computed using data from both methods were 

in close agreement.

The mechanical point-gage method consisted of 

reading the level of the water surface every 5 feet 

along the centerline of the flume. The point gage was 

mounted on a four-wheeled carriage that traveled on 

rails mounted on the walls of the flume. Levels were 

run on the gage at all locations for which watersurface readings were required. Three to eight sets of 

water-surface readings were made for each run after 

equilibrium was reached and during the period of data 

collection. The elevations for each point along the 

centerline may be plotted separately or averaged to 

obtain a mean slope. The average for each of the 

points was used to compute a least-squares regression 

for the runs with the 0.45-mm sand. The slope was 

determined graphically for the runs using the other 

sands. A study of the two methods indicated that both 

were sufficiently precise to yield slope values with no 

more error than is inherent in other variables.

Slope measurements taken after attainment of 

equilibrium conditions were used to determine the 

average slope. Also, water-surface elevations reflecting nonuniform flow at the entrance and exit of the 

flume were discarded.

The bubbler gage continuously recorded the difference in elevation of the water surface to within 0.001 

foot between two points, and from this difference the 

water-surface slope was computed. The bubbler-gage 

connections to the 8-foot-wide flume were 100 feet 

apart. The continuous record of slope, as computed 

from the bubbler-gage headings, was used to determine when equilibrium conditions were established. 

The bubbler gage was not used in the 2-foot-wide 

flume or in the 8-foot-wide flume for the 0.45-mm 

sand.

Any error in the mean-slope value reported for each 

run can be attributed to two major sources: (1) the 

plus or minus 0.001 foot accuracy for the bubbler gage 

or the individual point-gage readings, and (2) the 

variation about the mean for a series of readings for 

the bubbler gage or the point gage. If the error for 

the bubbler gage is 0.001 foot in 100 feet, the absolute

error for the gage is

1QS

For the finer sands, this

alone would be 5-10 percent for slopes where sediment 

particles move occasionally. A 0.001-foot error in the 

point-gage reading is much less significant when

plotted with several other readings. The variation 

about the mean for bubbler-gage readings is caused 

mostly by the effect of the bed forms moving near the 

orifices to the bubbler gage in the flume. Variation in 

the point-gage readings at a specific location is also due 

to the movement or shape of bed forms near the pointgage readings. This variation may cause errors of 

as much as 15-20 percent, depending on the size 

of the bed forms, the relative slope, and the number of observations.

DEPTH OF FLOW

The average depth of flow (col. 3, tables 2-11) was 

determined by observing the difference in elevation 

between the water surface and the sand bed with a 

point gage. Observations were made at preselected intervals down the length of the flumes. The selection 

of the interval depended upon the bed configuration 

that existed for the run, the intervals being closer 

spaced for a dune-bed configuration than for an antidune or a ripple-bed configuration. Only those depths 

observed in the part of the flume having uniform slope 

were used to establish the average depth. Because of 

the rapid changes in water-surface elevation at a point 

and the softness of the bed, especially for runs in the 

lower flow regime, many depth observations were required to obtain a reasonably accurate average value.

This method of observing depth was used for all the 

sands except the 0.45-mm size. Observations of depth 

for the 0.45-mm sand were made by determining the 

elevation of a screeded 30-to-40-foot central section of 

the sand bed and determining the average elevation of 

the water surface at times when the surface was relatively smooth. The two methods of observing depths 

yielded virtually the same results. The observations of 

average depth are considered accurate to plus or minus 

0.03 foot. At a depth of 0.60 foot, the observation is 

therefore accurate to plus or minus 5 percent.

WATEB DISCHARGE

Water discharge (col. 4, tables 2-11) was determined in the return-flow lines with calibrated orifice 

meters connected to water-air manometers. The orifice 

meters were located in the lines to avoid the possible 

effect of sand deposits on the calibration. They were 

checked periodically to determine if any change had 

occurred in the calibration from abrasion by the sand. 

The individual observations are considered accurate to 

plus or minus 2 percent. The mean discharge for each 

run is determined from the average of 5-15 readings 

made during the period of data collection.

"Water discharge" actually means the discharge of 

the water-sediment mixture. For example, a concen-
18 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

tration of 50,000 ppm (parts per million) of sediment 

means that 5 percent of the water-sediment mixture is 

sediment by weight, or nearly 2 percent of the mixture is sediment by volume. The orifice meters were 

calibrated in clear water. However, a study by Nobuhiro Yotsukura (written commun., 1961) proved 

that the use of clear water to calibrate the meters 

would not produce any appreciable error in the sediment concentrations used in the course of this study.

WATER TEMPERATURE

The water temperature (col. 5, tables 2-11) was 

measured to the nearest half of a degree centigrade 

with a mercury thermometer. The temperature reported for each run was based on an average of 5-10 

readings obtained during the data-collection phase of 

each run. The average temperature recorded for each 

run should be correct to plus or minus 3 percent.

SUSPENDED-SEDIMENT CONCENTRATION

Suspended-sediment concentration is defined as the 

ratio of the weight of solids to the weight of the 

water-sediment mixture. Suspended sediment (Col. 6, 

tables 2-9, and col. 7, tables 10, 11) was sampled 95- 

100 feet downstream from the headbox of the 8-footwide flume and 35 feet downstream from the headbox 

of the 2-foot-wide flume with a specially designed 

depth-integrating sampler. The sampler consisted of a 

brass nozzle 3 inches long and V4 inch in diameter 

attached to a "wading rod." The nozzle was connected 

to a flexible tube. A water-sediment sample was drawn 

through the tube to a container by means of a vacuum 

pump which was adjusted to draw in the fluid at a 

velocity approximately equal to the velocity of the 

flow. With this equipment, 5- to 8-pound samples of 

water-sediment mixture were collected from two to 

four times during each run by a mechanical integration of the flow in the cross section. The integration 

was attained by traversing the sampler through 

equally spaced verticals at an equal transit rate for 

each vertical.

Some suspended-sediment concentrations were found 

to be larger than corresponding concentrations of bedmaterial discharge. This difference was due, in part, 

to the inadequate number of suspended-sediment samples, and to the possibility that samples were taken in 

a region of flow where local shear stress and turbulence were much greater than average. The standard 

deviation given in column 7, tables 2-9, is based on 

the variation among the individual samples and has 

considerable range depending on the number of samples, the flow, and the bed conditions.

CONCENTRATION OF TOTAL-SEDIMENT DISCHARGE

The concentration of total sediment discharge (col. 

9, tables 2-11) was obtained with a width-depth integrating sampler located at the nappe where the flow 

dropped from the flume into the tailbox. For all sands 

except the 0.45-mm size, on a dune-bed configuration, 

eight or more samples were collected during a 2-hour 

period. For the 0.45-mm sand size, on a dune-bed configuration, and for all sands at all other bed configurations, four to six samples were taken in a 1-hour period. Each sample consisted of 70-110 pounds of the 

water-sediment mixture. For all sets of data except 

those for the 0.45-mm sand, the mean concentration 

obtained for each run is considered accurate to plus or 

minus 5-10 percent for concentrations in excess of 100 

ppm, and to plus or minus 10-50 percent for concentrations between 1 and 100 ppm. The standard deviation given in column 10 of tables 2-11 is based on the 

variation among the individual samples.

For the experiments using the 0.47- and 0.54-mm sand 

where fine sediment was added to the flow, the concentration of fine sediment was determined from a sample 

(about one liter) taken from the large 70- to 110-pound 

sample of the water-sediment mixture after the large 

sample settled for 1 minute. The bed-material fraction 

(col. 9, tables 2-11) of the total-sediment discharge 

was that material retained after washing on a No. 200 

sieve. To obtain the total-sediment discharge, the finesediment concentration (col. 6, tables 2-11) must be 

added to the bed-material discharge (col. 9, tables 

2-11). Of course, for those experiments where fine 

sediment was not added to the flow, the bed-material 

discharge was the total-sediment discharge.

SIZE GRADATION OF SEDIMENT

The median particle size and (or) the gradation distribution in terms of fall diameter of each suspendedand bed-material-discharge sample and each bedmaterial sample (cols. 8, 11, 12, and 13, tables 2-11) 

was determined by drying the total sample, splitting 

it into a workable size, and then analyzing it in the 

visual-accumulation tube (Inter-Agency Keport No. 

11, 1957). Each bed-material sample consisted of several 0.1-foot-diameter cores, about 0.6 foot in length, 

taken at random from the bed of the flume. In the 

sets of runs where fine sediment was added to the 

flow, the fine sediment was washed out of the sample 

before the sample was dried, split, and analyzed.

The particle-size distribution curves given in figures 

3 and 4, the average median diameter of the sand, and 

the gradation coefficient of the bed material were determined by averaging the results of the size analysis of
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 19

the bed material for all runs of a given set and sand. 

The gradation (a) is determined by the equation

. i/ (^ _i_ ^sA =% I j- + j- y

\«16 «50/

in which d^ is the median size and d\§ and c^4 are the 

respective sizes for which 16 and 84 percent of the 

sample is finer than the indicated size.

BED CONFIGURATION

The general bed configuration (col. 30, tables 2-11) 

was noted visually and recorded photographically 

through the observation window in the side of the 

flume, at the water surface through the central measuring section of the flume, and at the bed surface in the 

flume. The bed-surface observations were made either 

through the water, if the water was sufficiently clear, or 

from the flume at the end of the run after the water had 

been carefully drained out.

A sonic depth sounder was being developed during 

the collection of most of these data (Richardson and 

others, 1961). After development of the sounder, sonic 

data were obtained over ripple-and-dune runs by (1) 

setting the sounder at a stationary point and allowing 

the sand wave to move past the sounder, and (2) traversing the sounder over the length of the flume at a 

predetermined uniform velocity.

The length, height, and velocity of the sand waves 

(cols. 14-16, tables 2-11) were evaluated by:

1. Observations through the wall of the flumes marked 

by a grid.

2. Observations in the center of the flume by point 

gage and foot attachment.

3. Observations by a sonic sounder.

The sonic-sounder method was only applicable when 

the bed configuration was ripples, dunes, or transitiondunes. The number of observations made for each run 

was generally considered adequate to define within 

plus or minus 10 percent, the mean values reported.

MEAN VELOCITY OF FLOW

The velocity of flow of a stream is usually determined 

from a series of velocity readings in the stream section. 

In the flume, however, the mean velocity (col. 17, 

tables 2-11) was determined from the observed values 

of discharge (Q), depth (D), and width (W) by use of 

the continuity equation,

VV ~A~DXW _Q __Q_ 

The expected error of V from the above equation would 

be about 6 percent if, for example, Q and D had errors 

of 3-5 percent, respectively. A small error in W

791-597 O 66 2

would be constant for all runs and thereby be canceled 

with respect to evaluation of other variables.

VELOCITY PROFILE

Velocity-profile data, obtained from the horizontal 

movements of flow at specific verticals in the flow, are 

reported in tables 12-21. The observations were made 

with a standard Prandtl pitot tube which had been 

calibrated in a towing tank. Tables 12-21 show the 

velocity at various distances above the sand bed for 

most runs.

The magnitude and shape of the velocity profile in 

open-channel flow depend on the bed roughness and 

on the sediment-transport characteristics. The bed 

roughness and transport, in turn, depend on several 

waves. Figure 28 shows a breaking wave. The bed 

material, and viscosity of the water-sediment mixture.

Except for the plane-bed run, the velocity profiles 

were not constant with either time or space. As the 

bed configuration changed with time, so did the velocity profiles. In consideration of the time required to 

obtain a single velocity profile (5-15 min.), there was 

some change in the profile during the measurement. 

Also, the velocity profiles did not plot as a straight 

line on semilogarithmic paper (Vy = B log y + C) 

except for those for the plane-bed runs and some made 

on the back of the ripples or dunes near their crest.

The profile data were plotted on semilogarithmic 

paper with depth (log) as the ordinate and velocity as 

the abscissa. A "best fit" straight line was then used 

to define the relation between Vv and log y (that is, 

VV=B log ?/ + <7), where B defines the slope of the 

line in terms of velocity per log unit, and C defines the 

intercept of the line at a depth of 1.0 foot above the bed 

in terms of velocity. The values of B and (7, although 

of limited utility for the dune runs, are listed in 

columns 18 and 19 in tables 2-11.

SHEAR VELOCITY, V*

Shear velocity (col. 20, tables 2-11) is defined as 

 \lgDS, or VT/P- The error in V* would be about 7 

percent if D and S both have errors of 10 percent, 

or about 5 percent if D and S have errors of 10 and 4 

percent, respectively.

BED-MATERIAL DISCHARGE, q, AND g t

Bed-material discharge (cols. 21-22, tables 2-11) 

was computed from Q, Cs or Ct, and a constant. Since 

q_s and gt are expressed in pounds per second per foot

of width, &=^X<7*X0.0000624, and t=

X0.0000624. If Q, W, and Cs or Ct have average 

errors of 5, 2, and 10 percent, respectively, then the 

mean error for q_B or q t is about 10 percent.
110 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

KINEMATIC VISCOSITY, v

The kinematic viscosity (v) of the water-sediment 

mixture (col. 23, tables 2-11) was determined from the 

temperature of the water and appropriate standard 

tables. For runs in which fine material (bentonite) 

was added to the flow, the "apparent" kinematic 

viscosity was determined from figure 6. Dynamic 

viscosity values were determined by testing waterbentonite mixtures in a Stormer Viscometer (Simons 

and others, 1963, p. 17) for 0.5-, 1-, 2-, 3-, 5-, and 

10-percent concentrations and for a temperature range 

from 5° to 45° C. The "apparent" kinematic viscosities plotted in figure 6 were computed from the 

dynamic viscosity values (n) and the density of the

water-bentonite mixture (p); v=--

p

SHEAR STRESS AT BED, r

The shear stress (T) or tractive force at the bed 

(col. 24, tables 2-11) is a parameter commonly used as 

a measure of the intensity of forces related to resistance 

to flow and transport of sediment particles. It is 

computed 'by the formula

r=7DS,

where D and S are from columns 3 and 2, tables 2-11, 

respectively, and y is the specific weight of water 

(62.42 Ibs per cu ft at 0° C).

15.0

EXPLANATION

Concentration

Symbol of bentonite

(ppm x 104 )

0.5 and 1.0 

2.0 

3.0 

5.0 

10.0

0.6

10 15 20 25 30 35 

TEMPERATURE, IN DEGREES CELSIUS

FIGURE 6. Relationship of "apparent" kinematic viscosity of aqueous dispersions 

of bentonite to temperature.

REYNOLDS NUMBER, R

The Reynolds number, R (col. 25, tables 2-11) is a 

ratio of the viscous force to the total inertial force in 

the channel:

R - - 

VDP or VD

It is commonly used as a measure of the effect of viscosity on the flow pattern.

The Reynolds number is also often used with respect 

to a sediment particle:

R n = > or ,

where w is fall velocity of the particle and d is fall diameter of the particle.

FROUDE NUMBER, F

The effect of gravity on the flow pattern is commonly 

related to the Froude number, F (col. 26, tables 2-11), 

which is the ratio of the gravity force to the total inertial force. As commonly used and reported herein,

F=

RESISTANCE FACTORS, /, C/Vrf, n

Parameters related to average resistance to flow in 

channels are based on the variables S, D, and V. They 

are:

1. Darcy-Weisbach resistance coefficient, /= V^ 

2. The dimensionless Chezy discharge coefficient,

Tr V

(Jl^~g~~ or Note that the discharge coefficient is the inverse of resistance.

3. The Manning n, n= y > where D is nearly

equal to R the hydraulic radius. These resistance 

factors are listed in columns 27-29, tables 2-11.

DESCRIPTION OF INDIVIDUAL RUNS

This section of the report documents pertinent laboratory notes from general and unusual observations 

of the flow and transport phenomena during the period in which the run was approaching equilibrium 

and during the collection of the routine basic data. 

Most notes refer to methods used to set up the runs, 

the bed forms, the flow characteristics, and to unusual 

conditions relative to data collection. Many photographs were taken to show the flow and roughness 

characteristics. The photographs were generally taken 

either through the glass wall at the side of the flume, 

from above the. water surface, or from above the bed
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 111

surface after careful draining of the flume at the end 

of the run.

Notes and corresponding photographs, if any, for 

each run are headed by the respective run number. 

These make up the set of runs for a specific sand and 

flume size. The run numbers and the order of presentation (usually by increasing slope) correspond to the 

run numbers and order given in tables 2-11.

RUNS USING 0.19-MM SAND IN 8-FOOT-WIDE FLUME

The sand used in this set of runs was the finest 

used during the investigation. The runs were made between November 3, 1959, and January 21, 1960. The 

experimental variables and parameters are given in 

table 2, and the velocity-profile data in table 12.

Run %4- The data are an average from two runs 

during which slope, discharge, depth, and temperature 

remained nearly the same. Beginning of motion or 

transport occurred at a low slope (S = 0.00006) because of the fine sand and the 0.94-foot depth of flow. 

The error in the mean slope measurement was in the 

order of 10-20 percent. The problem of determining 

when beginning of motion occurred (Rubey, 1937) was 

further complicated by the effect of small local irregularities on the bed. Particle movement on the bed 

nearly ceased as very small ripples became established. 

The ripples, in turn, increased roughness and depth, 

and decreased velocity. Equilibrium was thus established.

Run 22A. The bed material was carefully screened 

to a plane, and then flow was established to a depth of 

0.6 foot. Slope was increased and depth decreased by 

opening the tailgate in small increments until beginning of sand particle motion was observed. With Q 

2.99, T = 17.5, S = 0.00010, and D = 0.48, there was 

some movement of lightweight particles. The coarse 

light-weight particles (0.5-1 mm) which moved on the 

bed surface were sand grains cemented with a clay 

material. This coarser material collected along with 

the fine material into isolated ridges about 0.005 foot 

high.

Run 2. The conditions for this ripple run were 

similar to those for run 1 (page 112) except that depth 

and discharge were doubled and slope was reduced. 

Movement of the bed material in the form of very 

slowly moving ripples occurred throughout the flume. 

No armor plating developed, as it did in runs using 

coarser sands. The ripple waves seemed very fluid and 

soft in comparison to the troughs. Depth measurements may have been too great, owing to the ease with 

which the probe penetrated the surface of the sand 

waves. The average concentration from eight samples 

was used to determine bed-material discharge. Longitudinal and transverse views of the ripples are shown 

in figures 7 and 8. The photographs were taken after 

the water was slowly drained from the flume, without 

disturbing the ripples. The troughs between many 

ripples appeared flat owing to water standing in the 

depressions.

Run 22B. This run was established from 22A by 

increasing the slope to 0.00016 and, thereby, decreasing 

the depth to 0.43 foot. All the particles moved occasionally, and then, very slowly as the slope was increased. Careful observation was required to detect 

such small amounts of movement. Slight indentations,

FIGURE 7. Longitudinal upstream view of the flume bed, showing ripple formation 

at end of run 2 after slowly draining the water from the flume.

FIGURE 8. Transverse view of ripple formation at end of run 2. The direction of 

flow was from left to right.
112 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

similar to those described by Bagnold (1956), formed 

on the bed as primary features (the beginning of ripple 

forms) . Ripples that formed upstream from station 15 

were caused by entrance effects and should not affect 

data relative to beginning of particle motion.

Run 26. Some particle movement occurred over the 

entire flume bed. Large particles moved farther than 

smaller particles. These larger particles (0.2-0.3 mm) 

collected together and formed very small ridges spaced 

about the same as those ordinarily formed by ripples. 

It may be concluded that this segregation was responsible for the formation of ripples, except that other 

investigators (Brooks, 1958; Liu, 1957) reported such 

ridges and ripples when using a more uniform sand.

Run 25. The conditions for this run were the same 

as for run 24 except that the slope was steeper. The 

bed was completely covered with very small ripples 

while the water surface was very tranquil. Ripples began to form wherever there was a slight bed irregularity, such as a large particle, and, motion having 

begun, continued to form progressively downstream 

and laterally from this point. A few coarse clay particles rolled freely on the sand surface until stopped 

by a depression or another large stationary particle. 

The ripple waves were fluidlike or soft to the probe. 

Figure 9 shows the smaller size of ripples formed in 

this run, in contrast with those formed in run 2. Note 

the absence of a plane with respect to the troughs of 

the ripples.

Run %%C. This run was a continuation of runs 22A 

and 22B, but at a slightly increased slope and decreased depth. Movement of sediment was general over

FIGURE 9. Upstream view of ripples formed during run 25. Ripples are smaller and 

more completely developed than those formed in run 2 (figs. 7, 8).

the entire bed, and thus ripples formed over most of 

the bed within about four hours after starting the run. 

Beginning of motion was best represented in run 22B. 

The rate of transport was very low; therefore, sediment samples were not taken.

Run 30. The bed was screeded prior to starting the 

run, and the slope of the bed was set parallel to an 

assumed water surface slope which would insure uniform flow over ripples at the desired depth of about 

1 foot. The ripples formed a more irregular pattern 

than did those of runs with less shear. The water surface was tranquil or mirrorlike. The individual ripples 

changed shape with time and moved very slowly. The 

bed-material discharge, determined from nine samples, 

ranged from 3.1 to 4.3 ppm (parts per million), and 

the suspended-sediment concentration of four samples 

was composited and equals 7.0 ppm.

Run 1. This run was started with the bed screeded 

level. Small ripples 0.3-0.4 foot long and 0.02 foot 

high covered the entire bed immediately after the run 

began. The ripples gradually increased in length and 

height to about 0.6 foot and 0.05 foot, respectively. 

Ripple crests were very soft and fluidlike in comparison with the intervening troughs. The transport rate 

was very low; so that the velocity of the ripples was 

extremely slow. The run had been in progress for 

about 40 hours before data were taken. The bed-material discharge, determined from eight samples, 

ranged from near 0 to 3 ppm. Suspended-sediment 

concentration was not measured.

Run 31. Ripples formed under the flow conditions 

of this run were larger and had more irregular patterns than those formed at lower slope and depth. 

The velocity was such that sand was eroded at the 

headbox and moved downstream as a wave. This wave 

affected the water-surface slope downstream to station 

45. The ripple waves in the test section seemed to be 

much softer than the underlying, nonmoving material. 

A transverse view through the flowing water (fig. 10) 

shows the more triangular shape of the ripples, in 

contrast with those shown in figure 8. The seven bedmaterial discharge samples ranged from 25.0 to 34.9 

ppm, and the four suspended-sediment samples was 

composited and equals 42 ppm.

Run 27. The shifting part of the bed was very 

fluid, but the underlying part was firm because of 

screeding. The seven bed-material discharge samples 

ranged from 3.1 to 5.1 ppm. Suspended-sediment 

movement was negligible; therefore, samples were not 

taken. The measured bed-material discharge was less 

than was expected for the given hydraulic conditions.

The pattern of ripple development for all runs suggested that flow conditions can easily be set up which
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 113

FIGUBE 10. Transverse view, through the flowing water, of ripples formed during 

run 31. The direction of flow is from left to right.

will form very uniform ripples of small amplitude that 

are nearly continuous across the flume. Then, slightly 

increasing shear stress by increasing depth or slope will 

cause larger more irregular ripples to form which are 

distinctly discontinuous across the flume.

Run 5. Run 4 was not completed because of a sand 

wave in the flume. The bed form of run 5 was large 

ripples. The bed was very soft, particularly on the 

crest of the ripples. The large ripples and consequent 

transverse currents caused very small boils, which 

could be seen by careful observation of the water surface. Flow tended to meander through the flume and 

cause somewhat uneven depth of flow across the flume 

at a particular across section. The seven bed-material 

discharge samples ranged from 110 to 144 ppm, and 

the four suspended sediment samples ranged from 95 

to 119 ppm.

Run 23. After runs 22A-C, the bed was raked crosswise to create artificial roughness. Ripples formed 

overnight on the entire bed. Seemingly, the run was 

not in perfect equilibrium; that is, minor slope, roughness, and depth adjustments were occurring which 

caused nonuniform flow. The water surface was very 

placid, although not as smooth as before beginning of 

motion. The seven bed-material discharge samples 

ranged from 1.8 to 2.8 ppm. As indicated for run 27, 

the measured sediment transport rate was much less 

than expected when the hydraulic factors were compared with those for runs of similar hydraulic conditions. Figure 11 shows the ripple pattern which 

formed during run 23.

FIGUBE 11. Upstream view of ripple pattern on flume bed at end of run 23.

Run 32. Bed roughness appeared to be small dunes 

with superposed ripples. The bed material to a depth 

of 0.1-0.2 foot was moved. Depth observations were 

very difficult to make because the rapidly moving material was very soft. Ripples changed shape rapidly: 

old ones vanished and new ones formed. Data on the 

length and height of ripples, from observations 

through the side windows, may be misleading because 

of the wall effect. The sonic recorder was used to determine the dimensions and velocity of the sand waves. 

The character of the bed configurations is indicated in 

figure 12.

Run 8. Bed roughness consisted of ripples superposed on dunes. The bed was soft as with dunes,

FIGUBE 12. Upstream view of bed configurations at the end of run 32. Light spots 

are reflection of lights on water left from incomplete drainage in ripple troughs.
114 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

particularly on the shifting parts. Boils associated 

with the dunes appeared on the water surface, but 

they were not very violent. Figure 13 is an upstream 

view of the bed form for this run. The upstream side 

of the dunes had no ripples where the depth was 

shallowest and the shear was greatest.

Run 28. Conditions for this run were similar to 

those for run 27 except that the slope was greater. 

The suspended-sediment discharge was still very small. 

The water surface was relatively smooth, but a brickworklike pattern of ripples formed on the bed. The 

bed was very soft in the zone of movement. Seven 

samples of bed-material discharge ranged from 28.4 to 

42.4 ppm.

Run 33. The bed configuration for this run was 

very large widely spaced dunes. Large strong eddies 

carried sand from the bed to the water surface just 

downstream of the dune crests. These eddies resulted 

in boils or local crowns at the water surface, from 

which moved small horizontal components of flow. 

The backs of most dunes, according to feel with a foot 

plate, were covered with ripples. The velocity of flow 

over the crest of a few very high dunes was sufficient 

to plane away all roughness on the crest. Slope and 

depth observations were difficult to make because of the 

rapid change in position and shape of the dunes. 

Small dunes were continually forming and moving onto the crest of the large dunes, thus changing the 

amplitude and rate of travel of the large dunes. Bedmaterial discharge, determined from nine samples of 

flow, ranged from 606 to 1,152 ppm; four suspendedsediment concentration samples ranged from 652 to 

1,460 ppm.

FIGURE 13 Upstream view of ripple-dune pattern at end of run 8

Run 29. The discharge was less than one-third, the 

depth was less than one-half, and the slope was nearly 

the same as that of run 33. The result was an increase 

in roughness, a decrease in velocity, and about one 

twenty-fourth as much sediment discharge. This effect 

of depth on the flow and bed-material discharge was 

found to be comparable to that shown by Colby 

(1961). The ripples moved faster and there was 

more sediment in suspension than in other ripple runs. 

The ripples, which were soft and fluid in their moving 

parts, formed a brickworklike pattern. The water surface was rather smooth, as in the preceding ripple 

runs. The eight samples of bed-material discharge 

ranged from 45.2 to 68.6 ppm. The four samples of 

suspended-sediment concentration were composited for 

a mean concentration of 30.6 ppm.

Run 3. The ripples were somewhat larger in amplitude and more widely spaced than those in runs 1 and 

2. The considerably increased sediment discharge 

caused the ripples to move faster and with greater 

irregularity of pattern. The irregular ripple pattern 

is shown in a photograph of the bed taken through thf> 

flow (fig. 14). The seven samples of bed-material discharge ranged from 61 to 120 ppm.

Run 11. At the beginning of the run, the bed was 

nearly plane; during the run large regular dunes 

formed, which in turn caused the slope to increase. 

This was the first run using the fine sand for which 

the form, the individual element, and bed roughness 

as a whole, was similar to that observed in runs using 

coarser sands. The amplitude of the dunes was about 

0.5 foot. Some ripples formed in the dune troughs

FIGURE 14. Downstream view through flow showing rippled-bed configuration 

during run 3.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 115

FIGURE 15. Upstream view of bed configuration at end of run 11. The small surface 

ripples formed during shutdown of the run. Note the scour hole to the floor of the 

flume in the foreground.

adjacent to the walls. The bed was very firm on the 

back of the dunes, where the surface was planelike; 

and it was very soft in the trough area, where the 

velocity was less and the sand was being deposited. 

When the flow was stopped and the flume drained, 

more ripples were seen on the dunes than were apparent when the run was in progress. (See fig. 15). 

Four observations of dune velocity were made through 

the window to show the range of velocity of the more 

prominent dunes. The results were 0.085, 0.181, 0.182, 

and 0.480 fpm (feet per minute). The eight bed-material discharge samples ranged from 1,140 to 1,560 

ppm, and the four suspended sediment samples ranged 

from 766 to 856 ppm.

Run 13. Discharge was about the same as in run 12, 

but the tailgate was slightly opened. The resultant increased slope and decreased depth caused the downstream dunes to be partly planed out and, thus, caused 

decreased resistance to flow. The upstream dunes near 

the flume entrance were fully developed, but decreased 

in amplitude downstream until, at station 100, planebed conditions prevailed. (See fig. 16.) A few small 

dunes, however, remained below station 100. The water 

surface was very smooth over the plane-bed area. Considerable sediment was carried into suspension by 

eddies in the dune area. Low, more streamlined, dunes 

offered less resistance to flow and, hence, caused less 

suspension of sediment than did the regularly shaped 

dunes at the upper end of the flume. Eight observations of bed-material discharge ranged from 1,180 to 

1,385 ppm, and four observations of suspended-sediment 

concentration ranged from 695 to 852 ppm.

FIGURE 16. Typical bed conditions at end of run 13. The small surface waves were 

caused by slow flow at the time of shutdown.

Run 14.. The shear stress was increased from that in 

run 13 by increasing slope. More of the bed was plane 

for this run than for run 13, and the dunes at the 

upper end of the flume were reduced to long flat sand 

waves about 0.1 foot high. (See fig. 17.) The resulting decreased resistance caused a decrease in depth 

from that observed for run 13. When core samples of 

the bed were taken, a crusty surface was noted. This 

indicated that the sand particles were more densely 

packed at the surface than at the lower levels. On the 

whole, the bed was much firmer than that for the 

ripple-and-dune runs. The variation in concentration 

of bed-material discharge was nearly the same as for 

run 13. The differential-bubbler-gage record of slope 

showed considerable variation. However, this varying 

of slope was not as great as that for a dune-bed configuration because it was caused by changes in watersurface elevation as dunes moved downstream.

FIGURE 17. Upstream view of bed conditions at the end of run 14. 

face ripples formed during shutdown.

The small sur-
116 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Run 15. Slope was greater and depth was less than 

in runs 13 and 14. The bed was plane throughout the 

flume except for very minor long flat sand waves. The 

bed was very firm and had a crustlike surface. The 

water surface was very plane and showed neither boil 

activity nor standing waves. Thus, data were easy to 

collect for this kind of flow condition. Through the 

side window, small chunks of sandstone were visible 

only 0.1-0.2 foot below the sand surface. This was 

the maximum depth at which the sand moved in this 

bed.

Run 34- The bed configuration for this run comprised small dunes with large ripples superposed, which 

caused considerable roughness of the water surface. A 

smoother surface would probably have resulted if 

depth had been greater under these conditions of 

roughness. Figure 18 is an upstream view of the water 

surface. Bed-material discharge ranged from 464 to 

543 ppm for eight samples and the suspended-sediment 

ranged from 342 to 467 ppm for four samples.

Run 12. The conditions for this run were very 

similar to those for run 11 except that both the slope 

and velocity were increased. Large dunes, spaced 15- 

30 feet apart, formed on the bed. The back of the 

dunes was very firm, the intervening troughs, soft. 

Some dunes had a rather flat avalanche face; consequently, upstream circulation over the bed in the 

trough was weak. This condition resulted in a lower 

roughness value for this run than for run 11, and a 

firmer bed in the trough area. Figures 19 and 20 show 

the water surface and the bed, respectively. Nine concentration measurements of bed-material discharge 

ranged from 1,180 to 1,540 ppm, and six concentration 

measurements of suspended sediment ranged from 887 

to 1,040 ppm.

FIGURE 18. Upstream view of water surface during run 34.

FIGURE 19. Upstream view of water surface during run 12.

FIGURE 20. Bed configuration at the end of run 12, viewed upstream. Note large 

rather streamlined dunes.

FIGURE 21. Upstream view of ripples on low dunes characteristic of run 6. The 

pools of water remained after incomplete drainage at the end of the run.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 117

Run 6. As is shown in figure 21, the bed roughness 

elements for this run consisted of ripples and irregularly spaced dunes about 6 feet long. The ripples had 

an irregular shape which changed rapidly. Some 

ripples had the usual triangular shape; others were 

rounded and symmetrical. The water-surface slope 

also varied considerably between the measurement 

points. Several slope measurements were averaged to 

get a value for the representative slope of this run. 

An upstream view of the water surface is shown in figure uie 99 &£.

Run 7. The principal bed configuration was dunes, 

although ripples formed in the deeper and lower velocity parts, as is indicated in figure 23. Turbulence at the 

water surface seemed to be less than in run 6, although 

many boils were seen which carried sand to the surface. Once during the run, a dune crest was seen. 

Downstream from the dune crest, at the zone of separation, ripples were orientated in the upstream direction.

Run 35. The conditions for this run were similar 

to those for run 34 except that slope and mean velocity 

were increased. The bed roughness elements were dunes 

with ripples superposed, but the dunes were larger 

than those in run 34. The water surface was not as 

rippled as in run 34, but much stronger eddies carried 

clouds of sand from the bed to the water surface. 

Transverse flow apparently formed long sand ridges 

parallel to the direction of flow. Sediment streaming 

off these ridges indicated greater than average sediment transport. The bed was very soft near the dune 

crests. A plane-bed condition with very intense sediment movement near the bed, existed on the upper 

part of the dunes, where the water was shallowest. 

Sediment transport differed widely, both from point 

to point on the bed and in suspension. The shapes of 

the dunes and ripples were very irregular and changed

FIGUKE 22. Upstream view of water surface during run 6.

FIGURE 23. Upstream view of bed configuration at the end of run 7.

quickly. Thus, tracking dunes either visually through 

the window or with the sonic sounder was difficult. 

This sand was much more fluidlike and more sensitive 

to probing forces than were the coarser sands.

Run 16. The slope was steeper, the velocity greater, 

and the depth less than in runs 13, 14, and 15. Upstream from station 110 the bed and water surface 

were essentially plane; downstream from this point, 

standing waves were inphase with bed waves. Figure 

24 shows these water-surface characteristics. The 

waves in the lower end of the flume had an amplitude 

of less than 0.1 foot and were about 3-4 feet apart.

Run 10. This was essentially a plane-bed run. Very 

long and low sand waves moved down the flume. A 

few ripples persisted at the walls of the flume downstream from the crests of these waves. The presence

FIGURE 24. Upstream view during run 16, taken from station 140. Standing waves 

can be seen in the part of the flume downstream from station 110, and plane con 

ditions, upstream from station 110.
118 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

of the sand waves was also shown by the cycling of 

the bubbler gage. The bed was firm and plane except near the ends of flume.

Run 9. The dunes formed in this run were very 

long and rather low but not as rounded as a sand 

wave. On the basis of observations though the window, 

some ripples apparently formed in the troughs. The 

back of the dunes (upstream from the crest) was very 

firm and plane; over which, the velocity was greater 

than in the deeper trough areas where the bed was 

irregular and very soft. Such variation in velocity 

caused considerable variation in elevation of the water 

surface at a point where the dunes passed. The water 

surface showed strong boils over the trough area. 

Nine sample measurements of bed-material discharge 

made in an 8-hour period ranged from 967 to 1,640 

ppm. Suspended-sediment concentration in six samples ranged from 497 to 1,070 ppm three samples 

taken from the back of the dune (plane area) averaged 

600 ppm, and three from the trough area averaged 

948 ppm.

Run 17. The slope was increased by opening the 

tailgate after run 16 without stopping the flow. Velocity increased from 3.84 to 4.14 fps (feet per second), 

and depth decreased from 0.72 to 0.67 foot. In the 

first 60-70 feet the flume had a plane bed. Downstream the bed condition became one of small standing 

waves and then, with an increase in wave size, antidunes in the vicinity of stations 90-100. The most consistent and greatest antidune activity was downstream 

from station 110. The bed was very firm in the planebed areas and got softer with increasing wave activity 

in the downstream direction. See description of runs 

18 and 19 for photographs showing these flow conditions.

Run 18. Slope was increased from that for run 17 

by further opening the tailgate. This resulted in a 

velocity increase from 4.14 to 4.33 fps and caused 

waves and antidunes to form from station 30 downstream to the end of the flume. Very symmetrical 

waves formed upstream from station 80 and extended 

all the way across the flume but did not break. Below station 80, waves were accented on one side of the 

flume or the other or extended the full width of the 

flume. The condition downstream from station 100 

(fig. 25) was the same as that below station 80 except 

that interfering waves caused a choppy water surface. 

In the .lower part of the flume, the water surface at 

a specific location went through the cycle of choppy, 

smooth, increasing wave, and breaking wave. When 

the waves broke, the flow in the area nearly stopped. 

The antidunes formed at a much lower slope than they 

did in runs using the coarser sands.

FIGURE 25. Upstream view of the water surface in the area of antidune activity 

during run 18.

Run 19. The slope was increased from 0.00300 (for 

run 18) to 0.00350, but the mean velocity remained un - 

changed. The antidunes traveled upstream faster than 

did those in runs using the 0.45-mm sand. Not more 

than three or four waves broke, and then, very gently. 

Sometimes waves built up and then subsided without 

breaking. Occasionally, at a section, wave interference 

from breaking waves upstream caused the water surface to be very choppy. As in the previous run, this 

choppy water surface smoothed and then waves developed again. Figure 26 shows the flow and bed 

characteristics during this run. View A shows a condition at near minimum depth (about 0.45 ft) and 

maximum velocity, and view B shows an area of 

deceleration where depth increases to about 0.75 foot. 

Both views A and B show that the stream bed remained relatively plane and uniform from scour 

despite the very large amount of sand being swept 

along near the bed. View C shows a breaking wave 

carrying a large amount of sand in suspension. The 

sand obscures the bed in the right part of the picture. 

The depth of the breaking wave is slightly less than 

twice the depth of the trough.

Run 39. Conditions for this run were similar to 

those for run 19 except that slope and velocity were increased. Antidunes formed throughout the entire 

width and length of the flume. The average length of 

waves from crest to crest was 4.8 feet for 12 observations. The average depth was 0.50 foot in the trough 

(21 observations) and 0.88 foot at the crest (27 observations) .

Run W. The intensity of turbulence due to antidune activity was nearly uniform through the flume. 

Most waves built up and broke, but a few waves built 

up and died down without breaking. Almost all waves
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 119

moved gradually upstream. The amount of sediment 

being moved, including both that in contact with the 

bed and that in suspension increased considerably. 

The amount of sediment in suspension was sometimes 

so great that the position of the bed was practically 

impossible to distinguish through the window. In the 

trough the bed was firm; but where the water surface 

was choppy in the areas of breaking waves, the bed 

was soft.

Run 21. For this run, the tailgate setting was left 

the same as for run 20, but the discharge was reduced 

from about 22 cfs to 16 cfs. Decreasing discharge 

caused the slope of the energy grade line and the alluvial bed to increase considerably. The antidune waves, 

shown in figure 27, formed both single trains occupying the full width of the flume and some double trains. 

A choppy water surface occasionally resulted from interference of upstream antidune waves or, when the 

waves were not quite at right angles to the flow and 

reflected off the sides of the flume, from criss-cross 

waves. Figure 28 shows a breaking wave. The bed 

surface is more irregular than it was in run 19 (fig. 

266/). In comparison to run 19, the depth of flow in 

the breaking waves was more than twice the depth of 

flow in the trough.

Run 38. The flow conditions for this run were nearly the same, as for run 21 even though discharge, 

depth, velocity, and slope were increased. Antidune 

activity was apparent throughout the flume, and a 

pool and small chute formed. (See description for runs 

36 and 37.) The pool, possibly the result of antidunes 

breaking, was only about 5 feet long, and the chute 

was indistinct.

Run 36. Chute-and-pool activity was very pronounced in this run. (See fig. 29.) As many as four

FIGURE 26. Flow and bed characteristics of antidune conditions during run 19, 

photographed through window in side of the flume. A, The trough of a water 

wave. B, The upstream side, or deceleration area, of a wave. C, A breaking 

wave, showing heavy concentration of suspended sand. FIGURE 27 Upstream view of antidune wave pattern during run 21
120 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 28. Side view of breaking antidune during run 21. FIGURE 29. Upstream view of chute-and-pool flow conditions during run 36. Note 

the air bubbles on the water surface downstream from the hydraulic jump in the 

foreground of the picture.

FIGURE 30. Side views of chute-and-pool flow conditions during run 37. A, The chute. B, The hydraulic jump. C, The pool. D, The acceleration of flow toward the

next chute. Photographs were taken through the window in the side of the flume.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 121

chutes and four pools formed in the flume at one time. 

The gradient into the pools was very steep. The storage of water in and the release of water from the pools 

caused the discharge of the pump to vary. The flow 

in the pool sections, which were as much as 30 feet 

long, was 0.5-0.8 foot deep and was tranquil (Froude 

No. less than 1); whereas, the flow in the shorter, chute 

sections was 0.2-0.3 foot deep and was rapid (Froude 

No. more than 1). The bed elevation changed about 

0.4 foot with time, but at no time was the floor of 

the flume exposed.

Run 37. A chute began to form at station 50, near 

the lower end of the flume, and moved upstream. 

When it reached station 100, another chute began to 

form at station 50; thus, the chutes were about 50 feet 

apart. The chutes and pools moved upstream at a rate 

of about 8 feet per minute. Figure 30 shows the flow 

conditions during run 37. The slope of the water surface was nearly 40 percent on the steepest part of the 

chute.

RUNS USING 0.27-MM SAND IN 8-FOOT-WIDE FLUME

The 0.27-mm sand was obtained by wet screening the 

0.28-mm sand and removing the fraction coarser than 

2.0 mm (table 1). These experiments were conducted 

during the period March-April 1959. The experimental variables and parameters are given in table 3, 

and the velocity-profile data, in table 13.

Run 50A. During this run the bed material was 

very close to beginning of motion. The bed was planed 

prior to starting flow and then once again after the 

water was flowing by moving the planer from upstream to downstream. Ripples formed on 3-4 percent 

of the bed. The formation of ripples may have been 

due to vibration of the flume. Vibrations of the flume

caused by very small water-surface waves to form, 

which made precise measurement of slope difficult.

Run SOD. The slope was increased to 0.00018, compared with 0.00007 for run 50A, and ripples formed. 

The mean velocity increased only a small amount (0.79 

to 0.84 fps) in consideration of the large increase in 

slope because of the increase in bed roughness from the 

plane bed in run 50A to the ripples formed in this 

run. The rippled bed was very soft. The sand in the 

trough between ripples felt and looked coarser than 

the sand in the back and the crest of the ripples. Apparently, only the finer sand moved up the incline to 

form the ripple. The coarse fraction tended to armorplate the trough and inhibit further growth of the 

ripples. This sorting, shown in figure 31, is opposite 

that indicated by Baghold (1941) for blown sand, in 

which the coarsest material collects at the crest and 

the finest in the trough.

Run 51. The amplitude and spacing of ripples were 

greater than in run 50D. The coarser particles moved, 

and the sand felt as if it were about the same diameter 

in both the trough and the crest of the ripples. Figure 32 shows that the ripples were more fully developed than those in run 50D (fig. 31) and that the 

coarse material was deposited at the base of the ripple 

face rather than being a residual in the trough of the 

ripple. The concentration of bed-material discharge 

ranged from 10 to 15 ppm for seven samples, and the 

suspended-sediment concentration averaged 9.0 ppm 

for four samples.

Run 52. The ripples formed were slightly larger 

than those formed in run 51, more sand was moving, 

the slope was steeper, and the velocity was greater. 

The bed seemed very fluidlike, and all sizes of particles

FIGURE 31. Upstream view of ripples on the bed of the flume at the end of run SOD.

FIGURE 32. Upstream view of ripples on the bed at end of run 51. Note that the 

ripples are better developed than those shown in figure 31.
122 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

were in motion sometime during the run. The rate of 

ripple movement was difficult to determine because of 

the rapid change of ripple shape. Some lateral shifting 

occurred as the ripples moved downstream. Figure 33 

shows the shape of the ripples formed under the flow 

conditions for run 52.

These ripples were more irregular in size and shape 

than those formed during run 51 (fig. 32). The sand 

movement over the bed was typical of ripples. It 

moved by sliding and bounding up the back side of 

the ripple and then sliding or leaping until it came 

to rest on the foreplane of the ripple. Some fine sand 

went into suspension at the ripple crest. The bedmaterial discharge ranged from 72 to 121 ppm for 

eight samples, and the suspended-sediment concentration ranged from 46 to 62 ppm for four samples.

Run 54- The bed form was one of dunes with 

ripples superposed. The ripples and dunes were irregular in form and changed shape rapidly as they 

moved past the observation window. The bed was soft, 

and particles of different size were well mixed, even 

in the troughs. The bed was firmest on the tiack of 

the larger dunes. Bed-material discharge ranged from 

163 to 287 ppm for eight samples and suspended-sediment concentrations ranged from 102 to 197 ppm for 

four samples.

Run 53. The back of some of the large dunes was 

plane where the depth was shallow and the shear was 

great. Most dunes were covered with small ripples or 

with sand waves nearly equivalent to ripples. The 

flow conditions were such that a slight increase in 

shear would cause the bed form to change to the nonrippled dune. The bed was much softer than in runs 

where only ripples formed. The dunes constantly 

changed shape and speed as small ones caught up with 

the larger ones. Some lateral shifting of dunes and

FIGURE 33. Upstream view of ripples on the bed at the end of run 52.

FIGURE 34. Upstream view of the bed configuration at the end of run 53.

formation on longitudinal ridges or fins parallel to the 

flow also occurred. Large amounts of sediment from 

those fins went into suspension. The characteristic 

shape of the dunes, ripples, and fins is shown in figure 

34.

Run 57. The shallow depth of flow caused the bed 

to revert to a rippled condition even though the slope 

had been increased from the previous run. The ripples 

were fully developed and soft, particularly near the 

crest. The bed was firmest just downstream from the 

ripple troughs. The bed looked very similar to that of 

run 51 (fig. 32). Bed-material discharge ranged from 

69 to 110 ppm for eight samples.

Run 56. The slope was the same for this run as for 

run 57, but discharge, depth, and velocity were greater. 

The bed form changed to dunes with superposed ripples. Again, no ripples formed on the back of the 

larger dunes, where depth of flow was shallow, the 

velocity high, and the bed very firm. The "plane" flow 

condition on the back of the dunes caused a rather 

compact crust, possibly as much as one-half inch thick, 

to form on the dune. At places where sand was being 

carried into suspension, the bed was very fluidlike or 

soft. Figure 35 shows the irregularity of the dune 

and ripple pattern of run 56. The variation of concentration among sediment samples was very high. 

Bed-material discharge ranged from 355 to 829 ppm, 

and suspended-sediment discharge ranged from 252 to 

852 ppm.

Run 55. The slope of the flume for this run was 

not changed from that for runs 56 and 57; but as the 

discharge, depth, and velocity were increased, the slope 

increased from 0.00126 to 0.00130 as equilibrium was
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 123

FIGURE 36. Upstream view of bed configuration at the end of run 56.

established. The dunes formed were rather large, 

and caused some troughs to extend to the floor of the 

flume. (See fig. 36.) The top layer of sand on the back 

of large dunes was firm, but it was very easily broken 

to expose the softer body of the dune. The bed was 

soft both at the crest and in the trough of the dunes. 

The condition of the water surface varied greatly with 

distance and time. It was very smooth and sloped 

downward where the velocity increased up the back 

side of the dune. A series of eddies and the reverse 

flow in the trough downstream from the dune caused a 

rapid increase in elevation of the water surface at the 

crest of the dune. Water-surface elevation varied

FIGURE 36. Upstream view of bed configuration at the end of run 55. Note the 

large dual fins in the left foreground.

0.035 foot within a 5-feet distance along the flume. The 

reverse flow in the troughs of the dunes was further 

substantiated by reverse-orientated ripples in these 

troughs.

Run 45- The bed was firm and felt plane except 

near scattered very low dunes or depressions. No eddies reached the surface from these depressions. Small 

symmetrical surface waves were seen near the headbox 

and occasionally near the tailbox.

Run 4$- The dunes formed in this run were very 

large. The bed was firm and very smooth on the back 

of dunes, and soft at the crest and through the trough 

of dunes. The reverse circulation in the trough of the 

large regularly-shaped dunes was very strong. The 

largest dune observed through the window, was 0.75 

foot high (fig. 37). This dune probably would have 

been even larger if the depth of the sand bed had 

been greater. Some segregation of coarse and fine sand 

was noted, but it was not as noticeable as in runs 

using the 0.28-mm sand, which contained more coarse 

material. Again, reverse-orientated ripples frequently 

formed in the dune trough. Bed-material discharge 

ranged from 583 to 1,310 ppm for eight samples, and 

suspended-sediment discharge ranged from 505 to 684 

ppm for three samples. Ten observations of the slope 

of the avalanche faces of dunes ranged from 24° to 32° 

and averaged 30°.

Run 44- The dunes were longer, lower, and more 

irregularly shaped than those of run 43. The irregular 

shapes made measurement of dune velocity at the window more difficult. The back of the typical dune was 

firm and smooth, and the trough was soft and rather 

rippled. The concentration of nine bed-material discharge samples ranged from 550 to 1,060 ppm, and of 

four suspended-sediment samples, from 501 to 843 

ppm. Concentrations of bed-material discharge were

FIGUBE 37. Sliding face of the largest dune (0.75 ft) observed during run 43, viewed 

from window. Direction of flow is from left to right. Foreslope of the dune 

is 30°.
124 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

considerably lower than normal for the given flow 

conditions.

Run 4^. This was a dune run that was very similar 

to run 43. The bed-material discharge of eight samples ranged from 629 to 809 ppm, and the suspendedsediment concentration of three samples ranged from 

378 to 481 ppm.

Run 46. The slope was the same as for run 42, but 

a substantial increase in discharge planed the bed. Low 

resistance to flow resulted in a 0.2-foot reduction in 

depth and an increase in velocity from 2.09 to 3.68 

fps. The increased tractive force caused the average 

bed-material discharge to increase from 704 to 1,670 

ppm. The sand bed was firm and smooth, similar to 

the back of dunes mentioned in descriptions of previous runs. Low (about 0.05 ft) standing waves formed 

on the water surface throughout the flume and then 

dissipated. The bed level at any point varied only 

about 0.03 foot. The concentration of eight bedmaterial discharge samples ranged from 1,400 to 1,880 

ppm, and the concentration of four suspended-sediment samples ranged from 771 to 1,000 ppm.

Run 58. The depth of flow was shallow and probably inhibited dune growth. Strong vortices in the 

flow affected the water surface, as is shown in figure 

38. The bed was firm except at the crest of the dunes. 

The troughs were much firmer than those in previous 

dune runs. The firmness in the troughs was probably 

caused by the shape of the trough and the height of 

the dune. Several minor roughness elements about the 

size of large ripples, but with greater length between 

crests were seen. After the water had been carefully 

drained from the flume at the end of the run, some 

longitudinal formations were noted. (See fig. 39.) The

R UK 58 

0*6.7

FIGURE 38. Upstream view of water surface during run 58.

FIGURE 39. Upstream view of the bed configuration at the end of run 58.

bed-material discharge ranged from 567 to 880 ppm 

for eight samples, and the suspended-sediment discharge ranged from 240 to 484 ppm for three samples.

Run 4^- This was an antidune run. Wave activity 

was slow and weak, but waves broke throughout the 

flume. Some waves moved upstream while others rose 

and fell without much migration. The concentration 

of seven bed-material discharge samples ranged from 

4,080 to 5,900 ppm, and the concentration of four suspended-sediment samples ranged from 3,230 to 4,360 

ppm.

Run 48. Increasing the slope from 0.00280 (for run 

47) to 0.00493 caused more antidune activity to occur 

than was noted in run 47. Considerable water was 

stored in the flume when waves broke, thus the level in 

the tailbox dropped and discharge decreased slightly. 

Bed level was difficult to locate in the areas where the 

waves were breaking, because of the large amount of 

suspended load. Between the breaking waves, in the 

rapid-flow areas, the suspended-sediment discharge was 

small but the bed-material discharge was very large. 

The surface flow conditions are shown in figure 40.

Run 39. The antidune activity in this run was considerably more violent than that in run 48. Some 

chute-and-pool activity was noted. (See description of 

runs 36 and 37, for the 0.19-mm sand.) The discharge 

was nearly the same as that in run 48, but the slope 

was increased considerably, the depth was decreased 

from 0.59 to 0.55 foot, the mean velocity was increased 

from 4.60 to 4.93 fps, and the mean concentration of 

bed-material discharge was increased from 9,080 to 

28,700 ppm.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 125

Run 41. Discharge and depth were decreased and 

slope was increased after run 39. The result was a 

typical chute-and-pool type of flow. The velocity of 

flow in the pools just downstream from the breaking 

waves was essentially zero. Suspended sediment moved 

in all directions in the pools, but it mainly settled to 

the bed. The unstable conditions caused very large 

variations in instantaneous values of velocity, slope, 

depth, suspended load, and bed load at any point in 

the flume. Velocity profiles could not be obtained with 

the available equipment. The concentration of six 

samples of bed-material discharge ranged from 23,200 

to 46,500 ppm, and that of four samples of suspended 

sediment ranged from 37,400 to 51,800 ppm.

Run 40- Increased flow and depth caused the flow 

conditions to be even more unstable than those of run 

41. During most of the run, three pools and three 

chutes could be seen. The rapid flow running into a 

large wave or pool looked exactly like a hydraulic 

jump. Air was entrained in the water as the waves 

broke, just as air is entrained in a hydraulic jump. 

Many waves were nearly 1 foot high just before they 

broke. Sediment movement in the area of the waves 

was so great that the boundary between the flow and 

the bed could not be located in fact, it appeared that 

part of the bed was moving. Figure 41 is a photograph 

showing a breaking wave or hydraulic jump in the 

foreground and a variety of flow conditions farther 

downstream.

RUNS USING 0.28-MM SAND IN 8-FOOT-WIDE PLUME

These experiments were conducted during the period November 1958-February 1959. The experimental 

variables and parameters are given in table 4, and the 

velocity-profile data, in table 14.

FIGURE 40. Downstream view of water-surface conditions during run 48. Note the 

breaking antidune near the center of the flume.

791-597 O 66 3

FIGURE 41. Downstream view of flow conditions (chute-and-pool flow) duringrun40.

Run 7. The bed was screeded in the direction of the 

water flow prior to the beginning of the run, so that 

the particles were arranged in a relatively stable pattern on the bed. A few small grains and an occasional 

large grain moved when the flow began. After 36 

hours, a few ripples had developed near the headbox 

because of the irregular flow conditions, but no sediment movement was observed in the data-observation 

area of the flume.

Run 8. The run was very close to beginning of 

motion, because small ripples formed downstream to 

station 40, a few formed at station 90, and a few 

formed near the end of the flume. In all, ripples covered about 15-20 percent of the flume bed. Ripples 

would probably have covered the entire bed if the run 

had been continued for several days.

Run 9. The bed was raked at the end of run 8. The 

discharge was unchanged from run 8. Ripples soon 

formed over the entire bed, and these caused resistance 

and slope to become greater than those of run 8. The 

ripples generally extended transversely across the 

flume, but not in a perfectly straight line. (See fig. 42.) 

The coarse material armored the troughs and gave the 

sand waves a starved appearance. The armored troughs 

were very firm, whereas the ripple waves were soft 

and thus were different from dunes, which have firm 

backs.

Run 10. Ripples formed which looked very much 

like those formed in run 9. The transverse pattern of 

the ripples, however, was more irregular, and the 

movement was more erratic. The stress on.the bed 

seemingly was somewhat greater than that in run 9;
126 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

'.i

FIGURE 42. Transverse view of rippled bed pattern at the end of run 9. Note the 

armor plate of coarse material in the ripple troughs and the rather regular transverse pattern of the ripples.

yet the armor of coarse material on the bed did not 

move. The resulting starved ripples did not yield as 

much sediment to transport as would normally be expected for this sediment, flow, depth, and slope. The 

run began about 44 hours prior to the beginning of 

data collection.

Run 5. The ripples formed in this run were more 

fully developed than those of the previous runs, but 

a thick layer of coarse particles was again noted in the 

troughs of the ripples. The sand was scoured out 

around the nonmoving coarse particles, and, as a result, the particles were lowered to the zone of lowest 

sand movement. No suspended sediment was present, 

and the water surface was very smooth; consequently, 

the bed was clearly visible through the flow. Eight 

measurements of bed-material discharge ranged from 

5 to 16 ppm.

Run 13. An extensive study of the effect of time 

on equilibrium was done during this run. Data collected December 11, about 24 hours after the start of 

the run, was not significantly different from data collected on December 15. The bed roughness was made 

up of fully developed ripples, few of which had characteristics almost like those of dunes. These few large 

forms caused some disturbance of the water surface. 

Many ripples not only moved downstream, but also, 

moved laterally several tenths of a foot. The rapidly 

changing form of the ripples made measurement of 

their velocity difficult. Also, observations of the velocity of specific ripples were ruined when the observed

ripple either was overtaken by a faster moving ripple 

from upstream, was invaded by a ripple from the side, 

or overtook another ripple. The ripple velocity is affected by the size of the ripple and the flow and transport conditions in the vicinity of the ripple. Bedmaterial discharge ranged from 58 to 88 ppm for 10 

observations. The sediment from four suspendedsediment samples was composited in the laboratory, so 

that a range cannot be given.

Run 4- This was a ripple run. Figure 43 is an upstream view of the ripples after the water had been 

carefully drained from the flume. The water surface 

had only a few minor surface disturbances. Little or 

no suspended sediment was present. Coarse particles 

moved slowly and intermittently, while the finer sand 

moved from around the larger particles.

Run 11. The ripples were more irregular than those 

formed in previous runs, at flatter slopes. They were 

deeper and the distance was greater from crest to 

crest. The coarse material did not influence the shape 

of the ripples, and movement occurred in the same 

manner as in previous runs of this set. Again, the finer 

sand was eroded away from the coarse particles, so 

that the rate of transport of the coarse particles was 

reduced. The bed-material discharge ranged from 18 

to 22 ppm for eight observations. There was no suspended sediment in the flow.

Run 33. This run was designed to provide data to 

fill a gap in those for the dune range of bed roughness. 

Ripples formed on the dunes except on the back of the 

very largest dunes. The top of most dunes rose and 

fell as ripples caught up with the dune crest. The 

counter-circulation in the dune troughs was very weak. 

The angle of the avalanche face of the dunes ranged 

from 23° to 30°, depending on the form of the dune

FIGURE 43. Upstream view of the rippled bed form at the end of run 4.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 127

and the amount of counter-circulation in the trough. 

The bed was very soft at all locations. Bed-material 

discharge ranged from 238 to 400 ppm for nine observations, and suspended-sediment concentration ranged 

from 195 to 558 ppm for four observations.

Run 1. The bed form consisted of relatively large 

dunes with a profuse pattern of ripples superposed. 

The ripple pattern was very hetrogeneous as a result 

of the irregular flow patterns around the dunes. Suspended-sediment concentration seemed very uniform 

vertically, and the eddies (boils) of the water surface 

downstream from the dune crests were not particularly 

strong. The slope for this run was poorly defined.

Run 12. The run began about 16 hours prior to data 

collection. The general bed roughness was classed as 

ripples, but it contained a few elements which looked 

like poorly developed dunes. The coarse particles did 

not influence the roughness elements. These coarse 

particles either settled in the sand as the finer material 

was eroded away from them, rolled downstream to the 

next trough, or, occasionally, rolled upstream into a 

deeper part of the ripple trough. The upstream movement occurred only in the zone of reverse flow in the 

trough of a dunelike form. The bed was very soft. The 

water surface was rougher than that of most ripple 

runs, and some suspended sediment was present, indicating that the flow was approaching the dune condition. The ripples rapidly changed form, size, and 

shape; thus, measurement of ripple velocity was very 

difficult.

Run 14- The run began December 15 and continued 

to December IT, when the final data were recorded. 

The mean slope at 0800 December 16, 1500 DecemFIGURE 44. Upstream view of the dune-bed configuration at the end of run 14

FIGURE 45. Upstream view of the dune-bed configuration at the end of run 20.

ber 16, 0800 December IT, and 1045 December IT was 

0.00122, 0.00109, 0.00122, and 0.00118, respectively. The 

roughness on the bed was mainly ripples and a few 

larger elements resembling dunes. (See fig. 44.) Some 

sediment moved in suspension. The water surface was 

more turbulent than in the preceding ripple runs; but, 

despite the small quantity of suspended sediment, the 

streambed could still be seen through the flow. The bed 

was very soft. Accumulation of coarse material on the 

bed was not excessive. Small ripples moved over larger 

ones and seemed to consist of sand finer than the average in the bed.

Run 20. The bed condition for this run consisted 

of dunes, as is shown in figure 45. The bed was very 

soft in the troughs but firm on the back of the dune 

upstream from the crest, where the depth was at a 

minimum and the velocity was at a maximum. The 

area in the trough and immediately downstream from 

the trough contained ripples. Some dune faces were 

very round, and the counter-circulation in such places 

was weak and intermittent. The dune face generally 

was of the normal type shown in figure 46. The angle 

of the dune face was generally between 25° and 2T°, 

but occasionally as low as 20° or as much as 30°, depending upon the strength of the counter-circulation in 

the dune trough. The coarse particles rolled readily 

from the downstream part of the trough area up the 

back of the dune and then slid down the face of the 

dune until they came to rest. After coming to rest 

they were buried and were not exposed again after 

passage of the dune. Such large particles were never 

seen in suspension. Twelve measurements of bedmaterial discharge ranged from 365 to T54 ppm, and 

3 measurements of suspended-sediment concentration 

ranged from 323 to 3T3 ppm.

Run 2. This run was very similar to run 20 except 

that the dunes formed were lower and longer. The
128 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 46. Avalanche face of a large dune formed during run 20. Direction of 

flow is from left to right.

flatness of the dunes, compared with those formed in 

run 20, was probably due to the shallower depth and 

somewhat greater slope during run 20. Again, the bed 

was firm and crusted on the back of the dunes and soft 

on the dune crest and in the trough. Boils on the water 

surface marked the separation zone, and large-scale 

eddies occurred downstream from the dune crest. The 

slope was poorly defined.

Run 21. Very few ripples were associated with the 

dune pattern for this run. As in runs 20 and 2, the 

distance between dunes was great, but the dune height 

was somewhat less than in runs 20 and 2. The water 

surface was relatively smooth over the back of the 

dunes; but it was very turbulent, because of large boils 

over the troughs and slightly downstream from the 

troughs. The water surface stood high over the trough, 

relative to that over the back of the dunes, because of 

the change of velocity head as the flow moved from 

one area to another.

Run 19. Except for flow depth, which was shallower, the flow conditions and bed forms were very 

similar to those of runs 2 and 21. The shallower mean 

depth caused the eddies and turbulence to be stronger 

and the dunes smaller.

Run 16. The large dunes moved faster than in preceding runs. The rate of transport of sediment by the 

sand waves was very high, but the limited sand depth 

on the bed of the flume seemingly was not adequate to 

allow full-scale roughness to develop some troughs 

extended to the floor of the flume. The dunes traveled 

through the flume at all elevations. Occasionally, a 

dune crest formed just upstream from a short trough 

that extended below the average downstream bed elevation. The jet from the crest of such a low dune, in 

its effort to "normalize" the dune and the trough, impinged on the downstream edge of the trough and 

caused very rapid erosion of the trough. Rate of dune 

movement for a given height of dune was not constant, 

because the main current was sometimes directed 

around an area by upstream forms, and because part 

of the sediment in transport was sometimes captured 

by a dune immediately upstream from the one being 

observed. The slope was poorly defined.

Run 23. This was a transitional run in which the 

bed forms oscillated between dunes and washed-out 

dunes. Dunes generally existed when resistance was 

relatively great and slope was steep. Then the dunes 

seemed to vanish, and resistance and slope decreased to 

the point where dunes again developed. The cycling 

between dunes and washed-out dunes probably resulted 

from the change in depth and slope that occurred when 

the resistance changed with a change in bed form. 

Some cycling may have resulted, however, from segregation of the bed material into different sizes for different dunes because it was observed that dunes of 

fine, coarse, and intermediate sized material passed by 

the observation window. Large boils resulting from 

eddies near the dune trough and the rapid flow over 

the irregular bed configuration caused the water surface to be very turbulent.

Run 17. The slope was nearly the same as that of 

run 16, but the depth of flow had been reduced considerably. Dunes formed which rapidly changed shape 

and direction of motion. The water surface had an 

appearance typical to that over a dune bed. More surface turbulence, in the form of small waves, occurred 

than in runs with greater depth of flow.

Run 3. With depth increased (at the same slope) 

over that for run 17, dune height and length increased. 

As in run IT, most dunes moved. Small dunes moved 

faster than large ones, and small dunes in shallow fast 

water moved faster than small dunes in deep slow 

water. When a small dune approached a large dune 

and began taking sediment from it, the large dune 

stopped (or nearly stopped) until the small dune 

caught up. The result was a new dune. The bed was 

firm on the back of the dunes upstream from the crest 

and was very soft on the crest, on the avalanche face, 

and in the trough. The slope for this run was poorly 

defined.

Run 18. The bed condition for this run was a 

typical dune bed. Ripples formed in some of the 

deeper troughs. Large eddies formed downstream from 

the dune crests, or over the troughs, and carried much 

sand to the water surface; the suspended load was 

large in these areas. On the back of the dunes, upstream from the crest, particles moved mostly in contact with the bed. Suspended-sediment concentration
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 129

was small enough in this zone that both the bed and 

the "sheet" of moving sand could be seen.

Run 30. The flow was tranquil, and the bed was 

nearly plane. An occasional dune or bar less than 0.1 

foot high was seen moving through the flume. The bed 

was not soft, but neither was it as firm as during a 

plane-bed run with greater velocity. The run was 

classed as transitional between dunes and plane bed.

Run §4- The depth of flow was shallow, and the 

bed configuration was reduced almost to ripples. Figure 47, a photograph taken after the water had been 

drained from the flume, shows ripples on the left and 

small dunes with ripples on the right. The slope was 

steeper than for previous runs having fully developed 

dunes. The suspended load was negligible, and the 

total load was small for this slope.

Run 22. A plane bed and little resistance to flow 

were the significant characteristics of this run. The 

elevation of the bed varied no more than 0.01 foot 

about the mean. Most sediment transport was near 

the bed, and the coarse material rolled along at a 

rather uniform rate. Run 22 has nearly the same slope 

as run 34, but the rate of flow has been increased from 

5.5 to 14.9 cfs. The increased flow caused the depth to 

increase from 0.44 to 0.60 foot even though the resistance decreased from 0.021 to 0.013 (Manning n). The 

rate of energy input, or in this case depth of flow, 

strongly affects other variables.

Run 15. Reducing discharge from that of run 22 

(14.92 to 12.87 cfs) caused the bed form to change to 

fully developed dunes. With this increased roughness, 

the mean depth increased from 0.60 to 0.75 foot and the 

mean velocity decreased from 3.11 to 2.14 fps. The

FIGURE 47. Upstream view of bed configuration at the end of run 34.

dunes ranged from 0.3 to 0.5 foot in height and were 

as much as 30 feet apart. The wide spacing of the 

dunes resulted in a large variation in the amount of 

bed-material discharge at the tailbox. Twelve samples, 

collected there over a long period of time (0820-1155), 

had concentrations ranging from 674 to 998 ppm. Suspended sediment in four samples ranged from 358 to 

419 ppm.

Run 24. The bed configuration was transitional between dunes and plane bed. The dunes were very irregularly spaced and had an amplitude of 0.2 to 0.4 

foot. The avalanche angle of a typical dune in this 

run was small, and the flat trough inhibited countercirculation. Occasionally a dune formed that had a 

more normal avalanche angle and a trough with some 

counter-circulation. The water surface was very 

choppy. The flow expanded, or decelerated, over the 

dune troughs and contracted, or accelerated, over the 

crests; hence, surface waves formed. Eddies in the 

dune troughs did not reach the water surface.

Run 25. The bed of sand in the flume was firm and 

plane. It fluctuated vertically no more than 0.05 foot 

at the window. The water surface was smooth compared with that in the dune runs and transitional runs. 

A minor disturbance on the water surface was generated downstream from station 50 by a wall roughness. Figure 48 shows the flow and bed conditions of 

this run. Much of the material that rolled along the 

bed was coarser than the average bed-material size. 

The windrow effect, or lines of coarse particles, may 

have been caused by secondary circulation.

Run 28. The flow variables and resulting plane-bed 

configuration were nearly the same as for run 25. Most 

sediment transport occurred close to the bed.

Run 29. For this plane-bed run, slope was increased 

from that for run 28. As a result, velocity increased 

from 3.57 to 3.77 fps and sediment transport increased 

from 2,760 to 3,120 ppm. The bed and water surfaces, 

as seen through the window, slowly varied about 0.1 

foot, approximating a standing-wave condition.

Run 26. The increased slope over that of run 29 

(from 0.00278 to 0.0032,8) resulted in a flow pattern of 

standing waves and an occasional breaking wave. The 

standing waves built up near stations 35^0 and 

traveled down the remainder of the flume to the tailbox. The largest waves formed near the tailbox. 

Waves extended the full width of the flume except 

when they were first forming. Some of the waves 

moved upstream; and, of these, some broke and some 

did not.

Run 82. The flow conditions (antidunes) were similar to those described for run 31, except that wave
130 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 48. Flow and bed conditions for run 25. A, Water surface during flow. 

B, View through the side window. C, Flume bed after draining the flume at the 

end of the run.

activity was not as great and the total-sediment transport was much less.

Run 27. This was an antidune run. Much breakingwave activity occurred, but seldom did more than three 

waves break at one time. Some waves moved upstream 

and subsided without breaking. The waves extended 

most of the way across the flume except when they 

first began to form. The coarse fraction of the bed 

material may be an important factor in causing the 

sand waves to move upstream, because much of the 

coarse material that eroded from the downstream part 

of the sand wave moved only to the upstream slope of 

the next sand wave.

Run 31. Violent antidune action occurred throughout the flume. The waves were large, and as many as 

six or none at all may have been breaking at a given 

instant. Figure 49 shows the flow conditions downstream from near the middle of the flume. Near breaking waves the mean velocity of the water was reduced 

to nearly zero, and sediment moving into this region 

was lifted into suspension. As the flow accelerated 

and smoothed out to a plane-bed condition, the zone of 

maximum transport shifted toward the bed. The planebed condition gradually evolved into a low-standing 

wave, and then into a higher wave that moved upstream prior to breaking. Small rollers turned from 

the flow toward the bed on the upstream side of the 

sand waves as they broke. The bed was firm in the 

trough, firm on the downstream side of the waves, 

softer on the upstream side of the sand wave, and much 

softer on the crest or peak of the sand wave.

Run 35. Conditions for this run were similar to 

those for run 31 except that slope was increased from

3f

FIGURE 49. Downstream view of antidune flow conditions during run 31.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 131

0.00593 to 0.00815. This caused a greater number of 

violent antidune waves of larger amplitude to form 

and caused the transport rate to be more than double 

that in run 31. The mean velocity and depth did not 

change appreciably from run 31, but resistance to flow 

increased.

Run 37. Discharge and depth were much less than 

in runs 35 and 31, and the size of the waves formed 

and the violence of the antidune activity were accordingly less. Breaking waves were farther apart. 

Many waves built up to near the breaking elevation, 

and then the sand appeared to be pushed out from 

under the water wave and the wave subsided without 

breaking.

Run 38. The discharge for this chute-and-pool run 

was intermediate between that of runs 37 and 36. Although the slope and the tailgate setting were not 

changed for the three runs, the slope and the flow conditions changed considerably as a result of the change 

of shear stress on the bed with the change in rate of 

discharge. The flow conditions were very violent. A 

series of three or four chutes and pools formed in the 

length of the flume, each with rapids, large standing 

waves, breaking waves, and a pool, in downstream 

order. Figure 50 is a sketch of this phenomenon as 

seen through the window. The pool was like a small 

hydraulic jump or stilling basin, where sediment was 

brought into full suspension and then settled onto the 

bed at the lower end of the pool, at the head of the 

next sand wave and chute. The sediment-transport 

rate was higher for specific slope, depth, and bed material than was expected for the antidune roughness.

Run 36. This run was similar to run 38 except that 

the discharge was increased and the chute-and-pool 

activity was, therefore, more intense.

RUNS USING 0.45-MM SAND IN 8-FOOT-WIDE FLUME

This was the first set of runs, completed for the 

project. The notes were not as complete as for other 

sets, and the data-collection system lacked some refinements which were developed later. The significant 

differences in data-collection methods between this set 

and other sets are:

1. For runs having antidune flow, depth was measured 

only in areas where the water surface was relatively smooth; thus, the measured depth is too 

shallow.

2. Fewer bed-material discharge samples were taken 

over a shorter period of time, causing a greater 

error in the mean.

3. Slope was determined by averaging the several 

readings taken at different times every 5 feet 

along the flume and then computing a leastFIGURE 50. Sketch of chute-and-pool phenomenon as viewed through the window 

in the wall of the flume. The vertical scale is exaggerated 3-5 times. Each chuteand-pool series is 20-30 feet long.

squares regression from these averages. The slope 

for other sets of runs was determined by plotting 

each and (or) the average of several slope measurements on graph paper and then visually drawing the mean slope line through these points. The 

water-surface elevation from which the slope was 

computed for antidune runs was only obtained 

when the water surface was relatively smooth. 

The water-surface elevation and depth for the 

other sets of runs were taken at random times at 

a given flume station. A system for taking good 

pictures was lacking for several runs in this set. 

These experiments were conducted during the period 

January-July 1957. The experimental variables and 

parameters are given in table 5, and the velocityprofile data, in table 15.

Run 14- The flow for this run was increased from 

1.84 cfs (run 13) to 3.94 cfs. The velocity increased 

from 0.65 to 0.81 fps, and the shear stress was below 

beginning of motion.

Run 13. The bed was planed to a slope of 0.00010 

prior to the beginnning of the run. The bed material 

did not move under the given flow conditions.

Run 17. The flow for this run had sufficient shear 

stress to move particles into a configuration of ripples, 

which averaged 0.77 foot long and 0.04 foot high. All 

transport was on or very close to the bed. No sediment was in suspension.

Run 16. The transport rate of 1.2 ppm for this run 

was in equilibrium with the low-ripple bed configuration. The ripple waves transported sand much finer 

than the sand remaining in the troughs. This made 

the ripples appear "starved," as in ripple runs with 

the 0.27- and 0.28-sands.

Run 15. The run began March 4, 1957. Several 

adjustments of the tailgate were made prior to 1700 

March 6, by which time ripples had formed over the 

full length of the flume. At 0800 March 7 the slope, 

transport, and bed configuration were stabilized 

throughout the flume. The bed slope was 0.00021, and 

the water-surface slope was 0.00023; thus, flow conditions were nearly uniform. The concentration of
132 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

five bed-material-discharge samples taken March 8 

ranged from 0.26 to 1.38 ppm. This large range reflected the uneven transport at the end of the flume 

caused by the transverse pattern of waves moving in 

the flume.

Run 18. The bed was not planed after run 17. The 

discharge was reduced from 6.22 to 3.62 cfs, and the 

slope was increased from 0.00020 to 0.00031. These 

changes did not alter the ripple-bed configuration appreciably from that of run 17. (See fig. 51.) The mean 

bed-material discharge was reduced from 0.7 to 0.4 

ppm.

Run 2. The bed was screeded to a slope of 0.00050 

before the run began. The mean bed-material discharge was 9.4 ppm, about 10 times greater than that 

for the previous runs. Eipples on the flume bed had 

greater spacing and amplitude than those for the runs 

already described. The ripples were more random with 

respect to size, shape, and location on the bed. They 

no longer had a well-arranged transverse pattern, and 

sorting of the sand was no longer noticeable.

Run 3. The flow conditions and ripples of this run 

were similar to those in run 2. The slope was increased 

and the velocity decreased because of increased resistance. The bed-material discharge was increased by 

less than 10 percent.

Run 9. The discharge of this run was reduced from 

7.90 cfs (run 3) to 3.84 cfs. The result was a ripple 

run with little bed-material discharge. The concentration of five bed-material discharge samples ranged 

from 0.8 to 1.8 ppm.

FIGURE 51. Transverse view of the ripples formed during run 18. The flow was 

from right to left, and the scale is 1.3 feet long. The crests of the ripples contain 

finer sand than is found in the troughs.

Run 1. This run was nearly the same as runs 2 

and 3, except that the slope was increased, and this 

caused a reduction in the resistance to flow. The reduced resistance to flow may have been the result of 

the longer, relatively lower and more rounded ripples. 

Either the measured bed-material discharge was too 

high or the slope was too low compared with other 

runs of similar bed-material characteristics and energy 

of flow.

Run 5. The bed was screeded to a slope of 0.00050 

before the run began. The mean slope of the water 

surface was 0.00047 at the time of data collection. The 

flow and bed-material-discharge conditions were nearly 

the same as those of run 1, but the ripples were smaller.

Run 11. The slope was set at 0.00070 until ripples 

formed, and then it was reduced to 0.00050. The final 

slope was 0.00049. Discharge was reduced from 7.93 

cfs (run 5) to 1.95 cfs. The shear stress was sufficiently low that the bed-material discharge was less than 

20 percent of that of run 5. The ripple pattern was 

very uniform, and the pattern of ripple waves was 

mostly perpendicular to the direction of flow.

Run 4- The bed configuration was low dunes and 

ripples. The resistance to flow was less than for regular ripple conditions and resulted in greater velocity 

and shallower depth than in previous runs of this set. 

Seventeen observations of bed-material discharge 

ranged from 67 to 140 ppm and had an 18-ppm standard deviation from the 92-ppm mean. Either the sediment concentration was too high, or the slope measurement was too flat in comparison with "normal" 

conditions found from similar runs.

Run 8. Reducing the rate of flow from that of run 

4 resulted in reduced velocity, depth, and bed-material 

discharge. The bed configuration was ripples.

Run 7. Bed features formed were dunes 4-8 feet 

long. Many of the dune troughs were 0.4 foot deep. 

Small ripples were seen on the crest of the dunes. 

Ripple waves were spaced about 0.3 foot from crest to 

crest and ranged from 0.02 to 0.06 foot in height. The 

reported concentration of bed-material discharge was 

about double the normal value for these flow conditions.

Run 10. The shallow depth and low rate of flow reduced the shear stress on the bed so that apparently, 

only ripples formed on the flume bed. The configuration was nearly that of a staggered pattern of individual ripples.

Run 6. The bed configuration was a transverse 

pattern of ripples across the flume. A diagonal pattern 

(about 45°) of slightly larger forms was also evident. 

The transverse bed waves were about 0.08 foot high 

and 0.7 foot apart. The diagonal waves were about
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 133

0.15 foot high and 2.5 foot from crest to crest. No 

sediment was in suspension.

Run 12. The shallow depth of this run caused a 

low bed-material discharge and a rippled bed configuration. The shallow depth also accentuated the effect 

of a backwater curve from the tailgate. This backwater curve reduced the bed-material discharge near 

the tailgate compared with the discharge near the 

central part of the flume. The total measured transport 

may be too low by a factor of 10-20. The other measurements of basic data probably were satisfactory.

Run 19. Dunes formed which were 3-8 feet long 

and almost completely covered with ripples. The dunes 

had a maximum height about equal to the mean flow 

depth. Many dune crests moving down the flume were 

normal to the flume walls, but some were 20-30° from 

the normal. The resistance to flow seemed to.be less 

than in runs in which fully developed dunes formed.

Run 21. Flow was increased from 4.24 cfs (run 19) 

to 12.12 cfs. This increase in flow caused the depth of 

flow to more than double and caused the velocity to 

increase from 1.30 to 1.58 fps. The bed-material-discharge also was nearly doubled. Figure 52 is a view 

of the dune-bed configuration in the flume after carefully draining the flume at the end of the run. The 

fin or longitudinal dune in the foreground is evidence 

of transverse-flow components resulting from either 

secondary circulation or flow diversion around the 

upstream dunes, or both. The spacing of the ripples 

on the dunes varied from close in the deep troughs to 

wide, and even obliteration, on the crest.

Run 22. The bed configuration and resistance to 

flow were nearly the same as for run 21. A small increase in flow rate caused the bed-material discharge 

to increase.

FIGURE 52. Upstream view of the dune-bed configuration at the end of run 21.

FIGURE 53. Upstream view of the dune-bed configuration at the end of run 25.

Run 25. Low discharge and shallow depth caused 

the dune height to be less than in runs 21 and 22. Figure 53 shows that the dune pattern was more regular 

than in the previous runs. The avalanche faces were 

normal to the flow and averaged about 6 feet in width. 

The orientation of the ripples, although not continuous 

on the dunes, indicated the direction of flow over the 

dunes.

Run 20. The flow and transport conditions resulted 

in a dune-bed configuration and an overall resistance 

to flow transitional between those of runs 25 and 21. 

The bed-material discharge was nearly the same as that 

of run 21, which had the deeper flow, because of the 

much higher slope.

Run 23. The flow rate for this run was about the 

same as that for runs 21 and 22, but the slope was 

about double. The dunes had a more natural appearance than those of run 25. Compare figures 53 and 54. 

The dunes appeared to consist of slightly coarser material than that seen on the surface of the trough. The 

finer material in the trough settled out of suspension 

as a result of the lower velocity of flow over the trough 

area.

Run 24- The dunes that formed on the bed were 

similar to those formed in run 23, but somewhat 

smaller. The resistance to flow and the bed-material 

discharge were greater than for the previous run.

Run 40. The water surface was extremely turbulent, 

and the waves were neither symmetrical nor smoothsurfaced. Some disturbances on the surface could be 

correlated with points of maximum roughness on the 

bed. Slope measurement was difficult because of the 

rough water surface. The water surface in the area
134 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 54. Upstream view of the dune-bed configuration formed during run 23. 

Note that the dune wave and avalanche face consist of coarser material than is 

in the trough.

of a boil stood several hundredths of a foot higher 

than in the surrounding area. Both horizontal and 

inclined bedding planes were observed through the 

window as the dunes moved by at different levels. The 

inclined bedding planes were on the avalanche face 

of the dunes and appeared to be formed of material 

somewhat coarser than the median diameter of the 

bed material. The horizontal layers were composed of 

suspended sediment deposited in the trough of some 

dunes and appeared to be somewhat finer than the 

median diameter of the bed material.

Run 39. Slope was 0.00364 and discharge was 2.58 

cfs per foot of width. All dune roughness was planed 

out. A train of well-rounded standing waves traveled 

from near the entrance of the flume to the exit. The 

water surface was much smoother and the bed was 

firmer than in the dune runs. A train of inphase sand 

waves formed under the water waves, the reverse of 

the phenomenon observed for the dune forms. The 

relative variation of bed-material-discharge concentration was much less than for the dune runs.

Run 26. This was a plane-bed run. The flow was 

essentially the same as described for run 39 except 

that no standing waves or undulations in the bed 

elevation occurred.

Run 28. The flow of this run was in a transition 

phase. One side of the flume had low washed-out 

dunes, where the water surface was out of phase with 

the sand waves; and the other side had low standing 

waves, where the surface was inphase with the bed 

waves. The amplitude of both kinds of sand waves 

was much smaller than that of the water waves. The 

proportion of the two kinds of flow changed considerably with time.

Run 29. Long flat dunes formed during this run, 

each with an avalanche face as much as 0.15 foot high. 

A typical observation showed smooth flow 0.25 foot 

deep on the back of the dune and, after the flow 

passed a 0.10 foot high avalanche face, turbulent flow 

0.42 foot deep in the trough area. The water surface 

was actually 0.07 foot higher over the dune trough 

than over the smooth back of the adjacent dune.

Run 31. The flow lines were relatively straight, and 

the water surface was relatively smooth, except for 

rounded standing waves which generally developed 

slowly into trains. Small ripples formed near the wall 

of the flume. They were probably due to the wall effect 

and did not extend into the flow more than 1 foot. 

Some water waves near the tailbox became steep and 

broke.

Run 27. The moving bed forms were low alternate 

bars, which caused the flow to meander. Some standing waves formed in the flume, and occasionally a 

wave would break gently. The standing-wave condition seemed to alternate with the plane-bed condition. (See fig. 55.)

Run 36. The low discharge (3.15 cfs) and shallow 

depth (0.19 ft) for this run accentuated formation of 

the alternate-bar type of flow mentioned for run 27. 

The bars were 0.1-0.2 foot high and generally occupied 

about half the flume width. Shallow flow over the bars 

moved sediment and deposited it at the downstream 

edge of the bar; thus, the bars slowly migrated downstream. In the deeper flow, which moved from side 

to side in the flume, around the bars, antidunes formed. 

Generally the antidunes were standing waves, but occasionally a wave broke. Figure 56 shows the water 

surface during this run and the bed condition at the 

end of the run, after the flume was drained.

Run J^l. A train of standing waves formed in the 

middle half of the flume. The standing waves were a 

train of sand waves under inphase water waves. The 

waves generally increased somewhat in height as they 

traveled along the flume. The waves occasionally migrated slowly upstream or downstream, but they generally were nearly stationary. The height of the water 

waves varied 0.20-0.25 foot from trough to crest, 

whereas the height of the sand waves varied 0.12-0.16 

foot from trough to crest. The bed was very firm 

where the water surface was smooth, but it was either 

soft or firm under waves.

Run 30. The flow in this run was similar to that 

described for run 36. The thalweg wandered from side 

to side along the flume and contained an occasional 

small antidune. The water surface was more wavy 

over the entire flume than it was for run 36. These 

waves averaged about 0.2 foot high and 1.2 feet from
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61

Of «

.-<:

135

w^^^W3l<^° **

FIGURE 55. Flume conditions for run 27. A, Water surface downstream from station 

100. B, Diagonal bars formed by flow upstream from station 100.

crest to crest. The alternate bars were 0.2-0.3 foot high 

on the downstream or avalanche edge. Waves on the 

bed under water-surface waves had a pattern similar to 

that of the surface waves, but they were less than half 

as high.

Run 35. This run was similar to run 30 except that 

the alternate bars which formed were not as prominent 

and the standing waves were more evenly spaced in the 

flume. Some standing waves occasionally moved upstream, but they generally remained in one position, 

growing in amplitude and then gently receding.

FIGURE 56. Upstream views during and after run 36. A, The water surface. B, 

The bed after the flume was drained. Note that the main thread of streamflow is 

on the left side of the flume in the area of the sign and then moves downstream 

toward the right side of the flume toward the 1 ower right corner of the photographs.

Run 34- The slope, depth, and velocity were greater 

than those of run 35. A series of standing waves 

formed.

Run 33. The mean velocity was 4.60 fps compared 

with 2.80 fps for run 35. The standing-wave flow pattern occurred at varying rates of mean velocity for 

several runs. Occasionally a train of small antidunes 

formed and moved upstream without breaking (standing waves). These waves grew in amplitude and then 

gently receded to a plane bed. The resistance to flow 

was very low.
136 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Run 38. The flow was deeper than for run 33, and 

standing waves formed from wall to wall across the 

flume at approximately right angles to the flow. More 

waves moved upstream than moved downstream. No 

waves broke.

Run 37. The flow conditions were very similar to 

those of run 38. The train of standing waves extended 

from wall to wall in the flume. The waves varied 

greatly in size, but never disappeared nor broke. The 

channel bed was very firm and, as seen through the 

window, appeared to be horizontally bedded. Clouds 

of suspended sediment extended up through about twothirds of the flow depth.

Run 32. The size of the water-surface waves increased with distance downstream in the flume. During most of the run, a train of antidunes existed between stations 40 and 95. These dunes continuously 

built up, broke, and then reformed. (See fig. 574.) 

From station 105 to the end of the flume, the dunes 

and resulting water waves extended the full width of 

the flume (See fig. 575.) The antidunes did not move 

upstream very much during their buildup. The waves 

on the bed surface under the main train of water waves 

were inphase with the water waves and had an amplitude about one-fourth that of the water waves. Most 

sediment moved near the bed, but some suspended sand 

was seen in the top part of the larger waves. Wave 

activity at the side window was mild compared with 

that in midstream; small inphase waves migrated 

downstream, and the amplitude of the bed undulations 

under them was about one-fourth that of the water 

waves. The bed undulations were still apparent after 

the flume had been drained at the end of the run. They 

extended all the way across the flume, were generally 

less than 0.1 foot high, and appeared to be parallel to 

each other and perpendicular to the flow direction.

Run 45. The water-surface condition varied widely, 

from plane, to antidune waves (either breaking or 

standing), to trains of waves extending nearly the full 

length of the flume. The sand bed was firm except 

where the antidunes broke (see fig. 58). Very heavy 

concentrations of sediment moved, mostly near the bed. 

Analysis of data showed that the concentration was 

about double that ordinarily expected for the imposed 

hydraulic conditions.

Run 44- Antidune waves formed just to the left of 

the center line of the flume, generally in a single train, 

but occasionally in a double train. The waves moved 

slowly upstream until they broke. New waves that 

formed downstream from the breaking position continued the process, so that net upstream movement 

was minor. The bed was firm except under the crest 

of a breaking wave. Mean flow depth for this run was 

shallow (0.28 ft), so a given antidune sand wave was

generally higher than the adjacent trough of the water 

wave.

Run 42. The flow condition and the bed configuration for this run are similar to run 44 even though the 

slope was steeper, the discharge, depth, and velocity 

were greater, and the bed-material discharge was less.

Run 4^. Wave activity was very diverse. The waves 

generally occupied the full width of the flume and 

formed and broke rather quickly compared with those 

formed in runs described previously. When several of 

these large waves broke at once, the flow velocity was 

greatly reduced and considerable water was stored in 

the flume. The result was a lowering of the water level 

in the tailbox and, consequently, a reduction of the discharge of the pumps. Thus, the rate and magnitude of 

discharge variation depended on the antidune activity.

RUNS USING 0.93-MM SAND IN 8-FOOT-WIDE FLUME

Data for these runs were collected during the period 

March-July 1960. The experimental variables and 

parameters are given in table 6, and the velocity-profile 

data, in table 16.

Run 19. The bed was screeded to a plane prior to 

this run. Then flow was carefully increased until several particles close to incipient motion had settled into 

a more stable position. No sediment was moving when 

the hydraulic data were collected. Resistance to flow 

due to the stationary sand grains was computed (table 

6).

Run 25. The flow depth was the same as for run 19, 

but the slope was greater and, consequently, the velocity was 1.22 instead of 1.00. No sediment movement 

occurred.

Run 26. Discharge was increased about 10 percent 

over that for run 25, and the resulting shear stress and 

a mean velocity of 1.32 fps were sufficient to cause 

some movement of particles finer than 1 mm. The 

movement of the grains was very random and infrequent. The rate of bed-material discharge was too low 

for reliable measurement.

Run 27. Further increase in the shear stress over 

that in run 26 caused general movement of all particles 

except those larger than about 2.0 mm. The bedmaterial discharge, determined from a composite of 

six samples, was 2.8 ppm.

Run 20. The slope for this run was the same as for 

run 27, but the discharge and velocity were less. The 

measured bed-material discharge was about 0.4 ppm, 

but data from other runs indicated that it should have 

been about 2 ppm. The slope was more than double 

that for run 19, and the velocity was about one-third 

greater. The bed seemed denser than that in run 19 

because of the fact that particles fell to a lower elevation on the bed as they moved in run 20.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 137

FIGURE 57. Flow conditions during run 32. A, View downstream showing train 

of antidunes near station 80. B, View upstream from station 125 showing large 

antidunes occupying full width of flume, and narrower antidunes from station 95 

to the head of the flume.

Run 21. The slope and discharge were increased for 

this run over those for run 20. Some particles moved 

constantly, but the largest ones moved only occasionally. The bed was very plane, and the largest grains 

were gradually buried. The water surface was smooth 

but not as glassy as in runs 19 and 20. The measured 

bed-material discharge (0.4 ppm) was about one-sixth 

that normally expected for the given flow conditions.

Run 18. A series of very low dunes or sand waves 

formed along the left wall of the flume. They tapered 

down to the plane bed along the right side of the 

flume. Some armoring occurred in the areas of greater 

boundary shear stress as a result of sorting of the fine 

material from the coarse. At least 99 percent of the 

bed-material discharge (21 ppm) moved in contact 

with the bed, so the water remained very clear.

Run 28. The discharge was about 10 percent greater than that in run 18, but the slope remained the 

same. Low dunes formed in a pattern similar to that 

in run 18. The dunes in this run, however, extended 

farther across the flume than did those in run 18.

Run 29. The slope was increased over that of run 

28, but no sediment moved because of the low shear 

stress. The low shear stress resulted from a reduction 

in velocity (from 1.75 to 1.16 fps) and in depth (from 

1.04 to 0.50 ft).

Run 22. This run was nearly identical with run 29.

Run 30. The velocity was increased to 1.25 fps by 

increasing both slope and discharge. Only particles 

less than about 1.0 mm in diameter moved.

Run 31. This was the first of the shallow-depth 

(about 0.5 ft) runs with the 0.93-mm sand during 

which there was general transport of the sand on the 

bed. No sand waves or dunes were seen, but some sorting of the fine and coarse material was noted. Movement of fine material occurred about 0.5 foot from the 

walls of the flume and was parallel to the direction of 

the flow. A few small depressions or pockets were 

eroded in the bed. No sand waves were seen downstream from such erosion pockets.

Run 15. Very small regular dunes about 0.10 foot 

high formed and moved slowly downstream. These 

dunes were typical of those obtained with finer sands, 

except that they were perhaps more regular and more 

closely spaced. They looked like those of run 14 shown 

in figure 59. The water surface was calm except downstream from dune crests, where small boils were generated by eddies. The bed was easily seen through the 

flow, because the amount of sand in suspension was 

very small.

Run 23. Conditions were similar to those in run 30 

except that the velocity was 1.30 instead of 1.25 fps. 

No particles larger than about 1.5 mm moved. The 

bed-material discharge was greater over patches of 

finer material. Even large particles rolled across these 

areas and then stopped when they reached the 'zone of 

normal gradation and other large particles.

Run 32. The bed was essentially a plane, and the 

bed-material discharge was 26 ppm. The bed-material 

discharge was nearly the same as for runs 18 and 28, 

but the hydraulic conditions were much different. 

Eight or nine bands of relatively fine material moved 

at equally spaced increments across the flume. Figure 

60 shows the bed after the flume had been drained at 

the end of the run.

Run 24. The discharge was about 10 percent less 

than that of run 32. The bed was plane, the depth was 

0.49 foot instead of 0.52 foot, and the velocity was 1.46 

fps instead of 1.50 fps. As in run 32, segregated move-
138 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 58. Upstream views of flow conditions for run 45. A, Train of antidune 

waves (sometimes called rooster tails). B, Bed configuration caused by the antidune flow.

ment occurred: the bed-material discharge was mostly 

composed of fine particles. Some small depressions or 

pockets were noted.

Run 14- The bed roughness for this run consisted 

of small dunes having an amplitude of less than 0.05 

foot and spaced 2.5-3.0 feet apart. This state of equilibrium was reached by washing out the large dunes 

formed in run 13, in which discharge and slope were 

much larger. The sand bed was very soft, particularly 

on the crest of the dunes. There was little or no suspended load, and the bed roughness did not affect the

water surface. The bed was plane adjacent to the flume 

walls. Figure 59 shows the bed after the flume had 

been drained at the end of the run. Evidence of differential transport can be seen in view B, which shows 

that the finer material is concentrated where the dunes 

are highest. Differential bed-material discharge was 

also indicated by the fact that the median diameter of 

the bed-material discharge was 0.00272 foot, whereas 

the median diameter of the bed material on or near 

the surface was 0.00325 foot;

Run 34- The flow conditions were similar to those 

described for run 14 (fig. 59) but the dunes that 

formed were slightly more irregular in shape. The increased shear stress caused the dune velocity and bedmaterial discharge to increase. The average particle 

size in the dunes or sand waves was smaller than that 

in the bed as a whole.

Run 16. The shear stress was sufficient to cause 

dunes to form that were more typical of natural dunes 

that those formed in runs 18, 28, 15, 14, and 34. The 

pattern of the dune faces was generally perpendicular 

to the direction of flow, but some advancement of the 

faces sometimes occurred near the centerline of the 

flume. Figure 61 shows the degree of dune development at the end of the run. Some sediment was carried 

in suspension, but not so much that the bed could not 

be seen through the water surface. Although the bed 

was very soft during flow, especially near the dune 

crests, the depth was much easier to measure than in 

runs using finer sands. As the size of the bed material 

increased, the avalanche face of the dunes grew steeper, 

recirculation downstream from the dune crest grew 

stronger, and the dunes moved in a more definite plane, 

were closer together, and had a more uniform shape.

Run 35. The depth of flow was shallow (0.53 foot) 

and slope, fairly steep (0.00130). Dunes formed that 

appeared to have characteristics between those of dunes 

formed in runs 16 and 34. (See fig. 60, 61 and 62.) The 

steeper slope caused an increase in the bed-material 

discharge and the dune velocity. The resistance to 

flow was about midway between those in runs 16 and 

34; yet, the water surface was more turbulent than in 

runs 16 and 34. Small boils were seen on the water 

surface downstream from the crest of the low dunes. 

Small fins of sediment that were parallel to the flow 

formed downstream from some avalanche faces. Many 

fins consisted of material finer than the average in 

transport.

Run 17. This run was similar to run 16 except that 

the slope and, consequently, the shear stress were increased by opening the tailgate. The dunes were well 

formed and moved faster because the shear stress was 

increased. The suspended bed-material discharge con-
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 139

B

FIGURE 59. Flume bed at end of run 14. A, View upstream. B, View downstream. 

Note in view B that the finer material is in the areas of maximum dune height.

sisted mainly of the finer particles, and the water was 

sufficiently clear that the bed could be seen through the 

flow. A few ripples moved on the backs of the largest 

dunes.

Run 33. The bed was raked and rough-screeded 

prior to the beginning of this run. Because of the 

shallower depth of flow, the dunes that formed were 

not as high as those formed in run 17. The water surface was rough and choppy, and a few boils were seen 

downstream from the dune crests. The dune height and 

the resistance to flow were greater than in runs 35 and

FIGURE 60. Upstream view of the plane bed at the end of run 32.

34. Figure 63 shows the bed at the end of run 33 and 

may be contrasted with figure 62, which shows the bed 

at the end of run 35.

Run 5. The dunes formed were larger and more 

irregularly shaped than those formed at nearly the 

same discharge but at lesser slope in runs 16 and 17. 

The rate of dune movement was nearly equal to that in 

run 17 (table 6), but the bed-material discharge was 

greater because the dunes were larger. The water surface was depressed in depth over the dune crests and 

was expanded over the troughs. Boils due to the strong 

counterflow in the troughs, could be seen on the water 

surface downstream from the dune crests. The bed

FIGURE 61. Upstream view of dunes formed during run 16.
140 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 62. Upstream view of the dune-bed condition at the end of run 36,

with these larger dunes was softer and more fluid than 

in the previous runs. The suspended-sediment co'ncentration was very small so the bed could be seen through 

the flow. Small fast-moving dunes moved on top of 

the large dunes, possibly causing the change in level of 

the major dune movement.

Run 10. The slope was steeper, the depth shallower, 

and the bed-material discharge greater than in run 33. 

The result was a low dune pattern. The relatively 

large amount of bed-material discharge near the bed 

and possibly also the increased strength of secondary 

circulations accentuated the "fins" downstream from 

the dune crest. (See fig. 64.) The irregularly shaped 

dunes and "fins" seemed to indicate that at such shallow depths, meandering might develop if slope and 

transport rate were increased.

FIGURE 64. Upstream view of the dune configuration at the end of run 10.

Run 37. The flow conditions in this run were similar to those in run 6, which will be described later.

Run 36. This was another shallow-depth run and 

was similar to run 10. The water surface was so turbulent that eddies, generated by the dunes, were indistinct. Waves generated in the flow by the dunes were 

reflected from the side walls, giving the appearance of 

additional roughness. The dunes were larger than 

those in other shallow-depth runs. The large dunes at 

this shallow depth caused much resistance to flow.

Run 6. This run was similar to run 37. As can be 

seen in figure 65, the bed consisted of large dunes. The

FIGURE 63. Upstream view of low dunes on the flume bed at the end of run 33. FIGURE 65. Upstream view of the dune-bed configuration formed during run 6
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 141

FIGURE 66. Upstream views of the flow conditions for.run 11. A, The water surface. 

B, The bed configuration at the end of the run.

dunes were very regular in form and had small dunes 

or ripples on their back. The bed was soft on the crest 

and firmer on the back, but in general it was softer and 

more porous than in runs having smaller dunes. The 

high velocity of flow over these large dunes resulted in 

a very rough water surface. If the depth had been 

greater, the surface waves would probably have been 

dampened and eddies and boils would have been more 

conspicuous. The turbulence was sufficient to cause 

some larger particles to be carried in suspension, and 

some of these were seen "jumping" from dune crest to 

dune crest. Most of the moving sediment was, however,

791-59T O 66 4

in nearly continuous contact with the bed. The dunes 

advanced by the processes of (1) sediment avalanching 

and deposition on the front of the dune crest and (2) 

erosion of the dune back and at the front of the 

trough. The amount of bed-material discharge varied 

greatly, depending on the position of the dune or dunes 

in relation to the flume exit.

Run 7. The slope was about the same as that for 

run 6, but the discharge was reduced to about 10 cfs. 

Compared with run 6, the velocity and depth were 

less, the dunes were smaller, and the water surface was 

smoother. Boils were conspicuous on the water surface 

downstream from the dune crests. As in other sets of 

runs, the large dunes moved much slower than the 

small dunes. The speed was directly proportional to 

the size or amplitude of the avalanche face, which 

varied with the volume of sediment in transport. The 

speed was also proportional to the shear stress, to the 

bed-material discharge over the back of the dune, 

which, in turn, was affected by the position of upstream dunes, and to the exposure or elevation at which 

the dune moved through the flume.

Run 38. The dunes formed in this run were similar 

to those formed in runs 6 and 37. Increasing the slope 

for this run caused the velocity of flow and the bedmaterial discharge to increase; consequently, the mean 

dune velocity was considerably greater. Many short 

dune troughs formed, in which the impinging flow 

from the crest of the dune at the upstream edge of the 

trough caused very rapid scour on the downstream 

part of the trough. The components of flow from this 

impingement, both forward and reverse, caused considerable suspension of sediment.

Run 11. The bed configuration consisted of large 

fast-moving dunes. The water surface was turbulent, 

and a few random surface waves were generated. Figure 66 shows the water-surface and bed conditions of 

this run. As can be seen in figure 662?, ripples or small 

dunelike sand waves formed on the back of the dunes. 

The distance between the major dunes seemed to in- 

. crease as they moved downstream. When the distance 

between dunes had increased to about 10 feet, either a 

new dune formed or the distance gradually decreased, 

depending on the position and shape of the dune pattern upstream.

Run 8. This run was similar to run 7 except that 

the slope was steeper and the velocity was higher. The 

discharge was increased over that of run 7 to maintain 

nearly the same depth. The dunes that formed were 

longer, lower, and traveled faster. The characteristics 

of the flow on the dunes seemed to represent the beginning stages of the transition between dunes and 

plane bed, although the energy of the flow was much
142 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

less than the rapid-flow condition in which F > 1. 

The wavy water surface effectively masked the typical 

dune-type boils on the water surface.

Run 12. The dunes were medium sized but moved 

rapidly and caused many surface waves. Some surface 

waves had white caps, but did not exhibit antidune 

characteristics. The bed increased in firmness as the 

velocity increased, especially on the back of the dunes. 

The dune shapes were sometimes observed to be very 

regular and consistent or, at other times and locations, 

change rapidly. Occasionally, a jet of flow moved over 

a dune that had a steep avalanche face, inpinged on 

the steep upstream face of the trough, or on the back 

of the next dune downstream, and caused very rapid 

erosion and the suspension of large quantities of sediment. Where such flow conditions occurred, very 

strong reversed flow originating from the eroding area 

and moving across the bottom of the trough was evident. Figure 67 shows these flow conditions.

Run 13. The slope for this run was steeper than 

that for run 12. Faster flow and more bed-material 

discharge resulted. The water surface was very rough, 

and short trains of irregularly shaped waves with 

white caps formed. The dunes were elongated and 

irregular in shape. Figure 68 shows the flow conditions of the run. The suspended-sediment concentration was greater than that in run 12. The dunes moved 

fast and changed shape rapidly; thus, useful data on 

dune velocity and amplitude were difficult to obtain 

through observation windows.

Run 9. The water surface was very rough, and the 

dunes were low and moving downstream very rapidly. 

This was a true transitional run. Standing waves inphase with the underlying bed configuration were common, but, more typically, the water waves were out of

FIGTJBE 67. Rapid flow from the dune crest on the left impinging on the downstream 

wall of the trough and causing rapid erosion and suspension of sediment during 

run 12.

FIGUBE 68. Upstream views of flow and bed conditions for run 13. A, Water-surface 

condition. B, Bed configuration at end of run.

phase with the bed configuration. Some trains of 

standing waves built up and then broke.

Run 3. The flow and roughness conditions of this 

run were similar to those described for run 9. Greater 

depth and velocity, however, caused much more suspension of sediment.

Run 1. The water surface was very rough, and 

some standing waves broke. The waves were less 

symmetrical and wider spaced than those in runs using 

smaller diameter sands. The water surface indicated
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 143

FIGURE 69. Flow conditions during run 2. A, An upstream view of a train of rough 

standing waves, and the water surface. B, A side view of inphase water and bed 

surfaces typical of standing waves.

a condition of an upper regime flow, but the bed consisted of low rapidly moving dunes. Very streamlined 

dunes indicated a transitional condition.

Run 2. In this run, the slope was steeper, the resistance was less, the velocity was higher, and the 

depth was less than in run 1. Trains of standing waves 

(fig. 69 J.) formed, but the waves generally disintegrated or washed out without breaking. The sand 

and water waves were inphase (fig. 69#) and generally 

were nearly stationary. Under these flow conditions, 

most sediment transport was close to the bed. As the 

sharpest and largest waves broke, "rooster's tails" 

formed on the water surface.

v I

FIGUBE 70. Upstream views of flow conditions for run 4. A, The rough water 

surface. B, The bed configuration at end of run.

Run 4- The conditions at the start of this run were 

the same as in run 2, except that the discharge was 

less. The reduced discharge caused the depth and the 

bed-material discharge to decrease, and the resistance 

to increase. The water surface was extremely rough, as 

is shown in figure 70. A variety of conditions, such as 

small elongated dunes rapidly advancing across a flat 

area and a few symmetrical or inphase waves, was 

visible from the side window. The symmetrical sand 

waves were very unstable and rapidly changed to 

dunes or planed out.

Run 41. This was another transitional run. Sometimes the bed and water surfaces were plane, sometimes 

they were undulating inphase, and sometimes they
144 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 71. Upstream views of flow conditions for runs 43 and 39. A, The water 

surface. B, The sand bed.

were out of phase. The out-of-phase condition was 

caused by small and rounded dunes having weak zones 

of flow separation. The resistance to flow was less than 

that in run 4; therefore, the water surface was 

smoother, and both the velocity and the bed-material 

discharge were greater.

Run 1$, The flow conditions over the bed were 

more plane than those of run 41. Small trains of large 

amplitude standing waves occasionally formed and 

then died out; but did not break. The bed was very 

firm except on the crest of dunes in a wave train.

Run 40. This run differed from run 42 by having 

more standing waves, greater resistance to flow, and 

more bed-material discharge. The wave trains sometimes built up nearly to the breaking point and then 

moved slightly upstream without breaking.

Runs 43 and 39. Input variables, resistance to flow, 

and bed-material discharge for these two runs were

nearly identical. The water and bed surfaces are 

shown in figure 71. Small-amplitude standing waves 

occasionally formed on the water surface, and these 

affected the bed. The bed was at least as firm as that 

in any other run or set of runs. The firmness of the 

bed may have been a major factor causing the low bedmaterial discharge noted for these two runs. Turbulence was reduced by the pavementlike bed.

RUNS USING 0.32-MM SAND IN 2-FOOT-WIDE FLUME

The purpose of this set was to determine the effect 

of viscosity on resistance to flow and bed-material discharge. The viscosity of the flow was varied for each 

run by changing the temperature of the flow. The 

temperature of the flow for a given run was maintained at a specific level by immersing a steam hose 

into the tailbox, thus warming the water before it 

was pumped back to the head of the flume. The sand 

used was the 0.27-mm sand used in the 8-foot-wide 

flume, but made coarser by washing away some of the 

fine particles. This set of experiments was conducted 

during the period November 1959-April 1960. The 

experimental variables and parameters are given in 

table 7, and the velocity profiles in table 17.

The order of presenting the runs in the following 

discussion and in table 7 is different from that used 

for the preceding sets because increasing slope cannot 

be used if the low- and high-temperature runs for a 

given discharge are to be compared. The low- and 

high-temperature paired runs are presented in the 

order of increasing discharge, the low-temperature run 

preceding the high-temperature run. For a specific 

temperature, the order approximated that of increasing 

slope, velocity, and bed-material discharge. Only water 

temperature and, hence, fluid viscosity were changed 

for any pair of runs. Changes in slope, depth, roughness, and bed-material discharge were the direct response to the change in fluid viscosity. In some sets 

the first run was made with cold water, and the second 

with heated water; in others the procedure was reversed.

Run 1. The run was started with the bed planed to 

a slope of about 0.00015. At a mean velocity of 0.90 

fps, small particles moved more steadily than large 

ones. When large particles moved, they generally became stabilized at a lower elevation, a very short distance, from where they started. The very small ripples 

formed from this kind of selective movement were most 

evident at the lower end of the flume, mainly because 

the depth of the flow there was less and the velocity 

was higher, but also because most of the fine sediment 

had been moved, by selective movement, from the 

upper to the lower end of the flume.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 145

Run 2. The conditions for this run were similar to 

those for run 1 except that the temperature of the flow 

was 23.4°C in contrast to 10.0°C in run 1. The sediment transport rate was slightly greater than in run 

1. Small particles moved constantly, medium particles 

moved intermittently, and large particles moved occasionally. The final bed form, very low ripples, caused 

somewhat greater resistance to flow and, in turn, lower 

velocity, than in run 1.

Run 3. Fully developed ripples as much as 0.2 foot 

high formed on the bed. Although these ripples moved 

downstream very rapidly, the water surface remained 

generally smooth. Clouds of sand occasionally swirled 

off the crests of the ripples, but no true suspended sediment extended from the bed to the water surface.

Run 4- The bed configuration of this run was ripples averaging 0.07 foot high and 0.66 foot long. The 

water surface was relatively smooth. Most sediment 

rolled or slid over the crest of each ripple. Small 

clouds of the finer particles were occasionally carried 

up into the flow. Few if any particles reached the surface, however, and the suspended concentration, for all 

practical purposes, was zero.

Run SO. Large and fairly uniform ripples formed 

throughout the length of the flume. Suspended sediment (24 ppm) was especially noticeable downstream 

from the ripple crests.

Run 29. The higher water temperature for this run 

caused a higher flow velocity and a higher bed-material 

discharge than run 30 at nearly the same slope. The 

dunes formed on the bed were smooth and flat and were 

partly covered with small ripples. Some dunes were 

almost indistinguishable. Ripples were the dominant 

bed form. Suspension of sediment was especially noticeable downstream from the ripple or dune crests. 

Suspended transport was only a small portion of the 

total transport as was attested by the smooth water 

surface.

Run 5. Both dunes and ripples formed on the bed 

of the flume. The water surface was undulating and 

was much rougher than in any other run previously 

described in this set. The bed sloped transversely near 

the larger dunes. Some bed-material discharge moved 

as suspended sediment, but most rolled and slid rapidly 

over the crest of the dunes.

Run 6. Rate of discharge was the same as in run 

5, but the water temperature was 17°C higher than in 

run 5. Depth of flow was greater than in run 5, but 

slope, velocity, and bed-material discharge are all 

significantly less. Again the bed features comprised 

low dunes with small ripples superposed. (See fig. 72.) 

Occasionally small vortices were seen carrying sand 

to the surface of the flow.

Runs 27 and 28. Fully developed dunes (and a few 

ripples) formed throughout the flume. In run 27 (cold 

water) the dunes were longer and more rounded and 

the water surface was smoother than in run 28 (warm 

water). The effect on depth, velocity, slope, and bedmaterial transport caused by changing water temperature seemed to be the inverse of that in the previous 

three pairs of runs, in which ripples were the dominant 

forms.

Runs 26 and 25. The dunes formed on the flume bed 

in runs 26 and 25 were generally of typical shape and 

were out of phase with water-surface undulations 

that is, the depression in the water surface was over 

the crest of a sand wave. Occasionally, some irregular 

dune troughs formed, such as an erosion pocket with 

both steep upstream and downstream slopes. Ripples 

formed in some dune troughs where the velocity was 

lowest. In run 25 the dunes increased in size downstream. As in runs 27 and 28, velocity and slope were 

higher in runs using warm water, whereas bed-material discharge was less.

Run 21. The run was typical of the transitional 

regime. The bed alternately was nearly a plane or 

comprised long low dunes. During the near-plane condition, the water surface conformed closely to any bed 

irregularities. Small irregularities slowly developed 

into low dunes, most of which did not extend uniformly across the flume. Dunes were 0.2-0.3 foot high on 

the left side of the flume but only 0.1 foot high on the 

right side. The bed was firm though easily scoured

FIGUBE 72. Downstream view of dune-bed configuration formed during run 6.
146 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

under the plane conditions, and very soft in the 

vicinity of the dune crests.

Run %%. The higher water temperature in this run 

resulted in a bed condition closer to that of dunes, although it was actually transitional. Long low very 

irregular dunes occupied about two-thirds of the flume. 

Most dunes were about 0.15 foot high, but at least one 

in each train of dunes that moved through the flume 

was about 0.3 foot high. The water surface was rough, 

and the depth of flow varied greatly. The more dunelike configuration caused the velocity and the slope to 

be lower and the bed-material discharge to be larger, 

especially the suspended part, than in run 21.

Runs %4 and 23. These runs were similar to runs 21 

and 22 except that the increased discharge resulted in 

a greater depth and somewhat lower velocity. The 

dunes formed in the warmer water (run 23) were more 

fully developed than those in run 22.

Run 7. The flow conditions for this run resulted in 

a smooth bed form of very long waves. The water 

surface was rough and followed the same pattern as 

the bed. Much of the bed-material discharge was 

rapidly rolled or slid along the bed, but some went 

into suspension very easily like dust swept by a broom. 

The bed-material discharge varied rapidly. Undulation of the bed surface caused stratification in the form 

of thin alternate layers of fine and coarse sediment in 

the bed, at least in the areas near the walls of the 

flume.

Run 8. The warm water caused the bed configuration to revert back to dunes from the nearly plane condition of run Y. About two-thirds of the length of the 

flume was covered with dunes, which started at the 

upper end of the flume and became progressively 

smaller as they moved downstream. In a few places 

the bed was intermittently scoured to the floor of the 

flume. The water surface was very rough, and the 

crest-to-crest distance between water waves was much 

less than the distance between dune crests. The downstream face of the dunes was not steep, so that any 

eddies downstream from the dunes were small. Figure 

73 is a side view of the dune configuration and flow 

of run 8. Sediment streaming from the crest of the 

dune can be seen in the photograph.

Run W. Downstream from station 35, very small 

antidunes formed. These moved upstream very slowly 

but did not break. The water and sand waves were 

inphase because the flow was in the upper regime.

Run 19- The higher temperature in comparison 

with run 20 caused the bed form and flow to change 

from one of mild antidunes to a plane bed. The downstream one-third of the flow surface had a slightly

FIGURE 73. Side view of dunes and flow conditions during run 8.

wavy appearance, but the rest was very smooth. The 

bed was very firm except in a few upstream areas of 

the flume. Even though the downstream water surface 

became increasingly wavy, it was very smooth compared with the surface in runs having greater slope.

Runs 10 and 9. The flow velocity and the amount of 

bed-material discharge were similar in these runs. The 

bed configuration was one of standing waves. Slope 

and resistance to flow were greater in run 10, seemingly 

because the viscosity of the water was greater (1.55 as 

opposed to 1.00). The standing waves were more 

persistent in runs 9 and 10 than in runs 19 and 20. 

They generally formed and remained for about 15 

seconds and then gradually diminished. Figure Y4 

shows the long low amplitude of the inphase sand and 

water waves. The amplitude of the water waves was 

greater than that of the sand waves.

Runs 12 and 11. The depth of flow was increased 

from that in runs 10 and 9, and for a given temperature 

a decrease in bed-material discharge and slope resulted. 

The bed was nearly plane in both runs, although standing waves formed in run 11. The water surface undulated gently in run 11. The magnitude of the 

undulations was about 0.1 foot at the downstream end 

of the flume. The bed-surface undulations were not as 

large as those of the water surface.

Runs 14 and 13. Antidunes formed in both runs. 

Those formed in run 14 (cold water) were better deFIGUBE 74. Side view of bed and flow during run 9.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 147

FIGURE 75. Side views of antidune flow conditions during run 15. A, Dune crest 

(left) and zone of flow acceleration (center and right). B, Trough of sand and 

water waves (left) and breaking wave and very heavy concentration of sediment 

near the bed (center and right).

veloped than those formed in run 13 (warm water), 

and they moved upstream at about 0.2 fps compared 

with 0.1 fps for those in run 13. The magnitude of 

the antidunes and their rate of movement decreased 

upstream in the flume. The bed-material discharge 

was greater in run 14 than in run 13 because the cold 

water resulted in greater antidune activity and, thus, 

more suspension of sediment.

Runs 15 and 16. The antidunes formed in these two 

runs were similar to those formed in runs 14 and 13. 

Bed-material discharge was greater in runs 15 and 16 

than in 14 and 13 because mean velocity and depth 

were greater and possibly because the water temperatures were lower. The suspension of bed material developed upward from a densely transported layer at 

the bed and was significantly greater than in runs 14 

and 13. Figure 75 shows two views of the flow conditions.

Rim 17. A chute-and-pool condition formed during 

this run that was nearly like that formed during runs 

using finer sands in the 8-foot-wide flume. Occasionally, an 8- to 10-foot-long chute formed in which flow 

accelerated downstream to a hydraulic jump or a 

strong downstream standing wave. Breaking antidunes

were seen all along the flume, and often the lower 20 

feet of the flume had a continuous series of breaking 

antidunes. The antidunes seemed to break when the 

crest of the sand wave was level with the water surface in the upstream trough.

Run 18. Flow in this run appeared similar to that 

in run 17 except that it was not as violent and no 

chutes and pools formed. The water surface was very 

rough; so reliable measurements of depth and slope 

were difficult to make. Eight measurements of the 

velocity of the upstream movement of the antidunes 

ranged from 0.020 to 0.082 fps and averaged 0.052 fps.

Run 31. This was a chute-and-pool run. The length 

of the chutes was possibly limited by the amount of 

sediment on the flume bed; that is, the lower part of 

the chute at the hydraulic jump may have been scoured 

to the floor of the flume. Nonuniform suspendedsediment concentration was indicated by analyses of 

four samples in which the mean concentration was 

41,600 ppm and the standard deviation was 27,800 

ppm. Four measurements of bed-material discharge 

averaged 49,300 ppm and had a standard deviation of 

7,700 ppm. A comparable high-temperature run was 

not made.

RUNS USING 0.33-MM (UNIFORM) SAND IN 2-FOOTWIDE FLUME

The sand used in this set of runs had a median 

diameter of 0.33 mm and as little size gradation as 

was practical to obtain. Table 1 and figures 4 and 5 

have more detailed information on the character of 

the sand. The runs were all made with temperature of 

the water close to 20°C and the depth of flow close 

to 0.50 foot. This set of experiments was conducted 

during the period January-April 1961. The experimental variables and parameters are given in table 8. 

Velocity-profile data are given in table 18. The runs 

are discussed on the following pages and are listed in 

table 8 in chronological order by increasing slope.

Run 7. The bed was planed smooth under quiet 

water and set at a slope of 0.00025 immediately prior 

to this run. When flow had been established, the resulting mean flow velocity was 1.14 fps. The shear 

stress was great enough to cause movement of sediment throughout the length of the flume but was not 

great enough to cause ripples to form anywhere but 

near the headbox.

Run 8. The slope was increased to 0.00087, and this 

increase caused much sediment movement; consequently, resistance to flow increased and ripples formed. 

The increase in resistance made it necessary to decrease 

the discharge and the velocity so that a depth of 0.50 

foot could be maintained. As is shown in figure 76 and
148 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

in columns 14 and 15 of table 8, the ripples had small 

amplitude and length. Ripples appeared to be slightly 

larger near the flume walls than at midstream. The 

bed-material discharge was only 6.6 ppm, and nearly 

all of it moved very close to the bed. The bed was 

very firm except on ripple crests, which were very 

soft and fluidlike.

Run 5. A continuous flow for 3 days was required 

to establish equilibrium in this run. Little or no 

change in flow conditions occurred during the last 

24 hours. The ripples were about twice as high as 

those formed in run 8, and their size and shape varied 

more widely. The bed-material discharge was 47 ppm, 

of which about 15 ppm was carried in suspension.

Run 11. The bed form consisted of dunelike highs 

and lows almost completely covered with ripples. The 

high areas did not have discernible crests, as one would 

expect for dunes. The entire bed was soft.

Run 10. The slope was 0.00213, more than double 

that for run 11. The consequent flow and transport 

variables achieved equilibrium with a bed form consisting of ripples superposed on dunes. Some shorter 

dunes, 1.5-2.0 feet long, did not have ripples on their 

surface. The sand bed felt soft and fluidlike.

Run 6. The flow characteristics were similar to 

those expected over a dune-bed configuration. The 

dunes varied greatly in size and shape, and some had 

ripples on their surface; some even had a very round 

crest. Figure 77 illustrates the bed and flow conditions 

in run 6. The rounded shape of some of the dunes apparently resulted from the specific dune being subjected to a jet of flow from over the next upstream 

dune.

FIGURE 76. Upstream view of rippled flume bed at the end of run 8.

B

FIGURE 77. Bed and flow conditions for run 6. A, Upstream view of the flume after 

the water had been drained from it at the end of the run. B, Side view of two 

dunes. The flow is from right to left.

Run h The slope and depth seemed to fluctuate 

considerably, and, with them, the bed condition from 

nearly plane to transitional dunes. The bed-material 

discharge remained relatively constant. The transitional dunes gradually built up from the plane-bed 

condition. At first they were long but had small amplitude; then they changed to short but with large 

amplitude. As the dunes built up, the resistance to flow 

increased and caused the depth and slope to increase 

also. The bed was softer than under normal plane-bed 

conditions.

Run 1. Plane-bed conditions of flow and transport 

existed during this run. The resistance to flow was 

low, and the water surface was relatively smooth. Most 

sediment transport occurred in close contact with the 

sand bed. The average bed-material discharge was 

3,090 ppm, of which only 12.7 percent was in suspension, in contrast to over 30 percent ordinarily in
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 149

suspension when dunes and ripples are present. The 

sand bed was very firm.

Run 9. The flow condition varied with the size and 

shape of the dunes formed. At times the dunes were 

as much as 8-12 feet long, and at other times they 

averaged 3-4 feet long. The height of the long dunes 

was about one-half that of the short dunes. The alternating from one kind of dune to another affected 

slope, depth, and concentration of bed-material discharge. The mean slope for this run was greater than 

that for run 1, but the velocity and bed-material discharge were much less.

Run 12. A plane-bed condition very similar to that 

in run 1 existed as long as the water was kept heated. 

When the water temperature was allowed to drop to 

15 °C, the bed condition converted to the one of antidunes.

Run 13. The increase in slope and shear stress for 

this run caused the flow velocity and bed-material discharge to be greater than in run 12. The result was a 

series of standing waves which built up slowly and 

then gently receded or broke. The sand and water 

waves were inphase, and the vertical distance between 

the crest and trough of the water waves was about 

twice that of the sand waves. None of the dunes upstream from station 40 broke, and only some of those 

downstream from station 40 broke.

Run 2. This was a typical antidune run of relatively mild activity. Antidunes formed and broke regularly in the downstream end of the flume, less frequently 

in the middle of the flume, and only occasionally in 

the upper end of the flume. The mild activity as the 

dunes broke did not cause much suspension of sand. 

After a series of waves broke, the bed usually planed 

out considerably and low-standing waves developed. 

The standing waves, in turn, moved upstream as they 

grew in size and developed into antidunes. Figure 78 

illustrates the nature of the standing-waves formed in 

run 2.

FIGURE 78. Side view of the standing waves most typical of flow conditions during 

run 2. Flow is from right to left.

FIGURE 79. Side view of an antidune beginning to break during run 3. Flow is from 

right to left.

Run 3. Antidunes were breaking somewhere in the 

flume at all times during this run, but they generally 

took longer to break than did those in run 2. The 

longer breaking time, plus the greatly increased frequency of breaking resulted in a large increase of 

suspended bed-material discharge over that in run 2. 

Sediment was deposited on and filled in the upstream 

slope of the sand waves. During and after breaking of 

an antidune, such deposition and filling occurred very 

rapidly. Figure 79 shows an antidune early in the 

breaking stage. The 0.1-foot-thick highly concentrated layer of sediment became a cloud of sand in the 

low velocity flow under the breaking crest of the water 

wTave.

Run 14- Increase in slope over that in run 3 caused 

greater velocity and more violent activity in the form 

of breaking antidunes. The bed-material discharge was 

nearly the same as that of run 3, but the part held in 

suspension was greater.

BUNS USING 0.33-MM (GRADED) SAND IN 2-FOOTWIDE FLUME

The 0.33-mm graded sand as described previously, 

was manufactured or assembled from several size fractions to obtain a nonuniform sand having a median 

diameter of 0.33 mm. Flow characteristics and bedmaterial discharge in runs using this sand were recorded for comparison with data for runs using the 

uniform 0.33-mm sand. The runs in this set are likewise presented in order of increasing slope. The following data were collected during the period JulySeptember 1961. The experimental variables and 

parameters are given in table 9, and the velocity-profile data, in table 19.

Run 11 A. The bed was planed smooth under several 

inches of quiet water prior to the beginning of the run. 

Flow was established at a slope of 0.00022 and a mean 

velocity of 1.08 fps. Some fine grains moved, mostly 

to positions at lower levels among coarser grains.
150 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Particles which protruded into the flow were affected 

by the greatest shear stress and usually were the first 

to move.

Run 11B. General movement of all particles was 

obtained by increasing the slope to 0.00027 and increasing the mean velocity to 1.28 fps. Ripples formed 

from stations 0 to 20, and some fine-grained particles 

moved as far as station 24. The remainder of the flume 

downstream from station 24 remained plane despite 

considerable particle movement.

Run 16. Data collection began 36 hours after the 

run was begun. A uniform pattern of ripples that resembled sand waves formed. It appeared that material 

finer than the median size was traveling over a bed of 

material coarser than the median size. Figure 80 shows 

the bed configuration after the water had been drained 

from the flume at the end of the run. (Compare the 

ripples shown in fig. 80 (graded sand) with those 

shown in fig. 76 (uniform sand of same median diameter). Several samples were taken from the sand 

waves and from the troughs. Analysis of the composited wave samples gave a median diameter of 0.20 

mm and a standard deviation of 1.96, whereas the composited trough samples gave a median diameter of 0.38 

mm and a standard deviation of 2.23. This analysis 

confirmed the visual observation that sorted bedmaterial discharge existed under this kind of ripple 

formation.

Run 6. The ripples formed in run 6 were more 

fully developed and in a more irregular pattern than 

those formed in run 16. (See fig. 81.) They caused

FIGURE 80. Upstream view of ripples at the end of run 16. Note that the sand in the 

ripple crests is finer than that in the troughs.

i/

FIGUEE 81. Upstream view of ripples formed during run 6.

greater resistance to flow and somewhat lower mean 

velocity than those in run 16, even though the slope 

had been increased from 0.00029 to 0.00047. The water 

surface was calm. The bed-material discharge (12 

ppm) moved in almost continuous contact with the 

bed.

Run S. Slope and discharge were increased over 

those in run 6. As a result, flow velocity in this run 

was much greater than that in run 6, and bed-material 

discharge was somewhat greater. The ripples seemed 

very small; their growth may have been restricted by 

the coarse bed material. (See fig. 82.) Sediment moved 

by sliding or by short hops. A mixture of coarse and 

fine particles moved near the center of the flume, 

whereas only fine particles moved closer to the flume 

walls. The coarser material formed an armor plate, 

and the fine material moved as ripples. Many coarser 

particles moved across several ripples without stopping, whereas the fine particles moved from ripple to 

ripple but had a long rest period between moves.

Run 1. Long low dunes and a few low ripples 

formed. (See fig. 83.) Generally, relatively low resistance to flow indicates a low percentage of suspended 

sediment, but this was not true for this run. The low 

resistance to flow in run 1 may be explained by the fact 

that the bed was very soft throughout the depth disturbed by the dune movement.

Run 10. The bed form in this run was mostly one 

of ripples superposed on dunes. Long low dunes occasionally formed, moved slowly downstream, and 

then died away. The bed-material discharge was some-
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 151

FIGURE 82. Upstream view of ripples formed during run 5.

what less than in run 1, and the suspended part was 

much less.

Run 8. Small rather rounded dunes formed. Ripples on these dunes were less prominent than on those 

formed under similar hydraulic conditions in runs 

using the uniform sand.

Runs 9 and 7. Low dunes of various sizes formed 

in both runs. (See fig. 84.) Some dunes had a few 

superposed ripples during the runs.

FIGURE 83. Upstream view of the dune-bed configuration at the end of run 1.

FIGURE 84. Upstream view of the dune-bed configuration formed during run 9. 

Most of the ripples were caused by flow disturbance during draining of the flume 

at the end of the run.

Run 2. Dunes formed that were similar to those of 

runs 9 and 7 but were somewhat rounded because of 

the increased slope and velocity in run 2. (See fig. 85.) 

The dunes moved through the flume very rapidly, so 

that there was much bed-material discharge.

Run 3. The flow pattern and bed-material discharge 

were characteristically those of a run in which the bed 

condition was transitional between dunes and plane

FIGURE 85. Upstream view of the dune-bed configuration at the end of run 2.
152 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

bed. The bed form varied from almost plane to fastmoving low dunes which rapidly changed form. Some 

segregation of particles occurred, but generally the 

sediment was well graded throughout most of the 

flume.

Run 4- The mean velocity of flow was 4.00 fps. The 

transitional dunes of run 3 were washed away, and a 

plane firm sand bed resulted. Most of the bed-material 

discharge was in a thin layer close to the bed.

Run 12.- The bed for this run was essentially plane, 

but some very small standing waves formed. These 

small waves can be seen in figure 86. Very heavy sediment transport took place near the bed.

Run 13. The, flow conditions for this run resulted 

in formation of standing waves and slow-moving antidunes, some of which broke.

Run 15. Violent antidunes broke in series and 

caused considerable suspension of sediment. The water 

surface was too rough to allow reliable depth and slope 

measurements.

Run 14- This was another antidune run, but the 

slope was steeper and the velocity lower than in run 

15. The antidunes alternately had small and large 

amplitude. The small antidunes broke gently, and the 

large ones, vigorously.

RUNS USING 0.47-MM SAND IN 8-FOOT-WIDE FLUME

The 0.47-mm sand used in this set of runs was derived from the 0.45-mm sand by washing away of 

some of the fine fractions. The main purpose of the 

set was to determine the effect of fine sediment, 6/, on 

the mean-flow and bed-material-discharge parameters

FIGURE 86. Upstream view of bed conditions at the end of run 12.

for a range of equilibrium-flow conditions similar to 

those in the set of runs using the 0.45-mm sand.

After equilibrium was established and the data collected for a given run, bentonite was either added to 

or extracted from the flow to establish a new concentration of fine sediment without stopping the flow. The 

change in the fine-sediment concentration generally 

caused a change in the flow and transport conditions, 

and these changes, in turn, caused a change in bed 

roughness, depth, slope, and bed-material discharge.

Bentonite was used as the fine sediment because it is 

commercially available in large quantities. The particle-size distribution of the bentonite down to 2 microns is shown in figure 87. Bentonite is composed of 

several different clay minerals, as is shown in figure 88. 

The mean specific gravity of the particles is about 2.8.

As Simons, Richardson, and Haushild (1963) pointed out, aqueous dispersions of bentonite are non-Newtonian; that is, the shearing stress is not directly proportional to the rate of shear. Therefore, the term 

"apparent" viscosity relates the shearing stress to the 

rate of shear. Figure 6 shows the relations of apparent 

kinematic viscosity (v) and temperature for dispersions of 0, 0.5, 1, 2, 3, 5, and 10 percent bentonite in 

distilled water as determined using a Stormer viscometer. One part sodium hexametaphosphate to 99 

parts bentonite, the ratio used in the flume experiments, prevented flocculation of the clay particles in 

the dispersions. The apparent kinematic viscosity is 

given in column 23 of tables 10 and 11 for each run.

After equilibrium had been established in each run, 

samples for determination of total sediment discharge 

(bed material plus fine material) were collected into a 

tank at the end of the flume with a width-depth integrating sampler. Eight samples were taken in the lower 

flow regime (ripples and dunes) during a 12-hour pe99.99

99.9

O _ QQ K yy.o

y 98 fc o 0 Z

uj~ 95 

o z 

< <

!- ^ on z: i- yu

UJ

O

ffi 80

70

DIAMETER, IN MILLIMETERS

FIGURES?. Particle-size distribution of bentonite used in flume studies with the 

0.47-mm and 0.54-mm sands. The sample was chemically and mechanically dispersed in water and analyzed by the sieve-pipette method.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 153

LLL

Clay (57 percent)

Silt (41 percent)

Sand (2 percent)

Estimated amount 

(parts per ten)

Montmorillonite 

Quartz 

Vermalite

Montmorillonite 

Quartz 

Feldspar 

Mica

Quartz 

Feldspar 

Mica

9 + 

Trace 

Trace

6 + 

2 + 

1- 

Trace

3

7- 

Trace

FIGURE 88. Mineralogy of bentonite for different size classifications as analyzed with 

an X-ray diffractometer by Paul D. Blackman, U.S. Geological Survey, Denver. 

The size distribution differs from that shown in figure 87 because no chemical dispersant was used to prevent flocculation after the sample had been mechanically 

dispersed.

riod, and four samples were taken in the upper flow 

regime (plane bed, standing waves, and antidunes) 

during a 1-hour period. Each sample consisted of 

70-110 pounds of the water-sediment mixture.

To separate the fine material, or "wash load," from 

the bed material, the sample was allowed to stand a 

few minutes so that the sand could settle. After the 

sand settled, the water-bentonite mixture was drained 

off, leaving the sand. The remaining fine material in 

the sand was removed by washing the sand over a 

No. 230 sieve. The concentration of the fines thus removed was added to the concentration of the fines removed from a pint sample of the water-bentonite 

mixture drained from the tank containing the flume 

sample. Then, all material coarser than 0.062 mm was 

considered bed material, and all finer material was 

considered fine material. The concentration of finematerial transport is listed in table 10, column 6, and 

bed-material transport, in column 9. The sum of these 

is the total concentration of sediment discharge.

Samples of concentration of suspended-sediment 

(col. 7, table 10) were obtained with the specially designed depth-integrating sampler in the flume section

95-100 feet downstream from the flume entrance. Generally, only one 5- to 8-pound sample was collected by 

the equal-transit-rate method for each run. Some concentrations were not recorded because the samples contained an excessive amount of bed material from 

contact of the sampler nozzle with the bed, particularly 

for the dune runs. Because only a single sample was 

collected during each run, the standard deviation 

could not be computed.

This set of experiments was conducted during the 

period January-May 1958. The experimental variables 

and parameters are given in table 10, and the velocityprofile data, in table 20.

The order of presenting the runs in table 10 and 

in the descriptions to follow is based on (a) increasing 

fine-sediment concentration within a series of runs, 

(b) increasing slope, and (c) the following order of 

bed form: ripples, dunes, transitional, plane, and antidunes. The run numbers were continued from the 0.45- 

mm set because of the close similarity of the bed 

material.

Runs Ifi, $ , 4$, wnd 4&- These runs were made 

using the 0.47-mm sand and clear water. Data collected were meant to fill gaps in the data for the runs 

using the 0.45-mm sand. Dunes with superposed ripples were formed in all four runs. As was expected, the 

mean velocity increased as depth increased and as the 

dunes became lower and longer. Runs 47 and 48 had 

low shear stress and a low rate of bed-material discharge; thus, there was no suspended-sediment movement, and the sand dunes moved very slowly.

Runs 85, 86, 87, and 88. The slope for this series of 

runs ranged from 0.00046 to 0.00049, and the concentration of fine-material discharge was 0, 4,800, 8,400, 

and 11,400 ppm, respectively. Under these conditions, 

ripples formed on the bed and flow velocity ranged 

from 1.13 to 1.20 fps. Fine material near the bottom 

(about 0.1 foot of flow) blocked visibility of the bed. 

Through the side window of the flume, however, it 

could be seen that the fine material was being deposited 

in the trough of the ripples and that the next ripple 

from upstream would ride over the lens of fine material ; subsequent ripple troughs passed above, through 

or below the lens deposit. Figure 89, photographed 

through the window, shows ripples and lenses formed 

during run 88. The lenses, as well as the shape and 

velocity of the ripples, seemed to offer some resistance 

to normal sand transport. When ripples became stationary or nearly so, they became rounded and had 

about the same slope on the upstream and downstream 

faces. The stationary ripples resulted from the space 

between the sand grains at the surface being filled with 

fine sediment. The fine material definitely caused the
154 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 89. Ripples and lenses oi fine material (light colored) in the bed during run 

88. The relatively round shape oi the ripples can be contrasted with the normalshaped ripples shown in figure 33.

ripple shapes and patterns to be more irregular than 

those formed in clear water. In collecting bed-material 

samples, it was noted that the layer of sand below the 

normal depth of movement of the ripple waves was 

much firmer for the fine-material runs than for the 

clear-water runs.

Runs 90 and 89. The slope was greater for these 

runs than for runs 85-88. Both the flow and the ripples 

were noticeably affected by the stabilization of the bed 

by the bentonite. In run 89 a crusty layer underlay the 

ripples throughout most the flume, and the ripples 

were the same height as those in the previous four 

runs but were longer and had a higher velocity. The 

bed was raked smooth to a depth of about 0.15 foot 

prior to run 90, but it was covered with loose sand 

ripples riding on a layer of clay-impregnated sand during the run. The sand moved more freely, at least near 

the windows in run 90, than in run 89.

Runs 93, 92, and 91. The slope was again increased 

for these runs and was sufficient to cause dunes and

FIGURE 90. Upstream view of the bed configuration typical of that formed during 

runs 93, 92 and 91.

FIGURE 91. Upstream views of the water surface during runs 51 (.A) and 96 (B) 

contrasting the increase in turbulence with increased flow stress and resistance.

overriding ripples to form on the bed. The bed form 

shown in figure 90 at the end of run 92 was typical for 

all three runs. The water surface was turbulent, and 

boils formed downstream from the major dunes. Resistance to the establishment of flow equilibrium due to 

the fine material in the bed seemed to increase as slope 

increased. In each run the slope was gradually increased over a period of several hours and then slightly 

reduced before the final equilibrium was obtained to 

insure that the more compact sand-clay layer would be 

below the zone of dune movement.

Runs 82, 51, 52, 73, 74, 76, 75, 53, 77, and 96. In this 

series of 10 runs, the slope ranged from 0.00199 to 

0.00248, the water discharge ranged from 8.01 to 8.76 

cfs, and the bed-material discharge ranged from 429 to 

761 ppm. The bed form in all the runs was one of
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 155

dunes with varying amounts of superposed ripples. 

The water surface in each run showed evidence of 

turbulence depending on the amounts of shear stress 

and resistance to flow. Figure 91 shows the water surface during runs 51 and 96. The dune shape ranged 

from rough in a relatively regular cross pattern (run 

51) to washed out in an irregular pattern (runs 82 and 

96). This range in dune shape is shown in figure 92. 

The resistance to flow in these runs as measured by 

Manning n ranged from n=0.034 (run 82) to n=0.023 

(run 96).

Many sizes of dunes and ripples were in motion at 

any given time. The small dunes often moved faster 

and, hence, caught up with the large dunes and drastically modified their shape, amplitude, and velocity. 

When a small dune caught up with a larger one, the 

new dune approximated the sum of the two amplitudes 

in height. The small dune moved faster than the large 

one only if it was behind the large dune. The fine 

sediment seemed to cause the dune form in these runs 

to be more irregular for a given slope and velocity of 

flow than that in the clear-water runs, possibly because of the cohesiveness of the mixture.

Run 94- This was a dune run with almost no fine 

sediment in the flow. The shape of the dunes was 

normal; however, the amplitude and the spacing varied 

considerably. The material on the bed appeared to 

move more freely than in runs with a large fine-sediment concentration.

Runs 83, 54, 56, 55, 57, 58, and 95. These runs had 

slopes ranging from 0.00180 to 0.00259, depths between 0.80 and 0.94 foot, bed-material discharge ranging from 588 to 1,600 ppm, and a bed form of dunes. 

The discharge of the water-sediment mixture ranged 

from 15.28 to 15.58 cfs, a variation of only 2.0 percent.. 

Fine-material concentration increased from 0 (run 83) 

to 28,300 ppm (run 95). Depth, slope, and roughness 

decreased as concentration of fine sediment increased. 

The water surface was turbulent and contained many 

boils caused by eddies downstream from the dune 

crests. The most turbulent surface flow occurred in 

run 95. (See fig. 93.) The bed roughness in run 95 became stabilized for brief periods of time (several minutes) and, when this happened, caused choppy waves 

on the water surface. However, the bed was soft (no 

lenses of clay), and the turbulence was great enough to 

cause the clay to act as a wash load, even at this concentration of 28,300 ppm. In run 83 (clear-water condition), dunes had a mean height of 0.43 foot, and some 

dune troughs exposed the floor of the flume. Watersurface waves and the sand waves were out of phase 

in all runs in this series; that is, a high (or crown) on 

the water surface was over a low area (or trough) of

FIGUEE 92. Upstream views contrasting dune shapes resulting from the flow during 

runs 82 04) and 96 (E).

the dune, and the low area on the water surface was 

over a dune crest.

Run 78. The flow for this run was in equilibrium 

with large dunes moving at a rapid rate. Strong eddies 

from the dune crests caused the water surface to be 

very turbulent. (See fig. 94.) The water stood high 

over the trough and low over the crest of dunes, as in 

the preceding runs, but to an even greater extent. The 

flow must have been nearly transitional, as indicated 

by the fact that often no major dunes could be seen 

near the flume windows.

Run 59. The flow stress in this run caused the 

dunes to be washed out; so this run, too, was transitional. The water surface was very irregular, as is 

shown in figure 95. The washed-out dunes formed a 

diagonallike crisscross pattern, which was also re-
156 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 93. Upstream view of water surface during run 95. The flow, at a velocity 

of 2.39 fps, is over a dune-bed form.

FIGUBE 94. Upstream view of water surface during run 78.

FIGUBE 95. Upstream view of water surface during run 59.

peated for the surface waves. The bed was very soft 

and fluid, particularly near the dunes.

Runs 60 and 61. These runs had plane-bed conditions. Occasionally a small dunelike form was seen, 

but these features were generally less than 0.01 foot in 

amplitude. These minor dunes seemed to extend diagonally across the flume, similar to those observed 

during run 59. The bed was firm except on the crest of 

the minor dunes. The character of the flow at the surface is shown in figure 96.

Runs 71, 72, and 70. The flow was typically that of 

plane-bed runs. Some small dunes, similar to those 

formed in runs 60 and 61, formed during run 71; the 

bed was very plane in run 72; and a few small standing waves formed at the lower end of the flume during 

run 70. The sand bed was firm, but not as firm as in 

runs in which higher velocities caused standing waves 

to form.

Runs 63, 64, 65, 66, and 80. The flow stress caused 

formation of bed features ranging from predominately 

standing waves during run 63 to double-train antidunes 

during runs 65, 66, and 80. Figure 97 shows a typical 

water-surface condition for this series of runs. The 

wave pattern in run 63 developed less vigorously and 

less frequently than that in run 80, in which the wave 

trains formed nearly continuously. The sand waves 

were symmetrical and inphase with the surface waves. 

The sand bed was firm and smooth except in the area 

of the breaking antidunes. For a given slope, antidune 

activity seemed to increase with fine-sediment concentration.

Runs 81, 62, 67, and 79. The slope ranged from 

0.00622 to 0.00651, the depth ranged from 0.53 to 0.55 

foot, the mean velocity was about 4.9 fps. Standing 

waves formed in each run. Figure 98 shows a typical 

view of the flow for these runs: at times the water

FIGURE 96. Upstream view of water surface during run 60.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 157

FIGURE 87. Upstream view of water surface typical of runs 64, 65, and 66.

surface was nearly plane in short reaches, and at other 

times low- to medium-height standing waves were 

evident. The bed was plane under the plane-flow areas 

and wavy under the standing waves with an amplitude 

of about one-half the amplitude of the water waves. 

The bed was firm at all locations. Most bed-material 

discharge occurred within 0.05 foot of the bed. Fine 

material was in the bed below the zone of sand movement.

Runs 84, 69, and 98. Varying amounts of antidune 

activity occurred during this group of runs. Figure 99 

illustrates the range of flow condition during run 84 

from standing waves to breaking antidunes. The highest concentration of the fine material (42,000 ppm) for 

this set occurred in run 98. Run 98 also had the largest, 

most frequent, and most violent antidunes. Figure 100 

illustrates the antidune activity during run 98.

Run 68. A single train of standing waves formed 

during this run. The standing waves were similar but 

slightly larger than those of run 67. The water waves 

had an amplitude of about 0.05 foot and the sand 

waves had an amplitude of about 0.04 foot. The inphase water and sand waves were spaced about 4 feet 

apart. The bed surface was firm.

Runs 100 and 99. These two runs were nearly identical with respect to slope, depth, and velocity. Run 

100 was a continuation of run 99 except that the finesediment concentration had been decreased by adding 

clear water to the flow and wasting the excess of the 

mixture. Run 100 had 106 ppm of fine sediment and a 

temperature of 13.3°C, whereas run 99 had 26,900 ppm 

of fine sediment and a temperature of 19.6°C. Run 100 

had a plane bed and a mean bed-material discharge of 

8,440 ppm; run 99 had violent antidunes and a mean 

bed-material discharge of 16,100 ppm. The decrease in

791-597 O 66 5

antidune activity with the decrease in fine-sediment 

concentration was very striking.

Run 97. The slope for this run was much steeper 

than that for runs 100 and 99, but the mean velocity 

was much less because of the shallower flow. The antidunes formed in run 97 were not as violent as those 

in run 99; and, consequently, the bed-material discharge was little more than half that of run 99.

BUNS USING 0.54-MM SAND IN 2-FOOT-WIDE FLUME

This set of runs complemented the previous set (0.47 

mm sand in 8-ft-wide flume) in determining the effect 

of fine sediment on resistance to flow and on sediment 

transport. The smaller, 2-foot-wide flume, made it 

practical to use much higher concentrations of bentonite in the flow. The characteristics of the bentonite are 

described on page I 52.

As in the previous set, equilibrium was established 

and data were collected for a given run, then without 

stopping the flow, bentonite was added to or extracted 

from the flow to establish a new concentration of fine 

sediment. The change of fine-sediment concentration 

generally affected the fluidity, which in turn caused a 

change in bed roughness, velocity, depth, slope, and 

bed-material discharge.

Samples for determination of total-sediment-transport concentration (bed material plus fine sediment) 

were collected with a width-depth integrating sampler 

at the end of the flume. From 8 to 12 samples were 

taken for the ripple and dune runs, and from 6 to 8 

samples were taken for the upper-regime flows. The 

method of analysis for separation of the fine material 

and bed material was described on page I 53. Depthintegrated suspended-sediment samples were not obtained for these runs.

FIGUBE 88. View of water surface typical of runs 81,62, 67, and 79.
158 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 99. Upstream views of standing waves {A) and breaking antidunes (B) 

during run 84.

This set of experiments was conducted during the 

period April-July 1959. Experimental variables and 

parameters are given in table 11, and velocity-profile 

data, in table 21.

The order for presenting this set of runs is identical 

with that used for presenting runs using the 0.47-mm 

sand.

Runs 1 and 2. Particles of sand moved under flow 

conditions during these runs, but the degree of movement was not sufficient to cause ripples to form. In 

run 1, particles moved only occasionally; but in run 2, 

many particles were in motion at any given time. Before run 2 was started, the material on the bed was 

thoroughly raked and ripples were introduced, but the 

flow and the characteristics of the sediment particle

FIGURE 100. Downstream view of the antidunes during run 98.

movement during the run caused the ripples to erode 

down to a plane bed after about 4 hours.

Run 3. The flow during this run caused considerably more sediment movement than occurred during run 

2. Irregular sand waves formed that were very different from ripples.

Run 4- In spite of the low bed-material discharge 

of 17 ppm, a rippled bed did not develop. The bed 

pattern, in general, comprised sand waves; but occasionally it included a very small avalanche face, 

such as normally would be associated with a dune.

Runs 6 and 5. The flow conditions in these runs 

caused normal steep-fronted dunes to form throughout 

the length of the flume. The dune fronts were continuous across the full width of the flume but were 

not always normal to the flume wall. If the dunes were 

diagonal to the flow, however, they were all in the 

same direction; and if they were normal to the flow, 

they all were normal. The continuous dune fronts 

caused increased resistance to flow, but not increased 

bed-material discharge, in contrast with the data for 

the 0.47-mm sand in the 8-foot-wide flume.

Run 20. This run should be classed as transitional, 

although it could be called a dune run. The dunes 

were irregular in shape and movement; sometimes 

there was a long flat area with no dunes. The water 

surface was generally rough, with choppy waves superposed on longer waves owing to the dunelike bed configuration.

Runs 8, 8A, 8E, 8B, 8C, and 8D. The discharge for 

this series of runs ranged from 3.69 to 3.84 cfs, and the 

fine-material concentration ranged from 0 to 63,700 

ppm. Runs 8, 8A, and 8E had bed forms of typical 

sharp-crested dunes. However, beginning with run 8B 

the fine-sediment concentration was increased to 20,600
SUMMARY OP ALLUVIAL CHANNEL DATA PROM PLUME EXPERIMENTS, 1956-61 159

ppm, and the dunes became irregular in shape. The 

irregularities ranged from long stretches of very low 

sharp-crested dunes to large round-crested dunes. Also 

beginning with 8B, some bentonite was layered in the 

bed by the dune action. The highest concentration of 

fine material was during run 8D, and the dunes formed 

during this run were very long and low and had small 

rounded ripplelike waves superposed. The bed in run 

8D was much firmer than that in the dune runs, but 

not as firm as is expected for the plane-bed condition.

Run 7. This clear-water run had a slope nearly 

double that for 8D; yet the bed had a rough dune 

configuration in contrast to the low smooth configuration of run 8D. The average bed-material discharge 

was 1,250 ppm for run 7 and 521 ppm for run 8D. 

The relatively high bed-material discharge for run 7 

was caused by the rapid movement of the dunes and 

by the suspension of sediment through the action of 

large eddies that originate from the dune crests. The 

water surface over the dunes was very turbulent. 

Small waves and boils formed over the dune trough 

and eddy areas and dissipated over the upstream slope 

of the next dune downstream.

Runs lit, 14A, HC, and l^B. The discharge for each 

of these runs was about 4.8 cfs, and the fine-sediment 

concentration ranged from 0 to 44,100 ppm. The bed 

condition varied from one of nearly normal dunes, for 

clear water (run 14), to plane bed, for the highest concentration of fine material (run 14B). The equilibrium 

slope decreased as the fine-sediment concentration increased, as in runs 8-8E.

Run 19. This run was set up to produce dunes at a 

discharge rate higher than that in run 7. The depth 

was first set at 0.6 foot but was increased as equilibrium became established. The dunes resulting from this 

flow had an unusual shape, especially the short ones, 

in that they were high and well-rounded toward the 

upper end but drawn down at the lower end, where 

the crest is ordinarily located. The avalanche face, 

where present, was less than half as high as the dune. 

The water surface was extremely rough, because of the 

turbulence caused by the dunes. A short dune trapped 

between two relatively long dunes was severely scoured 

by a jet of flow from the upper dune and, therefore, 

rapidly changed size and shape. This run was classed 

as transitional between dunes and plane bed.

Run 9. This run was transitional between dunes and 

plane bed. Generally one or more irregularly shaped 

dunes could be seen in the flume, but the conditions 

changed constantly. Dunes formed and then were 

erased by the flow. The roughness of the water surface 

varied with the roughness of the bed.

Run 10. The bed in this run was plane more than 

90 percent of the time. Sometimes smooth undulations 

developed throughout the length of flume and lasted 

2-3 minutes. Occasionally a very low dune with a small 

avalanche face formed and moved rapidly through 

the flume. This kind of flow caused most of the bedmaterial discharge to slide and to roll along the bed.

Runs 15, 15A, 15B, and 15C. The discharge for 

each of these runs was nearly 7.0 cfs, and the concentration of fine material ranged from 0 to 58,600 

ppm. The flow in all the runs was considered to have 

standing wave form, although the waves for run 15 

were often poorly defined. Unlike in dune runs 8-8D 

and 14-14B, an increase in fine-material concentration 

caused an increase in the equilibrium slope. Most 

bed-material discharge moved in relatively close contact with the sand bed.

Runs 13 and 11. These were clear-water runs which 

had standing-wave patterns of flow. Suspended sediment moving in the cross section of flow was much 

less a part of the bed-material discharge than that 

moving close to the bed. With the recirculating system and under these flow conditions, only the top few 

hundredths of a foot of the bed was disturbed. Specific sand particles from the bed moved downstream, 

but they were immediately replaced by other particles 

from the moving layer. The step length and rest 

period differed greatly for any group of particles or 

between specific particles.

Runs 18, ISA, 18B, and ISO. The discharge in this 

series of runs was about 7.6 cfs, and the fine-sediment 

concentration ranged from 0 to 58,700 ppm. The flow 

conditions ranged from standing waves when there 

was no fine sediment (run 18) to mildly breaking antidunes when the concentration of fine sediment was 

highest (run 18C). Equilibrium slope increased noticeably, and suspended-sediment concentration considerably, as fine-sediment concentration increased, especially when the flow shifted to the breaking antidunes of 

run 18C.

Runs 16A, 16B, and 16C. The discharge in each of 

these three runs was about 7.8 cfs, and fine-material 

concentrations ranged from 11,200 to 44,500 ppm. 

Slopes were considerably steeper than in runs 18-18C. 

The flow condition was one of antidunes in all three 

runs. The degree of antidune activity and resistance 

to flow in the runs increased with increasing fine-material concentration.

Runs 17,17A, and 17B. The discharge in this series 

was nearly the same as in the 16A-C series, but the 

slope was greater and antidunes formed in all runs. 

As bentonite was being added between periods of data 

collection ("runs"), it was noted that antidune activity
160 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

increased with increasing concentration of the fine material. A similar condition was noted by Langbein 

(1942) for natural streams. This increased antidune 

activity caused increased resistance to flow and greater 

slope to maintain the depth of flow. In run 17B, three 

or four waves occasionally broke simultaneously, scouring out a 16- to 20-foot-long pool and creating a steep

section draining the pool. Run 17B must have been 

transitional between antidunes and chute-and-pool flow. 

The increasing antidune activity caused the suspension and total transport of sand to increase rapidly. 

Run 12. This clear-water antidune run was made 

at high slope to allow comparison with runs having 

high concentrations of fine sediment.
BASIC DATA
162 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 2. Experimental variables and parameters

Run

(1)

24 

22A 

2 

22B 

26

25 

22C 

30 

1 

31

27 

5 

23 

32

8

28 

33 

29 

3 

11

13 

14 

15 

34 

12

6 

7 

35 

16 

10

9 

17 

18 

19 

39

20 

21 

38 

36 

37

Slope 

X10« 

S

(2)

0. 0055 

.010 

.015 

.016 

.017

.018 

.018 

.028 

.034 

.043

.057 

.058 

.062 

.066 

.070

.079 

.083 

.084 

.092 

.099

.100 

.106 

.112 

.127 

.130

.130 

.140 

.147 

.156 

.170

.194 

.196 

.300 

.350 

.390

.460 

.542 

.582 

.845 

.950

Depth 

(ft)

(3)

0.94 

.48 

1.06 

.43 

.30

.93 

.42 

1.00 

.58 

1.02

.55 

1.03 

.44 

.95 

.93

.54 

1.06 

.56 

.55 

1.09

.89 

.86 

.79 

.52 

1.02

.61 

.68 

.52 

.72 

.51

.49 

.67 

.64 

.64 

.61

.60 

.50 

.58 

.51 

.65

Water 

discharge

(cuft 

per sec)

(4)

6.52 

2.99 

6.68 

2.99 

2.00

6.45 

2.99 

8.91 

3.42 

10.62

4.08 

12.67 

2.99 

13.64 

14.81

4.49 

16.66 

5.08 

5.20 

20.47

21.98 

22.12 

21.84 

7.00 

21.96

8.14 

9.66 

7.52 

22.14 

11.68

8.22 

22.19 

22.16 

22.19 

22.33

22.17 

16.13 

22.00 

15.54 

21.84

Temperature 

T

(°C)

(5)

18.6 

17.5 

12.3 

17.8 

19.2

19.2 

18.0 

17.0 

13.6 

18.1

18.1 

16.4 

18.1 

18.2 

18.3

18.0 

17.4 

19.1 

12.3 

18.9

19.3 

19.4 

19.3 

16.6 

19.7

15.3 

18.0 

18.5 

18.8 

19.1

18.6 

19.1 

18.9 

18.7 

18.8

18.5 

18.7 

17.9 

16.8 

17.3

Suspended concentration

Sampled 

(ppm)

(6)

0 

0 

0 

0 

0

0 

0 

7 

0 

42

105 

0

506

748 

31

795

772 

950 

1,120 

393 

929

550 

567 

729 

1,350 

861

697 

4,030 

7,270 

13, 400 

20,100

23,300 

21,900 

31,600 

38,800 

57,300

Standard 

deviation 

C, 

(ppm)

(7)

0 

0 

0 

0 

0

0 

0

0

11

0

28

86

42

67 

56

84 

58 

58

88 

140 

154 

116 

157

260 

373 

473 

562 

2,080

4,620 

3,690 

10,000 

13,900 

14,500

Particle 

size 

dso 

(ftXIOS)

(8)

0.423

.462

.456 

.511

.482

.351

.371 

.413 

.482

.423

.429 

.452 

.462 

.528 

.433

.397 

.472 

.478 

.495 

.521

.485 

.469 

.508 

.518 

.561

Total bed-material discharge

Concentration 

Ct 

(ppm)

(9)

0 

0 

0.2 

0 

0

.3 

0 

3.7 

1.2 

29

4.0 

120 

2.0 

281 

519

34 

836 

58 

84 

1,300

1,240 

1,490 

2,000 

503 

1,270

861 

1,240 

999 

2,750 

2,480

1,210 

4,650 

9,240 

12,900 

16,200

23,900 

25,200 

26,600 

35,500 

47,300

Standard 

deviation 

Ct 

(ppm)

(10)

0 

0

0 

0

.2 

0 

.5 

1.0 

3.3

.7 

13 

.4 

17 

40

4.9 

174 

7.2 

18 

181

68 

168 

71 

26 

110

157 

192 

131 

296 

316

230 

1,770 

820 

3,060 

3,590

3,610 

4,720 

7,510 

4,120 

10,500

Particle 

size 

dm 

(ftXIOS)

(11)

6.321 

.712 

.433

.334 

.499 

. .499 

.456 

.427

.518 

.482 

.558 

.528 

.446

.453 

.522 

.561 

.518 

.436

.489 

.499 

.531 

.620

.548

.495 

.544 

.522 

.522 

.495

.512 

.502 

.522 

.541 

.512

Gradation 

a

(12)

1.80 

1.40 

1.59

1.61 

1.62 

1.38 

1.53 

1.67

1.32 

1.46 

1.45 

1.36 

1.55

1.54 

1.43 

1.38 

1.36 

1.54

1.42 

1.56 

1.40 

1.34 

1.40

1.46 

1.30 

1.29 

1.33 

1.30

1.33 

1.26 

1.33 

1.31 

1.31

Bed 

material 

particle 

size

<*50

(ftXlO")

(13)

0.656

.626

.613

.626 

.643 

.623

.623 

.640 

.597 

.649 

.630

.623 

.656 

.643 

.659 

.583

.590 

.564 

.584 

.653 

.593

.620 

.614 

.656 

.597

.587

.623 

.561 

.597 

.564

.590

.676 

.689

Sand waves

Length 

(ft)

(14)

0.6

.4

.6 

.5 

.6

.5 

.9 

.4 

4.0 

5.4

.6 

8.0 

.6 

.7 

11.6

13.4 

18.8 

20.5 

1.7 

17.7

5.1 

7.4 

4.5

24.0

5.2 

4.4 

4.9

Height 

H,

(ft)

(15)

6.03

.03

.03 

.02 

.04

.03 

.04 

.03 

.10 

.18

.04 

.65 

.04 

.04 

.39

.13 

.17 

.04 

.04 

.32

.18 

.31 

.13

.10

.20 

.10 

.10

Velocity

(ft per 

min)

(16)

0.00098

.024 

.00085

.080 

.0029 

.23 

.17

.13

.032 

.21

.20

.26 

.20

.10 

.24 

.24

.78 

.15
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 163

for 0.19-mm sand in 8-foot-wide flume

Run

(1)

24 

22A 

2 

22B 

26

25 

22C 

30 

1 

31

27 

5 

23 

32

8

28 

33 

29 

3 

11

13 

14 

15 

34 

12

6 

7 

35 

16 

10

9 

17 

18 

19 

39

20 

21 

38 

36 

37

Mean 

velocity 

V 

(ft per 

sec)

(17)

0.87 

.78 

.79 

.87 

.83

.87 

.89 

1.11 

.74 

1.30

.93 

1.54 

.85 

1.79 

1.99

1.04 

1.96 

1.13 

1.18 

2.35

3.09 

3.22 

3.46 

1.68 

2.69

1.67 

1.78 

1.81 

3.84 

2.89

2.10 

4.14 

4.33 

4.33

4.58

4.62 

4.03 

4.74 

3.81 

4.20

Velocity profile

Slope 

B

(18)

0.27

.38

.24

.53 

.36 

.51 

.47 

.76

.53 

1.01 

.34 

.72 

.83

.63 

.49 

.64 

.67 

.45

1.29 

1.37 

.77 

1.33

.80 

.83 

.63 

1.40 

1.29

1.18

Intercept 

C

(19)

1.19

1.16

1.18

1.24 

1.18 

1.52 

1.15 

1.86

1.51 

2.15 

1.40 

2.43 

2.66

1.72 

2.63 

1.77 

1.85 

3.13

3.85 

4.13 

4.50 

2.47 

3.84

2.30 

2.51 

2.71 

4.92 

4.22

3.68

Shear 

velocity 

V. 

(ft per 

sec)

(20)

0.041 

.039 

.072 

.047 

.041

.073 

.049 

.095 

.080 

.119

.100 

.139 

.093 

.142 

.145

.117 

.168 

.123 

.128 

.186

.169 

.171 

.169 

.146 

.207

.160 

.175 

.157 

.190 

.167

.175 

.206 

.249 

.269

.277

.298 

.295 

.330 

.373 

.446

Bed-material discharge

Sampled 

suspended 

Q> (Ib per sec 

per ft)

(21)

0 

0 

0 

0 

0

0 

0 

0.00049 

0

.0104 

0

.058

.097 

.00123

.127

.132 

.164 

.191 

.021 

.159

.035 

.043 

.043 

.233

.078

.045 

.70 

1.26 

2.32 

3.50

4.03 

2.76 

5.43 

4.71 

9.77

Total 

Qt 

(Ib per sec 

per ft)

(22)

0 

0 

0 

0.000010 

0

.000015 

0 

.00026 

.000032 

.0024

.00013 

.0119 

.000047 

.030 

.060

.0012 

.109 

.0022 

.0034 

.21

.21 

.26 

.34 

.027 

.22

.055 

.093 

.059 

.47 

.23

.078 

.80 

1.60 

2.23 

2.82

4.13 

3.17 

4.57 

4.30 

8.06

Kinematic 

viscosity 

Xios

(sqft 

per sec)

(23)

1.12 

1.16 

1.33 

1.15 

1.10

1.10 

1.14 

1.17 

1.28 

1.14

1.14 

1.19 

1.14 

1.13 

1.13

1.14 

1.16 

1.11 

1.33 

1.11

1.10 

1.10 

1.10 

1.18 

1.09

1.22 

1.14 

1.12 

1.12 

1.11

1.12 

1.11 

1.11 

1.12 

1.12

1.12 

1.12 

1.14 

1.18 

1.16

Shear 

stress 

at bed

T

(Ib per

sqft)

(24)

0.0032 

.0030 

.0099 

.0043 

.0032

.010 

.0047 

.017 

.012 

.027

.020 

.037 

.017 

.039 

.041

.027 

.055 

.029 

.032 

.067

.056 

.057 

.055 

.041 

.083

.049 

.059 

.048 

.070 

.054

.059 

.082 

.120 

.140 

.148

.172 

.169 

.211 

.269 

.385

Reynolds 

number X10-J 

R

(25)

730 

320 

625 

323

725 

325 

949 

328 

1,161

449 

1,330 

325 

1,499 

1,636

491 

1,788 

569 

482 

2,300

1,498 

2,514 

2,480 

736 

2,514

827 

1,061 

836 

2,473 

1,328

909 

2,502 

2,489 

2,475 

2,500

2,462 

1,796 

2,397 

1,650 

2,351

Froude 

number 

F

(26)

0.16 

.20 

.14 

.23

.16 

.24 

.20 

.17 

.23

.22 

.27 

.23 

.32 

.36

.25 

.34 

.27 

.28 

.40

.58 

.61 

.69 

.41

.47

.38 

.38 

.44 

.80 

.71

.53 

.89 

.95 

.95 

1.03

1.05 

1.00 

1.10 

.94 

.92

Resistance factor

DarcyWeisbach 

/

(27)

0.174 

.0203 

.0656 

.0234

.0570 

.0246 

.0585 

.0928 

.0669

.0934 

.0649 

.0957 

.0504 

.0423

.1016 

 .0590 

.0949 

.0936 

.0503

.0240 

.0226 

.0190 

.0603 

.0472

.0732 

.0774 

.0601 

.0196 

.0267

.0555 

.0197 

.0264 

.0308 

.0292

.0333 

.0430 

.0387 

.0765 

.0902

Chezy

c/V?

(28)

21.4 

19.8 

11.0 

18.5

11.8 

18.0 

11.7 

9.3 

10.9

9.3 

11.1 

9.1 

12.6 

13.7

8.9 

11.6 

9.2 

9.2 

12.6

18.2 

18.8 

20.5 

11.5 

13.0

10.4 

10.2 

11.5 

20.2 

17.3

12.0 

20.1 

17.4 

16.1 

16.6

15.5 

13.6 

14.4 

10.2 

9.2

Manning 

n (fti/6)

(29)

0.012 

.012 

.024 

.012

.022 

.013 

.022 

.026 

.024

.026 

.024 

.025 

.021 

.019

.027 

.023 

.026 

.026 

.021

.014 

.014 

.012 

.020 

.020

.023 

.024 

.020 

.012 

.014

.019 

.012 

.014 

.015 

.015

.016 

.017 

.017 

.023 

.026

Bed 

configuration

(30)

Plane. 

Do. 

Ripple. 

Plane. 

Do.

Ripple. 

Plane. 

Ripple. 

Do. 

Do

Do. 

Do. 

Do. 

Dune. 

Do.

Ripple. 

Dune. 

Ripple. 

Do. 

Dune.

Transition. 

Do. 

Plane. 

Dune. 

Do.

Do. 

Do. 

Do. 

Transition. 

Plane.

Dune. 

Antidune. 

Do. 

Do. 

Do.

Do. 

Do. 

Do. 

Chute-pool. 

Do.
164 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 3. Experimental variables and parameters

Run

(1)

50A 

50D 

51

52 

54

53

57 

56 

55 

45

43 

44

42 

46 

58

47 

48 

39 

41 

40

Slope

X102

S

(2)

0.007 

.018 

.046 

.065 

.084

.108 

.126 

.126 

.130 

.138

.140 

.163 

.167 

.167 

.185

.280 

.493 

.813 

.952 

1.022

Depth 

(ft)

(3)

0.96 

.91 

.99 

.94 

.93

1.02 

.48 

.75 

1.08 

.84

1.13 

1.03 

.94 

.74 

.46

.63 

.59 

.55 

.45 

.60

Water 

discharge

(ft s 

per sec)

(4)

6.09 

6.09 

9.86 

12.25 

13.62

15.58 

5.11 

11.09 

17.80 

21.84

19.23 

21.55 

15.68 

21.76 

6.75

21.79 

21.69 

21.71 

15.41 

21.35

Temperature 

T (°C)

(5)

14.5 

15.8 

16.0 

16.0 

18.3

16.9 

13.9 

15.3 

18.1 

17.8

17.4 

16.8 

14.8 

18.5 

14.2

13.6 

15.9 

10.2 

11.0 

10.8

Suspended concentration

Sampled 

C, 

(ppm)

(6)

0 

0 

9 

57 

157

396 

0 

407 

534 

679

556 

623 

416 

857 

331

3,770 

10,800 

34,000 

43,300 

41,400

Standard 

deviation 

C, 

(ppm)

(7)

0 

0

8 

40

100 

0 

297 

203 

136

112 

151

57 

98 

129

461 

1,150 

1,710 

2,020 

9,470

Particle 

size 

dso 

(ftXIOS)

(8)

0.584

.591 

.689 

.541

.640 

.820 

.902 

.554 

.689

.600 

.662 

.627 

.715 

.623

Total bed-material discharge

Concentration 

Ct 

(ppm)

(9)

0.5 

12 

98 

200

358 

93 

550 

639 

1,270

931 

833

704 

1,670 

753

4,760 

9,080 

28,700 

35,600 

35,800

Standard 

deviation 

C, 

(ppm)

(10)

0.2 

1.7 

16 

44

67 

16 

147 

173 

675

248 

157 

70 

172 

104

673 

1,020 

9,460 

7,920 

6,150

Particle 

size 

rise 

(ftXIOS)

(11)

0.705 

.696 

.607

.584 

.771 

.623 

.646 

.755

.686 

.630 

.656 

.853 

.702

.758 

.646 

.656 

.636 

.656

Gradation

a

(12)

1.71 

1.61 

1.56

1.49 

1.56 

1.58 

1.48 

1.76

1.60 

1.56 

1.60 

1.64 

1.53

1.73 

1.53 

1.46 

1.42 

1.45

Bed

material 

particle 

size 

dso 

(ftXIOS)

(13)

6.856 

.889 

.820 

.935

.902 

.951 

.823 

.886 

.951

.912 

.856 

.837 

.827 

.902

.863 

.856 

.787 

.955 

1.033

Sand waves

Length 

(ft)

(14)

0.4 

1.2 

1.7 

5.1

6.0

.7 

4.9 

9.2

9.7 

11.1 

8.5

9.0

3.4 

4.7 

5.0 

4.4

Height 

H,

(ft)

(15)

0.04 

.03 

.06 

.17

.28 

.05 

.20 

.36

.44 

.41 

.40

.15

.05 

.15 

.18 

.12 

.12

Velocity 

V, 

(ft per 

min)

(16)

0.0002 

.053 

.096 

.055

.29 

.080 

.16 

.13

.13

.18 

.086

.26

TABLE 4. Experimental variables and parameters

Run

(1)

7 

8 

9 

10 

5

13 

4 

11 

33

"1

12 

14 

20 

o 2 

21

19

« 16 

23 

17 

«3

18 

30 

34

22 

"15

24 

25 

28 

29 

26

32

27 

31 

35 

37

38 

36

Slope 

X102

S

(2)

0.007 

.011 

.023 

.041 

.045

.063 

.069 

.073 

.090 

.100

.108 

.116 

.120 

.131 

.131

.134 

.134 

.134 

.136. 

.136

.141 

.142 

.150 

.153 

.158

.172 

.199 

.229 

.278 

.328

.470 

.533 

.593 

.815 

.820

.930 

1.007

Depth 

D

(ft)

(3)

1.01 

1.00 

1.01 

.59 

1.00

1.00 

.86 

.59 

1.06 

.88

.57 

.62 

1.05 

.92 

1.07

.65 

1.02 

.91 

.65 

.88

.61 

.64

.44 

.60 

.75

.82 

.72 

.55 

.52 

.50

.58 

.43 

.56 

.54 

.30

.40

.57

Water 

discharge

(cuft 

per sec)

(4)

6.61 

7.76 

7.76 

4.16 

10.73

13.46 

10.73 

4.92 

15.74 

12.70

7!l9 

8.61 

18.14 

15.19 

20.39

9.90 

17.23 

22.02 

10.01 

15.28

11.96 

15.68 

5.50 

14.92 

12.87

21.98 

21.85 

15.72 

15.70 

15.51

21.76 

15.47 

21.34 

21.33 

8.34

15.26 

21.38

Temperature 

T (°C)

(5)

13.9 

11.9 

10.9 

15.1 

16.5

16.4 

14.6 

14.9 

17.6 

16.7

16.0 

15.6 

15.6 

15.8 

16.5

14.9 

15.8 

15.6 

14.7 

15.2

14.7 

14.5 

14.1 

12.7 

13.0

15.7 

14.7 

15.1 

15.4 

15.0

10.8 

15.1 

10.2 

10.9 

11.6

11.1 

11.5

Suspended concentration

Sampled 

C, 

(ppm)

(6)

0 

0 

0 

0 

0

99 

0 

0 

377 

403

74 

134 

347 

583 

528

423 

436 

60S 

262 

445

439 

548

442 

389

763

972 

750 

1,240 

1,740

9,490 

8,240 

16,400 

31,800 

7,820

33,800 

47,400

Standard 

deviation 

C. 

(ppm)

(7)

0 

0 

0 

0 

0

0 

0 

203

7

25 

62 

126

82 

89 

81 

44 

73

189 

63

53 

34

375 

328 

121 

118 

133

1,360 

251 

634 

5,080 

941

4,220 

8,660

Particle 

size 

dso 

(ftXIOS)

(8)

0.649

.672 

.570

.672 

.354 

.518

.655 

.449 

.492 

.600 

.383

.485 

.462

.511 

.446

.475 

.561 

.586 

.587 

.573

.590 

.557 

.613 

.619 

.639

.698 

.648

Total bed-material discharge

Concentration 

C, 

(ppm)

(9)

0 

0 

2.7 

1.0 

12

75 

51 

20 

330 

405

150 

298 

506 

664 

732

563 

549 

1,230 

505 

733

1,040 

1,370 

480 

1,540 

789

2,350 

2,710 

2,760 

3,120 

5,060

10,500 

11,500 

13,000 

27,600 

19,900

36,100 

42, 400

Standard 

deviation 

C, 

(Ppm)

(10)

0 

0 

1.8 

.2 

3.5

11 

16 

1.8 

54 

65

14 

55 

105 

158 

101

104 

144 

248 

79 

168

200 

102 

127 

59 

123

351 

363 

372 

135 

1,160

1,590 

866 

2,630 

3,810 

1,690

6,650 

11,400

Particle 

size 

dso 

(ftXIOS)

(11)

0.902 

.850

.663 

.650 

.906 

.630

.423

.751 

.725 

.607 

.554 

.591

.627 

.574 

.656 

.630 

.640

.699 

.627 

.788 

.755 

.620

.689 

.804 

.833 

.886 

.820

.676 

.682 

.591 

.650 

.885

.656 

.669

Gradation 

a

(12)

1.58 

2.08

1.82 

2.00 

1.60 

1.60 

2.13

1.92 

1.71 

1.62 

1.96 

1.64

1.69 

1.74 

1.64 

1.72 

1.91

1.68 

1.47 

1.69 

1.62 

1.68

1.77 

1.64 

1.51 

1.72 

1.62

1.71 

1.71 

1.34 

1.46 

1.91

1.48 

1.43

Bed

material 

particle 

size 

rfso 

(ftXIOS)

(13)

6.985 

.985 

.866 

.985

.949 

.902 

.951 

.853 

1.064

.886 

.853 

.928 

.918 

.866

.870 

.820 

.997 

.892 

.843

.814 

.975 

.951 

.951 

.837

.899 

1.031 

.873 

.929 

.886

.846 

.916 

.906 

.903 

.935

.912 

.984

Sand waves

Length 

L

(ft)

(14)

0.6 

.5

.7

1.2 

.8 

.6 

6.2 

7.1

.9 

1.5 

9.6 

11.2 

9.8

5.8 

7.8 

11.8 

6.2 

7.6

11.7

1.8

8.2 

16.2

2.5

3.4 

3.1 

3.8 

6.0 

3.0

4.5

5.7

Height 

H, 

(ft)

(15)

0.02 

.03 

.04

.06 

.06 

.03

.27 

.29

.04 

.07 

.46 

.35 

.31

.20 

.34 

.26 

.25

.27

.24 

04

.06

.35 

.23

.06

.07 

.14 

.22 

.25 

.13

.14 

.12

Velocity 

V, 

(ft per 

min)

(16)

0,029 

.055 

.040

.31

.077 

.027 

.10

.22 

.080 

.17

.16

.123 

.12 

.38 

.11 

.13

.20

.095

.098 

.36

Slope poorly defined.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 165

for 0.27-mm sand in 8-foot-wide flume

Run

(1)

50A

50D

51

52

54

53

57

56

55

45

43

44

42

46

58

47

48

39

41

40

Mean

velocity

V

(ft per

sec)

(17)

0.79

.84

1.24

1.63

1.83

1.91

1.33

1.85

2.06

3.25

2.13

2.62

2.09

3.68

1.83

4.32

4.60

4.93

4.28

4.45

Velocity profile

Slope

B

(18)

0.18

.20

.52

.58

.66

.45

.84

.93

.68

1.24

.37

.68

.50

1.40

.30

Intercept

C

(19)

1.23

1.27

1.70

2.03

2.22

2.18

1.67

2.70

2.63

4.07

2.15

3.24

2.26

4.74

2.07

Shear

velocity

V,

(ft per

sec)

(20)

0.047

.073

.121

.140

.159

.188

.140

.174

.213

.193

.226

.233

.225

.199

.166

.238

.306

.379

.371

.444

Bed-material discharge

Sampled

suspended

<7>

(Ib per sec

per ft)

(21)

0

0

.0007

.0055

.017

.048

0

.035

.074

.116

.084

.105

.051

.15

.017

.64

1.83

5.76

5.21

6.91

Total

Qt

(Ib per sec

per ft)

(22)

0

.000024

.00092

.0094

.021

.044

.0037

.048

.09

.22

.14

.14

.086

.28

.040

.81

1.54

4.86

4.28

5.98

Kinematic

viscosity

X106

V

(ft

per sec)

(23)

1.25

1.21

1.20

1.20

1.13

1.17

1.27

1.22

1.14

1.15

1.16

1.18

1.24

1.12

1.26

1.28

1.20

1.40

1.38

1.38

Shear

stress

at bed

T

(Ib per

ft)

(24)

0.0042

.010

.028

.038

.049

.069

.038

.059

.088

.072

.099

.105

.098

.077

.053

.110

.182

.279

.267

.383

Reynolds

number X10-2

R

(25)

607

631

1,023

1,277

1,506

1,665

503

1,137

1,052

2,374

2,075

2,287

1,584

2,431

668

2,126

2,262

1,937

1,396

1,935

Froude

number

F

(26)

0.14

.16

.22

.30

.33

.33

.34

.38

.35

.62

.35

.45

.38

.75

.48

.96

1.06

1.17

1.12

1.01

Resistance factor

DarcyWeisbach

/

(27)

0. 0277

.0598

.0763

.0592

.0600

.0778

.0881

.0711

.0852

.0283

.0898

.0630

.0926

.0235

. 0655

.0243

.0354

.0474

.0602

.0798

Chezy c/V7

(28)

17.0

11.6

10.2

11.6

11.5

10.1

9.5

10.6

9.7

16.8

9.4

11.3

9.3

18.4

11.0

18.1

15.0

13.0

11.5

10.0

Manning

n

(fti/6)

(29)

0.015

.022

.026

.022

.023

.026

.024

.024

.027

.015

.029

.023

.028

.014

.021

.014

.016

.018

.020

.024

Bed

configuration

(30)

Plane.

Ripple.

Do.

Do.

Dune.

Do.

Ripple.

Dune.

Do.

Transition.

Dune.

Do.

Do.

Plane.

Dune.

Antldune.

Do.

Do.

Chute-pool.

Do.

for 0.%8-mm sand in 8-foot-wide flume

Run

(1)

7 

8 

9 

10

5

13 

4 

11 

33 

1

12 

14 

20 

2 

21

19 

16 

23 

17 

3

18 

30 

34 

22 

15

24 

25 

28 

29 

26

32 

27 

31 

35 

37

38 

36

Mean 

velocity 

V 

(ft per 

sec)

(17)

0.82 

.97 

.96 

.88 

1.34

1.68 

1.56 

1.04 

1.86 

1.80

1.58 

1.74 

2.16 

2.06 

2.38

1.90 

2.11 

3.02 

1.92 

2.17

2.45 

3.06 

1.56 

3.11 

2.14

3.35 

3.79

3.57 

3.77 

3.88

4.69 

4.50 

4.76 

4.93 

3.48

4.77 

4.69

Velocity profile

Slope 

B

(18)

0.17

.45 

.59 

.69

1.01 

.76 

.47 

.36 

.32

.71 

.71

.55

.33

.39 

.31

1.07 

.46 

.91

.56 

1.06 

.34 

1.26 

.25

.82 

1.29 

1.22 

1.36

1.87

Intercept 

C

(19)

0.81

.84 

.85 

1.41

1.97 

1.80 

1.04 

2.22 

2.06

1.79 

2.15 

2.55

2.41

2.19 

2.28 

3.15 

1.67 

2.53

2.51 

3.95 

2.01 

3.91 

2.57

3.82 

4.89 

4.60 

4.97

5.48

Shear 

velocity

(ft p*er 

sec)

(20)

0.048 

.060 

.086 

.088 

.120

.142 

.138

.118 

.175 

.168

.141 

.152 

.201 

.197 

.212

.167 

.210 

.198 

.169 

.196

.166 

.171 

.146 

.172 

.195

.213 

.215 

.201 

.216 

.230

.296 

.272 

.327 

.376 

.281

.346 

.430

Bed-material discharge

Sampled 

suspended 

<7. 

(Ib per sec 

per ft)

(21)

0 

0 

0 

0 

0

.0104 

0 

0 

.046 

.040

.0042 

.0090 

.049 

.069 

.084

.033 

.059 

.105 

.020 

.053

.041 

.067

.051 

.039

.131 

.166 

.092 

.152 

.211

1.61 

.99 

2.73 

5.29 

.51

4.03 

7.91

Total 

Qi 

(Ib per sec 

per ft)

(22)

0 

0 

. 00016 

. 000032 

.0010

.0079 

.0043 

. 00077 

.041 

.040

.0084 

.020 

.072 

.079 

.116

.043 

.074 

.21 

.039 

.087

.097 

.168 

.021 

.179 

.079

.40 

.46 

.34 

.38 

.61

1.78 

1.39 

2.16 

4.60 

1.30

4.27 

7.08

Kinematic 

viscosity 

X10»

(sqft 2 

per sec)

(23)

1.27 

1.34 

1.38 

1.23 

1.19

1.19 

1.25 

1.23 

1.15 

1.18

1.20 

1.21 

1.21 

1.21 

1.19

1.23 

1.21 

1.21 

1.24 

1.22

1.24 

1.25 

1.26 

1.31 

1.30

1.21 

1.24 

1.23 

1.22 

1.23

1.38 

1.23 

1.40 

1.38 

1.35

1.37 

1.36

Shear 

stress 

at bed

T

(Ib per 

sqft)

(24)

0.0044 

.0069 

.014 

.015 

.028

.039 

.037 

.027 

.060 

.055

.038 

.045 

.079 

.075 

.087

.054 

.085 

.076 

.055 

.075

.054 

.057 

.041 

.057 

.074

.088 

.089 

.079 

.090 

.102

.170 

.143 

.207 

.275 

.154

.232 

.358

Reynolds 

number XlO-a 

R

(25)

652 

724 

703 

422 

1,126

1,412 

1,073 

499 

1,714 

1,342

750 

892 

1,874 

1,566 

2,140

1,004 

1,779 

2,271 

1,006 

1,565

1,205 

1,567 

545 

1,424 

1,235

2,270 

2,200 

1,596 

1,607

1,577

1,971 

1,573 

1,904 

1,929 

773

1,393 

1,966

Froude 

number 

F

(26)

0.14 

.17 

.17 

.20 

.24

.30 

.30 

.24 

.32 

.34

.37 

.39 

.37 

.38 

.41

.42 

.37 

.56 

.42 

.41

.55 

.67 

.41 

.71 

.44

.65 

.79 

.85 

.92 

.97

1.09 

1.21 

1.12 

1.18 

1.12

1.33 

1.09

Resistance factor

DarcyWeisbach 

/

(27)

0.0271 

.0301 

.0649 

.0804 

.0646

.0566 

.0628 

.1025 

.0710 

.0700

.0635 

.0612 

.0696 

.0732 

.0637

.0622 

.0791 

.0344 

.0618 

.0655

.0369 

.0250 

.0699 

.0244 

.0667

.0324 

.0257 

.0255 

.0262 

.0281

.0319 

.0292 

.0378 

.0466 

.0523

.0421 

.0672

Chezy 

C/V7

(28)

17.2 

16.3 

11.1 

10.0 

11.1

11.9 

11.3 

8.8 

10.6 

10.7

11.2 

11.4 

10.7 

10.5 

11.2

11.4 

10.1 

15.2 

11.4 

11.0

14.7 

17.9 

10.7 

18.1 

11.0

15.7 

17.6 

17.7 

17.5 

16.9

15.8 

16.6 

14.6 

13.1 

12.4

13.8 

10.9

Manning 

n (ft'/«)

(29)

0.015 

.016 

.024 

.024 

.024

.022 

.023 

.027 

.025 

.024

.021 

.021 

.025 

.025 

.024

.022 

.026 

.017 

.021 

.023

.016 

.014 

.021 

.013 

.023

.016 

.014 

.014 

.014 

.014

.015 

.014 

.016 

.018 

.017

.016 

.022

Bed 

configuration

(30)

Plane. 

Do. 

Ripple. 

Do. 

Do.

Do. 

Do. 

Do. 

Dune. 

Do.

Ripple. 

Dune. 

Do. 

Do. 

Do.

Do. 

Do.

Transition. 

Dune. 

Do.

Do.

Transition. 

Dune. 

Plane. 

Dune.

Transition. 

Plane. 

Do. 

Do. 

Antidune.

Do. 

Do. 

Do. 

Do. 

Do.

Chute-pool. 

Do.
166 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 5. Experimental variables and parameters

Run

(1)

14 

13 

17 

16 

15

18 

2 

3 

9 

1

5 

11

4

8 

7

10 

6 

12 

19 

21

22 

25 

20 

23 

24

40 

39 

26 

28 

29

31 

27 

36 

41 

30

35 

34 

33 

38 

37

32 

45 

44 

42 

43

Slope

X102

8

(2)

0.015 

.019 

.020 

.021 

.023

.031 

.036 

.039 

.040 

.042

.047 

.049 

.057 

.060 

.078

.088 

.088 

.106 

.112 

.114

.124 

.189 

.193 

.247 

.289

.301 

.364 

.368 

.366 

.369

.432 

.436 

.446 

.466 

.492

.494 

.546 

.607 

.619 

.620

.656 

.862 

.898 

.986 

1.01

Depth 

D

(ft)

(3)

0.61 

.35 

.98 

.81 

.80

.58 

.82 

.85 

.55 

.80

.75 

.35 

.69 

.51 

.70

.33

.46 

.29 

.41 

.96

1.00 

.42 

.61 

.65 

.62

.81 

.55 

.34 

.40 

.30

.44 

.33 

.19 

.54 

.27

.25 

.28 

.27 

.50 

.43

.37 

.28 

.28 

.31 

.43

Water 

discharge

(cuft 

per sec)

(4)

3.94 

1.84 

6.22 

5.11 

5.07

3.62 

7.90 

7.90 

3.84

7.85

7.93 

1.95 

7.94 

3.83 

7.98

1.95 

3.90 

1.95 

4.24 

12.12

13.54 

4.91 

8.14 

13.34 

8.73

21.41 

20.64 

14.45 

11.19 

4.54

14.85 

7.91 

3.15 

21.62 

5.33

5.58 

8.44 

10.02 

21.38 

18.87

14.96 

5.58 

10.83 

13.43 

21.42

Temperature 

T (°C)

(5)

10.2 

9.0 

12.0 

12.0 

11.0

11.3 

11.0 

11.5 

12.0 

9.0

11.0 

11.5 

10.0 

12.0 

11.5

10.5 

9.5 

11.7 

18.0 

16.0

15.7 

17.0 

16.4 

16.0 

17.0

19.0 

19.0 

17.0 

16.0 

17.4

17.5 

18.0 

19.0 

18.7 

17.2

17.0 

17.5 

16.0 

19.0 

18.5

18.0 

18.9 

19.4 

20.0 

18.5

Suspended concentration

Sampled 

C. 

(ppm)

(6)

189

388 

558

917

747

3,970

323 

907

2,680 

682

732

752

250 

3,020 

4,520

Standard 

deviation 

C, 

(ppm)

(7)

Particle 

size 

rfso 

(ftXlOS)

(8)

0.31 

1.33

.43 

.46 

1.11

.44 

.49 

.44 

1.08 

1.31

1.51 

1.12 

.65 

.65 

1.38

1.02 

.59 

1.71 

.68 

.66

1.56 

.66 

.98 

1.21

Total bed-material discharge

Concentration 

Ct 

(ppm)

(9)

0 

0 

.7 

1.2

.7

.4 

9.4 

10 

1.4 

23

27 

4.7 

92 

7.6 

268

16 

42 

1.0 

208 

380

554 

378 

508 

856 

917

2,460 

3,960 

4,580 

4,230 

1,850

4,750 

4,100 

1,370 

4,340 

3,550

4,610 

5,690 

6,810 

6,230 

5,570

6,180 

9,630 

15, 100 

11,400 

11, 500

Standard 

deviation 

C, 

(ppm)

(10)

0 

0 

.2 

.6 

.5

.1 

.3 

5.6

.8 

7

10 

3.9 

18 

2.5 

20

4.1 

16

.8 

52 

34

102 

77 

61 

206

711

657 

338 

275 

594 

241

409 

291 

795

785 

457

330 

1,050 

442 

844 

688

764 

1,440 

4,160 

1,890 

232

Particle 

size 

rfso 

(ftX103)

(11)

0.728 

.837

.968 

.935 

.361 

1.160

.863

1.030

.846 

.637

1.400 

1.440 

.771 

.951 

.820

.791 

1.100 

.663

.755 

.820

.810 

1.010 

1.140 

1.110 

1.190

1.250 

1.210 

1.350 

1.380 

1.350

1.330 

1.450 

1.360 

1.590 

1.740

1.670 

1.590 

1.570 

1.720 

1.280

Gradation 

a

(12)

2.70 

2.68

2.47 

2.79 

3.80 

3.95

2.77

2.29 

2.78 

3.36

1.64 

1.86 

3.70 

3.28 

2.81

2.58 

2.03 

2.84 

2.43 

2.29

1.97 

1.92 

1.87 

1.84 

2.08

1.80 

1.98 

2.10 

1.76 

1.85

1.71 

1.77 

1.85 

1.83 

1.83

1.84 

1.61 

1.60 

1.65 

1.80

Bed 

material 

particle 

size 

rfso (ftxio3)

(13)

1.44

1.35 

1.48 

1.54 

1.44

1.52 

1.46 

1.51 

1.39 

1.46

1.54 

1.64 

1.54 

1.57 

1.36

1.25 

1.50 

1.61 

1.40 

1.23

1.41 

1.51 

1.54 

1.65 

1.48

1.58 

1.66 

1.50 

1.14 

1.57

1.48 

1.31 

1.26 

1.36 

1.65

1.35 

1.33 

1.74 

1.30 

1.57

Sand waves

Length 

L

(ft)

(14)

0.8

.7

.7 

1.2 

1.4 

.7 

2.0

1.0 

.8 

4.2 

.7 

4.4

.8 

1.6 

.9

6.4 

4.8

7.5 

6.3 

5.4 

6.6 

5.5

7.4 

3.7

2.6 

6.4

3.2 

10.2 

.9 

3.9 

6.0

2.2 

2.5 

2.8 

3.8 

3.8

3.7 

1.6 

3.0 

3.6

5.8

Height 

H,

(ft)

(15)

0.04 

.06

.04 

.07 

.09 

.06 

.10

.07 

.06 

.15 

.06 

.20

.08 

.10 

.06 

.26 

.31

.52 

.26 

.36 

.41 

.31

.31 

.10

.05 

.23

.06 

.19 

.03 

.14 

.12

.07 

.08 

.10 

.09 

.08

.29 

.11 

.21 

.25 

.27

Velocity 

V. 

(ft per 

min)

(16)

,
SUMMARY OF ALLUVIAL CHANNEL DATA PROM FLUME EXPERIMENTS, 1956-61 167

for 0.45-mm sand in 8-foot-wide flume

Run

(1)

14 

13 

17 

16 

15

18 

2 

3 

9 

1

5 

11 

4

8 

7

10 

6 

12 

19 

21

22 

25 

20 

23 

24

40 

39 

26 

28 

29

31 

27 

36 

41 

30

35 

34 

33 

38 

37

32 

45 

44 

42 

43

Mean 

velocity 

V

(ft per 

sec)

(17)

0.81 

.65 

.80 

.79 

.79

.78 

1.20 

1.16 

.88 

1.23

1.32 

.70 

1.44 

.93 

1.43

.75 

1.07 

.85 

1.30 

1.58

1.70 

1.47 

1.68 

2.57 

1.76

3.32 

4.71 

5.38 

3.52 

1.89

4.24 

2.99 

2.04 

5.05 

2.47

2.80 

3.73 

4.60 

5.38 

5.54

5.03 

2.50 

4.78 

5.36 

6.18

Velocity profile

Slope 

B

(18)

0.221 

.108 

.161 

.261 

.32

.22

.36 

.30 

.35

.41 

.30 

.36 

.36 

.22

.38 

.64 

.41 

.56 

1.05

.61 

.32 

.61 

.32 

.85

.49 

1.80 

1.61 

1.60 

1.15

1.60 

1.17 

.73 

1.60 

1.70

2.07 

1.99 

1.62 

1.78 

1.99

1.29 

1.51 

1.79 

2.20

Intercept 

C

(19)

0.90 

.67 

.92 

.98 

.98

.86

1.49 

1.33 

1.68

1.79 

1.21 

1.86 

1.40 

1.80

1.32 

1.65 

1.45 

1.87 

1.75

1.91 

2.25 

2.06 

2.75 

2.57

3.83 

5.90 

5.03 

5.60 

3.35

5.32 

4.32

6.40 

4.34

4.93 

5.73 

5.48 

6.70 

6.15

5.95 

4.75 

6.80 

7.20

Shear 

velocity 

V, 

(ft per 

sec)

(20)

0.054 

.046 

.071 

.067 

.077

.076 

.097

.103 

.084 

.104

.107 

.074 

.113 

.099 

.133

.097 

.114 

.099 

.122 

.188

.200 

.160 

.195 

.227 

.240

.280 

.254 

.200 

.217 

.189

.247 

.215 

.165 

.285 

.207

.199 

.222 

.230 

.316 

.293

.280 

.279 

.285 

.314 

.374

Bed-material discharge

Sampled 

suspended 

?. 

(Ib per sec

per ft)

(21)

0. 0179

.025 

.058

.153 

.120

.35

.0079 

.153

.117 

.045

.122 

.111

.0109 

.255 

.47

Total 

Qt (Ib per sec 

per ft)

(22)

0 

0 

.000034 

.000048 

.000028

.000011 

.00058 

.00062 

.000042 

.00141

.00167 

.000071 

.0057 

.00023 

.0167

.00024 

.00128 

.000015 

.0069 

.036

.058 

.0145 

.032 

.089 

.062

.41 

.64 

.52 

.37 

.066

.55 

.25 

.034 

.73 

.148

.201 

.37 

.53 

1.04 

.82

.72 

.42 

1.28 

1.19 

1.92

Kinematic 

viscosity 

X10«

(sqft 

per sec)

(23)

1.40 

1.46 

1.34 

1.34 

1.38

1.36 

1.38 

1.36 

1.34 

1.46

1.38 

1.36 

1.41 

1.34 

1.36

1.39 

1.43 

1.35 

1.14 

1.20

1.21 

1.17 

1.19 

1.20 

1.17

1.11 

1.11 

1.17 

1.20 

1.16

1.16 

1.14 

1.11 

1.12 

1.16

1.17 

1.16 

1.20 

1.11 

1.12

1.14 

1.11 

1.10 

1.08 

1.12

Shear

at bed 

r 

(Ibper 

sqft)

(24)

0.0057 

.0041 

.012 

.0086 

.011

.011 

.018 

.021 

.014 

.021

.022 

.011 

.025 

.019 

.034

.018 

.025 

.019 

.029 

.068

.077 

.050 

.073 

.100 

.112

.152 

.125 

.078 

.091 

.069

.119 

.090 

.053 

.157 

.083

.077 

.095 

.102 

.193 

.166

.151 

.151 

.157 

.191 

.271

Reynolds 

number X10-2 

R

(25)

353 

156

585 

478 

458

333 

713 

725 

361 

674

717 

180 

705 

354 

736

178 

344 

183 

468 

1,264

1,405 

528 

861 

1,392 

933

2,423 

2,334 

1,563 

1,173 

489

1,608 

866 

349 

2,435

575

598 

900 

1,035 

2,423 

2,127

1,633 

631 

1,217 

1,539 

2,373

Froude 

number 

F

(26)

0.18 

.19 

.14 

.15 

.16

.18 

.23 

.22 

.21 

.24

.27 

.21 

.31 

.23 

.30

.23 

.28 

.28 

.36 

.28

.30 

.40 

.38 

.56 

.39

.65 

1.12 

1.63 

.98 

.61

1.13 

.92 

.82 

1.21

.84

.99 

1.24 

1.56 

1.34 

1.49

1.46 

.83 

1.59 

1.70 

1.66

Resistance factor

DarcyWeisbach 

/

(27)

0.0359 

.0405 

.0788 

.0568 

.0759

.0761 

.0528 

.0635 

.0732 

.0572

.0521 

.0902 

.0489 

.0911 

.0688

.1330 

.0911 

.1096 

.0700 

.1129

.1105 

.0946 

.1075 

.0626 

.1490

.0570 

.0232 

.0111 

.0304 

.0798

.0272 

.0415 

.0525 

.0254 

.0561

.0406 

.0283 

.0200 

.0275 

.0224

.0247 

.0995 

.0283 

.0274 

.0292

Chezy C/V0

(28)

14.9 

14.0 

10.1 

11.9 

10.3

10.2 

12.3 

11.2 

10.5 

11.8

12.4 

9.4 

12.8 

9.4 

10.8

7.8 

9.4 

8.5 

10.7 

8.4

8.5 

9.2 

8.6 

11.3 

7.3

11.8 

18.6 

26.9 

16.2 

10.0

17.1 

13.9 

12.4 

17.7 

11.9

14.0 

16.8 

20.0 

17.0 

18.9

18.0 

9.0 

16.8 

17.1 

16.6

Manning 

n (ft'/s)

(29)

0.016 

.016 

.026 

.021 

.025

.023 

.021 

.023 

.023 

.021

.020 

.024 

.019 

.025 

.023

.028 

.025 

.025 

.021 

.031

.031 

.025 

.028 

.022 

.033

.022 

.013 

.008 

.014 

.022

.013 

.016 

.016 

.013 

.018

.015 

.013 

.011 

.014 

.012

.012 

.024 

.013 

.013 

.014

Bed 

configuration

(30)

Plane. 

Do. 

Ripples. 

Do. 

Do.

Do. 

Do. 

Do. 

Do. 

Do.

Do. 

Do. 

Dune. 

Ripple. 

Dune.

Ripple.

Do! 

Dune. 

Do.

Do. 

Do. 

Do. 

Do. 

Do.

Do.

Standing wave. 

Plane. 

Transition. 

Dune.

Standing wave. 

Transition. 

Do. 

Standing wave. 

Transition.

Do. 

Standing wave. 

Do. 

Do. 

Transition.

Antidune. 

Do. 

Do. 

Do. 

Do.
168 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 6. Experimental variables and parameters

Run

(1)

19 

25 

26 

27 

20

21 

18 

28 

29 

22

30 

31 

15 

23 

32

24 

14 

34 

16 

35

17 

33 

5 

10 

37

36 

6 

7 

38 

11

8 

12 

13 

9 

3

1 

2 

4 

41 

42

40 

43 

39

Slope

X102

S

(2)

0.013 

.022 

.022 

.028 

.028

.030 

.037 

.037 

.043 

.043

.050 

.054 

.059 

.062 

.064

.068 

.071 

.080 

.112 

.130

.136 

.145 

.183 

.192 

.275

.304 

.313 

.339 

.356 

.393

.430 

.437

.587 

.600 

.65

.71 

.92 

.94 

1.12 

1.16

1.23 

1.26 

1.28

Depth

(ft)

(3)

1.01 

1.01 

1.02 

1.01 

1.03

1.01 

1.01 

1.04 

.50 

.49

.51 

.50 

1.05 

.49 

.52

.49 

.58 

.54 

1.04 

.53

1.00 

.56 

.93 

.46 

1.11

.55 

1.04 

.59 

1.02 

.92

.57 

.89 

.82 

.49 

.60

.68 

.53 

.51 

.44

.44

.38 

.44 

.43

Water 

discharge

(cuft 

per sec)

(4)

8.06 

9.88 

10.80 

11.86 

10.91

12.06 

13.42 

14.53 

4.62 

4.49

5.06 

5.42 

16.25 

5.10 

6.25

5.71 

7.41 

7.08 

16.85 

7.64

16.83

8.18 

16.41 

6.90 

22.58

8.96 

22.30 

10.10 

22.69 

22.22

11.20 

22.19 

22.09 

11.32 

16.46

22.33 

22.07 

15.64 

15.67 

20.44

15.53 

20.63 

20.88

Temperature 

T

(°C)

(5)

19.8 

19.3 

19.0 

22.7 

19.6

20.5 

18.0 

20.7 

18.9 

19.0

18.9 

16.8 

19.7 

19.2 

16.7

19.3 

17.4 

19.5 

19.4 

17.1

19.2 

19.0 

17.5 

19.0 

18.0

17.3 

19.1 

18.3 

18.9 

18.3

17.4 

18.5 

18.4 

18.5 

17.3

19.3

18.2 

18.0 

21.7 

20.4

19.6 

21.0 

20.5

Suspended concentration

Sampled 

C, 

(ppm)

(6)

0 

0 

0 

0 

0

0 

0 

0 

0 

0

0 

0 

4.1 

0 

0

0

12

30

14 

80 

12 

260

56 

281 

357 

422 

614

313

656 

1,190 

498 

2,820

3,770 

2,320 

2,340 

2,230 

1,610

1,470 

2,500 

2,300

Standard 

deviation 

C, 

(ppm)

(7)

0 

0 

0 

0 

0

0 

0 

0 

0 

0

0 

0

0 

0

0

37

117

135 

124 

220

121 

116 

572 

214 

1,360

529 

563 

875 

170 

741

498 

488 

520

Particle

size 

rfso 

(ftXlO")

(8)

2.62

1.38

2.23 

1.54 

.94

1.30 

2.34 

2.79 

2.65 

2.87

1.87 

1.79 

2.82 

1.48 

2.16

1.51 

2.30 

2.10

Total bed-material discharge

Concentration 

C, 

(ppm)

(9)

0 

0 

0 

2.8 

.4

.4 

21 

28 

0 

0

4.2 

65

26

15 

63 

73 

140 

201

211

253 

308 

450 

601

519 

537

822 

1,080 

1,180

1,490 

1,900 

2,750 

2,620 

3,110

4,020 

6,140 

5,090 

9,480 

7,320

10,200 

7,000 

7,010

Standard 

deviation 

Ct 

(ppm)

(10)

0 

0 

0

.2

3.6

8.7 

0 

0

.2 

30

9.8

3.7 

17 

20 

50 

52

58 

84 

65 

126 

259

70 

227 

199 

274 

630

646 

737 

840 

724 

723

724 

2,420 

1,600 

785 

1,280

1,740 

1,060 

460

Particle 

size

rfso 

(ftXIOS)

(11)

2.64 

2.95

2.58

2.79

2.72 

2.56 

2.69 

2.82

2.89 

2.53 

2.62 

2.76 

2.35

2.69 

2.16 

3.12 

2.41 

2.39

2.80 

2.49 

2.63 

3.05 

2.85

2.21 

2.82 

2.76 

2.68 

2.95

3.47 

3.45 

3.35

Gradation

a

(12)

1.43 

1.37

1.45

1.38

1.38 

1.40 

1.44 

1.48

1.50 

1.54 

2.42 

1.53 

2.40

1.62 

2.81 

1.84 

2.14 

2.74

1.53 

2.33 

1.84 

1.64 

2.02

2.28 

1.75 

2.11 

1.96 

1.51

1.34 

1.42 

1.50

Bed 

material 

particle 

size

^50

(ftXIOS)

(13)

2.79

3.15 

3.02

3.22 

3.28

2.98

3.25 

2.82 

3.18 

3.02

3.08 

2.99 

2.98 

3.22 

2.43

3.07 

2.92 

3.38 

2.48 

3.15

2.89 

3.02 

3.02 

3.17 

3.08

3.28 

3.02 

3.08 

3.41 

2.66

2.72 

2.49 

3.35

Sand waves

Length 

L

(ft)

(14)

2.1 

3.7

2.6

2.8 

2.9 

3.6 

2.9

3.5 

3.3 

5.2 

3.9 

6.6

3.5

5.8 

4.5 

6.3 

7.4

5.9 

4.8 

6.2 

2.7 

3.2

4.9

4.5

Height 

He 

(ft)

(15)

6.04 

.05

.09

.03 

.02 

.16 

.06

.18 

.08 

.28 

.12 

.34

.13 

.31 

.19 

.30 

.32

.17 

.23 

.25 

.12 

.19

.31 

.11

Velocity 

V, 

(ft per 

min)

(16)

0.06 

.07

.14

.07 

.12 

.13 

.20

.18 

.18 

.17 

.24 

.27

.32 

.45 

.44 

.58 

.60

.59 

1.16 

2.30 

1.37
SUMMARY OP ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 

for 0.98-mm sand in 8-foot-wide flume

169

Run

(1)

19

25

26

27

20

21

18

28

29

22

30

31

15

23

32

24

14

34

16

35

17

33

5

10

37

36

6

7

38

11

8

12

13

9

3

1

2

4

41

42

40

43

39

Mean

velocity

V

(ft per

sec)

(17)

1.00

1.22

1.32

1.47

1.32

1.49

1.66

1.75

1.16

1.15

1.25

1.36

1.93

1.30

1.50

1.46

1.60

1.64

2.03

1.80

2.10

1.83

2.21

1.88

2.54

2.04

2.68

2.14

2.78

3.02

2.46

3.12

3.37

2.89

3.43

4.10

5.20

3.83

4.45

5.81

5.11

5.86

6.07

Velocity profile

Slope

B

(18)

0.41

.48

.54

.60

.61

.67

.62

.58

.40

.42

.50

.54

.58

.57

.56

.60

.68

.73

.97

.63

.82

.64

.67

.37

1.28

.40

.27

1.58

1.10

1.26

2.03

1.30

3.97

2.96

2.49

2.64

3.34

Intercept

C

(19)

1.52

1.78

2.00

2.02

2.07

2.22

2.26

2.25

1.80

1.77

1.93

1.99

2.40

2.07

2.30

2.30

2.51

2.47

2.59

2.50

2.77

2.64

2.33

2.79

3.34

2.75

2.83

4.15

4.28

3.78

5.40

4.38

7.35

8.20

7.42

8.68

8.46

Shear

velocity

V*

(ft per

sec)

(20)

0.065

.085

.085

.095

.097

.098

.110

.111

.082

.082

.090

.093

.141

.098

.103

.104

.115

.118

.194

.149

.209

.162

.234

.169

.313

.232

.324

.254

.342

.341

.281

.354

.394

.308

.354

.394

.396

.392

.398

.405

.388

.423

.420

Bed-material discharge

Sampled

suspended

<?!

(Ib per sec

per ft)

(21)

0

0

0

0

0

0

0

0

0

0

0

0

.00052

0

0

0

.00158

.0039

.00089

.0102

.00083

.046

.0039

. 

fldQ LrrST

.028

.075

.106

.027

.114

.205

.044

.36

.66

.40

!27

.26

.178

.40

.38

Total

Qt

(Ib per sec

per ft)

(22)

0

0

0

.00026

.000034

.000038

.0022

.0032

0

0

. 000177

.0082

. 00127

.00067

.0036

.0040

.0184

.0120

.028

.0162

.039

.024

.106

.036

.093

.065

.191

.204

.130

.33

.47

.23

.40

.70

1.06

. 

fi9\}£i

1.16

1.17

1.24

1.13

1.14

Kinematic

viscosity X105

(sqft

per sec)

(23)

1.09

1.10

1.11

1.02

1.09

1.07

1.14

1.06

1.11

1.11

1.11

1.18

1.09

1.10

1.18

1.10

1.16

1.10

1.10

1.17

1.10

1.11

1.16

1.11

1.14

1.16

1.11

1.13

1.11

1.13

1.16

1.12

1.13

1.12

1.16

1.10

1.13

1.14

1.04

1.07

1.09

1.05

1.07

Shear

stress

at bed

r

(Ib per

sqft)

(24)

0.008

.014

.014

.018

.018

.019

.023

.024

.013

.013

.016

.017

.039

.019

.021

.021

.026

.027

.073

.043

.085

.051

.106

.055

.191

.104

.203

.125

.227

.226

.153

.243

.300

.183

.243

.301

.304

9QQ 

. Guv

.308

.319

.292

.346

.344

Reynolds

number X10-2

R

(25)

927

1,120

1,212

1,456

1,247

1,406

1,471

1,717

523

508

574

576

1,859

579

661

650

800

805

1,919

815

1,909

923

1,772

779

2,473

967

2,511

1,117

2,555

2,459

1,209

2,479

2,445

1,264

1,774

2,535

2,439

1,713

1,883

2,389

1,781

2,456

2,439

Froude

number

F

(26)

0.18

.21

23

.26

.23

.26

.29

.30

.29

.29

.31

.34

.33

.33

.37

.37

.37

.39

.35

.44

.37

.43

.40

.49

.43

.48

.46

.49

.49

.56

.57

.58

.65

.72

.78

.88

1.26

95

1.18

1.54

1.46

1.56

1.63

Resistance factor

DarcyWeisbach

f

(27)

0.0335

.0384

.0330

.0337

.0432

.0345

.0349

.0326

.0400

.0410

.0418

.0374

.0428

.0459

.0381

.0403

.0414

.0413

.0727

.0547

.0794

.0627

.0898

.0643

.122

.103

.117

.112

.121

.102

.104

.103

.109

.0941

.0853

.0739

.0464

.0841

.0640

.0389

.0461

.0415

.0474

Chezy

ci Vff"

(28)

15.4

14.4

15.6

15.4

13.6

15.2

15.1

15.7

14.2

14.0

13.8

14.6

13.7

13.2

14.5

14.1

13.9

13.9

10.5

12.1

10.0

11.3

9.4

11.2

8.1

8.8

8.3

8.4

8.1

8.9

8.8

8.8

8.6

9.2

9.7

10.4

13.1

9.8

11.2

14.3

13.2

13.9

13.0

Manning

n

(ftV6)

(29)

0.017

.018

.017

.017

.019

.017

.017

.017

.017

.017

.017

.016

.019

.018

.016

.017

.017

.017

.025

.020

.026

.021

.028

.021

.033

.027

.032

.029

.032

.029

.027

.029

.030

.025

.025

.024

.018

.024

.021

.016

.017

.017

.018

Bed

configuration

(30)

Plane.

Do.

Do.

Do.

Do.

Do.

Dune.

Do.

Plane.

Do.

Do.

Do.

Dune.

Plane.

Do.

Do.

Dune.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Transition.

Do.

Do.

Do.

Do.

Do.

Do.

Standing wave.

Do.

Do.

Do.
170 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 7. Experimental variables and parameters

Run

(1)

1

2 

3 

4 

30

29 

5 

6 

27 

28

26 

25 

21 

22 

24

23

7 

8 

20 

19

10 

9 

12 

11 

14

13 

15 

16 

17 

18

31

Slope

X102

S

(2)

0.014 

.017 

.112 

.086 

.110

.103 

.139 

.118 

.147 

.214

.201 

.210 

.184 

.166 

.172

.261 

.189 

.194 

.566 

.417

.710 

.493 

.456 

.408 

.865

.730 

.835 

.635 

.970 

.656

1.62

Depth 

D

(ft)

(3)

0.51 

.52 

.54 

.54 

.57

.56 

.56 

.59 

.58 

.63

.71 

.66 

.58 

.64 

.74

.73 

.60 

.72 

.55 

.56

.59 

.56 

.67 

.60 

.60

.60 

.63 

.62 

.62 

.61

.65

Water 

discharge 

Q (cuft 

per sec)

(4)

0.91 

.88 

1.31 

1.31 

1.56

1.57 

1.88 

1.88 

2.28 

2.29

2.67 

2.64 

3.13 

3.13 

3.48

3.48 

3.48 

3.50 

4.55 

4.55

4.78 

4.78 

5.32 

5.30 

5.70

5.70 

6.63 

6.64 

6.79 

6.82

6.71

Temperature 

T

(°C)

(5)

10.0 

23.4 

10.5

27.8 

14.7

33.8 

10.2 

27.2 

14.3 

34.3

13.1 

33.1 

12.4 

33.9 

12.1

32.8 

11.9 

26.9 

12.7 

28.4

7.0 

23.5 

7.9 

23.8 

12.5

31.7 

11.4 

26.7 

12.9 

27.9

14.5

Suspended concentration

Sampled 

C, 

(ppm)

(6)

0 

0 

0 

0 

24

9.1 

56 

33 

168 

251

80 

274 

196 

498 

307

227 

196 

248 

1,520 

735

2,020 

1,480 

1,480 

1,810 

5,340

2,100 

19,000 

14, 700 

29,900 

17, 400

41,600

Standard 

deviation 

C, 

(ppm)

(7)

0 

0 

0 

0

8.4

1.3

14

3.1 

101 

49 

218 

63

72 

38 

29 

139 

159

602 

86 

384 

310 

711

111 

3,140 

4,820 

6,060 

2,860

27,800

Particle 

size 

rfso 

(ftXIOS)

(8)

6.616

.626 

.715

.649 

.655 

.538 

.649 

.695

.646 

.613 

.567 

.708 

.767

.636 

.688 

.652 

.672 

.767

.737 

.793 

.737 

.816 

.777

.836

Total bed-material discharge

Concentration

ct

(ppm)

(9)

0 

0 

55 

61 

91

117 

226 

168 

455

787

854 

719 

907 

1,150 

706

1,150 

1,410 

1,820 

5,600 

4,340

5,180 

5,530 

3,960 

5,250 

12,300

8,780 

26,100 

21,000 

29,600 

20,800

49,300

Standard 

deviation 

Ct 

(ppm)

(10)

0 

0 

11 

16 

22

43 

62 

40 

238 

310

295 

180 

199 

286 

206

359 

194 

405 

527 

383

1,040 

870 

288 

812 

3,500

1,770 

5,810 

2,480 

5,120 

6,620

7,720

Particle 

size 

rfso 

(ftXIOS)

(ID

0.886 

.998 

.886

1.248 

.782 

.788 

.854 

.913

.933 

.867 

.847 

.886 

.847

.894 

.925 

.926 

1.012 

.831

1.015 

1.184 

.923 

1.035 

.906

.991 

.801 

.864 

.871 

.886

.833

Gradation

a

(12)

1.63 

1.60 

1.47

1.43 

1.57 

1.48 

1.36 

1.48

1.46 

1.56 

1.58 

1.63 

1.52

1.52

1.58 

1.57 

1.49 

1.48

1.54 

1.63 

1.46 

1.69 

1.51

1.43 

1.39 

1.44 

1.42 

1.62

1.47

Bed 

material 

particle 

size 

rfso 

(ftXIOS)

(13)

0.854 

1.021

1.019 

.837 

.854 

1.038 

1.035

1.071 

1.019 

1.035 

1.051 

.969

.916 

.950 

1.003 

1.001 

.979

1.001 

.935 

1.051 

1.051 

1.215

1.049 

1.160 

1.527 

1.103 

1.231

Sand waves

Length 

L

(ft)

(14)

0.7 

.6

3.3 

1.0 

1.6 

4.1 

4.5

4.6 

4.2

6.4

6.8

6.3

5.5

Height 

H,

(ft)

(15)

0.20

.07 

.07

.11 

.10 

.10 

.21 

.13

.18 

.23

.18 

.13

.20

.24

Velocity 

V. 

(ft per 

min)

(16)

0.060

.050 

.0050 

.0083 

.20 

.19

.14 

.28

.37 

.26

.32

.48
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 

for 0.82-mm sand in 2-foot-wide flume

171

Run

(1)

1

2 

3 

4 

30

29 

5 

6 

27 

28

26 

25 

21 

22 

24

23 

7 

8 

20 

19

10 

9 

12 

11 

14

13 

15 

16 

17

18

31

Mean 

velocity 

V 

(ft per

sec)

(17)

0.90 

.86 

1.24 

1.24 

1.39

1.43 

1.72 

1.62 

2.01

1.85

1.93 

2.05 

2.74 

2.48 

2.39

2.43 

2.95 

2.48 

4.23 

4.18

4.12 

4.35 

4.03 

4.51 

4.86

4.84 

5.36 

5.42 

5.58 

5.73

5.27

Velocity profile

Slope 

B

(18)

0.49 

.70

2.14 

2.10

.88

1.87 

.84 

2.00 

3.75

1.70 

2.91 

1.51 

2.13

Intercept 

C

(19)

2.00 

1.88

7.18 

6.91

4.05

4.82 

4.11 

6.76 

7.60

6.22 

7.26 

5.80 

6.78

Shear 

velocity

vt

(ft per 

sec)

(20)

0.048 

.053 

.139 

.122 

.142

.136 

.158 

.150 

.166 

.208

.214 

.211 

.185 

.185 

.202

.248 

.191 

.212 

.313 

.273

.367 

.298 

.314 

.281 

.408

.376 

.412 

.357 

.440 

.359

.580

Bed-material discharge

Sampled 

suspended 

Q> 

(Ib per sec 

per ft)

(21)

0 

0 

0 

0 

.0012

.00045 

.0034 

.0020 

.0122 

.0183

.0069 

.0231 

.0195 

.049 

.034

.025 

.021 

.028 

.22 

.107

.31 

.22 

.25 

.31 

.97

.38 

4.00 

3.08 

6.45 

3.79

8.89

Total 

Qt 

(Ib per sec 

per ft)

(22)

0 

0 

.0023 

.0025 

.0045

.0058 

.0136 

.0101 

.033 

.057

.073 

.061 

.090 

.114 

.078

.126 

.156 

.20 

.81 

.63

.79 

.84 

.67 

.89 

2.24

1.59 

5.49 

4.40 

6.38 

4.53

10.54

Kinematic 

viscosity xio«

(SC[ ft

per sec)

(23)

1.41 

1.00 

1.39 

.91 

1.24

.80 

1.40 

.92 

1.26 

.79

1.30 

.81 

1.32 

.80 

1.34

.81 

1.34 

.92 

1.31 

.90

1.55 

1.00 

1.51 

.98 

1.32

.84 

1.36 

.93 

1.30 

.90

1.25

Shear 

stress 

at bed

T

Ob per 

sqft)

(24)

0.045 

.0055 

.038 

.029 

.039

.036 

.049 

.043 

.053 

.084

.089 

.087 

.067 

.066 

.079

.119 

.071 

.087 

.194 

.146

.261 

.172 

.191 

.153 

.324

.273 

.328 

.246 

.375 

.250

.660

Reynolds 

number XlO-a 

R

(25)

325 

447 

482 

736 

639

1,001 

688 

1,039 

925

1,475

1,054 

1,670 

1,204 

1,984 

1,320

2,190 

1,321 

1,941

1,776 

2,601

1,568 

2,436 

1,788 

2,761 

2,209

3,457 

2,483 

3,613 

2,661 

3,884

2,740

Froude 

number 

F

(26)

0.22 

.21 

.30 

.30 

.32

.34 

.41 

.37

.47 

.41

.40 

.44 

.63 

.55 

.49

.50 

.67 

.52 

1.00 

.98

.95 

1.02 

.87 

1.03 

1.11

1.10 

1.19 

1.21 

1.25 

1.29

1.15

Resistance factor

DarcyWeisbach 

/

(27)

0.0227 

.0305 

.101 

.0777 

.0835

.0724 

.0677 

.0683 

.0518 

.101

.0986 

.0849 

.0366 

.0445 

.0573

.0830 

.0335 

.0585 

.0448 

.0425

.0635 

.0375 

.0484 

.0310 

.0567

.0510 

.0475 

.0348 

.0497 

.0314

.0980

Chezy °No

(28)

18.7 

16.2 

8.9 

10.1 

9.8

10.5 

10.9 

10.8 

12.1 

8.9

9.0 

9.7 

14.8 

13.4 

11.8

9.8 

15.4 

11.7 

13.4 

15.3

11.2 

14.6 

12.8 

16.1 

11.9

12.9 

13.0 

15.2 

12.7 

16.0

9.1

Manning 

n (fti/s)

(29)

0.012 

.015 

.027 

.023 

.024

.023 

.022 

.022 

.019 

.027

.028 

.025 

.016 

.018 

.021

.025 

.016 

.021 

.018 

.016

.021 

.016 

.019 

.015 

.020

.013 

.019 

.016 

.019 

.015

.027

Bed 

configuration

(30)

Plane. 

Do. 

Ripples.

Do'.

Dune. 

Do. 

Do. 

Do. 

Do.

Do. 

Do. 

Transition. 

Do. 

Do.

Do. 

Do. 

Do. 

Antidune. 

Plane.

Antidune. 

Do. 

Plane. 

Antidune. 

Do.

Do. 

Do. 

Do. 

Do. 

Do.

Chute-pool.
172 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 8. Experimental variables and parameters

Run

(1)

7 

8 

5 

11 

10

6 

4 

1 

9 

12

13 

2 

3 

14

Slope 

X102

s

(2)

0.025 

.087 

.088 

.102 

.213

.240 

.270 

.290 

.320 

.350

.620 

.800 

.910 

1.14

Depth 

D

(ft)

(3)

0.50 

.50 

.49 

.52 

.49

.52 

.49 

.51 

.52 

.51

.50 

.50 

.52 

.52

Water 

discharge

(cuft 

per sec)

(4)

1.12 

1.00 

1.12 

1.41 

1.69

1.96 

3.29 

4.01 

2.62 

4.24

4.42 

4.66 

5.40 

6.04

Temperature 

T

(°C)

(5)

20.2 

20.0 

20.0 

20.1 

20.0

20.0 

20.0 

20.0 

19.8 

20.0

20.3 

20.0 

20.3 

19.9

Suspended concentration

Sampled 

C, 

(ppm)

(6)

0 

0 

15 

54 

568

323 

648 

393 

2,070 

625

761 

5,140 

11,000 

15,300

Standard 

deviation 

C, 

(ppm)

(7)

0 

0 

3.5 

5.6 

258

50 

70 

8.5 

306 

80

171

978 

1,780 

2,760

Particle 

size 

dM 

(ftX103)

(8)

0.610 

.475 

1.016

.617

.934

.844

1.050 

.945 

.928 

.885

Total bed-material discharge

Concentration 

Ct 

(ppm)

(9)

0 

6.6 

47 

142 

460

732 

2,210 

3,090 

1,960 

3,280

4,990 

7,110 

18,400 

18,400

Standard 

deviation 

Ct 

(ppm)

(10)

0 

2.3 

17 

8.9 

129

160 

426 

397 

368 

240

386 

1,100 

2,530 

1,970

Particle

size

<*50

(ftXIOS)

(ID

1.000 

.912 

1.009 

1.033

.951 

.969 

1.085 

.918 

1.113

1.180 

1.115 

.990 

1.015

Gradation 

tr

(12)

1.52 

1.68 

1.73 

1.50

1.53 

1.57 

1.18 

1.50 

1.25

1.25 

1.26 

1.36 

1.46

Bed 

material 

particle 

size 

dso 

(ftXlO")

(13)

1.049 

1.075 

1.163 

1.163

1.016 

1.020 

1.115 

1.082 

1.180

1.120 

1.016 

1.049 

1.082

Sand waves

Length 

L

(ft)

(14)

0.8 

.9 

2.3

2.8

3.8

4.4

5.5 

6.1

Height 

H,

(ft)

(15)

6.02 

.04 

.05 

.06

.13

.14

.14 

.23

Velocity

(ft per 

min)

(16)

0.01 

.05 

.10 

.19

.27

.43

TABLE 9. Experimental variables and parameters

Run

(1)

11A 

11B 

16 

6 

5

1 

10

8 

9

7

2 

3 

4 

12 

13

15 

14

Slope X10"

S

(2)

0.022 

.027 

.029 

.047 

.063

.097 

.117 

.120 

.143 

.163

.188 

.343 

.433 

.447 

.695

.910 

.980

Depth 

D

(ft)

(3)

0.50 

.50 

.50 

.51 

.52

.50 

.48 

.51 

.52 

.53

.52 

.52 

.51 

.49 

.49

.52 

.51

Water 

discharge 

Q (cuft 

per sec)

(4)

1.06 

1.25 

1.05 

1.06 

1.46

1.95 

1.69 

2.11 

2.46 

2.32

2.62 

3.34 

4.00 

4.60 

5.38

6.46 

6.04

Temperature 

T

(°C)

(5)

18.3 

18.5 

20.5 

22.5 

22.6

22.1 

23.4 

24.1 

23.0 

23.2

22.1 

21.9 

21.8 

21.6 

19.6

19.6 

19.6

Suspended concentration

Sampled 

C, 

(ppm)

(6)

0 

0 

0 

0 

8.1

217 

56 

372 

888 

370

1,240 

3,370 

2,560 

3,610 

6,130

8,820 

3,770

Standard 

deviation 

C, 

(ppm)

(7)

0 

0 

0 

0 

3.8

9.9 

178 

298 

19

75 

1,550 

270 

410 

64

80 

73

Particle 

size 

dso 

(ftXlO")

(8)

0.282 

.335 

.373 

.429 

.370

.354 

.459 

.420 

.478 

.443

.459 

.452

Total bed-material discharge

Concentration 

C,

(ppm)

(9)

0 

0 

3.5 

12 

85

507 

452 

1,030 

1,520 

1,220

2,790 

4,320 

5,100 

7,900 

15,100

22,500 

14,600

Standard 

deviation 

C, 

(ppm)

(10)

0 

0 

1.5 

1.7 

11

137 

100 

345 

534 

391

542 

504 

824 

603 

1,100

7,000 

2,280

Particle 

size

dso 

(ftXlO")

(11)

0.449 

.443 

.985

.575 

.453 

.482 

.459 

.540

.423 

.443

.738 

.689 

.502

.557 

.715

Gradation 

a

(12)

1.90 

2.96 

2.14

2.25 

2.03 

2.31 

2.20 

2.49

2.12 

1.99 

2.12 

2.38 

2.68

2.20 

2.50

Bed 

material 

particle 

size 

dso 

(ftXIOS)

(13)

1.015 

.950 

1.100

1.050 

1.170 

1.445 

1.335 

1.408

1.110 

1.016 

.950 

.985 

.919

1.082 

1.147

Sand waves

Length 

L 

(ft)

(14)

0.41 

.50 

.29

4.0 

4.6 

3.4

5.8 

3.6

4.4

8.3

4.2

Height 

H.

(ft)

(15)

0.02 

.03 

.005

.15 

.15 

.12

.08 

.03

.12

.18 

.05

Velocity 

V, 

(ft per 

min)

(16)

0.004 

.004 

.017

.21 

.35 

.21

.54 

.89
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 173

for 0.38-mm (uniform) sand in 2-foot-wide flume

Run

(1)

7 

8 

5 

11 

10

6 

4 

1 

9 

12

13

2 

3 

14

Mean 

velocity 

V 

(ft per 

sec)

(17)

1.14 

1.02 

1.17 

1.38 

1.76

1.92 

3.43 

4.02 

2.57 

4.24

4.52 

4.76 

5.30 

5.93

Velocity profile

Slope 

B

(18)

0.45 

.70

1.10

Intercept 

C

(19)

1.40 

1.90

5.00

Shear 

velocity 

V. 

(ft per 

sec)

(20)

0.063 

.118 

.118 

.129 

.182

.200 

.206 

.218 

.231 

.240

.316 

.359 

.390 

.437

Bed-material discharge

Sampled 

suspended 

Q> 

(Ib per sec 

per ft)

(21)

0 

0 

.00052 

.0024 

.0300

.0198 

.066 

.049 

.169 

.083

.105

.75 

1.86 

2.88

Total 

?< 

(Ib per sec 

per ft)

(22)

0 

.00021 

.0017 

.0064 

.025

.046 

.23 

.39 

.16 

.44

.70 

1.06 

3.16 

3.54

Kinematic 

viscosity xio«

(sqft 

per sec)

(23)

1.08 

1.08 

1.08 

1.08 

1.08

1.08 

1.08 

1.08 

1.09 

1.08

1.07 

1.08 

1.07 

1.08

Shear 

stress 

at bed

T

(Ib per 

sqft)

(24)

0. 0078 

.027 

.027 

.032 

.064

.078 

.083 

.092 

.104 

.111

.193 

.250 

.295 

.370

Reynolds 

number X10-2 

R

(25)

528 

472 

531 

664 

799

924 

1,556 

1,898 

1,226 

2,002

2,112 

2,204 

2,576 

2,855

Froude 

number 

F

(26)

0.28 

.25 

.29 

.34 

.44

.47 

.86 

.99 

.63 

1.05

1.13 

1.19 

1.30 

1.45

Resistance factor

DarcyWeisbach 

/

(27)

0. 0248 

.1076 

.0811 

.0703 

.0855

.0871 

.0289 

.0236 

.0648 

.0256

.0391 

.0454 

.0434 

.0434

Chezy cH'g

(28)

18.0 

8.6 

9.9 

10.7 

9.7

9.6 

16.6 

18.4 

11.1 

17.7

14.3 

13.3 

13.6 

13.6

Manning 

n

(ftl/8)

(29)

0.013 

.027 

.023 

.022 

.024

.025 

.014 

.013 

.021 

.013

.016 

.018 

.017 

.017

Bed

configuration

(30)

Plane. 

Ripple.

Dune. 

Do.

Do.

Transition. 

Plane. 

Dune. 

Plane.

Antidune. 

Do. 

Do. 

Do.

for 0.88-mm (graded) sand in 2-foot-wide flume

Run

(1)

11A

11B

16

6

5

1

10

8

9

7

2

3

4

12

13

15

14

Mean

velocity

V

(ft per

sec)

(17)

1.08

1.28

1.07

1.06

1.43

1.99

1.80

2.11

2.42

2.23

2.57

3.27

4.00

4.79

5.61

6.34

6.05

Velocity profile

Slope

B

(18)

0.093

.088

.52

.91

.68

.52

.74

.41

.86

1.17

.95

2.08

Intercept

C

(19)

1.24

.65

1.60

.97

2.80

2.40

2.58

2.00

3.60

4.15

5.00

6.70

Shear

velocity

V,

(ft per

sec)

(20)

0.059

.066

.068

.088

.103

.125

.134

.140

.155

.167

.177

.240

.267

.265

.331

.390

.401

Bed-material discharge

Sampled

suspended

q,

(Ib per sec

per ft)

(21)

0

0

0

0

.00036

.013

.0029

.024

.068

.027

.101

.35

.32

.52

1.03

1.78

.71

Total

Qi

(Ib per sec

per ft)

(22)

0

0

.00012

.00041

.0040

.031

.024

.069

.12

.090

.23

.46

.65

1.16

2.59

4.63

2.81

Kinematic

viscosity xio»

(sqft

per sec)

(23)

1.13

1.12

1.07

1.02

1.02

1.03

1.00

.98

1.01

1.00

1.03

1.03

1.04

1.04

1.09

1.09

1.09

Shear

stress

at bed

T

(Ib per

sqft)

(24)

0.0069

0084

!0090

.015

.020

.030

.035

.038

.046

.054

.061

.111

.138

.137

.212

.295

.312

Reynolds

number X10-2

R

(25)

477

569

501

531

731

968

865

1,094

1,248

1,177

1,300

1,648

1,971

2,259

2,515

3,019

2,823

Froude

number

F

(26)

0.27

.32

.27

.26

.35

.50

.46

.52

.59

.54

.63

.80

.99

1.21

1.41

1.55

1.49

Resistance factor

DarcyWeisbach

f

(27)

0.0243

.0212

.0326

.0549

.0412

.0315

.0446

.0354

.0327

.0447

.0381

.0430

.0355

.0246

.0278

.0303

.0351

Chezy

ci^To

(28)

18.16

19.42

15.67

12.07

13.93

15.93

13.39

15.04

15.65

13.38

14.49

13.65

15.01

18.05

16.95

16.25

15.08

Manning

n

(ft 1/6)

(29)

0.013

.012

.015

.019

.017

.015

.017

.016

.015

.018

.016

.017

.016

.013

.014

.014

.016

Bed

configuration

(30)

Plane.

Do.

Ripples.

Do.

Do.

Dune.

Do.

Do.

Do.

Do.

Transition.

Do.

Plane.

Standing waves.

Antidunes.

Do.

Do.

791-597 O 6(
174 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 10. Experimental variables and parameters

Run

(1)

»46 

»47 

»48 

»49 

85

86 

87 

88

b90

b89

93 

92 

91 

82 

51

52 

73 

74 

76 

75

53 

77 

96 

94 

83

54 

56 

55 

57 

58

95 

78 

59 

60 

61

71 

72 

70 

63 

64

65 

66 

80 

81 

62

67 

79 

84 

69 

98

68 

100 

99 

97

Slope

X102

S

(2)

0.084 

.042 

.052 

.173 

.047

.046 

.046 

.049 

.053 

.065

.072 

.090 

.117 

.248 

.236

.222 

.222 

.215 

.203 

.204

.235 

.199 

.201 

.237 

.200

.240 

.242 

.237 

.259 

.233

.180 

.320 

.326 

.342 

.355

.531 

.550 

.640 

.570 

.578

.571 

.575 

.643 

.634 

.622

.646 

.651 

.740 

.734 

.821

.740 

.790 

.806 

.960

Depth 

D

(ft)

(3)

1.11 

.75 

1.23 

1.33

.78

.76 

.75 

.74 

.60 

.60

.62 

.63 

.58 

.64 

.62

.55 

.61 

.65 

.63 

.64

.57 

.65 

.53 

.81 

.91

.92 

.90 

.94 

.87 

.90

.80 

.72 

.65 

.62 

.61

.32 

.32 

.30 

.43

.41

.42 

.45 

.39 

.55 

.54

.53 

.55 

.41 

.43 

.44

.53 

.51 

.50 

.37

Water 

discharge

(cuft 

per sec)

(4)

14.54 

9.59 

15.26 

21.32 

7.11

6.92 

6.96 

7.10 

6.97 

7.08

7.20 

7.14 

7.12 

8.16 

8.11

8.01 

8.20 

8.18 

8.49 

8.24

8.01 

8.76 

8.31 

11.30 

15.58

15.36 

15.36 

15.36 

15.39 

15.28

15.38 

11.52 

15.36 

21.35 

21.32

8.22 

8.26 

8.14 

15.50 

15.61

15.60 

15.52 

15.27 

21.35 

21.23

20.87 

21.31 

15.36 

15.54 

15.80

20.94 

21.42 

21.27 

12.01

Temperature 

T

(°C)

(5)

13.1 

11.5 

11.5 

11.0 

12.7

17.0 

19.1 

18.3 

17.1 

18.5

14.7 

18.5 

18.0 

23.2 

13.1

16.0 

20.7 

21.0 

20.0 

21.2

17.2 

19.1 

18.6 

13.5 

16.2

16.6 

22.1 

18.5 

21.3 

20.1

18.7 

20.3 

21.7 

21.1 

23.2

21.4 

20.2 

20.2 

21.2 

21.2

21.6 

23.0 

21.8 

10.7

24.5

22.7 

21.0 

15.0 

22.4 

19.0

23.5 

13.3 

19.6 

19.5

Suspended concentration

Pine 

Material

cf

(ppm)

(6)

0

4,800 

8,400 

11,400 

6,950 

9,000

1 

6,070 

8,400 

133 

584

1,620 

5,670 

7,970 

9,330 

9,460

10,700 

12,500 

25,000 

7 

0

1,940 

2,860 

4,060 

4,320 

5,270

28,300 

12,000 

4,570 

3,600 

6,170

3,600 

7,100 

3,910 

3,020 

6,440

9,090 

12,300 

12, 100 

7 

4,790

11,200 

12,400 

7 

7,020 

42,000

7,620 

106 

26,900 

5,800

Sampled

c,

(ppm)

(7)

6

0

0

4,070 

7,100 

10,000 

6,690 

7,490

53

5,350 

8,050 

235 

553

1,830 

8,670 

23,800 

9,520 

22,900

2,750 

22,900 

28,600 

56 

503

2,590

3,140 

5,010 

4,220

43,400 

13,300 

5,820 

4,390 

7,910

3,040 

7,490 

3,840 

4,540 

8,400

11,600 

16,600 

14,000 

3,380 

7,320

11,400 

15,200 

3,700 

9,890 

57,700

12,400 

4,240 

42,300 

6,300

Particle 

size 

rfso 

(ftXIO3)

(8)

Total bed-material discharge

Concentration

ct

(ppm)

(9)

181 

23

59 

585 

6.0

1.6 

2.3 

2.5 

37 

31

99 

106 

195 

429 

545

578 

662 

534 

463 

625

571 

639 

761 

480 

588

657 

1,100 

765 

761 

807

1,640 

1,510 

2,920 

3,290 

3,390

5,250 

5,680 

6,310 

5,360 

5,480

5,160 

5,130 

7,140 

4,480 

4,490

4,390 

5,760 

7,100 

8,280 

17,700

6,760 

8,440 

16,100 

8,960

Standard 

deviation

ct

(ppm)

(10)

28 

15 

11 

169 

4.9

.3 

1.4 

1.2 

6.2 

8

21 

52 

44 

98 

145

137 

138 

151 

122 

184

191 

154 

135 

146 

170

271 

466 

202 

204 

204

239 

310 

820 

457 

564

1,178 

261 

156 

358 

302

445 

836 

37 

672 

428

202 

1,038 

135 

782 

2,620

461 

681 

2,000 

2,310

Particle 

size 

dm 

(ftX103)

(ID

1.141 

1.148 

.823 

1.364

.249 

.210 

.417 

1.345 

1.361

1.482 

1.509 

1.443 

1.463 

1.351

1.456 

1.509 

1.420 

1.387 

1.574

1.361 

1.246 

1.066 

1.404 

1.151

1.253 

1.148 

1.164 

1.325 

1.210

1.099 

1.089 

1.312 

1.427 

1.440

1.525 

1.505 

1.476 

1.633 

1.630

1.584 

1.647 

1.624 

2.076 

2.030

1.994 

2.204 

1.410 

1.601 

1.237

2.181 

2.322 

1.361 

2.165

Gradation 

a

(12)

1.85 

1.85 

1.96 

1.66

3.19 

4.37 

3.04 

1.70 

2.50

1.55 

1.93 

1.90 

1.64 

1.66

1.63 

1.83 

2.08 

2.00 

1.84

1.65 

2.91 

2.66 

1.77 

1.74

1.74 

1.70 

1.88 

1.91 

1.94

2.42 

2.88 

1.73 

1.64 

1.68

1.68 

1.55 

1.60 

1.60 

1.60

1.64 

1.76 

1.76 

1.61 

1.54

1.57 

1.82 

1.39 

1.71 

1.90

1.55 

1.40 

1.93 

1.50

Bed

material 

particle 

size 

rfso 

(ftXlQS)

(13)

1.502

1.437 

1.521 

1.640 

1.355 

1.509

1.742 

1.619 

1.610 

1.679

1.417 

1.565 

1.627 

1.456 

1.443

1.564 

1.581 

1.588 

1.624 

1.633

1.469

1.692 

1.518 

1.535

1.771 

1.453 

1.535 

1.699 

1.722

1.673 

1.588 

1.515 

1.535 

1.601

1.506 

1.526 

1.594 

1.584 

1.647

1.620 

1.355 

1.640 

1.430 

1.440

1.738 

1.561 

1.492 

1.597

Sand waves

Length 

(ft)

(14)

6.0 

8.2 

6.2 

7.3 

1.2

1.0 

.9 

1.0 

1.6 

1.6

6.0 

4.6 

4.3 

4.1 

5.6

5.3 

5.4 

5.5 

5.7 

4.4

5.8 

5.1 

4.3 

5.2 

5.8

6.5 

5.3 

5.9 

5.1 

5.4

8.6 

7.4 

7.50

3.4 

3.4

3.4 

3.3 

3.4

4.4

4.0 

3.9 

3.6 

3.7 

3.1

4.0

4.0 

3.4

Height 

H,

(ft)

(15)

0.41 

.22 

.32 

.35 

.07

.06 

.06 

.07 

.06 

.06

.17 

.25 

.25 

.28 

.20

.26 

.29 

.34 

.30 

.28

.34 

.29 

.24 

.32 

.43

.41 

.29 

.27 

29 

.26

.33 

.39

.07

.23 

.20

.20 

.20 

.26 

.04

.10 

.08 

.21 

.26 

.24

.05

.31 

.16

Velocity 

V, 

(ft per 

min)

(16)

0.035 

.030 

.080 

.0074

.0033 

.0055 

.0015 

.027 

.030

.039 

.050 

.084 

.17 

.19

.18 

.26 

.17 

.16 

1.5

.11 

.091 

.20

.28 

.16

.33 

.20 

.23 

.29 

.21

.31 

.34 

.72

* Run made to supply missing slope and depth data in the 0.45-mm set.

b Bed stabilized by bentonite.

c Computed on the basis of kinematic viscosity for distilled water.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 

/or 0.47-mm sand in 8-foot-wide flume

175

Run

(1)

 46

»47

»48

> 49

85

86

87

88

b90

b89

93

92

91

82

51

52

73

74

76

75

53

77

96

94

83

54

56

55

57

58

95

78

59

60

61

71

72

70

63

64

65

66

80

81

62

67

79

84

69

98

68

100

99

97

Mean

velocity

V

(ft per

sec)

(17)

1.64

1.60

1.55

2.00

1.13

1.14

1.16

1.20

1.45

1.47

1.45

1.43

1.53

1.60

1.62

1.81

1.67

1.58

1.69

1.60

1.77

1.68

1.94

1.74

2.14

2.08

2.14

2.04

2.20

2.11

2.39

2.00

2.96

4.28

4.36

3.21

3.26

3.41

4.48

4.76

4.63

4.34

4.91

4.85

4.89

4.91

4.82

4.67

4.48

4.51

4.95

5.28

5.32

4.07

Velocity profile

Slope

B

(18)

0.50

.43

.30

.52

.56

.53

.64

.59

.62

.46

.82

.71

.56

.53

.42

.38

.37

.71

.68

.65

1.36

1.55

.47

1.30

.76

1.51

2.52

1.80

1.90

1.87

1.35

2.77

1.95

3.20

3.02

1.20

2.27

2.35

2.20

2.60

2.40

2.20

2.69

4.46

3.21

Intercept

C

(19)

1.97

1.94

1.91

1.51

1.50

1.46

1.52

1.97

1.81

2.05

1.94

1.96

2.20

2.40

2.30

2.33

2.50

2.42

2.84

2.50

3.03

2.94

2.83

2.89

3.18

4.75

6.05

5.90

5.43

5.20

5.21

6.53

6.26

6.83

6.53

5.45

7.17

7.13

6.67

7.30

7.10

7.43

7.94

9.41

7.69

Shear

velocity

V.

(ft per

sec)

(20)

0.173

.101

.144

.272

.109

.107

.105

.108

.101

.113

.120

.135

.148

.226

.217

.198

.209

.212

.203

.205

.208

. 9fU4WX

.185

94Q 

. f/va

.242

.267

.265

.268

.269

.260,

.215

.272

.261

.261

.264

.234

.238

.249

.281

.276

.278

.289

.284

.335

.329

.332

.340

.313

.319

.341

.355

.360

.360

.338

Bed-material discharge

Sampled

suspended

3. (Ib per sec

per ft)

(21)

0

0

0

.22

.38

.56

.36

.41

.0030

.30

.45

.015

.035

.114

.55

1.52

.63

1.47

.172

1.57

1.85

.0049

.072

.31

.38

.60

.50

5.21

1.19

.70

.73

1.32

.195

.48

.24

.55

1.02

1.41

2.00

1.67

.56

1.21

1.85

2.53

.44

1.20

7.11

2.02

.71

7.02

.59

Total

Qt

(Ib per sec

per ft)

(22)

0.021

.0017

.0070

.098

.00033

. 0000087

.000:2

. 00014

.0020

.0017

.0056

.0059

.0108

.027

.034

.036

.042

.034

.031

. 

run WxV

.036

044

!049

. m&fU9 

.071

. 07Q U/ a

.132

nno 

. \JfJ4

.092

.096

.197

.136

.35

.55

.56

.34

.37

.40

.65

.67

.63

.62

.85

.75

.74

.71

.96

.85

1.00

2.18

1.10

1.41

2.67

.84

Kinematic

viscosity xio«

(sqft

per sec)

(23)

1.30

1.36

1.36

1.38

1.31

1.32

1.37

1.50

1.39

1.42

1.24

1.33

1.42

1.00

1.28

1.26

1.24

1.31

1.38

1.36

1.52

1.52

1.93

 I OO 1. 4O

1.19

1.25

1.11

1.26

1.19

1.25

2.03

1.41

1.20

1.18

1.20

1.18

1.31

1.20

1.16

1.26

1.34

1.38

1.43

1.38

1.12

1.36

1.46

1.23

1.24

2.46

1.23

1.29

1.96

1.29

Shear

stress

at bed

T

(Ibper

sqft)

(24)

0.058

.020

.040

.144

.023

.022

.022

.023

.020

.024

.028

.035

.042

.099

.091

.076

.085

.087

.080

. 081

.084

081

!066

ion * l^U

.114

.138

.136

.139

.141

.131

.090

.144

.132

.132

.135

.106

.110

.120

.153

.148

.150

.161

.156

.218

.210

.214

.223

.189

.197

.225

.245

.251

.251

.221

Reynolds

number X10-2

R°

(25)

1,400

882

1,402

1,928

673

741

784

786

744

788

725

804

778

1,024

785

833

961

978

986

975

870

984

918

1,101

1,636

1,622

1,870

1,348

1,823

1,758

1,707

1,346

1,850

2,503

2,660

988

966

947

1,835

1,859

1,870

1,934

1,841

1,933

2,694

2,551

2,525

1,557

1,889

1,788

2,624

2,087

2,440

1,369

Froude

number

F

(26)

0.27

.33

.25

.31

.23

.23

.24

.25

.33

.33

.32

.32

.35

.35

.36

.43

.38

.35

.38

.35

.41

.37

.47

.'4034

.38

.40

.37

.42

.39

.47

.42

.65

.96

.98

1.00

1.02

1.10

1.20

1.31

1.26

1.14

1.39

1.15

1.17

1.19

1.15

1.29

1.20

1.20

1.20

1.30

1.33

1.18

Resistance factor

DarcyWeisbach

/

(27)

0.0893

.0317

.0686

.1482

.0740

.0693

.0660

.0649

.0390

.0465

.0547

.0714

.0747

.1597

.1436

.0960

.1251

.1442

.1153

.1314

.1101

.1181

.0729

.1633

.1024

.1315

.1225

.1378

.1199

.1213

.0649

.1484

.0623

.0298

.0293

.0425

.0427

.0425

.0315

.0269

.0288

.0354

.0268

.0382

.0362

.0366

.0397

.0358

.0405

.0457

.0412

.0372

.0367

.0552

Chezy

/nf/-\/ 

Isll 3

(28)

9.5

15.9

10.8

7.4

10.4

10.7

11.0

11.1

14.3

13.1

12.1

10.6

10.4

7.1

7.5

9.1

8.0

7.4

8.3

7.8

8.5

8.2

10.5

7.0

8.8

7.8

8.1

7.6

8.2

8.1

11.1

7.3

11.3

16.4

16.5

13.7

13.1

13.7

16.0

17.2

16.7

15.0

17.3

14.5

14.9

14.8

14.2

14.9

14.0

13.2

13.9

14.7

14.8

12.0

Manning

n

(fti/6)

(29)

0.028

.016

.025

.038

.024

.024

.023

.023

.017

.018

.020

.023

.023

.034

.032

.026

.030

.033

.029

.031

.028

.030

.023

.036

.029

.033

.032

.034

.031

.032

.023

.034

.022

.015

.015

.016

.016

.016

.014

.013

.014

.015

.013

.016

.016

.016

.017

.015

.016

.01.7

.017

.016

.016

.019

Bed

configuration

(30)

Dunes.

Do.

Do.

Do.

Ripple.

Do.

Do.

Do.

Do.

Do.

Dimes.

Do

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Transition.

Plane.

Do.

Do.

Do.

Do.

Antidune.

Do.

Do.

Do.

Do.

Standing wave.

Do.

Do.

Do.

Antidune.

Do.

Do.

Standing wave.

Plane.

Antidune.

Do.
176 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 11. Experimental variables and parameters

Run

(1)

1 

2 

3 

4 

6

5 

20

8 

8A 

8E

8B 

8C 

8D 

7 

14

14A 

14C 

14B 

19 

9

10 

15 

15A 

15B 

15C

13 

11 

18 

ISA 

18B

ISO 

16A 

16B 

16C 

17

17A 

17B 

12

Slope

X102

s

(2)

0.016 

.019 

.026 

.038 

.170

.201 

.338 

.351 

.331

.248

.293 

.294 

.198 

.388 

.399

.366 

.377 

.339 

.408 

.433

.486 

.551 

.550 

.537 

.628

.565 

.768 

.520 

.508 

.790

.900 

.980 

1.075 

1.305 

1.175

1.365 

1.928 

1.438

Depth 

D

(ft)

(3)

0.61 

.60 

.62 

.59

.72

.81 

.72 

.78 

.84 

.88

.85 

.86 

.72 

.72 

.89

.82 

.87 

.70 

.76 

.72

.64 

.74 

.75 

.75 

.73

.72 

.66 

.71 

.76 

.69

.70 

.67 

.66 

.65 

.65

.65 

.68 

.64

Water 

discharge

(cuft 

per sec)

(4)

1.06 

1.12 

1.21 

1.59 

2.45

3.12 

4.74 

3.82 

3.82 

3.69

3.84 

3.83 

3.77 

3.42 

4.77

4.78 

4.80 

4.84 

3.82 

4.16

5.33 

6.94 

6.99 

6.96 

6.99

6.37

7.48 

7.62 

7.57 

7.59

7.59 

7.82 

7.84 

7.86 

7.89

7.83 

7.86 

7.84

Temperature 

T (°C)

(5)

15.9 

17.4 

16.9 

18.0 

18.6

19.2 

20.2 

18.9 

18.7 

23.3

21.5 

22.4 

25.0 

20.6 

19.3

24.3 

22.2 

22.3 

21.5 

17.7

20.3 

21.7 

22.5 

23.7 

24.0

18. J 

19.9 

22.6 

22.5 

23.3

23.7 

23.5 

25.0 

25.1 

22.5

22.3 

24.0 

16.9

Suspended concentration

Fine 

material

cf

(ppm)

(6)

0 

0 

0 

0 

0

0 

0 

0 

5,740 

14,500

20,600 

24,300 

63,700 

0 

0

9,580 

22,400 

44,100 

0 

0

0 

0 

14,200 

40,900 

58,600

0 

0 

0 

13,200 

37,900

58,700 

11,200 

31,500 

44,500 

0

39,600 

51,900 

0

Sampled 

C, 

(ppm)

(7)

Particle 

size 

dso 

(ftXlO")

(8)

Total bed-material discharge

Concentration 

C, 

(ppm)

(9)

0 

0 

.6 

17 

387

408 

2,620 

1,200 

1,050 

720

904 

1,100 

521 

1,250 

1,790

1,970 

1,950 

2,960 

1,200 

1,520

2,690 

3,330 

4,350 

4,710 

7,640

3,350 

5,690 

3,330 

3,400 

9,730

22,300 

5,600 

10,300 

15,800 

9,180

21,800 

50,000 

26,000

Standard 

deviation 

C, 

(ppm)

(10)

0 

0 

.2 

5.8 

124

217 

785 

370

194

362 

349 

78 

415 

475

697 

556 

316 

323 

404

945 

416 

350 

449 

1,330

299 

931 

717 

349 

3,990

5,420 

520 

1,720 

1,940 

945

2,400 

1,900 

10,300

Particle 

size 

dso 

(ftXIOS)

(11)

1.647 

1.539

1.499 

1.621 

1.585 

1.417 

1.673

1.483 

1.594 

1.787 

2.224 

1.667

1.532 

1.739 

1.296 

1.463 

1.421

1.706 

1.821 

1.519 

1.476 

1.247

1.847 

2.067 

1.870 

1.804 

1.558

1.421 

2.198 

1.496 

1.132 

1.460

1.214 

1.460 

1.486

Gradation

a

(12)

1.34 

1.66

1.60 

1.52 

1.55 

1.58 

1.47

1.67 

1.75 

2.92 

1.55 

1.45

1.64 

1.64 

2.91 

1.56

1.53 

1.88 

3.17 

2.69

1.60 

1.46 

1.61 

1.62 

1.61

1.40 

1.33 

1.73 

2.22 

1.74

1.63 

1.30 

1.74

Bed 

material 

particle 

size 

dso 

(ftXIOS)

(13)

1.585 

1.526 

1.640

1.575 

1.716 

1.903 

1.699 

1.968

1.949 

1.772 

1.706 

1.804 

1.903

1.837 

1.837 

1.837 

1.788 

1.549

1.824

1.732 

1.854 

1.837 

1.722

1.713 

1.509 

1.870 

1.837 

1.837

1.919

1.713 

1.837 

1.690

1.837 

2.100 

1.847

Sand waves

Length 

L 

(ft)

(14)

0.5

4.6

5.0 

4.3 

3.6 

3.8 

3.6

3.6 

4.4

3.3 

4.0

5.8 

5.8

4.2 

4.2

Height 

(ft)

(15)

0.03 

.10 

.35

.26 

.17 

.23 

.20 

.19

.20 

.24

.17 

.20

.20 

.19

.16 

.18

Velocity 

V, 

(ft per 

min)

(16)

0.0001 

.0004 

.0047

.0080 

.036 

.012 

.012 

.0073

.010 

.011

.012 

.021

.030 

.034

.018 

.022

 Computed on the basis of kinematic viscosity for distilled water.
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61

for 0.54-inm sand in %-foot-wide flume

177

Bun

(1)

1

2 

3

4 

6

5 

20 

8 

8A 

8E

8B 

8C 

8D 

7 

14

14A 

14C 

14B 

19 

9

10 

15 

15A 

15B 

15C

13 

11

18 

ISA 

18B

ISO 

16A 

16B 

160 

17

17A 

17B 

12

Mean 

velocity 

V 

(ft per 

sec)

(17)

0.89 

.96 

1.00 

1.37 

1.74

1.95 

3.36 

2.51 

2.33 

2.15

2.30 

2.28 

2.65 

2.44 

2.74

2.95 

2.82 

3.51 

2.58 

2.93

4.30 

4.75 

4.76 

4.73 

4.85

4.52 

5.80 

5.44 

5.11 

5.62

 5.54 

5.92 

6.03 

6.14 

6.21

6.17 

5.87 

6.27

Velocity profile

Slope 

B

(18)

0.295 

.294 

.422 

.428 

.825

.645 

.329 

.238 

1.90

.98 

1.79

.370

.99 

.85

2.88 

2.96

2.13

3.34 

4.38 

1.78

Intercept 

C

(19)

1.25 

1.34 

1.45 

1.95 

3.13

2.62 

6.00 

4.40 

4.15

3.64 

4.20

3.15

4.16 

3.91

6.88 

7.42

6.90

7.51 

8.40 

6.60

Shear 

velocity 

Yf 

(ft per 

sec)

(20)

0.056 

.061 

.072 

.085 

.198

.230 

.280 

.297 

.299 

.265

.283 

.285 

.215

.299 

.338

.312

.325

.277

.315 

.317

.315 

.363 

.365

.360 

.385

.362 

.403 

.346 

.352

.419

.450

.461

.480

.524

.495

.535

.651

.543

Bed-material discharge

Sampled 

suspended 

Q> 

(Ib per sec 

per ft)

(21)

Total 

Qt 

(Ib per sec 

per ft)

(22)

0 

0 

.000023 

.000864 

.030

.040 

.40 

.146 

.128 

.085

.110 

.134 

.063 

.136

.272

.30 

.298 

.46 

.146 

.201

.46 

.74 

.97 

1.04 

1.70

.68 

1.36 

.81 

.82 

2.35

5.39 

1.39 

2.57 

3.95 

2.31

5.43 

12.51 

6.49

Kinematic 

viscosity xio«

(sqft 

per sec)

(23)

1.20 

1.16 

1.17 

1.14 

1.12

1.10 

1.08 

1.11 

1.31 

1.46

1.70 

1.79 

3.20 

1.06 

1.10

1.27 

1.74 

2.41 

1.04 

1.15

1.07 

1.04 

1.47 

2.27 

2.98

1.14 

1.08 

1.02 

1.44 

1.70

3.00 

1.35 

1.93 

2.32 

1.02

2.27 

2.60 

1.17

Shear 

stress 

at bed

T

(Ib per 

sqft)

(24)

0.0061 

.0071 

.010 

.014 

.076

.102 

.152 

.170 

.173 

.136

.155 

.158 

.089 

.173 

.221

.188 

.204 

.149 

.192 

.195

.193 

.256 

.258 

.251 

.287

.254 

.314 

.231 

.240 

.340

.392 

.412 

.446 

.532

.475

.554 

.820 

.571

Eeynolds 

number X10-2 

fi»

(25)

449 

495 

526 

711 

1,115

1,438 

2,245 

1,755 

1,741 

1,884

1,878 

1,914 

1,985 

1,640 

2,207

2,480 

2,386 

2,413 

1,871 

1,841

2,545 

3,408 

3,508 

3,573 

3,606

2,862 

3,507 

3,814 

3,796 

3,870

3,894 

4,002 

4,160 

4,168 

3,949

3,917 

4,060 

3,400

Froude 

number 

F

(26)

0.20 

.22 

.22 

.31 

.37

.38 

.70 

.50 

.45 

.40

.44 

.43 

.55 

.51 

.51

.57 

.53 

.74 

.52 

.61

.95 

.97 

.97 

.96 

1.00

.94 

1.26 

1.14 

1.04 

1.19

1.17 

1.27 

1.30 

1.34 

1.36

1.35 

1.25 

1.39

Resistance factor

DarcyWeisbach 

/

(27)

0. 0315 

.0320 

.0413 

.0309 

.1040

.1108 

.0555 

.1117 

.1313 

.1213

.1213 

.1249 

.0524 

.1200 

.1214

.0893 

.1060 

.0499 

.1192 

.0938

.0430 

.0468 

.0470 

.0464 

.0504

.0513 

.0386 

.0323 

.0379 

.0446

.0527 

.0485 

.0506 

.0582 

.0509

.0600 

.0983 

.0599

Chezy 

cHg

(28)

16.0 

15.8 

13.9 

16.1

8.8

8.5 

12.0 

8.5 

7.8 

8.1

8.1 

8.0 

12.4 

8.2 

8.2

9.5 

8.7 

12.7 

8.2 

9.2

13.6 

13.1 

13.0 

13.1 

12.6

12.5 

14.4 

15.7 

14.5 

13.4

12.3 

12.8 

12.6 

11.7 

12.5

11.5 

9.0 

11.6

Manning 

n

(ft i/6)

(29)

0.015 

.015 

.018 

.015 

.028

.030 

.021 

.030 

.033 

.032

.032 

.032 

.020 

.030 

.032

.027 

.030 

.020 

.031 

.027

.018 

.019 

.019 

.019 

.020

.020 

.017 

.016 

.017 

.018

.020 

.019 

.020 

.021 

.020

.021 

.027 

.021

Bed 

configuration

(30)

Plane. 

Do. 

Eipple. 

Do. 

Dune.

Do.

Transition. 

Dune. 

Do. 

Do.

Do. 

Do.

Transition. 

Dune. 

Transition.

Do. 

Do.

Plane. 

Transition. 

Do.

Plane. 

Standing wave,s. 

Do. 

Do. 

Do.

Do. 

Do. 

Do. 

Do. 

Do.

Antidune . 

Standing waves. 

Antidune. 

Do. 

Do.

Do. 

Do. 

Do.
178 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 12. Velocity-profile data for 0.19-mm sand in 8-foot-wide flume 

[The lateral section used for measuring was 95-115 ft. from the headbox. w.s.=water surface]

Run

24--- .

2 ....

26..-- .

25. 

22C.. ... 

30... 

I.-... ........

31..... 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

1.030 

1.000 

.800 

.600 

.400 

.200 

.100 

.075 

.050 

.025

.909 

.859 

.709 

.559 

.409 

.309 

.259 

.209 

.159 

.109 

.079 

.049 

.019

.415 

.390 

.360 

.310 

.260 

.210 

.160 

.110 

.085 

.060 

.035 

.010

1.027 

.988 

.818 

.718 

.618 

.518 

.418 

.318 

.218 

.168 

.118 

.078 

.048 

.018

.564 

.547 

.447 

.347 

.247 

.197 

.147 

.097 

.047

1.048 

1.020 

.950 

.850 

.750

Velocity 

(fps)

w.s. 

1.08 

1.11 

1.08 

.99 

.87 

.78 

.78 

.71 

.68

w.s. 

1.23 

1.22 

1.10 

1.04 

.98 

.94 

.88 

.82 

.78 

.73 

.69 

.63

w.s. 

.93

.84 

.84 

.83 

.83 

.79 

.77 

.73 

.70 

.62 

.58

w.s. 

1.52 

1.53 

1.55 

1.49 

1.41 

1.32 

1.24 

1.16 

1.13 

1.14 

1.04 

1.03 

.95

w.s. 

.88 

.76 

.76 

.68 

.68 

.58 

.52 

.52

W.s. 

1.82 

1.82 

1.76 

1.74

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.936 

.910 

.810 

.710 

.610 

.510 

.410 

.310 

.260 

.210 

.160 

.110 

.080 

.050 

.020

1.025 

1.000 

.800 

.600 

.400 

.200 

.100 

.070 

.050 

.025

.274 

.250 

.230 

.190 

.150 

.110 

.080 

.050 

.020

.890 

.864 

.764 

.614 

.464 

.364 

.214 

.164 

.114 

.084 

.054 

.024

.401 

.375 

.325 

.275 

.225 

.175 

.125 

.100 

.075 

.050 

.010

.971 

.910 

.810 

.660 

.510 

.410 

.310 

.210 

.160 

.110 

.070

.535 

.506 

.406 

.306 

.206 

.156 

.106 

.056 

.006

1.028 

.980 

.880 

.730 

.'580

Velocity 

(fps)

w.s. 

1.24 

1.19 

1.15 

1.12 

1.10 

1.05 

1.05 

1.02 

1.02 

.97 

.94 

.91 

.86 

.76

w.s. 

1.16 

1.15 

1.11 

1.03 

.96 

.80 

.69 

.46 

.35

w.s. 

1.05 

1.03 

1.00 

.98 

.93 

.90 

.84 

.77

w.s. 

1.26 

1.22 

1.13 

1.13 

.99 

1.01 

.87 

.89 

.81 

.70 

.68

w.s. 

1.11 

1.07 

1.01 

.99 

.96 

.90 

.88 

.84 

.77 

.66

w.s. 

1.55 

1.53 

1.50 

1.40 

1.31 

1.25 

1.16 

1.12 

.98 

.50

,w.s. 

1.15 

1.07 

.91 

.91 

.77 

.77 

.52 

.38

W.S.

1.86 

1.80 

1.78 

1.76

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

1.050 

.983 

.783 

.583 

.385 

.185 

.085 

.043 

.023

.912 

.901 

.801 

.651 

.501 

.351 

.251 

.201 

.151 

.121 

.091 

.071 

.051

.418 

.405 

.305 

.255 

.205 

.145 

.105 

.080 

.055 

.030 

.010

.972 

.940 

.870 

.720 

.570 

.420 

.320 

.220 

.150 

.100 

.060 

.030

.523 

.492 

.392 

.292 

.192 

.142 

.092 

.042

.976 

.910 

.810 

.710 

.560

Velocity 

(fps)

w.s. 

1.11

1.10 

1.03 

1.00 

.84 

.78 

.75 

.71

w.s. 

1.27 

1.21 

1.12 

1.07 

1.07 

.91 

.92 

.83 

.76 

.67 

.62 

.58

w.s. 

1.12 

1.03 

.99 

.95 

.92 

.87 

.79 

.75 

.69 

.62

w.s. 

1.48 

1.52 

1.39 

1.43 

1.30 

1.19 

1.06 

.98 

.91 

.83 

.70

w.s. 

1.09 

1.09 

.91

.84 

.76 

.80 

.76

w.s. 

1.85 

1.83 

1.77 

1.71

Run

31 Con.

27--. 

5.. ...... 

23.-.. 

32... 

8.-.. ...

28... 

QO

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.650 

.550 

.450 

.350 

.250 

.200 

.150 

.110 

.090 

.070 

.040

.479 

.429 

.379 

.329 

.279 

.229 

.179 

.129 

.079 

.049 

.019

1.063 

1.028 

.828 

.628 

.428 

.328 

.228 

.128 

.078 

.028

.372 

.350 

.300 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.868 

.820 

.720 

.620 

.520 

.420 

.320 

.220 

.170 

.120 

.080 

.050 

.020

.990 

.948 

.898 

.748 

.548 

.348 

.248 

.148 

.098 

.048 

.023

.557 

.455 

.335 

.255 

.205 

.155 

.105 

.075 

.045

.980 

.920 

,820 

.720

Velocity 

(fps)

1.64 

1.61 

1.53 

1.34 

1.20 

1.14 

1.11 

.88 

.64 

.40 

.31

w.s. 

1.34 

1.31 

1.31 

1.26 

1.16 

1.15 

1.08 

.93 

.84 

.80

w.s. 

2.11 

2.10 

1.96 

1.79 

1.68 

1.54 

1.42 

1.24 

1.07

w.s. 

1.24 

1.19 

1.08 

1.05 

1.03 

.92 

.90 

.82 

.79

w.s. 

2.41 

2.39 

2.36 

2.29 

2.02 

1.96 

1.90 

1.86 

1.76 

1.70 

1.56 

1.46

w.s. 

2.48 

2.48 

2.39 

2.33 

2.12 

1.95 

1.68 

1.44 

1.38 

1.30

w.s. 

1.49 

1.34 

1.28 

1.15 

1.08 

.93 

.79 

.55

w.s.

2.57 

2.59 

2.56

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.480 

.380 

.280 

.180 

.130 

.080 

.040

.516 

.472 

.422 

.372 

.322 

.272 

.222 

.192 

.162 

.132 

.102 

.072 

.042

1.028 

.998 

.798 

.598 

.398 

.298 

.198 

.148 

.098 

.073 

.048

.371 

.344 

.294 

.244 

.194 

.144 

.094 

.069 

.044 

.019

.922 

.890 

.790 

.690 

.590 

.490 

.390 

.290 

.240 

.190 

.140 

.110 

.080 

.050 

.020

.812 

.775 

.625 

.425 

.225 

.125 

.075 

.050 

.025

.460 

.430 

.380 

.330 

.280 

.230 

.180 

.130 

.080 

.030 

.020

.870 

.820 

.720 

.620

Velocity 

(fps)

1.60 

1.60 

1.48 

1.39 

1.31 

1.19 

.97

w.s. 

1.35 

1.31 

1.28 

1.23 

1.19 

1.15 

1.06 

1.08 

1.02 

.92 

.84 

.66

w.s. 

2.00 

2.02 

1.92 

1.74 

1.68 

1.50 

1.43 

1.24 

1.19 

.93

w.s. 

1.32 

1.29 

1.25 

1.16 

1.12 

1.06 

1.02 

.98 

.90

w.s. 

2.47 

2.41 

2.40 

2.33 

2.23 

2.16 

2.07 

2.02 

1.95 

1.90 

1.80 

1.70 

1.67 

1.37

w.s. 

2.69 

2.63 

2.50 

2.29 

2.07 

1.98 

1.88 

1.38

w.s. 

1.50 

1.48 

1.46 

1.47 

1.43 

1.31 

1.21 

1.17 

1.08 

.97

w.s. 

2.62 

2.57 

2.50

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.410 

.310 

.210 

.160 

.110 

.070 

.040 

.020

.517 

.455 

.405 

.355 

.305 

.255 

.205 

.155 

.105 

.075 

.045 

.015

.365 

.348 

.298 

.248 

.198 

.148 

.098 

.073 

.048 

.023

.893 

.860 

.780 

.680 

.580 

.480 

.380 

.280 

.180 

.130 

.090 

.050 

.020

.926 

.900 

.800 

.700 

.500 

.300 

.200 

.100 

.050 

.025

.475 

.445 

.395 

.345 

.295 

.245 

.195 

.145 

.095 

.065 

.035 

.010

Velocity 

(fps)

1.61 

1.56 

1.41 

1.30 

1.23 

1.15 

1.11 

1.07

w.s. 

1.31 

1.28 

1.23 

1.19 

1.14 

1.08 

1.05 

.92 

.85 

.85 

.86

w.s. 

1.36 

1.29 

1.23 

1.20 

1.16 

1.12 

1.06 

1.03 

.98

w.s. 

2.43 

2.40 

2.36 

2.30 

2:15 

2.10 

2.00 

1.82 

1.72 

1.53 

1.35 

1.30

W.S.

2.61 

2.61 

2.59 

2.45 

2.32 

2.27 

1.91 

1.66 

1.33

w.s. 

1.48 

1.44 

1.37 

1.33 

1.31 

1.26 

1.18 

1.09 

.97 

.93 

.87
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 

TABLE 12. Velocity-profile data for 0.19-mm sand in 8-foot-wide flume Continued

179

Run

33 Con. 

29. ...........

3 .

11-. ........ .

13........ .

14-- ......

15...........

34 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.620 

.520 

.420 

.320 

.220 

.120 

.070 

.030

.513 

.490 

.440 

.339 

.340 

.290 

.240 

.190 

.140 

.100 

.060 

.030 

.010

.516 

.475 

.375 

.275 

.175 

.125 

.075 

.050 

.025

.793 

.721 

.621 

.421 

.221 

.121 

.071 

.046 

.021

.900 

.800 

.650 

.450 

.350 

.250 

.150 

.100 

.050 

.025

.856 

.807 

.707 

.507 

.307 

.207 

.107 

.057 

.027

.780 

.710 

.610 

.410 

.310 

.210 

.110 

.060 

.030

.498 

.450 

.370 

.300 

.230 

.180 

.130

Velocity 

(fps)

2.54 

2.52 

2.49 

2.45 

2.37 

2.26 

2.04 

1.43

w.s. 

1.60 

1.59 

1.55 

1.52 

1.44 

1.35 

1.29 

1.19 

1.12 

1.08 

1.01 

.92

w.s. 

1.58 

1.55 

1.47 

1.35 

1.25 

1.07 

.95 

.40

w.s. 

3.09 

3.07 

3.05 

3.03 

2.88 

2.75 

2.60 

2.44

w.s. 

3.69 

3.65 

3.60 

3.48 

3.27 

3.06 

2.88 

2.50 

2.20

w.s. 

3.90 

3.84 

3.68 

3.43 

3.27 

3.09 

2.73 

2.43

w.s. 

4.13 

3.97 

3.70 

3.54 

3.25 

3.05 

2.54 

2.23

w.s. 

2.24 

2.02 

1.88 

1.85 

1.80 

1.86

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.520 

.420 

.320 

.220 

.170 

.120 

.090 

.060 

.030

.480 

.445 

.345 

.245 

.195 

.145 

.095 

.065 

.035 

.010

.490 

.444 

.344 

.244 

.144 

.094 

.069 

.044 

.019

.948 

.885 

.785 

.685 

.485 

.285 

.185 

.135 

.085 

.050 

.025

.886 

.850 

.750 

.650 

.450 

.350 

.250 

.150 

.100 

.050 

.025

.872 

.810 

.710 

.510 

.310 

.210 

.110 

.060 

.030

.785 

.710 

.610 

.410 

.310 

.210 

.110 

.060 

.030

.495 

.450 

.380 

.310 

.260 

.210 

.170

Velocity 

(fps)

2.47 

2.44 

2.40 

2.23 

2.18 

2.08 

2.03 

1.94 

1.90

w.s. 

1.58 

1.55 

1.42 

1.30 

1.26 

1.12 

1.09 

1.00 

.91

w.s. 

1.60 

1.57 

1.44 

1.15 

1.02 

.97 

.97 

.97

w.s. 

3.07 

2.98 

3.03 

2.91 

2.91 

2.86 

2.75 

2.64 

2.45 

2.29

w.s. 

3.74 

3.70 

3.70 

3.64 

3.50 

3.40 

3.17 

2.98 

2.63 

2.42

w.s. 

4.11 

4.00 

3.86 

3.54 

3.30 

2.87 

2.13 

.95

w.s. 

4.49 

4.31 

4.14 

3.95 

3.71 

3.20 

2.91 

2.17

w.s. 

2.29 

2.24 

2.20 

2.01 

1.81 

1.73

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

.528 

.495 

.395 

.295 

.245 

.195 

.145 

.095 

.065 

.035 

.015

.575 

.547 

.447 

.347 

.247 

.197 

.147 

.132 

.097 

.072

1.236 

1.180 

1.080 

.880 

.680 

.480 

.280 

.180 

.130 

.080 

.055 

.030

.851 

.798 

.698 

.598 

.398 

.298 

.198 

.098 

.048 

.023

.890 

.810 

.710 

.510 

.310 

.210 

.110 

.060 

.030

.745 

.710 

.610 

.510 

.310 

.210 

.110 

.060 

.030

.485 

.460 

.360 

.310 

.260 

.210 

.160

Velocity 

(fps)

w.s. 

1.60 

1.49 

1.31 

1.28 

1.17 

1.11 

.98 

.83 

.65 

.46

w.s. 

1.61 

1.59 

1.51 

1.47 

1.40 

1.38 

1.26 

1.20 

1.09

W.S. 

3.20 

3.18 

3.15 

3.03 

2.86 

2.75 

2.66 

2.60 

2.49 

2.37 

2.12

W.S.

3.80 

3.77 

3.69 

3.64 

3.49 

3.24 

2.97 

2.41 

2.26

w.s. 

3.98 

3.91 

3.75 

3.43 

3.07 

2.80 

2.44 

2.20

w.s. 

4.33 

4.29 

4.20 

3.80 

3.54 

3.34 

3.00 

2.73

w.s. 

2.24 

2.12 

2.07 

1.98 

1.81 

1.75

Eun

34 Con. 

12....- 

6..- .....

7---. 

35--- 

16--. 

10.... .

9

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.090 

.060 

.030

.924 

.875 

.775 

.675 

.575 

.475 

.375 

.275 

.175 

.075 

.025

.f>41 

.622 

.522 

.422 

.322 

.222 

.122 

.072 

.047 

.022

.727 

.697 

.597 

.397 

.297 

.197 

.147 

.097 

.047 

.012

.349 

.317 

.297 

.267 

.237 

.207 

.177 

.147 

.117 

.087 

.057 

.027

.700 

.625 

.500 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.452 

.393 

.323 

.223 

.173 

.123 

.073 

.048 

.023

.411 

.400 

.350 

.300 

.250 

.200 

.150 

.125 

.100 

.075 

.050 

.025

Velocity 

(fps)

1.72 

1.44 

1.38

w.s.

3.60 

3.51 

3.37 

3.26 

3.02 

2.41 

2.10

W.S. 

2.52 

2.42 

2.28 

2.21 

2.07 

1.78 

1.38 

1.15 

.75

w.s. 

2.27 

2.25 

2.00 

1.84 

1.79 

1.83 

1.60 

1.43 

1.07

w.s. 

2.68 

2.73 

2.75 

2.82 

2.79 

2.77 

2.68 

2.63 

2.49 

2.22 

2.09

w.s. 

4.70 

5.00 

4.09 

3.82 

3.82 

3.68 

3.37 

3.28 

2.74

w.s.

3.60 

2.39 

3.17 

2.96 

2.66 

2.12

w.s. 

2.95 

2.99 

2.94 

2.86 

2.67 

2.67 

2.59 

2.51 

2.43 

2.35 

2.15

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.130 

.100 

.070 

.030

.859 

.800 

.700 

.600 

.400 

.200 

.100 

.050 

.025

.511 

.490 

.390 

.290 

.240 

.190 

.140 

.090 

.040 

.015

.647 

.621 

.521 

.321 

.221 

.171 

.121 

.071 

.021

.522 

.480 

.410 

.340 

.280 

.240 

.200 

.160 

.120 

.090 

.060 

.030

.705 

.650 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.438 

.425

.325 

.225 

.175 

.125 

.100 

.075 

.050 

.025

.441 

.397 

.347 

.247 

.197 

.147 

.122 

.097 

.072 

.047 

.022

Velocity 

(fps)

1.70 

1.83 

1.85 

1.76

w.s.

3.93 

3.64 

3.45 

3.03 

2.55 

2.11 

1.39

w.s. 

2.46 

2.46 

2.40 

2.36 

2.23 

2.10 

1.86 

1.59 

.87

w.s. 

2.30 

2.26 

2.06 

1.96 

1.88 

1.84 

1.77 

.91

w.s. 

2.25 

2.16 

2.13 

2.13 

2.10 

2.15 

2.11 

1.93 

1.97 

1.98 

1.78

w.s. 

4.75 

4.63 

5.01 

4.18 

3.95 

3.82 

3.52 

3.37 

3.20 

2.69

w.s.

3.68 

3.43 

3.31 

3.13

2.98 

2.80 

2.76 

2.58

w.s. 

3.30 

3.25 

3.04 

2.87 

2.67 

2.54 

2.31 

2.15 

1.98 

1.73

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.120 

.080 

.050 

.020

1.162 

1.100 

1.050 

.850 

.650 

.450 

.250 

.150 

.100 

.050 

.025

.620 

.600 

.550 

.450 

.250 

.050

.651 

.625 

.525 

.425 

.325 

.225 

.125 

.075 

.050 

.025

.522 

.475 

.405 

.335 

.265 

.205 

.165 

.125 

.085 

.055 

.025

.695 

.625 

.525 

.375 

.275 

.175 

.125 

.075 

.050 

.025

.458 

.395 

.325 

.225 

.175 

.125 

.100 

.075 

.050 

.025

.385 

.350 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

1.58 

1.51 

1.43 

1.29

w.s. 

3.43 

3.41 

3.31 

3.26 

3.16 

2.76 

2.55 

2.39 

2.21 

2.16

W.S.

2.33

2.24 

2.30 

2.00 

1.84

w.s. 

2.50 

2.47 

2.36 

2.23 

2.08 

1.64 

1.48 

1.39 

.64

w.s. 

2.40 

2.22 

2.14 

2.06 

2.00 

1.97 

1.84 

1.68 

1.53 

1.36

w.s. 

4.64 

5.02 

4.28 

4.02 

3.90 

3.68 

3.28 

3.12 

2.60

w.s. 

3.66 

3.52 

3.42 

3.19 

3.06 

2.98 

2.85 

2.64 

2.57

W.S. 

3.15 

3.09 

2.81 

2.68 

2.49 

2.38 

2.28 

2.04
180 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 13. Velocity-profile data for 0.27-mm sand in 8-foot-wide flume 

[The lateral section used for measuring was 95-115 ft from the headbox. w.s.=water surface]

Run

50A -

50D... .......

51............

52.... .....

54-- 

53-- .. .

57. 

56- 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.965 

.920 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.890 

.835 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.995 

.950 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.965 

.925 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.830 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.940 

.700 

.650 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.489 

.445 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.800 

.760 

.600 

.400 

.300 

.200 

.150 

.100

Velocity 

(fps)

w.s. 

1.25 

1.21 

1.18 

1.14 

1.11 

1.05 

1.04 

1.03 

.98 

.96

w.s. 

1.28 

1.23 

1.21 

1.16 

1.13 

1.09 

1.07 

1.05 

1.03 

.99

w.s. 

1.69 

1.64 

1.58 

1.49 

1.36 

1.27 

1.16 

1.08 

1.05 

1.01 

.99

W.S.

1.68 

1.66 

1.60 

1.41 

1.36 

1.23 

1.19 

1.05 

1.05 

1.03 

1.00

w.s. 

2.26 

2.20 

2.20 

2.07 

2.07 

2.07 

2.05 

1.94 

1.83 

1.80

w.s. 

2.14 

2.14 

2.11 

2.04 

1.88 

1.82 

1.79 

1.75 

1.65 

1.41

w.s. 

1.42 

1.20 

1.10 

1.01 

.74 

.66 

.82 

.60

w.s. 

2.30 

2.30 

2.27 

2.23 

2.13 

1.96 

1.89

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.960 

.925 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.900 

.845 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.960 

.920 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.100 

.970 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.890 

.870 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.050 

.025

.950 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.494 

.450 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.750 

.725 

.600 

.400 

.300 

.200 

.150 

.100

Velocity 

(fps)

w.s. 

1.22 

1.15 

1.15 

1.13 

1.07 

1.06 

1.05 

1.03 

1.02 

.96

w.s. 

1.25 

1.25 

1.22 

1.19 

1.15 

1.12 

1.09 

1.07 

1.03 

.99

w.s. 

1.67 

1.66 

1.60 

1.52 

1.48 

1.41 

1.38 

1.36 

1.28 

1.24 

1.24

W.S.

1.98 

1.84 

1.66 

1.60 

1.54 

1.49 

1.47 

1.45 

1.38 

1.40

W.S.

2.16 

2.12 

2.10 

2.04 

1.99 

1.76 

1.76 

1.76 

1.70 

1.70

w.s. 

2.19 

2.17 

2.13 

2.08 

1.99 

1.90 

1.64 

1.30 

1.21 

.70

w.s. 

1.27 

1.12 

.85 

.70 

.63 

.52 

.37 

.30

w.s. 

2.57 

2.57 

2.37 

2.26 

2.11 

1.71 

.92

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.975 

.920 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.915 

.860 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.940 

.890 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.050 

1.000 

.800 

.600 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.130 

1.020 

1.000 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.444 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.730 

.700 

.500 

.400 

.300 

.200 

.150 

.100

Velocity 

(fps)

w.s. 

1.24 

1.19 

1.15 

1.12 

1.10 

1.07 

1.06 

1.02 

.99 

.96

w.s. 

1.23 

1.23 

1.22 

1.19 

1.14 

1.10 

1.09 

1.06 

.94 

.92

W.S. 

2.07 

1.98 

1.86 

1.80 

1.74 

1.67 

1.61 

1.31 

1.36 

1.17

w.s. 

2.24 

2.15 

2.08 

2.04 

1.95 

1.76 

1.65 

1.58 

1.40 

1.36 

1.24 

1.24

w.s. 

2.27 

2.23 

1.99 

1.98 

1.82 

1.67 

1.64 

1.59 

1.57 

1.52 

1.49 

1.49

w.s. 

1.48 

1.43 

1.35 

1.13 

.88 

.90 

.74 

.66

w.s. 

2.58 

2.56 

2.19 

1.89 

1.49 

1.30 

.96

Run

56 Con. 

55.. 

45.. . 

43.. .-

44.. - 

42. 

46. ._-_._-

eo

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.075 

.050 

.025

1.540 

1.500 

1.350 

1.150 

.950 

.750 

.550 

.450 

.350 

.300 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.785 

.720 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.670 

.525 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.784 

.700 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.915 

.885 

.700 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.687 

.660 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.440 

.430 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

1.86 

1.52 

1.31

w.s. 

2.52 

2.47 

2.41 

2.41 

2.39 

2.30 

2.23 

1.91 

1.88 

1.76 

.96 

1.00 

1.03 

1.00 

1.00 

1.00

w.s. 

4.04 

3.95 

3.78 

3.56 

3.26 

3.17 

3.05 

2.84 

2.73 

2.32

w.s. 

2.24 

1.95 

1.86 

1.84 

1.82 

1.90 

1.90 

1.90 

1.90

w.s. 

2.77 

2.95 

3.11 

3.13 

3.11 

3.08 

3.00 

2.82 

2.27 

2.15

W.S.

2.20 

2.18 

2.18 

2.05 

2.09 

2.09 

1.98 

1.90 

.95 

1.07

w.s. 

4.77 

4.64 

4.39 

4.17 

3.96 

3.68 

3.68 

3.54 

3.30 

2.88

w.s. 

1.97 

2.06 

2.10 

2.16 

2.07 

1.99 

1.77 

1.61

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.075 

.050 

.025

.980 

.910 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.810 

.760 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.470 

1.450 

1.350 

1.150 

.950 

.750 

.550 

.350 

.250 

.150 

.100 

.075 

.050 

.025

.945 

.875 

.675 

.475 

.275 

.175 

.125 

.100 

.075 

.050 

.025

.890 

.855 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.717 

.700 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.370 

.350 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

1.23 

1.96 

1.58

w.s. 

2.47 

2.48 

2.56 

2.59 

2.60 

2.60 

2.59 

2.53 

2.40 

2.24 

1.73

w.s. 

3.77 

3.71 

3.58 

3.34 

3.25 

2.85 

2.57 

2.39 

2.21 

1.72

w.s. 

2.04 

2.00 

1.97 

1.94 

1.90 

1.53 

1.61 

1.55 

1.55 

1.55 

1.56 

1.54 

1.48

W.S.

3.33 

3.14 

3.04 

2.89 

2.69 

2.68 

2.33 

2.23 

2.23

w.s. 

2.05 

1.68 

1.68 

1.76 

1.77 

1.79 

1.79 

1.75 

1.68 

1.38

w.s. 

4.60 

4.50 

4.17 

4.09 

3.63 

3.40 

3.10 

2.94 

2.82 

2.23

W.S.

1.65 

1.62 

1.69 

1.58 

1.59 

1.51

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.075 

.050 

.025

.930 

.875 

.675 

.475 

.375 

.275 

.175 

.125 

.075 

.025

.815 

.765 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.315 

1.295 

1.175 

.975 

.775 

.575 

.375 

.275 

.175 

.125 

.075 

.050 

.025

.860 

.750 

.650 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.925 

.890 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.682 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

0.86 

.70 

.60

w.s. 

2.48 

2.46 

2.44 

2.28 

2.35 

2.42 

2.46 

2.26 

2.35

W.S.

3.86 

3.68 

3.53 

3.39 

3.26 

3.05 

2.81 

2.65 

2.56 

2.41

w.s. 

2.37 

2.36 

2.34 

2.33 

2.31 

2.26 

2.18 

2.11 

1.91 

1.69 

1.66 

1.65

w.s. 

2.86 

2.82 

2.77 

2.64 

2.56 

2.43 

2.31 

2.19 

2.08 

2.05 

2.05

W.S.

2.33 

2.34 

2.33 

2.29 

2.18 

2.01 

1.82 

1.54 

1.16 

1.14

W.S. 

4.13 

3.96 

3.85 

3.54 

3.40 

3.21 

3.09 

2.90 

2.70

...
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 181

TABLE 14. Velocity-profile data for 0.28-mm sand in 8-foot-wide flume 

[The lateral section used for measuring was 95-115 ft from the headbox. w.s.=water surface]

Run

7-- 

9 

10. 

5--.. .....

13.... 

4......... 

11.. 

2. Oft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.985 

.970 

.940 

.840 

.740 

.540 

.340 

.240 

.140 

.090 

.040 

.010

.980 

.900 

.700 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.580 

.530 

.400 

.300 

.250 

.200 

.175 

.150 

.125

1.025 

.950 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.020 

.960 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.820 

.780 

.650 

.500 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.521 

.480 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

w.s. 

0.82 

.81 

.82 

.76 

.68 

.67 

.58 

.51 

.51 

.50 

.46

w.s. 

.84 

.78 

.76 

.73 

.71 

.66 

.53 

.43 

.35 

.35 

.34

w.s. 

.70 

.58 

.49 

.44 

.43 

.38 

.25 

.21

w.s. 

1.35 

1.27 

1.18 

1.08 

.98 

.76 

.61 

.50 

.48 

.50 

.57

w.s. 

1.81 

1.77 

1.56 

1.53 

1.43 

1.08 

.74 

.64 

.72 

.48 

.35

w.s. 

1.66 

1.62 

1.56 

1.51 

1.49 

1.38 

1.35 

1.33 

1.31 

1.30 

1.30

w.s. 

.88 

.87 

.82 

.70 

.62 

.58 

.54 

.50 

.48

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.990 

.890 

.790 

.690 

.490 

.390 

.290 

.240 

.190 

.140 

.090 

.065 

.040 

.030 

.020 

.010

1.000 

.950 

.700 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.580 

.540 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.982 

.940 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.013 

.960 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.895 

.850 

.700 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.644 

.600 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

w.s. 

0.86 

.76 

.74 

.73 

.72 

.70 

.70 

.68 

.68 

.66 

.64 

.58 

.54 

.52 

.49

W.S.

.78 

.74 

.68 

.65 

.60 

.47 

.37 

.33 

.30 

.30 

.30

w.s. 

.74 

.65 

.52 

.50 

.42 

.40 

.34 

.26 

.23 

.21

w.s. 

1.39 

1.35 

1.29 

1.20 

1.02 

.85 

.78 

.75 

.75 

.71 

.70

w.s. 

1.87 

1.79 

1.63 

1.60 

1.55 

1.29 

1.18 

1.05 

1.05 

1.05 

1.05

w.s. 

1.75 

1.72 

1.64 

1.46 

1.27 

1.09 

.95 

.59 

.57 

.46 

.43

w.s. 

.88 

.86 

.76 

.66 

.60 

.52 

.51 

.50 

.47 

.44

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.985 

.970 

.940 

.840 

.740 

.540 

.340 

.240 

.140 

.090 

.040 

.010

1.015 

.965 

.775 

.625 

.475 

.375 

.275 

.175 

.150 

.100 

.075 

.050 

.025

.580 

.540 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.993 

.930

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.885 

.835 

.700 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.522 

.480 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

w.s. 

0.80 

.80 

.80 

.78 

.77 

.75 

.72 

.71 

.69 

.66 

.50

w.s. 

.85 

.79 

.76 

.68 

.59 

.55 

.50 

.44 

.37 

.34 

.28 

.25

w.s. 

.71 

.63 

.61 

.51 

.44 

.35 

.30 

.23 

.19

w.s. 

1.88 

1.86 

1.77 

1.72 

1.49 

1.28 

1.02 

.72 

.62 

.58 

.55

w.s. 

1.69 

1.66 

1.60 

1.50 

1.28 

1.14 

1.04 

.93 

.86 

.73 

.61

w.s. 

.94 

.93 

.85 

.76 

.72 

.64 

.59 

.55 

.51

Run

33 

I... 

14. . 

20.- 

21-. .

19-..- 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

1.005 

.950 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.740 

.690 

.590 

.490 

.390 

.340 

.290 

.240 

.190 

.140 

.090 

.040

.628 

.580 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.580 

.530 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.960 

.930 

.750 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.015

.855 

.815 

.575 

.375 

.275 

.175 

.125 

.075 

.050 

.025

.515 

.490 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

w.s. 

2.11 

2.11 

2.09 

2.09 

2.09 

2.07 

2.01 

1.93 

1.86 

1.82 

1.66

w.s. 

2.04 

2.04 

2.00 

2.06 

2.08 

2.08 

2.08 

2.02 

1.93 

1.84 

1.70

w.s. 

1.58 

1.51 

1.43 

1.24 

1.18 

1.15 

1.09 

.99 

.84 

.82

w.s. 

1.95 

1.86 

1.84 

1.82 

1.78 

1.72 

1.47 

1.44 

1.28 

1.15

W.S. 

2.46 

2.50 

2.51 

2.41 

2.36 

2.10 

1.86 

1.72 

1.48 

1.25 

.57

w.s. 

2.67 

2.67 

2.71 

2.67 

2.67 

2.67 

2.65 

2.48 

2.16

w.s. 

1.98 

1.95 

1.97 

1.91 

1.91 

1.84 

1.77 

1.64 

1.47

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.930 

.875 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.010 

.960 

.860 

.760 

.660 

.560 

.460 

.360 

.260 

.210

.601 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.610 

.550 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

1.030 

.990 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.025 

.980 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.510 

.475 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

w.s. 

2.12 

1.98 

2.00 

1.95 

1.94 

1.86 

1.86 

1.75 

1.70

w.s. 

1.69 

1.74 

1.80 

1.85 

1.79 

1.72 

1.69 

1.48 

.96

w.s. 

1.66 

1.48 

1.40 

1.19 

1.16 

1.08 

.84 

.73 

.70

w.s. 

1.86 

1.77 

1.66 

1.46 

1.40 

1.33 

1.32 

1.33 

1.36 

1.35

w.s. 

2.51 

2.47 

2.41 

2.21 

2.08 

2.02 

1.91 

1.72 

1.60 

1.46 

1.30

w.s. 

2.46 

2.39 

2.39 

2.39 

2.39 

2.31 

2.29 

2.22 

2.21 

2.09 

1.70

w.s. 

2.10 

2.11 

2.08 

2.02 

2.00 

1.98 

1.97 

1.91 

1.88

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

1.035 

.970 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.892 

.870 

.770 

.670 

.620 

.570 

.520 

.470 

.420 

.370 

.320 

.270 

.220 

.170 

.120 

.070 

.020

.580 

.530 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.580 

.530 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.960 

.920 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.025 

.960 

.800 

.600 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.615 

.580 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

W.S.

2.15 

2.24 

2.24 

2.16 

2.10 

2.00 

1.77 

1.68 

1.65 

1.59 

1.51

w.s. 

1.89 

1.85 

1.94 

1.62 

1.73 

1.74 

1.69 

1.74 

1.74 

1.73 

1.54 

1.61 

1.55 

1.29 

1.13 

1.03

w.s. 

1.65 

1.57 

1.48 

1.39 

1.33 

1.27 

1.10 

.99 

.99 

.99

w.s. 

1.94 

1.94 

1.91 

1.78 

1.65 

1.61 

1.56 

1.39 

1.30 

1.16

w.s. 

2.31 

2.30 

2.21 

2.15 

2.18 

2.21 

2.06 

2.08 

2.07 

1.93 

1.85

w.s. 

2.33 

2.36 

2.33 

2.35 

2.32 

2.23 

2.10 

1.98 

1.97 

1.88 

1.13

w.s. 

2.05 

2.04 

2.01 

1.93 

1.85 

1.81 

1.80 

1.73 

1.46
182 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 14. Velocity-profile data for 0.28-mm sand in 8-foot-wde flume Continued

Run

16___ 

23...........

17............

3.............

18... .

30 . 

34.---.. ......

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.915 

.850 

.600 

.450 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.950 

.900 

.700 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050

.925 

.870 

.700 

.500 

.400 

.300 

.250 

.200 

.175 

.150 

.125 

.100

1.180 

1.015 

.815 

.665 

.465 

.365 

.265 

.200 

.150 

.100 

.075 

.050 

.025

.740 

.700 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.665 

.620 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.450 

.425 

.325 

.225 

.175 

.125 

.100 

.075

Velocity 

(fps)

w.s. 

2.21 

2.15 

2.18 

2.20 

2.15 

2.14 

2.10 

2.01 

1.51 

1.40

W.S. 

3.13 

3.02 

2.91 

2.80 

2.75 

2.55 

2.13 

1.93 

1.76 

1.56

w.s. 

1.84 

1.66

1.58 

1.57 

1.54 

1.36

1.29 

1.28 

1.27 

.54 

.52

W.S. 

2.50 

2.50 

2.50 

2.40 

2.21 

1.95 

1.28 

.63 

.74 

.58 

.62 

.66

w.s. 

2.16 

2.05 

1.60 

1.37 

1.59 

1.59 

1.23 

1.25 

1.26 

1.25

w.s. 

3.76 

3.59 

3.40 

3.30 

3.10 

2.88 

2.70 

2.64 

2.51 

2.23

w.s. 

1.79 

1.78 

1.68 

1.55 

1.39 

1.35 

1.36

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.875 

.800 

.600 

.450 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.945 

.900 

.700 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.595 

.540 

.400 

.300 

.200 

.150 

.100 

.060 

.050 

.025

.805 

.750 

.600 

.450 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.750 

.720 

.600 

.500 

.400 

.350 

.300 

.275 

.250 

.225

.625 

.580 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.395 

.360 

.300 

.250 

.200 

.150 

.100 

.075

Velocity 

(fps)

w.s. 

2.45 

2.47 

2.43 

2.34 

2.32 

2.29 

2.31 

2.22 

2.10 

1.80

w.s. 

3.14 

2.98 

2.85 

2.70 

2.64 

2.57 

2.51 

2.31 

2.23 

2.14 

2.12

w.s. 

1.72 

1.70 

1.56 

1.52 

1.52 

1.46 

1.35 

1.03 

.98

w.s. 

2.33 

2.33 

2.26 

2.21 

2.16 

2.12 

1.90 

1.78 

1.74 

.1.74

w.s. 

2.84 

2.81 

2.76 

2.56 

2.47 

2.03 

1.70 

1.19 

.79

w.s. 

3.68 

3.68 

3.49 

3.40 

3.20 

2.99 

2.76 

2.51 

2.07

w.s. 

1.98 

1.96 

1.87 

1.87 

1.77 

1.72 

1.61

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.895 

.800 

.600 

.450 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.158 

1.100 

1.000 

.900 

.800 

.700 

.600 

.500 

.400 

.300 

.200 

.100 

.050 

.025

.690 

.635 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.870 

.800 

.700 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.600 

.560 

.450 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.720 

.675 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.345 

.320 

.250 

.200 

.150 

.100 

.075 

.050

Velocity 

(fps)

w.s. 

2.10 

2.02 

1.84 

1.81 

1.83 

1.74 

1.68 

1.54 

1.47 

1.42

w.s. 

3.18 

3.16 

3.10 

3.08 

2.98 

2.90 

2.70 

2.61 

2.44 

2.10 

1.34 

.30 

.30

w.s. 

1.62 

1.50 

1.48 

1.14 

1.10 

1.08 

1.07 

1.04 

1.04 

1.03

w.s. 

2.21 

2.21 

2.21 

2.18 

2.04 

1.95 

1.88 

1.80 

1.60 

1.55 

1.55

w.s. 

2.85 

2.84 

2.80 

2.73 

2.69 

2.57 

2.45 

2.33 

2.13

w.s. 

3.76 

3.76 

3.49 

3.40 

3.20 

2.64 

2.07 

1.70 

1.70 

1.48

w.s. 

1.96 

1.94 

1.90 

1.75 

1.66 

1.64 

1.64

Run

34 Con.

22.... .

15.... 

24..... .

25.... 

28.... 

29 

26.... 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.050 

.025

.630 

.580 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.810 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.650 

.610 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.670 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.550 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.540 

.490 

.440 

.400 

.300 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.505 

.470 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

1.36 

1.37

w.s. 

3.55 

3.50 

3.38 

2.98 

2.87 

2.85 

2.67 

2.56 

2.31 

1.93

w.s. 

2.32 

2.29 

2.18 

2.01 

1.83 

1.85 

1.89 

1.94 

1.94 

1.90

w.s. 

3.68 

3.78 

3.82 

3.78 

3.68 

3.45 

3.23 

2.96 

2.64 

2.31

w.s. 

4.74 

4.46 

4.39 

4.17 

4.01 

3.85 

3.40 

3.20 

2.76

w.s. 

4.39 

4.24 

4.08 

3.93 

3.76 

3.40 

3.30 

3.10 

2.76

w.s. 

4.24 

4.39 

4.39 

4.16 

4.08 

4.01 

3.76 

3.49 

3.10 

3.20 

2.88

W.S.

4.81 

4.46 

4.46 

3.93 

3.76 

3.59 

3.10 

2.fi4 

2.37

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.050 

.025

.610 

.560 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.595 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.810 

.760 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.670 

.650 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.550 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.490 

.440 

.400 

.300 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.485 

.430 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

1.61 

1.61

w.s. 

3.59 

3.58 

3.50 

3.31 

3.07 

2.92 

2.73 

2.66 

2.40 

2.20

w.s. 

2.47 

2.44 

2.38 

2.31 

2.25 

2.14 

2.07 

1.88 

1.82

w.s. 

3.70 

3.70 

3.68 

3.62 

3.48 

3.29 

3.10 

2.98 

2.79 

2.48

W.S. 

4.74 

4.53 

4.46 

4.24 

4.01 

3.85 

3.50 

3.40 

3.20 

2.88

w.s. 

4.32 

4.16 

4.08 

4.01 

3.68 

3.59 

3.30 

3.10 

2.64

w.s. 

4.67 

4.32 

4.32 

4.24 

4.08 

3.93 

3.59 

3.40 

3.20 

2.76

w.s. 

4.81 

4.53 

4.32 

4.16 

3.49 

3.40 

3.30 

2.07

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.025

.595 

.560 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.515 

.470 

.400 

. - . . 300 .200" 

.150 

.100 

.075 

.050 

.025

.800 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.700 

.650 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.550 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.490 

.440 

.400 

.300 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.475 

.410 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

1.61

w.s. 

3.43 

3.33 

3.27 

3.12 

2.94 

2.75 

2.55 

2.43 

2.14 

1.89

w.s. 

2 43 

2.40 

2.31 

2.25 

2.25 

2.25 

2.19 

2.16 

2.10

w.s. 

3.56 

3.42 

3.17 

3.09 

3.07 

2.97 

2.78 

2.74 

2.61 

2.43

w.s. 

4.46 

4.46 

4.24 

4.09 

3.93 

3.85 

3.59 

3.40 

2.88 

2.76

w.s. 

4.32 

4.08 

3.93 

3.85 

3.59 

3.49 

3.30 

3.20 

2.76

w.s. 

4.81 

4.39 

4.39 

4.16 

4.01 

4.08 

3.68 

3.59 

3.40 

3.10

w.s. 

4.60 

4.46 

4.32 

4.08 

3.93 

3.76 

3.40 

2.88
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 183

TABLE 15. Velocity-profile data for 0.45-mm sand in 8-foot-wide flume 

[The lateral section used for measuring was 95-115 ft from the headbox. w.s.=water surface]

Run

14.............

13- .

17............

16.-.-.. ...

15....... .....

18.. ...-. .

2.....

 2.. .

Distance 

above sand 

bed (ft)

8. 6 ft from 

of flu 

0.613 

.563 

.463 

.363 

.263 

.213 

.163 

.113 

.063 

.013

.356 

.306 

.256 

.206 

.156 

.106 

.081 

.056 

.031 

.006

.902 

.852 

.802 

.602 

.402 

.202 

.152 

.102 

.077 

.052 

.027 

.002

1, H ft from 

offlu 

0.792 

.742 

.692 

.492 

.292 

.192 

.142 

.092 

.067 

.042 

.017 

.010 

2.6 ft from 

offlu 

0.776 

.726 

.676 

.476 

.276 

.176 

.126 

.101 

.076 

.051 

.026

.673 

.623 

.573 

.473 

.373 

.273 

.173 

.073 

.048 

.023 

.010 

1.8 ft from 

offlu 

0.703 

.603 

.503 

.403 

.303 

.203 

.103 

4.0 ft from

Offll 

0.727 

.627 

.527 

.427 

.327 

.227

Velocity 

(fps)

left watt 

me 

w.s. 

0.84 

.83 

.81 

.76 

.75 

.73 

.69 

.59 

.46

w.s. 

.63 

.62 

.61 

.60 

.58 

.57 

.56 

.53 

.48

w.s. 

.91 

.91 

.90 

.87 

.81 

.79 

.75 

.74 

.73 

.71 

.70

left watt 

me 

w.s. 

0.97 

.98 

.96 

.87 

.82 

.78 

.73 

.69 

.67 

.62 

.60 

left wall 

me 

w.s. 

0.95 

.90 

.87 

.86 

.75 

.73 

.69 

.65 

.63 

.67

w.s. 

.74 

.78 

.78 

.77 

.72 

.67 

.60 

.52 

.49 

.39 

left watt 

me 

w.s. 

1.34 

1.32 

1.27 

1.25 

1.24 

1.22 

left watt 

ime 

w.s. 

1.44 

1.38 

1.29 

1.29 

1.26

Distance 

above sand 

bed (ft)

4.0 ft from 

offlu 

0.613 

.563 

.463 

.363 

.263 

.213 

.163 

.113 

.063 

.013

.363 

.313 

.263 

.213 

.163 

.113 

.088 

.063 

.038 

.013

.937 

.887 

.837 

.637 

.437 

.237 

.187 

.137 

.112 

.087 

.062 

.037 

.012

.787 

.737 

.687 

.487 

.287 

.187 

.137 

.087 

.062 

.037 

.012

.804 

.754 

.704 

.604 

.504 

.404 

.304 

.204 

.104 

.079 

.054 

.029 

.004

.697 

.647 

.597 

.497 

.397 

.297 

.197 

.097 

.072 

.047 

.022

.861 

.761 

.661 

.561 

.461 

.411

Velocity 

(fps)

left wall 

me 

w.s. 

0.86 

.84 

.80 

.79 

.76 

.75 

.70 

.64 

.41

w.s. 

.63 

.62 

.61 

.59 

.58 

.57 

.57 

.54 

.45

w.s. 

.92 

.92 

.91 

.90 

.83 

.78 

.74 

.74 

.73 

.72 

.70 

.69

W.S.

.94 

.94

.92 

.88 

.80 

.79 

.77 

.69 

.67 

.60

w.s. 

.97 

.92 

.90 

.90 

.86 

.82 

.77 

.65 

.52 

.46 

.43 

.30

w.s. 

.80 

.80 

.79 

.78 

.77 

.68 

.58 

.51 

.49 

.43

w.s. 

1.44 

1.43 

1.39 

1.31 

1.27

Distance 

above sand 

bed (ft)

6.8 ft from 

offlu 

0.621 

.571 

.471 

.371 

.271 

.221 

.171 

.121 

.071 

.021

.353 

.303 

.253 

.203 

.153 

.103 

.078 

.053 

.028 

.003

.938 

.888 

.838 

.638 

.438 

.238 

.188 

.138 

.113 

.088 

.063 

.038 

.013

.813 

.763 

.713 

.513 

.313 

.213 

.113 

.063 

.138 

.013 

.413

.771 

.721 

.671 

.471 

.271 

.171 

.121 

.096 

.071 

.046 

.021 

.010

5.4 ft from 

offli 

0.656 

.606 

.556 

.456 

.356 

.256 

.156 

.106 

.056 

.031 

.010

4.0 ft from 

offlu 

0.758 

.658 

.558 

.458 

.358 

.258

Velocity 

(fps)

left wall 

me 

w.s. 

0.83 

.85 

.82 

.77 

.75 

.73 

.69 

.65 

.47

w.s. 

.56 

.56 

.56 

.53 

.52 

.49 

.47 

.46 

.40

w.s. 

.90 

.89 

.89 

.87 

.86 

.83 

.80 

.78 

.75 

.74 

.74 

.68

w.s. 

.98 

.98 

.87 

.80 

.74 

.65 

.60 

.53 

.45 

.86

w.s. 

.94 

.94 

.92 

.82 

.77 

.71 

.63 

.58 

.58 

.46 

.35

left wall 

ime 

w.s. 

.82 

.79 

.79 

.79 

.76 

.74 

.69 

.62 

.57 

.46

left watt 

me 

w.s. 

1.44 

1.43 

1.46 

1.42 

1.37

Run

» 2 Con. 

3.-.. 

9.-. -

9... 

1. ...... .-_

5... . ....

5.... . .

11.... 

Distance 

above sand 

bed (ft)

4.0 ft from 

offlu 

0.127

.741 

.641 

.577 

.513 

.449 

.385 

.321 

.257 

.193 

.161 

.129 

.097 

.065 

.033 

1.2 ft from 

offlui 

0.551 

.501 

.401 

.351 

.301 

.251 

.201 

.151 

.101 

.051 

.026 

5.4 Jt from 

offlu 

0.581 

.531 

.431 

.381 

.331 

.281 

.231 

.181 

.131 

.081 

8.0ft from 

offlu 

0.650 

.625 

.525 

.425 

.325 

.225 

.125 

.025 

2.5 ft from 

offlu 

0.737 

.637 

.537 

.437 

.337 

.287 

.237 

.187 

.137 

.087 

.037 

7. Oft from 

offlu 

0.757 

.657 

.557 

.457 

.357 

.257 

.207 

.157 

.107 

.057 

1. H ft from I 

flur 

0.310 

.260 

.210 

.160 

.135 

.110 

.085 

.060 

.035 

.010

Velocity 

(fps)

left watt 

me 1.24

w.s. 

1.42 

1.43 

1.43 

1.38 

1.29 

1.29 

1.29 

1.20 

1.16 

1.13 

1.16 

1.11 

1.02 

left wall 

ne 

w.s. 

1.25 

1.23 

1.20 

1.18 

1.18 

1.16 

1.11 

.99 

.87 

.84 

left watt 

me 

w.s. 

1.22 

1.11 

1.08 

1.05 

1.02 

.90 

.87 

.80 

.73 

left wall 

me 

w.s. 

1.62 

1.59 

1.55 

1.50 

1.41 

1.36 

1.33 

left watt 

me 

w.s. 

1.65 

1.62 

1.57 

1.57 

1.51 

1.45 

1.43 

1.25 

1.13 

.94 

left watt 

,me 

w.s. 

1.68 

1.67 

1.65 

1.65 

1.62 

1.55 

1.35 

1.29 

1.02 

eft wall of 

ne 

w.s. 

1.00 

.97 

.90 

.90 

.87 

.87 

.80 

.77 

.69

Distance 

above sand 

bed (ft)

4.0 ft from 

offlu 

0.361 

.261 

.161 

.061

2.6 ft from 

offlui 

0.587 

.537 

.437 

.337 

.287 

.237 

.187 

.137 

.087 

.037 

.012 

6.8ft from 

offlu 

0.540 

.490 

.390 

.290 

.240 

.190 

.140 

.090 

.040 

.015 

4.0ft from 

offlu 

0.650 

.625 

.525 

.425 

.325 

.225 

.125 

.025

.667 

.567 

.467 

.367 

.317 

.267 

.217 

.167 

.117 

.067 

.042

2. 6 ft from I 

flurt 

0.357 

.311 

.261 

.211 

.186 

.161 

.136 

.111 

.086 

.061 

.036 

.011

Velocity 

(fps)

kft watt 

me 

1.28 

1.24 

1.09 

.95

left wall 

ne 

w.s. 

1.20 

1.18 

1.13 

1.05 

.99 

.97 

.94 

.84 

.55 

.49 

left watt 

me 

w.s. 

1.25 

1.23 

1.16 

1.11 

1.08 

1.05 

1.02 

.97 

.87 

left wall 

me 

w.s. 

1.63 

1.60 

1.49 

1.45 

1.39 

1.35 

1.34

w.s. 

1.70 

1.63 

1.62 

1.60 

1.60 

1.57 

1.49 

1.42 

1.33 

1.25

eft wall of 

ie 

w.s. 

1.00 

1.02 

.84 

.90 

.84 

.80 

.77 

.77 

.74 

.74 

.60

Distance 

above sand 

bed (ft)

4.0 ft from 

offlu 

0.158 

.058

0.543 

.493 

.393 

.343 

.293 

.243 

.193 

.143 

.093 

.043 

.018

6.0 ft from 

offlu 

0.650 

.625 

.525 

.425 

.325 

.225 

.125 

.025 

5.5ftfror 

offlu 

0.743 

.643 

.543 

.443 

.343 

.243 

.193 

.143 

.093 

.043

4.0 ft from I 

flur 

0.314 

.274 

.224 

.174 

.149 

.124 

.099 

.074 

.049 

.024

Velocity 

(fps)

left watt 

me 

1.28 

.87

w.s. 

1.20 

1.11 

1.08 

1.02 

.97 

.90 

.87 

.84 

.84 

.80

left wall 

me 

w.s. 

1.62 

1.62 

1.55 

1.52 

1.44 

1.30 

1.01 

it left watt 

me 

w.s. 

1.78 

1.70 

1.70 

1.70 

1.53 

1.55 

1.49 

1.35 

1.25

eft wall of 

ne 

w.s. 

1.02 

.97 

.94 

.90 

.90 

.84 

.80 

.80 

.77

See footnote at end of table, p. 186.
184 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 15. Velocity-profile data for 0.45-mm sand in 8-foot-wide flume Continued

Run

11 Con. 

4...... ....

4

8_._._ 

8.. ..... ...

1. ............

10..... .-.

10-.... ....

Distance 

above sand 

bed (ft)

6.4 ft from I 

flui 

0.390 

.340 

.290 

.240 

.215 

.190 

.165 

.140 

.115 

.090 

.065 

.040 

.015 

1.2 ft from I 

flun 

0.648 

.548 

.448 

.348 

.298 

.248 

.198 

.148 

.098 

.048 

5.5 ft from I 

flun 

0.665 

.565 

.465 

.365 

.265 

.215 

.165 

.115 

.065 

.015

Ltft from I 

flun 

0.461 

.411 

.311 

.261 

.211 

.161 

.111 

.061 

.011 

5. 4 ft from I 

flun 

0.421 

.419 

.319 

.219 

.169 

.119 

.069 

.019

2.5 ft from I 

flum 

0.632 

.532 

.432 

.332 

.232 

.182 

.132 

.082 

.032 

1.2 ft from I 

flun 

0.279 

.229 

.179 

.154 

.129 

.104 

.079 

.054 

.029 

.004

64 ft from I 

flur 

0.273 

.223 

.173 

.148 

.123 

.098 

.073 

.048 

.023 

.008

Velocity 

(fps)

eft wall of 

le 

w.s. 

1.00 

.90 

.90 

.90 

.87 

.87 

.80 

.84 

.77 

.77 

.77 

.69

eft wall of 

le 

w.s. 

1.87 

1.84 

1.79 

1.81 

1.76 

1.72 

1.65 

1.51 

1.47 

eft watt of 

ie 

w.s. 

1.73 

1.73 

1.70 

1.62 

1.53 

1.51 

1.45 

1.29 

1.25 

eft wall of 

le 

w.s. 

1.29 

1.27 

1.20 

1.08 

1.05 

.99 

.87 

.73 

eft watt of 

ie 

w.s. 

1.25 

1.22 

1.18 

1.08 

1.02 

.97 

.84

eft wall of 

e 

w.s. 

1.60 

1.62 

1.60 

1.62 

1.53 

1.58 

1.57 

1.29 

eft wall of 

ie 

w.s. 

1.08 

1.02 

.99 

.94 

.90 

.87 

.80 

.35 

.28

eft watt of 

ne 

w.s. 

1.13 

1.11 

1.08 

1.02 

.99 

.97 

.90 

.80 

.65

Distance 

above sand 

bed (ft)

6.8 ft from I 

flui

0.271 

.221 

.171 

.121 

.096 

.071 

.046 

.021 

.001

$.5 ft from I 

flun 

0.648 

.548 

.448 

.348 

.298 

.248 

.198 

.148 

.098 

.048 

7. Oft from I 

flun 

0.678 

.578 

.478 

.378 

.278 

.228 

.178 

.128 

.078 

.028 

2.6 ft from I 

flun 

0.444 

.393 

.293 

.243 

.193 

.143 

.093 

.043

6.8 ft from I 

flun 

0.511 

.461 

.361 

.261 

.211 

.161 

.111 

.061 

.Oil 

4.0 ft from I 

flu 

0.698 

.598 

.498 

.398 

.298 

.198 

.158 

.098 

.058 

2.6 ft from I 

flur 

0.302 

.252 

.202 

.177 

.152 

.127 

.102 

.077 

.052 

.027 

.002 

8.8 ft from I 

flun 

0.346 

.296 

.246 

.196 

.171 

.146 

.121 

.096 

.071 

.046 

.021

Velocity 

(fps)

eft watt of

rie

w.s. 

0.99 

.97 

.90 

.87 

.84 

.80 

.80 

.49

eft watt of 

ne 

w.s. 

1.81 

1.79 

1.78 

1.73 

1.78 

1.72 

1.62 

1.62 

1.58 

eft wall of 

ie 

w.s. 

1.55 

1.53 

1.43 

1.42 

1.42 

1.35 

1.33 

1.31 

1.29 

eft wall of 

ie 

w.s. 

1.33 

1.31 

1.27 

1.25 

1.16 

1.11 

1.02

°,ft wall of 

ie 

w.s. 

1.27 

1.25 

1.11 

1.08 

1.02 

.99 

.90 

.35 

eft wall of 

me 

w.s. 

1.88 

1.93 

1.79 

1.84 

1.82 

1.84 

1.79 

1.78 

eft wall of 

ne 

w.s. 

0.99 

.94 

.90 

.90 

.84 

.84 

.80 

.80 

.77 

.35 

eft wall of 

ne 

w.s. 

1.08 

1.08 

.99 

.99 

.97 

.94 

.87 

.84 

.69 

.42

Distance 

above sand 

bed (ft)

4.0ftfrom 

of fl-u

0.661 

.561 

.461 

.361 

.261 

.211 

.161 

.111 

.061 

.011

.493 

.450 

.350 

.300 

.250 

.200 

.150 

.100 

.050

------

6.1 ft from I 

flun 

0.606 

.506 

.406 

.306 

.206 

.156 

.106 

.056 

.006 

4.0 ft from le 

flun 

0.245 

.195 

.145 

.120 

.095 

.070 

.045 

.020 

.010

Velocity 

(fps)

left wall 

me

w.s. 

1.76 

1.76 

1.72 

1.55 

1.57 

1.53 

1.53 

1.49 

1.47

w.s. 

1.25 

1.22 

1.20 

1.18 

1.11 

1.02 

.99 

.84

eft wall of 

ie 

w.s. 

1.75 

1.65 

1.65 

1.62 

1.60 

1.49 

.84 

.49 

ft watt of 

ie 

w.s. 

1.18 

1.11 

1.05 

.97 

.94 

.90 

.87 

.73

Run

6..-- .... --

6.... 

19

19.... - 

21.... - 

20-- 

23.... -

Distance 

above sand 

bed (ft)

1 .2 ft from I 

flur

0.445 

.395 

.345 

.295 

.245 

.195 

.145 

.095 

.070 

.045

5.5 ft from I 

flur 

0.477 

.427 

.377 

.327 

.277 

.227 

.177 

.127 

.102 

.077 

.052

4.0 ft from I 

flur

0.237 

.189 

.139 

.114 

.089 

.064 

.039 

.014

2. Oft from I 

flui 

0.423 

.408 

.308 

.208 

.158 

.108 

.083 

.058 

.033

1.016 

.916 

.866 

.816 

.716 

.516 

.416 

.316 

.266 

.216 

.166 

.116

.555 

.540 

.440 

.340 

.240 

.140 

.090 

.040 

.015

.660 

.610 

.510 

.410 

.310 

.210 

.160 

.110 

.060 

.035

Velocity 

(fps)

eft watt of 

ne 

w.s. 

1.45 

1.43 

1.42 

1.40 

1.33 

1.31 

1.02 

.84 

.65

eft watt of 

ne 

w.s. 

1.38 

1.33 

1.33 

1.20 

1.16 

1.11 

.99 

.94 

.87 

.69

eft watt of 

ne

W.S.

1.22 

1.16 

1.11 

1.08 

1.05 

.97 

.90

eft watt of 

ie 

w.s. 

1.49 

1.58 

1.51 

1.42 

1.33 

1.22 

1.20 

.80

w.s. 

1.58 

1.60 

1.60 

1.58 

1.62 

1.67 

1.20 

1.11 

.73 

.55 

.49

w.s. 

1.81 

1.84 

1.79 

1.58 

1.47 

1.35 

1.20 

.97

w.s. 

2.78 

2.88 

2.82 

2.86 

2.78 

2.76 

2.70 

2.62 

2.60

Distance 

above sand 

bed (ft)

2.5 ft from I 

flur 

0.500 

.450 

.400 

.350 

.300 

.250 

.200 

.175 

.150 

.125 

.100

7.0ftfroml 

flui 

0.486 

.436 

.386 

.336 

.286 

.236 

.186 

.136 

.086 

.061 

.036

4.0 ft from I 

flur

0.433 

.418 

.318 

.268 

.218 

.193 

.168 

.143 

.118 

.093 

.068 

.043 

.018

.760 

.660 

.560 

.460 

.360 

.260 

.160 

.060 

.010

.740 

.720 

.620 

.520 

.470 

.420 

.370 

.320 

.270 

.220 

.170 

.145 

.120 

.095 

.070 

.045 

.010

1.080 

1.030 

.930 

.830 

.730 

.630 

.580 

.530 

.480 

.455

Velocity 

(fps)

eft wall of 

ne 

w.s. 

1.47 

1.45 

1.38 

1.33 

1.29 

1.23 

1.20 

1.11 

1.05 

.90

eft watt of

ne

w.s. 

1.31 

1.23 

1.27 

1.18 

1.20 

1.13 

1.05 

.94 

.84 

.65

eft watt of 

ne 

w.s. 

1.42 

1.53 

1.55 

1.42 

1.55 

1.47 

1.42 

1.35 

1.25 

1.16 

1.18 

1.18

w.s. 

1.92 

1.86 

1.75 

1.58 

1.51 

1.51 

1.38 

1.27

w.s. 

1.70 

1.88 

1.85 

1.79 

1.72 

1.72 

1.68 

1.68 

1.57 

1.43 

1.60 

1.56 

1.38 

1.40 

1.13 

.87

w.s. 

2.44 

2.44 

2.50 

2.48 

2.46 

2.40 

2.37 

2.40 

2.54

Distance 

above sand 

bed (ft)

4.0 ft from 

of flu 

0.457 

.350 

.250 

.200 

.150 

.100 

.050 

.025

6. Oft from I 

flur 

0.285 

.270 

.170 

.120 

.095 

.070 

.045 

.020 

.010

1.095 

.995 

.895 

.795 

.745 

.695 

.595 

.495 

.395 

.295 

.195 

.145 

.095

.655 

.635 

.535 

.435 

.335 

.285 

.235 

.185 

.160 

.135 

.110 

.085 

.060 

.035 

.010

.700 

.650 

.550 

.450 

.350 

.250 

.200 

.150 

.100 

.050

Velocity 

(fps)

left watt 

me 

w.s. 

1.42 

1.31 

1.23 

1.16 

1.02 

.97 

.69

eft watt of 

ie 

w.s. 

1.58 

1.67 

1.63 

1.51 

1.45 

1.33 

1.20 

.94

w.s. 

1.70 

1.75 

1.70 

1.65 

1.61 

1.60 

1.55 

1.22 

1.22 

1.22 

.99 

.69

w.s. 

1.75 

1.90 

1.91 

1.91 

1.85 

1.73 

1.63 

1.65 

1.55 

1.47 

1.38 

1.29 

1.16 

1.05

w.s. 

2.62 

2.68 

2.70 

2.60 

2.76 

2.70 

2.64 

2.60 

2.31
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 

TABLE 15. Velocity-profile data for 0.45-mm sand in 8-foot-wide flume Continued

185

Run

23 Con. 

22 - 

25--. .

24.. .

40--.. ..

39....-- .

26-.. ....

28-- ______

29-... ..

Distance 

above sand 

bed (ft)

S.Oftfrom 

of flu 

0.010

.965 

.865 

.765 

.665 

.465 

.265 

.215 

.165 

.115 

.065

.484 

.409 

.384 

.334 

.284 

.234 

.184 

.159 

.134 

.109 

.084 

.059 

.034

.570 

.470 

.370 

.320 

.270 

.220 

.170 

.120 

.070 

.020

1.300 

1.280 

1.180 

.980 

.780 

.580 

.480 

.380 

.280 

.180

.570 

.550 

.500 

.400 

.300 

.200 

.100 

.050 

.025

.500 

.480 

.410 

.310 

.210 

.160 

.110 

.060 

.040 

.020

.408 

.358 

.308 

.258 

.208 

.158 

.108 

.058

.304 

.254 

.204 

.154 

.129 

.104

Velocity 

(fps)

left wall 

me 

2.37

w.s. 

1.75 

1.85 

1.75 

1.68 

1.67 

1.60 

1.55 

1.55 

1.55

w.s. 

1.78 

1.78 

1.76 

1.68 

1.73 

1.78 

1.76 

1.79 

1.78 

1.72 

1.55 

1.45

w.s. 

2.80 

2.82 

2.66 

2.56 

2.48 

2.48 

2.36 

2.22 

2.12

w.s. 

3.96 

3.83 

3.64 

3.87 

3.45 

2.15 

1.82 

.00 

.00

w.s. 

5.45 

5.19 

5.22 

5.04 

4.85 

4.27 

3.74 

2.54

w.s. 

4.71 

4.26 

3.83 

3.73 

3.65 

3.50 

2.98 

2.46 

1.35

w.s. 

5.10 

5.10 

4.32 

4.55 

3.87 

3.98 

3.49

w.s. 

2.70 

2.60 

2.54 

2.31 

2.40

Distance 

above sand 

bed (ft)

4.0 ft from 

of flu 

0.430 

.405 

.330 

.230 

.130

1.088 

.988 

.888 

.788 

.588 

.388 

.288 

.238 

.188 

.138 

.088 

.038

.351 

.301 

.251 

.201 

.151 

.126 

.101 

.076 

.051 

.026

.750 

.650 

.600 

.500 

.400 

.300 

.250 

.200 

.150 

.100 

.050 

.023

.936 

.900 

.700 

.500 

.400 

.300 

.200 

.100 

.050 

.025

.540 

.500 

.400 

.300 

.200 

.100 

.050 

.025

.460 

.450 

.350 

.250 

.200 

.150 

.100 

.050 

.030 

.010

.343 

.323 

.273 

.223 

.173 

.123 

.073 

.023

.370 

.320 

.270 

.270 

.220 

.170

Velocity 

(fps)

left wall 

me 

2.40 

2.37 

2.44 

2.29 

2.42

W.S. 

1.95 

1.92 

1.94 

1.79 

1.72 

1.65 

1.62 

1.35 

1.51 

1.47 

1.22

W.S. 

2.02 

1.98 

1.91 

1.94 

1.92 

1.91 

1.76 

1.72 

1.58

w.s. 

1.95 

1.82 

1.68 

1.67 

1.79 

1.76 

1.68 

1.20 

.77 

.73 

.60

w.s. 

3.08 

3.36 

3.30 

3.34 

3.08 

3.18 

3.05 

2.62 

2.05

w.s. 

5.60 

5.34 

5.20 

4.59 

4.04 

3.63 

2.52

w.s. 

4.47 

4.48 

4.23 

4.07 

3.98 

3.50 

3.24 

2.96 

1.25

w.s. 

4.25 

3.85 

3.86 

3.74 

3.73 

3.71 

3.09

W.S. 

2.96 

2.64 

2.35 

2.37 

2.66

Distance 

above sand 

bed (ft)

6. Oft from 

of flu 

0.025 

.010

1.114 

1.014 

.914 

.814 

.714 

.514 

.464 

.414 

.314 

.214 

.114 

.010

.270 

.220 

.170 

.120 

.070 

.045 

.020 

.005

.294 

.194 

.144 

.094 

.044 

.019

.728 

.650 

.600 

.550 

.450 

.350 

.250 

.150 

.100 

.050 

.025

.640 

.600 

.550 

.450 

.350 

.250 

.150 

.100 

.050 

.025

.485 

.455 

.405 

.305 

.205 

.155 

.105 

.055 

.035 

.015

.395 

.345 

.295 

.245 

.195 

.145 

.120 

.095 

.070 

.045 

.020

.325 

.275 

.225 

.175 

.125 

.100

Velocity 

(fps)

left wall 

me 

2.16 

1.88

w.s. 

1.98 

1.94 

2.05 

2.03 

1.73 

1.63 

1.33 

1.27 

1.20 

1.13 

.84

W.S. 

2.11 

2.09 

2.10 

2.09 

1.91 

1.73 

1.67

w.s. 

2.94 

2.92 

2.70 

2.50 

2.05

w.s. 

3.42 

3.67 

3.60 

3.44 

3.75 

3.79 

3.71 

3.32 

2.92 

2.56

w.s. 

5.40 

5.10 

5.00 

4.80 

4.74 

4.20 

3.85 

3.41 

1.18

w.s. 

4.53 

4.62 

4.27 

4.21 

3.78 

3.61 

3.19 

2.62 

2.68

w.s. 

4.35 

4.17 

3.89 

3.75 

3.58 

3.39 

3.35 

3.21 

2.78 

1.35

w.s. 

2.44 

2.35 

2.42 

2.24 

1.98

Run

29 Con. 

31--. 

97

36.- 

41. 

30- 

35.. ...

34.. 

33.. -

38.. 

Distance 

above sand 

bed (ft)

H. Oft from 

of flu 

0.079 

.054 

.029 

.004

.293 

.243 

.193 

.143 

.093 

.068 

.043 

.018

.190 

.130 

.115 

.090 

.065 

.040 

.020 

.010

2.5 ft from \ 

flun 

0.614 

.550 

.500 

.400 

.300 

.200 

.150 

.100 

.050 

025 

2.0 ft from I 

flun 

0.225 

.175 

.150 

.125 

.100 

.075 

.050 

.025

.260 

.200 

.175 

.150 

.125 

.100 

.075 

.050 

.025

.280 

.200 

.150 

.100 

.050 

.025

.340 

.280 

.230 

.180 

.130 

.080 

.055 

.030

.510 

.450 

.400 

.300 

.200 

.150 

.100 

.050 

.025

Velocity 

(fps)

left wall 

me 

1.97 

1.78 

1.35 

.73

w.s. 

3.75 

3.55 

3.41 

3.24 

3.02 

2.82 

2.00

W.S.

1.97 

2.06 

1.87 

1.95 

1.53 

1.53 

1.47

eft wall of 

ie 

w.s. 

5.50 

5.50 

5.40 

5.19 

4.86 

4.80 

4.17 

3.74 

1.45 

ft wall of 

ie 

w.s. 

3.06 

2.90 

2.62 

2.60 

2.46 

2.12 

1.68

w.s. 

3.76 

3.71 

3.52 

3.25 

3.40 

2.54 

2.44 

2.06

w.s. 

4.33 

3.97 

3.58 

3.44 

3.39

w.s. 

4.34 

4.45 

4.08 

3.97 

3.74 

3.52 

3.10

w.s. 

6.13 

6.08 

5.70 

5.19 

5.18 

5.09 

5.02 

3.89

Distance 

above sand 

bed (ft)

4.0ftfrom 

of flu 

0.145 

.120 

.095 

.070 

.045 

.020

.335 

.325 

.275 

.225 

.175 

.125 

.075 

.050 

.025

.323 

.273 

.223 

.173 

.123 

.073 

.048 

.023

.170 

.150 

.130 

.105 

.080 

.055 

.030 

.020 

.010

.510 

.490 

.450 

.350 

.250 

.200 

.150 

.100 

.050 

.025

.281 

.231 

.181 

.131 

.081 

.056 

.031 

.006

.203 

.173 

.173 

.148 

.123 

.098 

.073 

.048

.250 

.200 

.150 

.100 

.050 

.025

.305 

.225 

.175 

.125 

.075 

.050 

.025

.500 

.450 

.350 

.250 

.200 

.150 

.100 

.050 

.025

Velocity 

(fps)

left wall 

me 

2.52 

2.40 

2.38 

2.19 

1.92 

1.60

w.s. 

4.87 

4.84 

4.61 

4.60 

4.38 

3.87 

3.33 

2.29

w.s. 

3.71 

3.64 

3.51 

3.46 

2.74 

2.39 

2.36

w.s. 

2.44 

2.24 

2.08 

1.87 

1.67 

1.05 

1.38 

1.55

w.s. 

6.09 

5.82 

5.61 

5.39 

5.02 

4.82 

4.38 

3.77 

2.64

w.s. 

3.31 

3.27 

2.90 

2.54 

2.60 

1.87 

2.25

w.s. 

3.12 

3.57 

3.17 

3.16 

3.18 

2.82 

2.12

W.S.

4.53 

4.27 

3.60 

3.27 

2.54

w.s. 

4.52 

4.30 

3.85 

3.50 

3.10 

2.83

w.s. 

5.57 

5.70 

5.50 

5.33 

5.02 

4.89 

4.73 

3.56

Distance 

above sand 

bed (ft)

6.0 ft from 

of flu 

0.075 

.050 

.025

.370 

.300 

.250 

.200 

.150 

.100 

.050 

.025

.319 

.269 

.169 

.119 

.069 

.044 

.019

.160 

.140 

.115 

.090 

.065 

.040 

.020 

.010

.499 

.479 

.450 

.350 

.250 

.200 

.150 

.100 

.050 

.025

.265 

.225 

.200 

.175 

.150 

.125 

.100 

.075 

.050 

.025

.229 

.200 

.175 

.150 

.125 

.100 

.075 

.050 

.025

.300 

.250 

.200 

.150 

.100 

.050 

.025

.300 

.250 

.190 

.150 

.100 

.050 

.025

.490 

.450 

.400 

.350 

.250 

.200 

.150 

.100 

.050 

.025

Velocity 

(fps)

left wall 

me 

1.98 

1.92 

1.31

W.S.

4.61 

4.38 

4.38 

3.91 

4.09 

3.64 

3.50

W.S.

3.83 

3.19

2.78 

2.28 

1.79 

1.25

w.s. 

2.31 

2.44 

2.42 

2.42 

2.21 

2.31 

1.73

W.S.

5.74 

5.65 

5.30 

5.35 

5.03 

4.75 

4.43 

3.85 

3.35

w.s. 

3.13 

2.72 

3.06 

2.98 

2.97 

2.76 

2.60 

2.12 

1.25

w.s. 

3.45 

3.23 

3.28 

3.01 

2.86 

2.64 

1.90 

1.72

W.S. 

4.23 

4.20 

3.90 

3.59 

3.16 

2.52

w.s. 

4.40 

4.40 

4.33 

3.76 

3.60 

3.06

w.s. 

6.13 

6.06 

6.19 

5.69 

5.45 

5.30 

4.83 

4.56 

3.44
186 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 15. Velocity-profile data for 0.45-mm sand in 8-foot-wide flume Continued

Run

37.. 

32-.. .....

45.. 

Distance 

above sand 

bed (ft)

2.0 ft from 

of flu 

0.500 

.450 

.350 

.250 

.200 

.150 

.100 

.050 

.025

.185 

.160 

.135 

.110 

.085

Velocity 

(fps)

left watt 

me 

w.s. 

6.10 

5.81 

5.75 

5.75 

5.20 

4.57 

3.77 

1.58

w.s. 

3.94 

3.95 

3.79 

3.58

Distance 

above sand 

bed (ft)

4.0 ft from 

of flu 

0.500 

.450 

.425 

.325 

.225 

.125 

.075 

.050 

.025

.345 

.275 

.225 

.175 

.125 

.075 

.050 

.025

.190 

.160 

.135

.110 

.085

Velocity 

(fps)

left wall 

me 

w.s. 

5.65 

5.71 

5.54 

5.15 

4.66 

4.38 

3.60 

3.15

w.s. 

5.44 

5.24 

4.93 

4.81 

4.53 

4.29 

3.95

w.s. 

4.08 

3.85 

3.79 

3.52

Distance 

above sand 

bed (ft)

e.Oftfrom 

of flu 

0.480 

.425 

.400 

.350 

.300 

.200 

.100 

.050 

.025

.380 

.340 

.290 

.240 

.190 

.140 

.090 

.050 

.025

.215 

.200 

.175 

.150 

.125

Velocity 

(fps)

left watt 

me 

w.s. 

5.20 

5.20 

5.49 

5.49 

4.95 

4.56 

4.32 

4.06

w.s. 

5.03 

5.25 

5.25 

4.85 

4.62 

4.53 

4.03 

2.60

w.s. 

3.97 

3.87 

3.68 

3.50

Run

45 Con. 

44...-.-.-.-.

42-- 

Distance 

above sand 

bed (ft)

B.Oftfrom 

of flu 

0.660 

.035 

.010

.302 

.200 

.175 

.125 

.075 

.050 

.025

Velocity 

(fps)

left watt 

me 

3.49 

3.34 

2.94

w.s. 

5.70 

5.70 

4.81 

5.20 

4.45 

4.36

Distance 

above sand 

bed (ft)

4.0ftfrom 

of flu 

0.060 

.035 

.010

.300 

.239 

.214 

.189 

.164 

.139 

.089 

.064 

.039 

.024

Velocity 

(fps)

left watt 

me 

3.63 

3.31

2.72

W.S. 

5.40 

5.30 

5.45 

5.02 

5.15 

4.39 

4.25 

4.15 

3.67

Distance 

above sand 

bed (ft)

e.Oftfrom 

of flu 

0.100 

.075 

.050 

.025

.255 

.210 

.185 

.135 

.085 

.060 

.035

.295 

.275 

.225 

.175 

.150 

.125 

.100 

.075 

.050 

.025

Velocity 

(fps)

left watt 

me 

3.26 

2.98 

2.48 

1.65

w.s. 

5.29 

5.11 

4.93 

4.66 

4.79 

3.97

W.S.

5.85 

5.84 

5.21 

5.20 

5.42 

5.31 

4.76 

4.23 

3.68

 These profiles taken 80,100, and 124 feet from headbox.

TABLE 16. Velocity-profile data for 0.93-mm sand in 8-foot-wide flume 

[The lateral section used for measuring was 95-115 ft from the headbox. w.s.=water surface]

Run

19.- 

25-- 

26

27..-- ...

20...........

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.980 

.930 

.830 

.680 

.530 

.380 

.230 

.130 

.080 

.040 

.020

Velocity 

(fps)

w.s. 

1.47 

1.50 

1.50 

1.44 

1.38 

1.32 

1.22 

1.11 

1.04 

.94

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.974 

.894 

.697 

.547 

.397 

.297 

.197 

.147 

.097 

.057 

.027

.982 

.905 

.855 

.755 

.655 

.555 

.455 

.355 

.255 

.155 

.105 

.065 

.030

1.008 

.955 

.855 

.755 

.655 

.555 

.455 

.355 

.255 

.155 

.105 

.065 

.030

1.005 

.975 

.875 

.775 

.625 

.525 

.475 

.375 

.275 

.175 

.125 

.075 

.035 

.005

.980 

.950 

.900 

.800 

.700 

.600 

.500 

.400

Velocity 

(fps)

w.s. 

1.58 

1.55 

1.52 

1.41 

1.35 

1.30 

1.25 

1.13 

1.00 

.93

w.s. 

1.82 

1.81 

1.75 

1.74 

1.70 

1.66 

1.62 

1.51 

1.47 

1.33 

1.28 

1.10

W.S.

1.98 

1.97 

1.92 

1.91 

1.86 

1.78 

1.70 

1.67 

1.55 

1.47 

1.39 

1.15

w.s. 

2.02 

1.97 

1.97 

1.93 

1.87 

1.83 

1.77 

1.71 

1.67 

1.55 

1.35 

1.09 

.69

w.s. 

2.00 

2.00 

2.01 

1.96 

1.92 

1.86 

1.81

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.972 

.930 

.830 

.680 

.530 

.380 

.280 

.180 

.130 

.080 

.050 

.020

Velocity 

(fps)

w.s. 

1.49 

1.51 

1.48 

1.45 

1.40 

1.36 

1.27 

1.25 

1.13 

1.02 

.91

Run

20 Con. 

21.... .

1Q

28

29- 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

.900 

.870 

.770 

.670 

.520 

.370 

.270 

.170 

.120 

.070 

.020

1.045 

.995 

.895 

.695 

.495 

.395 

.295 

.195 

.145 

.095 

.055 

.025

Velocity 

(fps)

w.s. 

2.23 

2.22 

2.18 

2.10 

2.06 

1.94 

1.81 

1.72 

1.63 

1.06

w.s. 

2.25 

2.21 

2.15 

2.06 

2.00 

1.97 

1.84 

1.78 

1.72 

1.56 

1.44

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.300 

.200 

.150 

.100 

.050 

.030 

.010

1.060 

1.030 

.900 

.750 

.650 

.550 

.450 

.350 

.250 

.200 

.150 

.100 

.060 

.030

1.040 

.950 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.060 

.030

.480 

.450 

.400 

.350 

.300 

.250 

.200 

.150 

.100 

.070 

.040

Velocity 

(fps)

1.75 

1.64 

1.57 

1.44 

1.25 

1.16 

.80

w.s. 

2.23 

2.22 

2.13 

2.13 

2.06 

.97 

.92 

.88 

.84 

.74 

.49 

1.37 

1.23

w.s. 

2.33 

2.27 

2.19 

2.12 

2.02 

1.90 

1.83 

1.72 

1.60 

1.40

w.s. 

1.65 

1.64 

1.63 

1.60 

1.53 

1.49 

1.45 

1.40 

1.34 

1.21

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.985 

.955 

.905 

.805 

.705 

.605 

.505 

.405 

.305 

.205 

.165 

.125 

.085 

.045 

.025 

.015

1.012 

.982 

.882 

.782 

.682 

.582 

.482 

.382 

.282 

.182 

.132 

.082 

.052 

.022

1.025 

.975 

.825 

.675 

.575 

.475 

.375 

.275 

.175 

.125 

.075 

.035

Velocity 

(fps)

w.s. 

2.23 

2.21 

2.17 

2.14 

2.10 

2.06 

1.99 

1.86 

1.80 

1.79 

1.68 

1.53 

1.31 

1.19 

1.01

w.s. 

2.29 

2.30 

2.27 

2.25 

2.22 

2.16 

2.07 

1.98 

1.91 

1.81 

1.68 

1.65 

1.41

w.s. 

2.30 

2.30 

2.25 

2.17 

2.13 

2.09 

2.00 

1.85 

1.75 

1.64 

1.46
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 

TABLE 16. Velocity-profile data for 0.9-8mm sand in 8-foot-wide flume Continued

187

Run

29 Con. 

22....... ......

30-- 

31.... 

15 

23-- 

32--. 

24.... 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.485 

.450 

.420 

.370 

.320 

.270 

.220 

.170 

.120 

.080 

.050 

.020

.935 

.900 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.060 

.030

.510 

.490 

.440 

.390 

.340 

.290 

.240 

.190 

.140 

.100 

.070 

.040 

.030 

.010

Velocity 

(fps)

w.s. 

1.80 

1.78 

1.76 

1.74 

1.72 

1.64 

1.62 

1.49 

1.45 

1.29 

.96

w.s. 

2.48 

2.51 

2.51 

2.40 

2.24 

2.18 

2.13 

2.09 

1.87 

1.82

W.S. 

2.03 

2.03 

2.05 

2.01 

1.99 

1.97 

1.91 

1.86 

1.76 

1.65 

1.51 

1.39 

1.23

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.020 

.010

.459 

.429 

.379 

.329 

.279 

.229 

.179 

.129 

.079 

.044 

.024

.496 

.466 

.416 

.366 

.316 

.266 

.216 

.166 

.116 

.076 

.046 

.026 

.008

.505 

.470 

.400 

.340 

.290 

.240 

.190 

.140 

.090 

.050 

.020

1.013 

.950 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.060 

.030

.490 

.470 

.430 

.380 

.330 

.280 

.230 

.180 

.130 

.090 

.060 

.030 

.010

Velocity 

(fps)

1.10 

1.01

w.s. 

1.65 

1.62 

1.61 

1.59 

1.54 

1.52 

1.41 

1.32 

1.25 

1.16

W.S. 

1.78 

1.75 

1.74 

1.68 

1.66 

1.61 

1.56 

1.49 

1.38 

1.28 

1.13 

.99

w.s. 

1.80 

1.76 

1.74 

1.68 

1.63 

1.60 

1.48 

1.43 

1.23 

1.08

w.s. 

2.50 

2.41 

2.26 

2.26 

2.01 

1.91 

1.91 

.88 

1.85 

1.83

W.S. 

2.08 

2.06 

2.00 

1.97 

1.95 

1.90 

1.84 

1.75 

1.67 

1.55 

1.29 

1.22

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.500 

.470 

.420 

.370 

.320 

.270 

.220 

.170 

.130 

.090 

.060 

.040 

.020

1.077 

1.050 

.950 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.060 

.030

.480 

 .450 

.400 

.350 

.300 

.250 

.200 

.150 

.120 

.090 

.060 

.030 

.010

.500 

.470 

.420 

.370 

.320 

.270 

.220 

.170 

.130 

.100 

.070 

.040 

.010

.490 

.460 

.410 

.360 

.310 

.260 

.210 

.160 

.110 

.070 

.040 

.020

Velocity 

(fps)

w.s. 

1.80 

1.78 

1.77 

1.77 

1.68 

1.68 

1.62 

1.55 

1.45 

1.37 

1.24 

1.12

W.S. 

2.60 

2.52 

2.39 

2.30 

2.14 

2.08 

1.98 

1.93 

1.80 

1.73 

1.75

w.s. 

1.87 

1.83 

1.82 

1.76 

1.70 

1.64 

1.62 

1.55 

1.48 

1.40 

1.20 

.95

w.s. 

2.01 

2.02 

2.00 

.98 

.95 

.92 

.85 

.80 

.71 

.63 

.47 

.21

w.s. 

1.98 

2.01 

1.92 

1.91 

1.88 

1.78 

1.73 

1.60 

1.49 

1.37 

1.21

Run

14

34 

16. 

35- 

17 .

33 

5-... 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.562 

.540 

.480 

.430 

.380 

.330 

.280 

.240 

.200 

.160 

.130 

.100 

.070 

.040 

.020

.540 

.510 

.460 

.410 

.360 

.310 

.260 

.210 

.160 

.110 

.060 

.030 

.010

1.006 

.950 

.800 

.700 

.600 

.500 

.400 

.300 

.200 

.150 

.100 

.060 

.030

.580 

.540 

.490 

.440 

.390 

.340 

.290 

.240 

.190 

.140 

.110 

.080 

.050 

.010

1.196 

1.160 

1.060 

.960 

.860 

.760 

.660 

.560 

.460 

.360 

.310 

.260 

.210 

.160 

.160 

.060

.500 

.470 

.440 

.390 

.340 

.290 

.240 

.190 

.140 

.090 

.050 

.020

1.105 

1.050 

.950 

.750 

.600 

.500

Velocity 

(fps)

w.s. 

2.16 

2.13 

2.10 

2.06 

2.03 

1.94 

1.92 

1.85 

1.80 

1.72 

1.66 

1.56 

1.35 

1.26

w.s. 

2.21 

2.20 

2.18 

2.15 

2.10 

2.02 

.98 

.88 

.78 

.66 

.47 

.31

w.s. 

2.55 

2.46 

2.44 

2.39 

2.26 

2.15 

2.00 

.90 

.76 

.57 

.37 

.30

w.s. 

2.20 

2.21 

2.28 

2.24 

2.25 

2.16 

2.16 

2.12 

2.00 

1.86 

1.81 

1.56 

.74

w.s. 

2.67 

2.62 

2.55 

2.51 

2.47 

2.44 

2.34 

2.21 

2.11 

2.11 

2.08 

1.88 

.84 

.64 

.58

w.s. 

2.34 

2.30 

2.31 

2.26 

2.23 

2.18 

2.15 

2.15 

2.05 

1.88 

1.62

w.s. 

2.85 

2.75 

2.52 

2.52 

2.48

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.548 

.530 

.480 

.430 

.380 

.330 

.290 

.250 

.210 

.180 

.150 

.120 

.090 

.060 

.030

.530 

.500 

.450 

.400 

.350 

.300 

.250 

.200 

.150 

.110 

.070 

.040 

.020

.993 

.966 

.866 

.666 

.466 

.316 

.216 

.166 

.116 

.066 

.016

.560 

.510 

.460 

.410 

.360 

.310 

.260 

.210 

.160 

.110 

.070 

.040 

.010

.948 

.900 

.800 

.700 

.600 

.500 

.400 

.300 

.200 

.150 

.100 

.060 

.030

.460 

.420 .370- 

.320 

.270 

.220 

.170 

.120 

.080 

.050 

.020

1.025 

1.000 

.845 

.695 

.545 

.395

Velocity 

(fps)

w.s. 

2.17 

2.18 

2.16 

2.13 

2.08 

1.99 

1.98 

1.97 

1.89 

1.84 

1.77 

1.68 

1.62 

1.49

w.s. 

2.28 

2.24 

2.18 

2.13 

2.11 

1.99 

1.90 

1.86 

1.79 

1.58 

1.38 

.96

w.s. 

2.71 

2.66 

2.60 

2.36 

2.13 

1.94 

1.88 

1.83 

1.75 

1.43

w.s. 

2.43 

2.42 

2.34 

2.32 

2.36 

2.26 

2.20 

1.98 

1.47 

1.12 

.98 

.93

w.s. 

2.66 

2.65 

2.57 

2.55 

2.55 

2.47 

2.33 

2.12 

2.00 

2.02 

1.99 

1.84

w.s. 

2.63 

2.67 

2.65 

2.61 

2.53 

2.42 

2.36 

2.20 

2.08 

1.79

w.s. 

2.74 

2.65 

2.61 

2.40 

2.26

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.577 

.560 

.520 

.470 

.420 

.370 

.320 

.280 

.240 

.200 

.160 

.130 

.100 

.070 

.040 

.020

.510 

.480 

.430 

.380 

.330 

.280 

.230 

.180 

.130 

.080 

.050 

.030 

.010

.995 

.900 

.700 

.500 

.400 

.300 

.250 

.200 

.150 

.100 

.060 

,030

.550 

.520 

.470 

.420 

.370 

.320 

.270 

.220 

.170 

.120 

.070 

.040 

.010

.890 

.860 

.780 

.690 

.590 

.490 

.390 

.290 

.240 

.190 

.140 

.090 

.060 

.030

.510 

.450 

.400 

.350 

.300 

.250 

.200 

.150 

.100 

.060 

.030

.955 

.875 

.675 

.525 

.375 

.275

Velocity 

(fps)

w.s. 

2.13 

2.14 

2.14 

2.09 

2.08 

1.99 

1.98 

1.92 

1.86 

1.79 

1.70 

1.62 

1.54 

1.41 

1.37

w.s. 

2.30 

2.27 

2.24 

2.12 

2.04 

2.04 

1.92 

1.82 

1.71 

1.60 

1.45 

1.22

W.S.

2.74 

2.66 

2.50 

2.40 

2.23 

2.30 

2.07 

2.02 

1.95 

1.94 

1.79

w.s. 

2.42 

2.44 

2.36 

2.32 

2.29 

2.14 

2.06 

1.97 

1.78 

1.58 

1.48 

1.33

w.s. 

2.99 

2.96 

2.91 

2.90 

2.87 

2.84 

2.71 

2.60 

2.37 

2.32 

2.18 

2.11 

1.85

W.S. 

2.56 

2.52 

2.48 

2.30 

2.31 

2.18 

2.16 

2.01 

2.00 

1.80

w.s. 

2.71 

2.76 

2.64 

2.47 

2.51
188 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 

TABLE 16. Velocity-profile data for 0.98-mm sand in 8-foot-wide flume Continued

Run

5 Con. 

10- - -

37.. -.

36- 

6- 

7.- 

38- .

11. 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.400 

.300 

.200 

.150 

.100 

.060 

.030

.380 

.350 

.300 

.250 

.210 

.170 

.140 

.110 

.080 

.050 

.020

.425 

.380 

.330 

.280 

.230 

.180 

.130 

.080 

.050 

.020

1.010 

.950 

.800 

.650 

.500 

.460 

.300 

.200 

.150 

.100 

.060 

.030

.411 

.350 

.300 

.250 

.200 

.150 

.100 

.060 

.030

.870 

.750 

.700 

.550 

.400 

.300 

.200 

.150 

.100 

.060 

.030

Velocity 

(fps)

2.44 

.71 

.52 

.51 

.41 

.45 

.49

w.s. 

2.63 

2.63 

2.60 

2.59 

2.56 

2.53 

2.49 

2.37 

2.32 

2.25

w.s. 

2.67 

2.69 

2.76 

2.49 

2.58 

2.51 

2.47 

2.43 

2.15

w.s. 

3.53 

3.53 

3.37 

3.11 

2.64 

1.74 

2.42 

2.08 

2.16 

2.04 

2.23

w.s. 

3.19 

3.18 

3.13 

3.06 

3.03 

2.57 

2.30 

2.40

w.s. 

4.09 

4.09 

3.75 

3.98 

3.82 

3.59 

3.53 

3.06 

2.60 

0.80

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.295 

.195 

.145 

.095 

.055 

.025

.452 

.390 

.340 

.300 

.260 

.220 

.180 

.140 

.100 

.070 

.030

.950 

.860 

.760 

.610 

.460 

.310 

.210 

.110 

.060 

.030

.450 

.420 

.390 

.340 

.290 

.240 

.190 

.140 

.090 

.050 

.020

.965 

.900 

.700 

.550 

.400 

.300 

.200 

.150 

.180 

.050

.505 

.470 

.420 

.370 

.320 

.270 

.220 

.170 

.120 

.100 

.060 

.030

1.010 

.880 

.800 

.650 

.500 

.350 

.200 

.100 

.060

.900 

.850 

.700 

.550 

.400 

.300 

.200 

.150 

.100 

.060 

.030

Velocity 

(fps)

2.13 

1.95 

1.58 

.58 

.58 

.73

w.s. 

2.72 

2.70 

2.67 

2.70 

2.47 

2.47 

2.49 

2.49 

2.47 

2.52

w.s. 

3.26 

3.10 

3.03 

2.99 

2.69 

2.50 

2.07 

1.29 

1.09

w.s. 

2.24 

2.66 

2.52 

2.35 

2.36 

2.36 

2.26 

2.43 

2.12 

2.05

w.s. 

3.20 

3.11 

3.20 

2.94 

3.11 

2.64 

2.85 

2.42 

1.70

w.s. 

3.23 

3.19 

2.98 

2.82 

2.54 

2.44 

1.97 

1.53 

1.82 

1.84 

1.76

w.s. 

3.64 

4.02 

3.68 

3.52 

3.39 

2.60 

2.41 

.51

w.s. 

3.90 

4.09 

4.02 

3.90 

3.75 

3.53 

3.57 

3.18 

3.34 

2.88

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.175 

.125 

.075 

.050 

.025

0.425 

.370 

.320 

.270 

.220 

.170 

.120 

.080 

.050 

.020

.555 

.520 

.420 

.320 

.220 

.170 

.120 

.080 

.050 

.020

.830 

.750 

.650 

.450 

.300 

.200 

.150 

.100 

.060 

.030

Velocity 

(fps)

2.36 

2.23 

2.01 

1.98 

2.14

w.s. 

1.66 

2.70 

2.61 

2.27 

2.43 

2.61 

2.55 

2.51 

2.80

w.s. 

2.81 

2.75 

2.76 

2.70 

2.57 

2.66 

2.60 

2.55 

2.48

w.s. 

3.34 

3.98 

4.16 

3.59 

2.70 

2.55 

1.34 

1.80 

1.75

Run

8-. -

13-- 

9--.- 

41 -. -

42..... 

40--.- 

43

39-.-.-- 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.550 

.500 

.450 

.410 

.370 

.330 

.290 

.250 

.210 

.170 

.130 

.090 

.060 

.030

.410 

.350 

.250 

.150 

.100 

.050

.440 

.410 

.360 

.310 

.260 

.210 

.160 

.120 

.090 

.060 

.030

.430 

.390 

.340 

.290 

.240 

.190 

.140 

.100 

.060 

.030

.360 

.310 

.260 

.210 

.160 

.110 

.060 

.030

.410 

.380 

.330 

.280 

.230 

.180 

.130 

.080 

.030

.470 

.430 

.390 

.340 

.290 

.240 

.190 

.140 

.100 

.060 

.030

Velocity 

(fps)

w.s. 

3.20 

3.24 

3.31 

3.23 

3.07 

3.00 

2.91 

2.94 

2.71 

2.61 

2.35 

2.07 

.88

w.s. 

5.92 

5.42 

4.52 

4.29 

4.22

w.s. 

6.72 

6.24 

5.21 

3.95 

3.60 

3.25 

2.52 

2.05 

1.14 

2.17

w.s. 

6.88 

6.80 

6.61 

6.38 

6.12 

5.82 

5.42 

4.96 

3.52

W.S. 

6.17 

5.92 

5.60 

5.01 

3.95 

2.66 

1.36

w.s. 

7.02 

6.91 

6.76 

6.53 

6.37 

5.87 

5.27 

3.12

w.s. 

7.09 

6.84 

6.63 

6.76 

6.41 

6.16 

5.64 

5.32 

2.64 

1.36

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.422 

.390 

.340 

.300 

.260 

.220 

.180 

.140 

.100 

.060 

.030

.750 

.550 

.450 

.350 

.250 

.150 

.100 

.050

.400 

.360 

.310 

.260 

.210 

.160 

.110 

.060 

.030

.430 

.380 

.330 

.280 

.230 

.180 

.130 

.090 

.060 

.030

.340

.300 

.260 

.210 

.160 

.110 

.060 

.030

.420 

.380 

.330 

.280 

.230 

.180 

.130 

.090 

.060 

.030

.410 

.390 

.340 

.290 

.240 

.190 

.140 

.100 

.060 

.030

Velocity 

(fps)

w.s. 

3.52 

3.52 

3.52 

3.20 

3.08 

2.77 

2.60 

2.41 

2.37 

2.41

w.s. 

4.85 

4.85 

4.09 

4.22 

3.52 

3.37 

2.64

w.s. 

5.64 

5.78 

5.56 

4.85 

4.58 

3.94 

2.94 

2.18

w.s. 

7.20 

6.88 

6.68 

6.49 

6.21 

5.74 

5.17 

3.95 

1.36

w.s. 

6.61 

6.25 

6.08 

5.74 

5.32 

4.75 

2.18

w.s. 

7.23 

7.23 

7.02 

6.65 

6.27 

5.92 

5.52 

4.40 

5.13

w.s. 

7.35 

7.16 

6.99 

6.68 

6.30 

5.87 

5.46 

4.22 

2.18

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.372 

.350 

.300 

.250 

.210 

.170 

.130 

.090 

.060 

.030

.540 

.450 

.350 

.250 

.150 

.100 

.050

.500 

.450 

.400 

.350 

.300 

.250 

.200 

.150 

.100 

.060 

.030

.420 

.350 

.300 

.250 

.200 

.150 

.100 

.060 

.030

.470 

.430 

.380 

.330 

.280 

.230 

.180 

.130 

.090 

.060 

.030

.300 

.280 

.260 

.210 

.160 

.110 

.060 

.030

.400 

.360 

.310 

.260 

.210 

.160 

.110 

.060 

.030

.450 

.420 

.400 

.350 

.300 

.250 

.200 

.150 

.100 

.060 

.030

Velocity 

(fps)

w.s. 

3.20 

3.20 

3.52 

3.12 

3.12 

2.94 

3.20 

3.28 

.76

w.s. 

4.96 

4.63 

3.95 

3.54 

3.52 

3.12

w.s. 

3.75 

3.52 

3.83 

3.45 

3.52 

2.42 

2.65 

2.93 

3.03 

2.75

w.s. 

5.96 

5.17 

4.85 

5.12 

4.70 

4.46 

3.82 

3.20

w.s. 

7.35 

7.13 

6.95 

6.74 

6.46 

6.25 

5.63 

4.02 

1.12 

0.38

w.s. 

6.53 

5.79 

5.37 

5.17 

4.70 

4.19 

1.36

w.s. 

7.61 

7.44 

7.30 

7.02 

6.63 

6.04 

5.01 

3.45

w.s. 

7.41 

7.37 

7.23 

7.06 

6.64 

6.37 

5.78 

4.64 

3.89 

.58
SUMMARY OF ALLUVIAL CHANNEL DATA FEOM FLUME EXPERIMENTS, 1956-61 189

TABLE 17. Velocity-profile data for O.S2-mm sand in 2-foot-wide flume

[w.s.=water surface]

Run

3-... 

4 _ -

5 __ .........

6...........

21............

7.............

8..... . .

0.5 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.522 

.480 

.410 

.310 

.210 

.110 

.060 

.035 

.023 

.010

.600 

.550 

.450 

.350 

.250 

.150 

.125 

.100 

.075 

.040 

.025

.570 

.520 

.420 

.320 

.220 

.120 

.095 

.070 

.045 

.024

.595 

.545 

.445 

.345 

.245 

.145 

.095 

.045 

.020

.615 

.565 

.465 

.365 

.265 

.165 

.115 

.090 

.065 

.040 

.019

.562 

.512 

.412 

.312 

.212 

.112

Velocity 

(fps)

w.s. 

2.04 

2.04 

2.04 

2.04 

2.04 

2.04 

2.04 

1.95 

1.94

w.s. 

1.49 

1.56 

1.45 

1.40 

1.28 

1.24 

1.17 

1.05 

1.09 

.85

w.s.

a 57

6.68 

6.28 

6.02 

5.29 

4.85 

4.70 

4.60 

4.64

w.s. 

5.88 

5.96 

5.86 

5.72 

5.30 

5.18 

2.76 

1.42

w.s. 

3.96 

4.05 

3.70 

3.68 

3.36 

3.37 

3.00 

2.86 

2.60 

.87

W.S.

3.65 

3.97 

3.98 

3.51 

3.61

1.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.610 

.510 

.410 

.310 

.210 

.180 

.135 

.110 

.080 

.060 

.019

.575 

.525 

.425 

.325 

.225 

.125 

.075 

.050 

.025

.675 

.625 

.525 

.425 

.325 

.225 

.175 

.150 

.125 

.100 

.075 

.050 

.026

.545 

.495 

.445 

.345 

.245 

.195 

.145 

.120 

.095 

.070 

.045 

.020

.600 

.550 

.450 

.350 

.250 

.150 

.100 

.075 

.050 

.022

.620 

.570 

.520 

.470 

.420 

.320

Velocity 

(fps)

w.s. 

1.73 

1.72 

1.58 

1.52 

1.54 

1.24 

1.13 

.97 

.90 

.74

w.s. 

6.63 

6.69 

6.41 

6.21 

5.12 

4.12 

4.28 

4.60

w.s. 

6.56 

6.60 

6.68 

6.42 

6.07 

5.60 

5.25 

4.78 

4.45 

3.64 

2.88 

2.29

W.S.

3.80 

3.69 

3.64 

3.44 

3.28 

3.29 

3.01 

3.28 

3.07 

2.75 

1.75

WJ5.

3.96 

4.14 

4.06 

3.99 

3.47 

3.28 

2.96 

2.94 

2.13

w.s. 

3.60 

3.69 

4.41 

4.35 

4.01

1.5 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.500 

.450 

.350 

.250 

.150 

.100 

.050 

.025

.550 

.500 

.400 

.300 

.200

.660 

.610 

.510 

.410 

.310 

.210 

.160 

.110 

.085 

.060 

.025

.650 

.600 

.500 

.400 

.300 

.200 

.150 

.125 

.100 

.075 

.050 

.021

.610 

.565 

.465 

.365 

.265 

.165 

.115 

.090 

.065 

.040 

.019

.675 

.625 

.525 

.425 

.325 

.225

Velocity 

(fps) "

w.s. 

1.76 

1.66 

1.54 

1.30 

1.22 

1.10 

.91

w.s. 

1.59 

1.61 

1.57 

1.31

w.s. 

5.90 

6.20 

5.98 

5.69 

5.20 

5.16 

4.07 

3.80 

3.64 

2.81

w.s. 

5.75 

5.97 

5.91 

5.86 

5.56 

5.24 

4.35 

4.15 

3.96 

3.72 

2.76

W.S.

3.67 

3.99 

3.98 

3.63 

3.21 

2.86 

2.63 

2.75 

2.27 

1.05

W.S.

2.88 

3.14 

3.57 

3.84 

3.32

Run

8 Con. 

20---. 

10---. 

9--... 

19

11.-.. 

0.5 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.062 

.037 

.019

.511 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025 

.010

.531 

.450 

.350 

.250 

.150 

.100 

.050 

.025 

.012

.585 

.535 

.435 

.335 

.285 

.235 

.210 

.185 

.160 

.135 

.110 

.085 

.060 

.035 

.008

.643 

.575 

.475 

.375 

.275 

.175 

.125 

.075 

.050 

.025 

.010

.546 

.525 

.475 

.375 

.275 

.175 

.125 

.075 

.050 

.025 

.010

Velocity 

(fps)

3.26 

3.15 

2.27

w.s. 

5.63 

5.76 

5.66 

5.27 

5.27 

4.74 

4.53 

4.06 

3.39 

2.50

w.s. 

5.81 

5.70 

5.24 

4.91 

4.85 

4.18 

3.66 

2.17

W.S.

5.77 

5.85 

5.83 

5.76 

5.63 

5.38 

5.28 

5.26 

4.93 

4.62 4:42

3.78 

1.92 

1.15

w.s. 

5.20 

5.27 

5.16 

4.96 

4.80 

4.56 

4.04 

3.70 

3.20 

2.30

w.s. 

5.98 

6.07 

6.09 

5.86 

5.37 

5.24 

4.59 

4.05 

2.89 

1.88

1.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.220 

.120 

.070 

.045 

.020

.506 

.450 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025 

.012

.585 

.535 

.435 

.335 

.235 

.185 

.135 

.085 

.060 

.035 

.010

.540 

.475 

.375 

.275 

.175 

.125 

.075 

.050 

.025 

.009

.544 

.486 

.436 

.386 

.336 

.286 

.236 

.186 

.136 

.111 

.086 

.061 

.036 

.011

.632 

.575 

.475 

.375 

.275 

.175 

.125 

.075 

.050 

.025 

.011

.562 

.525 

.475 

.375 

.275 

.175 

.125 

.075 

.050 

.025 

.012

Velocity 

(fps)

3.88 

3.70 

3.69 

3.00 

2.62

w.s. 

6.03 

5.98 

6.08 

5.80 

5.36 

4.91 

4.77 

4.31 

3.31 

2.60

WJ5.

5.93 

5.86 

5.63 

5.36 

5.13 

4.55 

4.09 

2.48 

1.56 

1.98

w.s. 

5.21 

5.15 

4.83 

4.80 

4.58 

4.48 

3.96 

3.05 

2.16

W.S.

a 14

6.00 

6.09 

6.07 

5.82 

5.91 

5.68 

5.31 

5.18 

4.82 

4.20 

3.16 

1.75

WJ5.

5.25 

5.26 

5.24 

5.18 

4.98 

4.60 

4.26 

3.84 

3.41 

2.27

W.S.

6.03 

5.86 

5.61 

5.45 

5.08 

4.80 

4.40 

3.90 

3.15 

2.60

1.5 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.175 

.125 

.075 

.050 

.025

.592 

.440 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025 

.009

.529 

.475 

.375 

.275 

.175 

.125 

.075 

.050 

.025 

.008

.544 

.444 

.344 

.294 

.244 

.194 

.144 

.219 

.094 

.074 

.050 

.025 

.011

.642 

.575 

.475 

.375 

.275 

.175 

.125 

.075 

.050 

.025 

.009

.540 

.525 

.475 

.375 

.275 

.175 

.125 

.075 

.050 

.025 

.009

Velocity 

(fps)

3.35 

3.33 

3.21 

2.62 

2.20

W.S.

5.93 

5.79 

5.68 

5.11 

5.01 

4.64 

4.50 

3.92 

3.64 

2.85

w.s. 

5.80 

5.61 

5.29 

4.96 

4.66 

4.48 

4.08 

3.38 

2.36

W.S.

5.81 

5.61 

5.48 

5.47 

5.30 

5.08 

4.65 

4.36 

3.96 

3.04 

2.11 

1.85

W.S.

5.22 

5.28 

5.21 

5.02 

4.74 

4.46 

4.12 

3.81 

3.13 

2.40

W.S.

6.01 

6.14 

6.03 

5.88 

5.48 

5.61 

4.97 

4.58 

3.61 

1.68

791-597 O 66
190 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 18. Velocity-profile data for 0.88-mm (uniform) sand in ^-foot-wide flume

[w.s.=water surface]

Run

8. . _ ......

5....... ... ...

0.5 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

Velocity 

(fps)

1.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.435 

.390 

.340 

.290 

.240 

.190 

.140 

.090 

.065 

.040 

.015

.456 

.420 

.400 

.350 

.250 

.200

Velocity 

(fps)

w.s. 

1.29 

1.24 

1.26 

1.17 

1.17 

.95 

.90 

.80 

.71 

.72

w.s. 

1.66 

1.62 

1.58 

1.44 

1.35

1.5 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

Velocity 

(fps)

Run

5 Con. 

1 . 

0.5 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

Velocity 

(fps)

1.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.150 

.100 

.060 

.030

.520 

.495 

.445 

.395 

.345 

.295 

.245 

.195 

.145 

.095 

.045 

.020

Velocity 

(fps)

1.31 

1.25 

1.13 

.83

w.s. 

4.60 

4.70 

4.60 

4.55 

4.49 

140 

4.19 

4.06 

3.83 

3.42 

3.11

1.5 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

Velocity 

(fps)

TABLE 19. Velocity-profile data for 0.8S-mm (graded) sand in 2-foot-wide flume

[w.s.=water surface]

Run

16... ... ..

6.. ......,..._

5-. .

1 .. ..

Distance 

above sand 

bed (ft)

Velocity 

(fps)

O.C ft from left wall of 

flume

1.0 ft from I 

flun 

0.493 

.490 

.460 

.410 

.360 

.310 

.260 

.210 

.160 

.110 

.070 

.040 

.020

0.6 ft from I 

flur 

0.480 

.430 

.380 

.330 

.280 

.230 

.180 

.130 

.080 

.050 

.030 

.020

eft watt of 

ie 

w.s. 

1.40 

1.36 

1.42 

1.39 

1.34 

1.30 

1.26 

1.14 

1.07 

.93 

.79 

.68

eft wall of 

ne 

w.s. 

2.62 

2.62 

2.59 

2.51 

2.43 

2.33 

2.23 

1.98 

1.83 

1.56 

1.38

Distance 

above sand 

bed (ft)

1.0 ft from I 

flun 

0.510 

.490 

.450 

.400 

.350 

.300 

.250 

.200 

.150 

.100 

.060 

.040 

.020

.548 

.528 

.493 

.480 

.430 

.380 

.330 

.280 

.230 

.180 

.130 

.090 

.060 

.040 

.020

.533 

.510 

.460 

.410 

.360 

.310 

.260 

.210 

.160 

.110 

.070 

.040 

.020

.498 

.460 

.410 

.360 

.310 

.260 

.210 

.160 

.110 

.060 

.020 

.010

Velocity 

(fps)

eft wall of 

ie 

w.s. 

1.25 

1.25 

1.19 

1.16 

1.13 

1.13 

1.10 

1.10 

1.10 

1.10 

1.19 

1.22

w.s. 

0.62 

.63 

.60 

.60 

.61 

.59 

.58 

.58 

.56 

.53 

.52 

.52 

.51 

.50

W.S.

1.39 

1.37 

1.44 

1.38 

1.33 

1.28 

1.25 

1.20 

1.11 

1.05 

.90 

.77

w.s. 

2.63 

2.66 

2.66 

2.56 

2.56 

2.50 

2.38 

2.25 

2.07 

1.89 

1.64

Distance 

above sand 

bed (ft)

Velocity 

(fps)

1.5 ft from left wall of 

flume

0.530 

.490 

.440 

.390 

.340 

.290 

.240 

.190 

.140 

.090 

.050 

.030 

.020

w.s. 

2.51 

2.64 

2.67 

2.64 

2.61 

2.49 

2.36 

2.15 

2.02 

1.77 

1.36 

1.15

Run

10-.. 

9-- 

7--. - 

Distance 

above sand 

bed (ft)

1.0 ft from I 

flur 

0.444 

.425 

.375 

.325 

.275 

.225 

.175 

.125 

.075 

.060 

.040 

.020

.515 

.495 

.440 

.390 

.340 

.290 

.240 

.190 

.140 

.090 

.050 

.030 

.020

.534 

.514 

.490 

.440 

.390 

.340 

.290 

.240 

.190 

.140 

.090 

.060 

.040 

.020

.630 

.600 

.540 

.490 

.440 

.390 

.340 

.290 

.240 

.190 

.140 

.090 

.060 

.040 

.020

Velocity 

(fps)

eft watt of 

ne 

w.s. 

2.51 

2.51 

2.43 

2.47 

2.37 

2.30 

2.31 

1.95 

1.99 

1.90 

1.62

w.s. 

2.59 

2.69 

2.66 

2.59 

2.51 

2.44 

2.37 

2.36 

2.15 

1.90 

1.78 

1.62

w.s. 

1.98 

2.09 

2.11 

2.11 

2.11 

2. 15 

2.13 

2.00 

1.91 

1.78 

1.65 

.99 

1.14

w.s. 

1.93 

1.92 

1.85 

1.81 

1.77 

1.75 

1.72 

1.72 

1.64 

1.60 

1.58 

1.58 

1.41 

1.31

Distance 

above sand 

bed (ft)

Velocity 

(fps)

1 .0 ft from left wall 

of flume

0.640 

.620 

.550 

.500 

.450 

.400 

.350 

.300 

.250 

.200 

.150 

.100 

.060 

.040 

.020

.560 

.540 

.490 

.440 

.390 

.340 

.290 

.240 

.190 

.140 

.100 

.060 

.040 

.020

W.S.

1.94 

1.85 

1.78 

1.74 

1.68 

1.67 

1.63 

1.54 

1.49 

1.44 

1.43 

1.43 

1.43 

1.43

w.s. 

2.66 

2.81 

3.00 

2.88 

2.97 

2.98 

3.02 

2.97 

2.75 

2.39 

2.14 

1.97 

1.80

Distance 

above sand 

bed (ft)

Velocity 

(fps)

1.0 ft from left watt 

of flume

0.621 

.601 

.540 

.490 

.440 

.390 

.340 

.290 

.240 

.190 

.140 

.090 

.060 

.040 

.020

w.s. 

2.06 

2.08 

2.08 

2.04 

2.04 

1.98 

1.96 

1.92 

1.61 

1.60 

1.39 

1.36 

1.31 

1.33
SUMMARY OP ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 

TABLE 19. Velocity-profile data for 0.33-mm (graded) sand in 2-foot-wide flume Continued

191

Run

2. ...... ......

Distance 

above sand 

bed (ft)

Velocity 

(fps)

1.0 ft from left watt 

of flume

Distance 

above sand 

bed (ft)

1.0 ft from 

of flu 

0.528 

.485 

.450 

.400 

.350 

.300 

.250 

.200 

.150 

.100 

.060 

.040 

.020

Velocity 

(fps)

left watt 

me 

w.s. 

3.40 

3.36 

3.23 

3.12 

3.09 

2.96 

2.94 

2.97 

2.85 

2.73 

2.61 

2.08

Distance 

above sand 

bed (ft)

Velocity 

(fps)

1.5 ft from left wall 

of flume

Run

3-..._ 

Distance 

above sand 

bed (ft)

Velocity 

(fps)

1.0 ft from left watt 

of flume

Distance 

above sand 

bed (ft)

1.0 ft from 

of flu 

0.540 

.490 

.440 

.390 

.340 

.290 

.240 

.190 

.140 

.090 

.040 

.020

Velocity 

(fps)

left watt 

me 

w.s. 

3.88 

3.75 

3.82 

3.45 

3.52 

3.52 

3.45 

3.12 

2.84 

2.64 

2.18

Distance 

above sand 

bed (ft)

Velocity 

(fps)

1.5 ft from left watt 

of flume

TABLE 20. Velocity-profile data, for 0.47-mm sand in 8-foot-mde flume 

[The lateral section used for measuring was 95-115 ft from the headbox. w.s.=water surface; r.f., reversed flow as indicated by negative pressure on manometer]

Run

46.... .. 

47--.. 

48...- ..

49 .. 

85.. 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.938 

.843 

.743 

.643 

.543 

.443 

.343 

.293 

.243 

.193 

.143 

.093 

.068 

.043 

.018

.710 

.673 

.573 

.473 

.373 

.273 

.223 

.173 

.148 

.123 

.098 

.073 

.048 

.023

1.232 

1.147 

1.047 

.847 

.647 

.447 

.347 

.247 

.197 

.147 

.122 

.097 

.072 

.047 

.022

1.240 

1.180 

1.130 

.930 

.730 

.530 

.430 

.330 

.286 

.255 

.230 

.205 

.180 

.130 

.030

.795 

.750 

.600

Velocity 

(fps)

W.S.

.94 

.95 

.92 

.86 

.74 

.23 

0.96 

1.00 

0.94 

1.56 

1.49 

1.22 

1.31 

1.30

w.s. 

1.78 

1.74 

1.70 

1.65 

1.63 

1.62 

1.55 

1.46 

1.44 

1.44 

1.56 

1.56 

1.48

w.s. 

1.91 

1.88 

1.85 

1.81 

1.79 

1.78 

1.70 

1.71 

1.69 

1.66 

1.58 

1.51 

1.43 

1.28

w.s. 

3.02 

3.07 

2.99 

2.89 

2.81 

2.51 

1.84 

1.10 

.96 

.63 

.63 

.42 

r.f. 

r.f.

w.s. 

1.47 

1.36

4.0 ft from left waU 

of flume

Distance 

above sand 

bed (ft)

1.489 

1.400 

1.200 

1.000 

.800 

.600 

.225 

.050 

.025

.659 

.618 

.518 

.418 

.318 

.268 

.218 

.168 

.118 

.093 

.068 

.043 

.018

1.247 

1.157 

.957 

.757 

.557 

.357 

.257 

.207 

.157 

.132 

.107 

.082 

.057 

.032

1.220 

1.160 

1.100 

.900 

.700 

.500 

.300 

.200 

.150 

.100 

.075 

.050

.770 

.700 

.550

Velocity 

(ftfs)

w.s. 

2.24 

2.27 

2.26 

2.10 

r.f. 

r.f. 

r.f. 

.35

w.s. 

1.98 

1.95 

1.94 

1.92 

1.89 

1.82 

1.81 

1.80 

1.80 

1.77 

1.69 

1.62

w.s. 

1.81 

1.81 

1.79 

1.75 

1.75 

1.49 

1.30 

1.08 

.90 

.77 

.79 

.92 

1.05

w.s. 

2.93 

2.93 

2.97 

2.97 

2.87 

2.58 

2.34 

2.16 

2.20 

2.41 

1.86

w.s. 

1.43 

1.36

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

1.576 

1.481 

1.381 

1.181 

.981 

.781 

.581 

.481 

.381 

.281 

.081 

.006

.803 

.753 

.653 

.553 

.453 

.353 

.303 

.253 

.228 

.203 

.178 

.153 

.128 

.103 

.078 

.053 

.028

1.011 

.918 

.718 

.518 

.318 

.218 

.168 

.118 

.093 

.068 

.043 

.018

1.710 

1.675 

1.475 

1.075 

.875 

.675 

.575 

.475 

.425 

.375 

.350 

.325 

.275

.075

.035

.775 

.700 

.550

Velocity 

(fps)

w.s. 

2.05 

2.05 

1.86 

1.68 

1.62 

1.62 

1.31 

.25 

r.f. 

r.f. 

r.f.

w.s. 

1.92 

1.88 

1.87 

1.78 

1.72 

1.74 

1.70 

1.65 

1.63 

1.62 

1.58 

1.56 

1.53 

1.38 

1.18 

1.15

W.S.

1.84 

1.86 

1.84 

1.89 

1.77 

1.75 

1.74 

1.69 

1.66 

1.56 

1.28

w.s. 

3.21 

3.21 

3.12

2.86

w.s. 

1.43 

1.36

Bun

85 Con. 

86.. _ . _

87- 

88-. .

QO

QQ

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.450 

.350 

.250 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.800 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.785 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.780 

.730 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.600 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.625 

.600 

.500 

.400 

.300 

.200 

.150 

.100 

.075

Velocity 

(fps)

1.28 

1.22 

1.15 

1.03 

.93 

.86 

.93 

.93 

.89 

.93

w.s. 

1.40 

1.40 

1.24 

1.21 

1.13 

1.02 

.91 

.77 

.65 

.51 

.57

w.s. 

1.45 

1.34 

1.25 

1.13 

1.03 

.98 

.90 

.92 

.74 

.45 

.00

w.s. 

1.49 

1.43 

1.29 

1.24 

1.09 

1.01 

.93 

.88 

.72 

.50

w.s. 

1.65 

1.59 

1.55 

1.49 

1.45 

1.38 

1.35 

1.12 

.90

w.s. 

1.58 

1.53 

1.41 

1.36 

1.23 

1.12 

1.08 

.97

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.400 

.300 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.810 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.775 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.775 

.725 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.595 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.630 

.600 

.500 

.400 

.300 

.200 

.150 

.100 

.075

Velocity 

(fps)

1.31 

1.23 

1.16

1.08 

.99 

.97 

.86

.78 

.72

w.s. 

1.43 

1.32 

1.24 

1.21 

1.07 

1.02 

.99 

.96 

.92 

.34 

.34

w.s. 

1.41 

1.26 

1.15 

1.16 

1.05 

1.05 

.88 

.86 

.83 

.80 

.74

w.s. 

1.48 

1.39 

1.33 

1.20 

1.06 

.91 

.78 

.73 

.56 

.61

W.S.

1.84 

1.76 

1.62 

1.63 

1.52 

1.45 

1.37 

1.24 

1.57

w.s. 

1.69 

1.65 

1.63 

1.59 

1.47 

1.36 

1.25 

1.19

6.0 ft from uleft waU 

of flme

Distance 

above sand 

bed (ft)

0.400 

.300 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.800 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.770 

.740 

.550 

.400 

.300 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.740 

.710 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.570 

.530 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.620 

.590 

.500 

.400 

.300 

.200 

.150 

.100 

.075

Velocity 

(fps)

1.30 

1.28 

1.13 

1.12 

1.05 

1.01 

.99 

.90 

.82

w.s. 

1.41 

1.31

1.22 

1.16 

1.02 

.98 

.87 

.85 

.84 

.71 

.30

w.s. 

1.59 

1.45 

1.36 

1.28 

1.14 

1.07 

1.03 

.99 

r.f. 

r.f. 

r.f.

w.s. 

1.49 

1.44 

1.28 

1.14 

1.09 

.97 

.82 

.74 

.61 

.51

W.S. 

1.95 

1.91 

1.83 

1.79 

1.74 

1.56 

1.47 

1.26 

.63

w.s. 

1.79 

1.76 

1.72 

1.69 

1.57 

1.52 

1.46 

1.34
192 SEDIMENT TRANSPORT IN ALLDVIAL CHANNELS

TABLE 20. Velocity-profile data for 0.47-mm sand in 8-foot-wide flume Continued

Run

89 Con. 

93 

92.... ..

91 

82 

51. .....

52. , .

73 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.050 

.025

.640 

.600 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.755 

.700 

.550 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.605 

.550 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.765 

.740 

.600 

.500 

.400 

.350 

.300 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.364 

.304 

.254 

.204 

.154 

.104 

.079 

.054 

.029

.897 

.847 

.697 

.597 

.497 

.397 

.347 

.297 

.272 

.247 

.222 

.197 

.147 

.097 

.047 

.022

.802 

.750 

.650 

.550 

.450 

.350 

.300 

.250

Velocity 

(fps)

0.51 

.42

w.s. 

1.80 

1.81 

1.79 

1.74 

1.67 

1.62 

1.64 

1.57 

1.48 

1.40

w.s. 

1.84 

1.81 

1.68 

1.31 

1.08 

1.06 

1.06 

1.10 

.96 

.90 

.95

w.s. 

1.84 

1.78 

1.64 

1.28 

1.28 

.97 

.71 

1.03 

.82 

.92

W.S.

2.03 

1.84 

1.72 

1.64 

1.68 

1.53 

.81 

.00 

.00 

.00 

.39 

.61 

.63

w.s. 

2.62 

2.63 

2.53 

2.61 

2.39 

2.23 

.88 

.69

w.s. 

2.09 

1.77 

1.64 

1.19 

.59 

.86 

.84 

.72 

.79 

.90 

1.14 

.00 

r.f. 

r.f. 

r.f.

w.s. 

2.23 

2.26 

2.16 

2.08 

1.93 

1.51 

.37

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.050 

.025

.540 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.740 

.700 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.530 

.490 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.795 

.750 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.417 

.357 

.307 

.257 

.207 

.157 

.107 

.082 

.057 

.042 

.027

.560 

.500 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.482 

.430 

.400 

.300 

.200 

.150 

.100 

.080

Velocity 

(fps)

1.08 

.50

W.S.

1.95 

1.93 

1.86 

1.82 

1.76 

1.72 

1.68 

1.60 

1.46

W.S.

1.79 

1.74 

1.63 

1.46 

1.32 

1.27 

1.23 

1.12 

.97 

.88

w.s. 

.50 

.53 

.51 

.43 

.35 

.19 

.05 

.98 

.74

w.s. 

2.12 

2.13 

2.13 

1.91 

1.80 

1.74 

1.82 

1.78 

1.46 

.59

w.s. 

2.12 

2.05 

1.97 

2.22 

2.22 

2.25 

1.97 

1.54 

.76 

.69

w.s. 

2.08 

2.09 

2.13 

2.02 

1.98 

1.85 

1.61 

1.30 

.80

W.S.

2.23 

2.57 

2.41 

2.33 

2.29 

2.20 

1.90

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.050 

.025

.530 

.500 

.350 

.250 

.150 

.100 

.075 

.050 

.025

.515 

.470 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.660 

.620 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.620 

.560 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.550 

.520 

.470 

.420 

.370 

.320 

.270 

.220 

.170 

.120 

.095 

.070 

.045 

.020

.507 

.490 

.460 

.410 

.360 

.310 

.260 

.210 

.160 

.110 

.060 

.035 

.015

.402 

.350 

.300 

.250 

.200 

.150 

.125 

.100

Velocity 

(fps)

1.22 

1.03

W.S.

2.07 

2.00 

1.86 

1.78 

1.67 

1.43 

.99 

.88

W.S.

1.80 

1.78 

1.74 

1.58 

1.22 

.73 

.76 

.82 

.86

w.s. 

1.93 

1.90 

1.82 

1.76 

1.66 

1.62 

1.55 

1.45 

1.38 

1.19

w.s. 

2.37 

2.44 

2.44 

2.36 

2.41 

2.16 

.99 

.33 

.48 

.30

w.s. 

2.11 

2.13 

2.10 

2.23 

2.08 

2.10 

2.13 

2.10 

2.23 

2.08 

1.81 

1.65 

1.51

w.s. 

2.17 

2.13 

2.23 

2.12 

2.12 

2.11 

2.07 

2.04 

1.97 

1.95 

1.96 

1.93

w.s.

2.48 

2.50 

2.47 

2.59 

2.56 

2.51 

2.50

Run

73 Con. 

74-.. __

76 - 

75 

53 

77 -

96

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.200 

.150 

.125 

.100 

.075 

.050 

.025

.695 

.640 

.570 

.470 

.370 

.320 

.270 

.220 

.170 

.130 

.100 

.080 

.060 

.040 

.020

.625 

.580 

.460 

.360 

.260 

.210 

.160 

.135 

.110 

.085 

.060 

.040 

.020

.655 

.590 

.500 

.400 

.300 

.250 

.225 

.200 

.175 

.150 

.125 

.100 

.080 

.060 

.040 

.020

.600 

.570 

.490 

.390 

.290 

.240 

.190 

.140 

.100 

.075 

.050 

.025

.690 

.620 

.450 

.350 

.250 

.200 

.150 

.125 

.100 

.080 

.060 

.040 

.020

.350 

.315 

.250 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

0.37 

.35 

.38 

.44 

.41 

.41 

.41

w.s. 

2.40 

2.55 

2.57 

2.55 

2.50 

2.29 

.37 

.35 

.35 

.35 

.33 

.31 

.30 

.28

w.s. 

2.29 

2.43 

2.46 

2.53 

2.34 

2.10 

1.93 

1.62 

.53 

.44 

.43 

.53

w.s. 

2.16 

2.24 

2.23 

2.31 

2.30 

2.21 

1.66 

.43 

.43 

.43 

.41 

.41 

.39 

.44 

.50

w.s. 

2.33 

2.39 

2.35 

1.97 

1.71 

1.78 

1.71 

1.64 

.83 

.35 

0

w.s. 

2.36 

2.36 

2.27 

2.21 

2.07 

1.90 

1.64 

1.51 

.52 

.43 

.42 

.43

w.s. 

2.39 

2.38 

2.37 

2.36 

2.33 

2.27 

2.00 

1.28

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.060 

.040 

.020

.635 

.600 

.450 

.350 

.250 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.625 

.580 

.460 

.360 

.260 

.160 

.110 

.085 

.060 

.040 

.020

.640 

.590 

.550 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.464 

.434 

.364 

.314 

.264 

.214 

.164 

.114 

.089 

.064 

.039 

.014

.895 

.855 

.825 

.725 

.625 

.525 

.425 

.325 

.275 

.225 

.175 

.135 

.100 

.075 

.050 

.025

.525 

.495 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

1.59 

.58 

.50

w.s. 

1.98 

1.97 

1.74 

1.68 

1.66 

1.58 

1.39 

.66 

.57 

.57 

.62

w.s. 

2.33 

2.36 

2.33 

2.30 

2.26 

2.13 

2.13 

2.05 

1.94 

1.90

w.s. 

1.84 

1.76 

1.70 

1.66 

1.86 

2.02 

1.98 

1.76 

.69 

.47 

.61

w.s. 

2.31 

1.95 

1.75 

1.63 

1.67 

1.64 

1.76 

1.71 

1.63 

1.53 

1.21

w.s. 

2.13 

2.10 

2.07 

1.97 

1.97 

1.78 

1.64 

1.57 

1.25 

.54 

.54 

.50 

.50 

.51 

.54

w.s. 

2.56 

2.55 

2.40 

1.55 

.96 

.50 

.57 

.79 

.84

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.075 

.050 

.025

.570 

.520 

.400 

.300 

.250 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.690 

.650 

.530 

.430 

.330 

.280 

.230 

.180 

.130 

.100 

.075 

.050 

.025

.630 

.600 

.500 

.400 

.300 

.250 

.200 

.150 

.125 

.100 

.075 

.050 

.025

.472 

.437 

.367 

.317 

.267 

.217 

.167 

.117 

.092 

.067 

.042 

.017

.510 

.470 

.400 

.300 

.250 

.200 

.150 

.125 

.100 

.080 

.060 

.040 

.020

.545 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

2.27 

2.27 

1.48

W.S.

2.23 

2.20 

2.15 

2.08 

1.97 

1.93 

1.97 

2.00 

1.93 

1.80 

1.66

W.S.

2.44 

2.39 

2.29 

2.30 

2.27 

.61 

.74 

.65 

.55 

.55 

.67 

.73

W.S.

2.26 

2.23 

2.20 

1.91 

1.62 

.84 

.74 

1.07 

.51 

.52 

.58 

.63

w.s. 

2.24 

2.24 

2.19 

2.06 

1.94 

2.09 

2.08 

1.96 

1.89 

1.67 

.54

w.s.

2.48 

2.48 

2.46 

2.43 

.51 

.50 

.50 

.75 

.67 

.67 

.66 

.57

w.s. 

2.44 

2.34 

2.37 

2.44 

2.36 

2.24 

2.15 

1.78 

1.16
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 

TABLE 20. Velocity-profile data for 0.47-mm sand in 8-foot-wide flume Continued

193

Run

94............

83............

54............

56............

55........ ....

57. ...........

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.745 

.680 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.095 

1.015 

.845 

.645 

.545 

.445 

.395 

.345 

.295 

.270 

.245 

.220 

.170 

.130 

.100 

.075 

.050 

.025

.873 

.833 

.733 

.533 

.433 

.333 

.283 

.233 

.183 

.133 

.083 

.058 

.033 

.018

.830 

.800 

.750 

.600 

.500 

.400 

.300 

.250 

.200 

.150 

.125 

.100 

.075 

.050 

.025

1.054 

1.024 

.874 

.724 

.574 

.474 

.374 

.324 

.274 

.224 

.174 

.124 

.099 

.074 

.049 

.024

.885 

.825 

.625 

.425 

.325 

.225 

.175 

.125 

.100 

.075 

.050 

.025

Velocity

(fPS)

w.s. 

2.59 

2.57 

2.56 

2.52 

2.37 

2.07 

.87 

.80 

.80 

.99

w.s. 

1.00 

.99 

.92 

.90 

2.53 

2.02 

.49 

.43 

.45 

.50 

.66 

.29 

.39 

.54 

.74 

.58 

.58

w.s. 

3.01 

3.01 

2.93 

2.61 

2.51 

1.37 

1.00 

1.71 

1.23 

1.56 

.61 

.68 

.96

w.s. 

2.61 

2.46 

2.46 

2.22 

2.00 

1.44 

1.48 

1.48 

1.44 

1.25 

.92 

.41 

.57 

.79

w.s. 

2.64 

2.52 

2.41 

2.46 

2.13 

1.91 

1.66 

1.48 

1.62 

1.46 

1.72 

1.91 

2.02 

2.08 

1.84

w.s. 

2.66 

2.57 

2.46 

2.34 

1.90 

1.62 

1.91 

2.61 

.84 

.88 

.84

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.755 

.700 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.845 

.800 

.650 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.815 

.755 

.655 

.555 

.455 

.355 

.255 

.205 

.155 

.105 

.080 

.055 

.030

.690 

.650 

.600 

.550 

.500 

.400 

.300 

.200 

.150 

.100 

.050 

.025

.585 

.535 

.485 

.385 

.285 

.235 

.185 

.135 

.100 

.075 

.050 

.025

.970 

.880 

.680 

.480 

.380 

.330 

.280 

.230 

.180 

.130 

.105 

.080 

.055 

.030

Velocity 

(fps)

w.s. 

2.13 

2.21 

2.15 

2.04 

2.04 

1.90 

1.68 

.81 

.63 

.69

W.S.

2.43 

2.43 

2.45 

2.45 

2.48 

2.48 

2.33 

2.23 

2.26 

2.04 

.96

w.s. 

2.53 

2.42 

2.47 

2.59 

2.43 

2.07 

1.60 

1.46 

.65 

.65 

.80 

1.08

W.S. 

2.56 

2.76 

2.94 

3.02 

3.02 

2.94 

2.82 

2.60 

2.41 

2.02 

1.84

w.s. 

2.50 

2.67 

2.66 

2.50 

2.42 

2.32 

2.32 

2.30 

2.37 

1.51 

1.38

W.S. 

2.60 

2.34 

2.37 

2.30 

2.36 

2.33 

1.93 

.50 

.50 

.63 

.63 

.72 

.96

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.840 

.800 

.700 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.965 

.900 

.800 

.650 

.500 

.400 

.300 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.888 

.825 

.775 

.725 

.675 

.575 

.475 

.375 

.275 

.225 

.175 

.125 

.075 

.050 

.025

1.015 

.975 

.900 

.800 

.700 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

1.060 

1.030 

.830 

.630 

.530 

.430 

.380 

.330 

.280 

.230 

.180 

.130 

.105 

.080 

.055 

.030

1.250 

1.160 

.960 

.760 

.560 

.460 

.360 

.310 

.260 

.210 

.160 

.120 

.090 

.060

Velocity 

(fps)

w.s. 

2.02 

1.98 

2.02 

2.13 

2.20 

2.04 

2.11 

1.98 

1.86 

1.78 

.79

w.s. 

2.81 

2.80 

2.77 

2.65 

2.46 

2.27 

1.25 

.92 

.72 

.46 

.41 

.79 

.66

w.s. 

2.88 

2.80 

2.87 

2.78 

2.86 

2.76 

2.71 

2.57 

2.27 

1.90 

1.23 

1.23 

.96 

.69

W.S. 

2.62 

2.71 

2.71 

2.76 

2.71 

2.78 

2.85 

2.64 

2.01 

.50 

.41 

.30 

.41

W.S.

3.28 

3.25 

3.20 

3.13 

2.75 

2.50 

1.23 

1.28 

1.28 

1.36 

1.07 

1.07 

1.42 

1.42 

1.50

W.S. 

2.89 

2.50 

2.29 

2.15 

1.88 

2.00 

.69 

.45 

.45 

.41 

.41 

.41 

.45

Run

57 Con. 

68 

Of.

78.. ....... ...

59 

60 

61 

71 

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.720 

.680 

.550 

.450 

.350 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.680 

.630 

.550 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.870 

.800 

.650 

.600 

.400 

.300 

.250 

.200 

.175 

.150 

.125 

.100 

.075 

.050 

.025

.510 

.490 

.440 

.340 

.290 

.240 

.190 

.150 

.125 

.100 

.075 

.050 

.025

.635 

.605 

.505 

.405 

.305 

.255 

.205 

.155 

.105 

.080 

.060 

.040 

.020

.590 

.560 

.460 

.360 

.260 

.210 

.160 

.110 

.085 

.060 

.040 

.020

.340 

.310 

.280 

.230 

.180 

.140 

100 

.080

Velocity 

(fps)

w.s. 

2.74 

2.82 

2.78 

2.89 

2.65 

2.73 

2.73 

2.65 

2.57 

2.24 

2.20

w.s. 

2.96 

2.98 

2.89 

2.92 

2.87 

2.80 

2.80 

2.54 

2.11 

1.90

W.S. 

2.61 

2.61 

2.65 

2.65 

2.56 

2.30 

1.61 

1.19 

1.19 

1.25 

1.07 

1.04 

1.19 

1.19

w.s. 

4.13 

4.01 

3.93 

3.81 

3.68 

3.85 

3.77 

3.50 

3.35 

3.10 

2.51 

0.00

W.S.

5.69 

5.69 

5.47 

4.99 

4.60 

4.53 

4.01 

3.50 

2 99 

2.' 37 

.88 

.88

W.S.

5.58 

5.51 

5.30 

4.99 

4.90 

4.60 

4.31 

4.09 

3.54 

3.50 

3.20

W.S. 

4.46 

4.31 

4.31 

4.09 

3.93 

3.50 

3.10

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.960 

.920 

.700 

.500 

.400 

.300 

.250 

.200 

.150 

.125 

.100 

.075 

.050 

.025

.630 

.580 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.625 

.530 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.535 

.496 

.415 

.315 

.265 

.215 

.165 

.115 

.090 

.066 

.040 

.015

.605 

.666 

.465 

.365 

.265 

.215 

.165 

.135 

.105 

.080 

.055 

.035 

.015

.550 

.540 

.460 

.360 

.260 

.210 

.160 

.110 

.085 

.060 

.040 

.020

.286 

.230 

.190 

.160 

.130 

.100 

.080 

.060

Velocity 

(fps)

W.S.

2.87 

2.63 

2.51 

2.33 

2.48 

2.37 

2.07 

2.10 

1.98 

1.91 

2.04 

2.04 

1.84

w.s. 

2.66 

2.65 

2.59 

2.19 

1.90 

1.86 

1.72 

1.74 

1.46

W.S. 

2.99 

2.92 

2.84 

2.75 

2.81 

2.78 

2.59 

2.20 

.92 

.92

W.S.

4.17 

4.05 

3.85 

4.01 

3.77 

3.68 

3.20 

2.07 

2.64 

2.64 

1.22

W.S. 

5.42 

5.24 

5.24 

4.87 

4.67 

4.53 

4.31 

4.17 

3.77 

1.90 

.88 

.88

W.S. 

5.42 

5.33 

5.12 

4.93 

4.67 

4.46 

4.39 

4.39 

4.24 

3.89 

3.40

W.S.

4.31 

4.31 

4.17 

4.01 

4.17 

3.77 

3.63

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.025

.900 

.860 

.730 

.630 

.430 

.330 

.230 

.180 

.155 

.130 

.105 

.080 

.055 

.030

1.130 

1.080 

.900 

.700 

.550 

.400 

.300 

.200 

.160 

.100 

.075 

.050 

.025

.610 

.560 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.640 

.610 

.550 

.450 

.350 

.300 

.250 

.200 

.150 

.125 

.100 

.075 

.050 

.025

.590 

.660 

.460 

.360 

.260 

.210 

.160 

.110 

.085 

.060 

.040 

.020

.600 

.560 

.460 

.360 

.260 

.210 

.160 

.110 

.085 

.060 

.040 

.020

.345 

.310 

.280 

.230 

.180 

.140 

.100 

.080

Velocity 

(fps)

0.30

W.S.

2.76 

2.67 

2.67 

2.60 

2.29 

2.26 

2.21 

1.93 

.88 

.45 

.60 

.41 

.57

W.S.

2.97 

2.87 

2.64 

2.34 

2.13 

2.02 

1.78 

1.44 

1.16 

1.10 

.99 

.96

W.S. 

2.29 

2.33 

2.26 

2.20 

2.60 

2.67 

2.67 

2.60 

1.22

w.s. 

3.50 

2.99 

2.99 

3.20 

3.30 

3.63 

3.50 

2.88 

2.99 

2.94 

2.88 

.74 

.88

W.S. 

5.42 

5.24 

4.93 

4.74 

4.32 

4.31 

3.93 

3.59 

3.10 

2.76 

1.48

W.S. 

5.24 

5.21 

4.93 

4.60 

4.43 

4.28 

4.17 

3.35 

3.50 

2.99 

1.90

W.S.

4.31 

4.21 

4.17 

3.89 

3.68 

3.20 

2.88
194 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 20. Velocity-profile data for 0.47-mm sand in 8-foot-wide flume Continued

Run

71 Con.

72.. -......

70 __ -

63.. 

65. ......

66 __ ... _ ..

80.. ..........

81......... ...

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.060 

.040 

.020

.310 

.270 

.220 

.170 

.130 

.100 

.080 

.060 

.040 

.020

.305 

.290 

.240 

.200 

.160 

.130 

.100 

.080 

.060 

.040 

.020

.400 

.350 

.300 

.250 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.320 

.270 

.220 

.170 

.120 

.090 

.060 

.040 

.020

.325 

.305 

.255 

.205 

.155 

.105 

,075 

.055 

.035 

.015

.330 

.300 

.270 

.240 

.200 

.160 

.130 

.100 

.080 

.060 

.040 

.020

.295 

.250 

.200 

.150 

.125 

.100 

.075 

.050 

.025

.500 

.485 

.385 

.285 

.185 

.135 

.085 

.060

Velocity 

(fps)

1.90 

.63 

.63

w.s. 

4.39 

4.24 

4.17 

3.96 

3.93 

3.63 

3.30 

2.23 

1.48

W.S.

4.46 

4.39 

4.39 

4.39 

4.17 

4.09 

3.77 

3.68 

3.40 

2.76

W.S.

4.80 

4.53 

4.31 

4.67 

4.53 

3.68 

3.85 

2.64 

..00 

1.48

w.s. 

4.87 

4.31 

4.60 

3.68 

4.01 

3.20 

4.60 

.88

w.s. 

5.12 

4.67 

5.30 

3.68 

3.93 

3.40 

3.10 

2.76 

0

w.s. 

4.81 

5.06 

4.57 

4.24 

4.60 

4.24 

4.81 

4.24 

3.93 

2.07 

2.07

w.s. 

5.18 

4.40 

4.50 

4.50 

3.70 

4.30 

4.00 

3.82

w.s. 

6.45 

6.31 

6.21 

5.42 

5.06 

4.53 

4.09

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.040 

.020 

.020

.320 

.275 

.225 

.175 

.125 

.100 

.080 

.060 

.040 

.020

.260 

.240 

.200 

.160 

.130 

.100 

.080 

.060 

.040 

.020

.450 

.400 

.350 

.300 

.250 

.210 

.180 

.150 

.120 

.100 

.080 

.060 

.040 

.020

.256 

.205 

.155 

.105 

.095 

.076 

.056 

.035 

.015

.355 

.305 

.255 

.205 

.155 

.105 

.075 

.055 

.035 

.015

.345 

.295 

.245 

.195 

.145 

.120 

.095 

.070 

.045 

.020

.430 

.400 

.350 

.300 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.505 

.420 

.360 

.260 

.210 

.160 

.110 

.085

Velocity 

(fps)

3.50 

3.20 

2.99

w.s. 

4.31 

4.17 

4.01 

3.85 

3.85 

3.68 

3.50 

3.20 

1.70

w.s. 

4.53 

4.46 

4.31 

4.09 

4.01 

3.77 

3.68 

3.20 

2.51

w.s. 

4.93 

4.31 

4.93 

3.77 

5.24 

4.24 

3.68 

3.59 

1.90 

2.23 

0 

0 

0

W.S.

5.36 

6.01 

5.24 

4.93 

4.39 

4.46 

4.93 

3.40

w.s. 

4.74 

4.81 

4.31 

4.09 

3.85 

4.60 

3.30 

.88 

.63

w.s. 

4.93 

4.74 

4.39 

3.40 

4.17 

4.24 

3.68 

1.90 

2.07

w.s. 

6.20 

5.10 

4.90 

4.50 

5.38 

4.70 

4.25 

.85 

.85 

3.65

w.s. 

6.38 

6.31 

6.01 

5.96 

5.64 

5.47 

5.18

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.060 

.040 

.020

.360 

.330 

.300 

.250 

.200 

.160 

.130 

.100 

.080 

.060 

.040 

.020

.275 

.240 

.200 

.160 

.130 

.100 

.080 

.060 

.040 

.020

.405 

.355 

.255 

.205 

.155 

.105 

.085 

.065 

.045 

.025

.250 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.425 

.355 

.305 

.255 

.205 

.155 

.105 

.075 

.055 

.035 

.015

.405 

.350 

.300 

.250 

.200 

.150 

.125 

.100 

.075 

.050 

.025

.395 

.375 

.275 

.225 

.175 

.125 

.100 

.075 

.050

.545 

.515 

.435 

.335 

.235 

.185 

.135 

.085

Velocity 

(fps)

2.64 

1.90 

.00

w.s. 

4.17 

4.17 

3.93 

3.81 

3.68 

3.50 

3.20 

2.99 

2.64 

.00 

.00

w.s. 

4.39 

4.31 

4.09 

4.01 

3.93 

3.77 

3.68 

3.50 

3.30

w.s. 

5.12 

5.64 

5.06 

4.74 

5.06 

4.67 

4.81 

4.09 

1.90

w.s. 

5.96 

4.60 

4.60 

4.74 

4.60 

4.39 

4.09

w.s. 

5.42 

5.06 

4.87 

4.67 

4.24 

3.59 

4.46 

1.22 

.63 

.63

w.s. 

5.47 

4.46 

4.99 

5.64 

4.09 

4.24 

3.68 

1.70 

0.00 

0.00

W.S. 

5.65 

5.50 

5.10 

5.80 

5.20 

3.85 

3.00 

.64

w.s. 

6.36 

6.16 

5.91 

5.53 

5.47 

4.93 

4.39

Run

81 Con. 

62-- 

67----. __ -

79--- 

84

68..-- 

100-.-- .

99 ___ ......

97

2.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.035 

.015

.535 

.505 

.435 

.335 

.235 

.185 

.150 

.125 

.100 

.075 

.055 

.035 

.015

.465 

:430 

.380 

.330 

.280 

.230 

.180 

.130 

.105 

.080 

.060 

.040 

.020

.520 

.480 

.400 

.300 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.340 

.300 

.250 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.404 

.380 

.330 

.280 

.230 

.180 

.130 

.100 

.080 

.060 

.040 

.020

.470 

.430 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.400 

.300 

.200 

.150 

.100 

.050

.302

.287 

.237 

.187 

.137 

.087 

.057 

,017

Velocity 

(fps)

3.77 

0

w.s. 

6.45 

6.26 

6.06 

5.80 

5.58 

5.91 

5.53 

4.99 

4.67 

4.39 

4.17 

3.93

w.s. 

6.41 

6.11 

6.06 

5.85 

5.53 

5.42 

4.87 

4.60 

3.77 

3.59 

1.90 

.87

w.s. 

6.50 

6.36 

6.21 

6.06 

5.53 

5.06 

4.24 

4.24 

.88 

1.07

w.s. 

6.15 

6.50 

6.05 

5.50 

5.40 

5.30 

4.90 

4.25 

1.38

w.s. 

6.69 

6.69 

6.69 

6.26 

6.21 

5.75 

6.06 

5.69 

5.36 

5.24 

4.31

w.s. 

7.38 

6.61 

6.31 

6.06 

5.69 

5.18 

4.31 

2.76

w.s. 

7.43 

7.05 

7.35 

5.53 

4.24

W.S.

5.18 

5.06 

4.67 

5.47 

5.91 

4.74 

3.30

4.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.060 

.035 

.015

.540 

.500 

.440 

.340 

.240 

.190 

.140 

.105 

.080 

.060 

.040 

.020

.480 

.445 

.345 

.295 

.245 

.195 

.145 

.095 

.070 

.045 

.025

.565 

.475 

.400 

.300 

.250 

.200 

.150 

.100 

.075 

.050 

.025

.385 

.350 

.300 

.250 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.458 

.430 

.380 

.330 

.280 

.230 

.180 

.130 

.100 

.080 

.060 

.040 

.020

.515 

.450 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.520 

.500 

.400 

.300 

.200 

.150 

.100 

.050

.250 

.232 

.182 

.132 

J)82 

.052 

.022

Velocity 

(fps)

4.60 

4.67 

3.77

w.s. 

6.01 

6.31 

6.01 

5.53 

5.36 

4.87 

4.67 

4.09 

3.77 

1.70 

1.22

w.s. 

6.21 

6.11 

5.91 

5.80 

5.59 

5.47 

4.99 

4.09 

4.24 

.63

W.S.

6.31 

6.01 

5.96 

6.01 

5.58 

5.58 

4.99 

4.74 

4.53 

.63

W.S.

5.90 

5.85 

5.65 

5.65 

4.91 

4.50 

4.40 

3.30 

1.45 

.65

w.s. 

6.64 

6.36 

6.26 

6.31 

6.11 

5.85 

5.53 

5.12 

5.06 

4.99 

4.09 

.69

W.S.

7.05 

6.65 

6.26 

6.06 

5.36 

4.74 

3.77 

1.49

w.s. 

7.05 

7.17 

6.65 

4.60 

5.18 

4.17 

r.f.

W.S.

5.58 

5.30 

5.12 

4.60 

2.99 

2.07

6.0 ft from left wall 

of flume

Distance 

above sand 

bed (ft)

0.060 

.035 

.015

.530 

.490 

.430 

.330 

.230 

.180 

.130 

.105 

.080 

.060 

.040 

.020

.515 

.480 

.430 

.330 

.280 

.230 

.180 

.130 

.100 

.075 

.050 

.025

.550 

.480 

.430 

.330 

.280 

.230 

.180 

.130 

.080 

.060 

.040 

.020

.285 

.250 

.200 

.150 

.100 

.080 

.060 

.040 

.020

.500 

.480 

.430 

.380 

.330 

.280 

.230 

.180 

.130 

.100 

.080 

.060 

.040 

.020

.515 

.450 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.480 

.350 

.250 

.150 

.100 

.050

.311 

.251 

.201 

.151 

.101 

.076 

.051 

.020

Velocity 

(fps)

4.31 

3.10 

.63

w.s. 

6.11 

6.01 

5.75 

5.64 

5.36 

5.12 

4.87 

4.87 

4.31 

3.93 

1.36

w.s. 

6.16 

6.01 

5.59 

5.47 

5.36 

5.12 

4.81 

4.67 

4.09 

3.30 

.87

W.S.

6.31 

6.41 

6.01 

5.85 

5.53 

5.58 

5.30 

4.53 

4.46 

3.77 

3.10

w.s. 

5.15 

4.50 

5.25 

4.10 

4.10 

3.60 

3.10 

.65

w.s. 

6.31 

6.31 

6.16 

6.06 

6.01 

5.80 

5.53 

5.06 

4.74 

4.39 

3.59 

3.77 

1.48

w.s. 

6.69 

6.46 

6.01 

5.47 

5.24 

4.60 

3.85 

3.77

W.S.

7.00 

5.91 

5.86 

5.85 

1.23

w.s. 

5.36 

5.24 

5.06 

4.74 

4.01 

3.93 

2.37
SUMMARY OF ALLUVIAL CHANNEL DATA FROM FLUME EXPERIMENTS, 1956-61 195

TABLE 21. Velocity-profile data for 0.54-mm sand in S-foot-wide flume 

[w.s.=water surface. Measurement taken 1.0 ft from left wall of flume]

Ron

1 _ . __ . .....

2. _ ...... ....

3....... .......

4... _ ........

6.... .......

Distance 

above sand 

bed (ft)

0.605

.565 

.500

.400 

.300

.200 

.150 

.100 

.075 

.050 

.025 

.010

.600

.565 BAA

.400 

.300 

200

.150 

.100 

.075 

.050 

.025 

.010

.610

.581 

.575

.500 

.400

.300 

.200 

.150 

.100 

.075 

.050 

.025 

.010

.548

530

.520

.500 

400

.300 

.200 

.150 

.100 

.075 

.050 

.025 

.010

.622

.600 

.569

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

w.s.

1.22 

1.16

1.14 

1.06

1.02 

.96 

.94 

.90 

.81 

.74 

.63

w.s.

1.26

1 99

1.22 

1.18

1

-10

1.11 

1.07 

1.01 

.99 

.88 

.75

w.s.

1.46 

1.50

1.31

1.25 

1.13 

1.07 

1.02 

.99 

.90 

.77 

.60

w.s.

1.85

1 7d

1.78

1.77

1.73 

1.65 

1.57 

1.47 

1.46 

1.41 

1.29 

1.16

2.07 

2.16

2.28 

2.30 

2.69 

2.61 

2.99 

3.20 

2.77 

2.04 

1.56

Bun

6 Con.

5... ...... ..

20-.. 

8...-. .... 

8A-. .......

8B- ....

Distance 

above sand 

bed (ft)

0.010

.774

.745 

.500

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025 

.010

.700

.682 

.600 

.500

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.808

.770 

.700

.600 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.796

.760 

.700

.600 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.833

.785 

.700 

.600 

.500 

.400 

.300 

.200 

.150 

.100

Velocity 

(fps)

1.36

2.36 

2.42

2.40 

2.38 

2.24 

2.12 

2.13 

2.11 

1.82 

1.28 

1.19

4.67 

5.36 

5.30

5.12 

4.60 

3.85 

3.30 

2.88 

1.48 

1.22 

1.22

2.99 

3.40

3.59 

3.77 

3.68 

3.40 

3.10 

2.64 

.88 

.88 

1.48 

2.64

3.40 

3.10

3.30 

3.50 

3.68 

3.10 

2.99 

2.76 

2.07 

2.37 

2.23 

.88

2.51 

2.76 

2.76 

3.10 

3.20 

3.10 

2.76 

2.76 

3.20

Run

8B Con.

8C-... .....

T. ....... ......

19.. ........

9. ..

10 ............

Distance 

above sand 

bed (ft)

0.075

.050 

.025

.832

.780 

.700 

.600 

.500 

.400 

.300 

.200 

.150 

.100

.075 

.050

.025 

.558

.510 

.400 

.300 

.200 

.150 

.100 

.075 

.050

.025 

.010

.643

.605 

.570 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050

.025

.010

.630

.610 

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.638

.600 

.500 

.400 

.300 

.200 

.150 

.100 

.025 

.050

Velocity 

(fps)

3.20

2.99 

.88

3.20 

3.20 

3.50 

3.50 

3.40 

3.20 

3.30 

3.20 

3.20

2.51 

1.22

.88

3.05 

3.04 

2.96 

2.81 

2.76 

2.75 

2.76 

2.75

2.56 

2.02

3.59 

3.97 

4.00 

4.05 

4.41 

3.47 

3.40 

3.23 

2.99 

2.82

2.64

2.12

3.30 

3.40 

3.30 

3.30 

3.54 

3.40 

3.25 

3.10 

2.82 

2.37

w.s.

5.80 

5.96 

5.91 

5.75 

5.36 

5.18 

4.53 

3.96 

2.15

Run

10 Con.

15.. ........

16B.... .

13.. .

11... .

18.. 

Distance 

above sand 

bed (ft)

0.025

7AR

.680 

.600

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.754

.670 

.600

Win

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.707

.672 

.600

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.684

.636

.600 

.500

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

.752

.670 

.600

.500 

.400 

.300 

.200 

.150 

.100 

.075 

.050 

.025

Velocity 

(fps)

1.36

w s

6.41 

6.50

6.46 

6.41 

6.21 

5.91 

5.42 

4.93 

4.09 

3.30 

2.07

6.06 

6.06 

6.11

6.11 

6.06 

5.75 

5.58 

4.99 

4.46 

4.01 

3.20

6.26 

6.31

6.36 

6.36 

6.21 

5.30 

5.47 

4.74 

3.85 

2.07 

1.22

W.S.

7.67

7.63 

7.50

7.20 

7.01 

6.16 

5.52 

3.48 

2.60 

1.51 

1.53

w.s.

6.16 

6.16

6.16 

6.11 

5.85 

5.36 

5.12 

4.39 

3.59 

4.66 

4.60
196 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 

REFERENCES

Bagnold, R. A., 1941, The physics of blown sand and desert

dunes: London, Methuen and Co., 145 p. 

 1956, The flow of cohesionless grains in fluids: Royal

Soc. [London] Philos. Trans., v. 249, no. 964, p. 256-260. 

Barron, E. G., 1963, New instruments for surface-water investigations: U.S. Geol. Survey Water-Supply Paper

1669-Z, p. Z4-Z8. 

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

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

526-549. 

Colby, B. R., 1961, Effect of depth of flow on discharge of bed

material: U.S. Geol. Survey Water-Supply Paper 1498-D,

12 p. 

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

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

Langbein, W. B., 1942, Hydraulic criteria for sand-waves:

Am. Geophys. Union Trans., p. 615-618.

Liu, H. K., 1957, Mechanics of sediment-ripple formation:

Am. Soc. Civil Engineers Jour., v. 83, paper 1197, 23 p. 

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

Sonic depth sounder for laboratory and field use: U.S.

Geol. Survey Circ. 450, 7 p. 

Rubey, W. W., 1938, The force required to move particles on a

stream bed: U.S. Geol. Survey Prof. Paper 189-E, 21 p. 

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

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

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

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

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

Geol. Survey Water-Supply Paper 1498-G, 45 p. 

U.S. Inter-Agency Report No. 11, 1957, The development and

calibration of the visual-accumulation tube: Minneapolis,

Minn., St. Anthony Falls Hydraulic Laboratory.

o