Summary of Turbulence Data From 

Rivers, Conveyance Channels, 

and Laboratory Flumes 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 802-B 

Summary of Turbulence Data From 

Rivers, Conveyance Channels, 

and Laboratory Flumes 

By R. S. McQUIVEY 

TURBULENCE I N WATER 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 802-B 

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1973 
UNITED STATES DEPARTMENT OF THE INTERIOR 

ROGERS C. B. MORTON, Secretary 

GEOLOGICAL SURVEY 

V. E. McKelvey, Director 

Library of Congress catalog-card No. 73-600286 

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

Washington, D.C. 20402- Price $1.55 (paper cover) 

Stock Number 2401-02429 
CONTENTS 

Page 

Abstract------------------------------------------------------------------------------------- B1 Description of experimental variables and parameters 

Introduction............................................................................... 1 -Continued 

Equipment ........ ------------------------------------------------------------------------- 2 Energy spectra ................................................................ . 

Constant-temperature anemometer............................... 2 Suspended-sediment concentration ............................... . 

Hot-film sensors................................................................ 3 Size and gradation of sediment ..................................... . 

Signal-conditioning equipment....................................... 4 Fall velocity ...................................................................... . 

Mean-velocity measuring equipment............................. 4 Total bed-material discharge ......................................... . 

Sonic depth sounders........................................................ 6 Shear velocity ................................................................... . 

Bed- and suspended-sediment samplers........................ 6 Shear stress at the bed ................................................... . 

Operating procedure and data reduction............................. 8 Kinematic viscosity ......................................................... . 

Description of experimental variables and parameters..... 9 Reynolds number ............................................................. . 

Water surface and energy slopes.................................. 9 Froude number ................................................................ . 

Width of flumes and channels........................................ 9 Chezy discharge coefficient ............................................. . 

Water discharge............................................................... 9 Bed configuration ............................................................ . 

Water temperature.......................................................... 10 Description of individual studies .......................................... . 

Depth at a verticaL......................................................... 10 20-centimeter-wide flume, rigid boundary ................... . 

Average depth of cross section...................................... 10 20-centimeter-wide flume, alluvial boundary .............. . 

Relative depth................................................................... 10 2-foot-wide flume, block roughness ............................... . 

Cross-sectional average velocity.................................... 10 4-foot-wide flume, rock roughness ................................. . 

Mean-velocity profile........................................................ 10 8-foot-wide flume, block roughness ............................... . 

Longitudinal turbulence intensity................................. 10 8-foot-wide flume, alluvial boundary ............................ . 

Vertical turbulence intensity----------············------------------- 11 A trisco feeder canal ........................................................ . 

Relative turbulence intensity......................................... 11 Rio Grande conveyance channeL .................................. . 

Eulerian integral time scale........................................... 11 Columbia River estuary .................................................. . 

Macroscale of turbulence................................................ 11 Missouri River ................................................................. . 

Microscale of turbulence................................................. 11 Mississippi River ............................................................. . 

Calculated turbulent shear stress.................................. 12 Current meter results ..................................................... . 

Measured turbulent shear stress................................... 12 References ................................................................................ . 

Relative turbulent shear stress...................................... 12 Basic data ................................................................................. . 

ILLUSTRATIONS 

FIGURE 1. Photographs of electronic equipment used in obtaining data at the 8-foot-wide flume and the Atrisco feeder 

Page 

B12 

12 

12 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

14 

15 

15 

16 

17 

20 

21 

22 

24 

24 

25 

28 

28 

29 

Page 

canal................................................................................................................................................................................. B2 

2. Schematic diagram of the equipment used in obtaining the turbulence data.......................................................... 3 

3. Sketches of the wedge, cylinder, and parabolic hot-film sensors used in these studies............................................ 3 

4-10. Photographs showing: 

4. Pitot tube and hot-film sensor arrangement used in the 20-centimeter-wide flume study........................ 4 

5. Modified propeller meter used to obtain local mean velocity and turbulence intensity during the 8-footwide flume, Atrisco feeder canal, and Rio Grande conveyance channel studies.................................... 4 

6. Stack of current meters and digital counter used during the Rio Grande conveyance channel study.... 5 

7. Large propeller meter used in obtaining local mean velocity during the Columbia River study.............. 5 

8. Current meter and hot-film sensor arrangement used in the Missouri River and Mississippi River 

studies................................................................................................................................................................... 6 

9. Pump and suspended-sediment sampler used during the Missouri River study............................................ 7 

10. Suspended-sediment sampler used during the Columbia River study.............................................................. 7 

11. Schematic diagram of the 20-centimeter-wide flume at Colorado State University.................................................. 14 

12. Photograph showing lead-shot roughness used in the 20-centimeter-wide flume study......................................... 14 

13. Photograph showing ripples formed in the 20-centimeter-wide flume........................................................................ 15 

14. Schematic diagram of the 2-foot-wide flume at Colorado State University.............................................................. 16 

15. Sketch of the block roughness and spacing pattern used in the 2-foot-wide flume, showing lh-inch-, %-inch-, 

and 1 Vs-inch-high blocks............................................................................................................................................... 17 

III 
IV CONTENTS 

Page 

FIGURE 16. Photograph of block roughness in the 2-foot-wide flume.............................................................................................. B17 

17. Schematic. diagram of the 4-foot-wide flume at Colorado State University.............................................................. 18 

18. Photographs of boundary roughnesses in the 4-foot-wide flume, showing %-inch rock roughness and riverbed 

roughness......................................................................................................................................................................... 18 

19. Schematic diagram of the 8-foot-wide flume at Colorado State University............................................................. 19 

20. Sketch of the block roughness and spacing pattern used in the 8-foot-wide flume.................................................. 19 

21-25. Photographs of 8-foot-wide flume, showing: 

21. Block roughness and honeycomb section installed near headbox................................................................... 19 

22. Typical ripple bed..................................................................................................................................................... 20 

23. Typical flat bed......................................................................................................................................................... 20 

24. Typical three-dimensional dune bed....................................................................................................................... 21 

25. Transitional bed, showing three-dimensional features near headbox and two-dimensional features 

near tailbox............................ ............................................................................................................................. 21 

26. Map showing location of the Atrisco feeder canaL......................................................................................................... 22 

27. Photograph showing upstream view of the Atrisco feeder canaL.............................................................................. 22 

28. Photograph of hot-film sensor used during the Atrisco feeder canal study.............................................................. 22 

29. Map showing location of the Rio Grande conveyance channel.................................................................................... 23 

30. Photograph of downstream view of the Rio Grande conveyance channel.................................................................. 23 

31. Photograph of upstream view of the Rio Grande conveyance channeL.................................................................... 23 

32. Photograph of data collection at the Rio Grande conveyance channel, showing turbulence equipment and 

other supportive equipment.......................................................................................................................................... 24 

33. Map showing location of the Columbia River estuary study........................................................................................ 25 

34. Photograph showing southward cross-section view of the Columbia River estuary.................................................. 25 

35. Map showing location of the Missouri River study......................................................................................................... 26 

36. Photograph of downstream view of the Missouri River from the study section....................................................... 27 

37. Photograph of upstream view of the Missouri River from the study section.......................................................... 27 

38. Map showing location of the Mississippi River study..................................................................................................... 27 

39. Photograph of upstream view of the Mississippi River from study section 444.0...................................................... 27 

40. Photograph of cross section of the Mississippi River at study section 441.6............................................................... 28 

TABLE la. 

lb. 

lc. 

2. 

3a. 

3b. 

3c. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12a. 

12b. 

12c. 

TABLES 

Page 

20-centimeter-wide flume, rigid boundary........................................................................................................................... B31 

20-centimeter-wide flume, rigid boundary, yawed-film results...................................................................................... 32 

20-centimeter-wide flume, rigid boundary, %, -inch. rock roughness.............................................................................. 32 

20-centimeter-wide flume, alluvial boundary, yawed-film results................................................................................... 34 

2-foot-wide flume, rigid boundary.......................................................................................................................................... 35 

2-foot-wide flume, rigid boundary, developing flow............................................................................................................ 36 

2-foot-wide flume, rigid boundary, yawed-film results...................................................................................................... 48 

4-foot-wide flume, rigid boundary......................................................................................................................................... 50 

8-foot-wide flume, rigid boundary ............................................................................................................................ -............ 52 

8-foot-wide flume, alluvial boundary...................................................................................................................................... 56 

Atrisco feeder canal................................................................................................................................................................. 59 

Rio Grande conveyance channel........................................................................................................................................... 60 

Columbia River estuary......................................................................................................................................................... 62 

Missouri River......................................................................................................................................................................... 63 

Mississippi River..................................................................................................................................................................... 64 

Current meter results, Atrisco feeder canal..................................................................................................................... 65 

Current meter results, Rio Grande conveyance channel.................................................................................................. 66 

Current meter results, Mississippi River............................................................................................................................. 66 
Symbol 

A 

Be 

Clvg 

Cs 

Ct 

D 

D 

d1s 

d;;o 

Dso 

d84 

E 

v~ 

f 

fc 

F(n) 

F 

g 

Lx 

n 

Q 

R 

R(t') 

R 

s 

v 

v~ 

v 

uv 

w 

w 

y 

'Y 

p. 

., 

p 

u 

1' 

w 

Ax 

CONTENTS 

SYMBOLS 

Definition 

Area of flow cross section, in (feet)2• 

Effective band width. 

Chezy discharge coefficient, VI U*. 

Concentration of suspended sediment, in milligrams per liter. 

Concentration of total bed material, in milligrams per liter. 

Total depth of flow in a vertical, in feet. 

Average depth of flow, in feet. 

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

Median particle size of suspended sediment, in millimeters. 

Median particle size of the bed material, in millimeters. 

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

Mean voltage, in volts. 

Root mean square of the voltage output, in volts. 

Resistance coefficient. 

Cutoff frequency, in (seconds)- 1 

Normalized energy spectrum function, in seconds. 

Froude number, f11Vgl5. 

Acceleration of gravity, in feet per second per second. 

Macroscale of turbulence, in feet. 

Frequency, in (seconds)- 1• 

Discharge of water-sediment mixture, Q=AV, in cubic feet per second. 

Hydraulic radius, in feet. 

Autocorrelation function. 

Reynolds number, VD I v. 

Slope of the energy gradient. 

Time, in seconds. 

Delay time, in seconds. 

Eulerian integral time scale, in seconds. 

Temperature, in oc. 

Velocity fluctuation in the x direction, in feet per second. 

Local mean velocity, in feet per second. 

Shear velocity, in feet per second. 

Longitudinal turbulent intensity, in feet per second. 

Velocity fluctuation in they direction, in feet per second. 

Vertical turbulent intensity, in feet per second. 

Av'erage velocity, QIA, in feet per second. 

Reynolds stress, in (feet)2 per (second)2• 

Lateral turbulent intensity, in feet per second. 

Flume or channel width, in feet. 

Depth above the bed, in feet. 

Specific weight of water, in pounds per cubic foot. 

Dynamic viscosity, in pounds-seconds per square foot. 

Kinematic viscosity, in square feet per second . 

Mass density of water, in slugs per cubic foot. 

A f d. . l . d . l(d;;o d84) measure o se 1ment partie e stze gra atwn, 2 d

16 

+ dso · 

Shear stress force on bed, in pounds per square foot. 

Fall velocity of dso, in feet per second. 

Microscale of turbulence, in feet. 

v 
VI CONTENTS 

ENGLISH-METRIC CONVERSION TABLE 

Metric unit 

Area of cross section.................................................. sq ft.. ............................................. 929 :~929()~~~~:::::::::::::::::::::::: ~rr:2 

~=i~~!io~:t:~;-~~~ti-~i~~:::::::::::::::::::::::::::::::::::::::::::}ft per sec .... -----------------------------------{ ~:!~~~:::::::::::::::::::::::::::::: 

{ 

0.005080 .... ----------------------

Velocity of bed configuration.................................... ft per min..................................... .5080 ........ --------·--·----------

.0 1829----------------------------

m/sec 

em/sec 

m/sec 

em/sec 

km/hr 

Water discharge .......... -----------------------------------------------· cu ft per sec ( cfs) -----------------------{ ~:~~~~io-~::::::::::::::::::::::: ~~~ ~:~c 

Sediment discharge..................................................... lb per sec per ft .......................... . 1.488 ................................ kg/sec/m 

Acceleration of gravity ............................................. . ft per sec per sec ......................... { ~:!~~~:::::::::::::::::::::::::::::: m/sec/sec 

em/sec/sec 

Shear stress ........ -------------------------------------------------------··· lb per sq ft .................................... r ~:!::~::::::::::::::::::::::::::::: dynes/cm2 

g/cm2 

kg/m2 

Kinematic viscosity--------·····---------------------------·----------- sq ft per sec.................................. 929.0 .... -------------------------------- cm2/ sec (Stokes) 

Dynamic viscosity ....................................................... lb sec per sq ft { 0.04788 ............................ g/cm-sec (Poise) ·--------···········--·--·--· .4482 .............................. g-sec/cm2 

Specific weight............................................................. lb per cu ft ................................... . 0.01602 ............................ g/cms 

Mass density................................................................ slug per cu ft .............................. . 0.5154 .............................. g/cms 
TURBULENCE IN WATER 

SUMMARY OF TURBULENCE DATA FROM RIVERS, CONVEYANCE 

CHANNELS, AND LABORATORY FLUMES 

By R. S. McQmvEY 

ABSTRACT 

The primary purpose of this report is to summarize and 

make available to other investigators some turbulence characteristics of turbulent shear flows obtained by use of hot-film 

anemometry. Related hydraulic and sediment data were also 

collected and are included. Data were collected from the study 

of flow in 20-centimeter-, 2-foot-, 4-foot-, and 8-foot-wide recirculating flumes, at the Colorado State University, over 

rigid and alluvial boundaries. Alluvial boundary data were 

also collected in the Atrisco feeder canal near Bernalillo, 

N. Mex., the Rio Grande conveyance channel near Bernardo, 

N. Mex., the Columbia River estuary near Astoria, Oreg., the 

Missouri River near Omaha, Nebr., and the Mississippi River 

near Vicksburg, Miss. 

The data collected and reported include such variables and 

parameters as the longitudinal and vertical components of 

the turbulent intensity, the macroscale and microscale of turbulence, the Eulerian integral time scale, the measured turbulent shear stress, the local mean velocities, the slope, the 

depth, the width, the discharge, the temperature, the suspended-sediment concentration, and the total bed-material discharge. Power spectra, some space-time, and space-correlation 

relations were obtained but are not included in this report. 

Also, not all the above characteristics were collected at each 

location. 

Some longitudinal turbulence intensities were obtained from 

a standard Price current meter and a small propeller meter 

at three of the field locations. These data are reported along 

with the hot-film anemometer measurements. 

INTRODUCTION 

As a part of the research program of the U.S. 

Geological Survey, several projects have been organized over the years to study the mechanics of water 

and sediment movement in open-channel flow. Answers to problems on resistance to flow, sediment 

transport, diffusion, dispersion, reaeration, and related problems were sought. Solutions to these problems are complicated by the multitude of variables 

and parameters involved and by the complex interdependence of those variables. 

Turbulence is a major factor in each of the abovementioned problems. Certain general items might be 

mentioned to indicate the effect of turbulence on various flow phenomenon. Sediment transport is controlled largely by turbulence. Both the movement of 

bed load and the carrying of material in suspension 

are apparently the result of the action of turbulent 

eddies in the flowing water. Even the bed forms and 

the nature and magnitude of resistance to flow in 

alluvial channels seem to be byproducts of the turbulence mechanism. Another significant phenomenon is 

that of turbulent mixing. This is simply the ability 

of turbulence to transfer momentum, heat, and mass 

from one region of the fluid to another. This depends 

on how fast eddies move transversely to the stream 

and their mean travel distance. The movement of 

eddies is undoubtedly dependent on the turbulence 

intensity, and their travel depends both on how many 

are present and on their size. 

Only recently has it become possible to measure 

turbulence in water. The development of constanttemperature anemometry has finally given the 

experimenter a tool for studying the turbulence phenomenon in water flows. Because of the complexities 

of the flow and of the experimental equipment involved, many inconsistencies are still present in the 

reported measurements. Need exists for all types of 

information on turbulence in water flow, not only to 

verify existing data, but also to provide new information on various flow conditions. The production 

of turbulence and its growth, dissipation, and distribution in the flow are fundamental to a sound concept of fluid motion involving friction, drag, and the 

dispersion and diffusion of heat, mass, and momentum. 

The objectives of these experiments were to obtain 

as much information on turbulence in water under 

as many different flow conditions as possible. Specifically, the main objective was to be able to measure 

turbulence in water under a variety of conditions, 

using hot-film anemometers, and to obtain reasonable 

and reliable results. Ultimately, the writer hopes to 

relate the measured turbulence characteristics to 

the problems of resistance to flow, sediment transBl 
B2 TURBULENCE IN WATER 

port, reaeration, diffusion and dispersion, to verify 

the equations of motion and energy for open-channel 

flow, and to develop a scaling parameter for various 

hydraulic systems. Several of these objectives will 

be topics of other reports. 

This report is a compilation of turbulence, hydraulic, and sediment data. Data were collected from the 

study of flow in 20-centimeter-, 2-foot-, 4-foot-, and 

8-foot-wide recirculating flumes, at the Colorado 

State University, over rigid and alluvial boundaries. 

Alluvial boundary data were also collected in the 

Atrisco feeder canal near Bernalillo, N. Mex., the 

Rio Grande conveyance channel near Bernardo, 

N. Mex., the Columbia River estuary near Astoria, 

Oreg., the Missouri River near Omaha, Nebr., and 

the Mississippi River near Vicksburg, Miss. 

The data collected and reported include such variables and parameters as the longitudinal and vertical 

components of the turbulent intensity, the macroscale and microscale of turbulence, the Eulerian integral time scale, the measured turbulent shear 

stress, the velocity, the depth, the slope, the width, 

the discharge, the temperature, the suspended-sediment concentrations, and the total bed-material discharge. However, not all these data were collected 

at each location. 

Some longitudinal turbulence intensities were obtained by using a standard Price current meter and 

a small propeller meter in three of the above field 

locations., A direct comparison of these intensities 

with the turbulence intensities measured with the 

hot-film anemometer is possible. 

No detailed analyses, comparisons, or conclusions 

are included in this report. The data contained are 

a basis for a series of U.S. Geological Survey reports 

on turbulence in water. 

The writer expresses his gratitude to members of 

the U.S. Geological Survey research staffs at Fort 

Collins, Colo., Albuquerque, N. Mex., and Portland, 

Oreg., and to the Corps of Engineers at Omaha, 

Nebr., and Vicksburg, Miss., for their support of the 

project with the proper logistics and for their aid 

in the collection of data. 

EQUIPMENT 

The constant-temperature anemometer is the basic 

instrument used to obtain the turbulence measurements. However, to obtain the desired turbulence 

characteristics, additional signal conditioning equipment is required. The electronic equipment used in 

obtaining the data in the flumes and in the field are 

shown in figure 1. Figure 2 is a schematic diagram 

of the equipment. 

A variety of equipment was used to obtain the 

B 

FIGURE 1. - Electronic equipment usea m obtaining data: 

A, 8-foot-wide flume; B, Atrisco feeder canal. 

hydraulic and sediment data location. A brief description of the data-collection equipment follows. 

CONSTANT-TEMPERATURE ANEMOMETER 

The anemometer used in this study is a commercially available constant-temperature compensating 

unit. When considering the use of an anemometer, 

two basic considerations should be investigated--the 

signal to noise ratio and the frequency response. The 

manufacturer reports that its unit has reasonably 

undistorted frequency response from 0 to 20 kHz. 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B3 

STRIPOSCILLOSCOPE 1 CHART 

RECORDER OUTPUT 

HOT-FILM 

SENSOR ANEMOMETER 

'---

FM 

TAPE -

-

0:::: 

w 0:::: 

w 0:::: 

X c:q- w 

w -- - t--

....J 00:::: :) RECORDER £L. .._w OUTPUT 

> £L. 

t-- <(Z ~ ....J 0 0 :) u u ~ 

- FIGURE 2.- Schematic diagram of the equipment used in obtaining the turbulence data. 

WEDGE HOT FILM 

QUARTZ-COATED PLATINUM 

FILM 

A 

CYLINDRICAL HOT FILM 

QUARTZ-COATED PLATINUM-FILM SENSOR 

ON GLASS ROD 

B 

PARABOLIC HOT FILM 

PLATINUM FILM 

ON LEADING EDGE 

c 

END VIEW 

FIGURE 3.- Hot-film sensors used in these studies: A, Wedge 

sensor; B, cylindrical sensor; C, parabolic sensor. 

The signal to noise ratio for the voltage output (several hundred millivolts) and frequency range (0 to 

100 Hz) in water flow is certainly no problem. 

Therefore, no problems are associated with the anemometer itself. To successfully use an anemometer 

for making a specific fluid-mechanics measurement, 

the selection of a sensor is, then, of primary importance. 

For a detailed explanation and description of hotfilm anemometry, the selection and the limitations of 

hot-film sensors, and the operational procedures, 

refer to McQuivey (1973). 

HOT-FILM SENSORS 

The three types of commercially available sensors 

used in these studies are shown in figure 3. The 

wedge-shaped hot-film sensor was used only in the 

20-centimeter-wide flume studies. The cylindricalshaped hot-film sensor was used in the 20-centimeter-, 2-foot-, ·and 8-foot-wide flume studies where 

foreign matter in the flow could be filtered or 

screened out. The frequency-response characteristics 

of the cylindrical sensor makes it the most desirable 

sensor to use. However, its shape is not desirable 

because of the tendency of foreign contaminants to 

wrap around or to collect on it, and the sensor is 

much too fragile for data collection in natural and 

sediment-laden channels. 

The parabolic-shaped hot-film sensor was used almost exclusively in the 4-foot- and 8-foot-wide flume 

studies, as well as in all the field studies. Because 

of its shape it remains fairly clean of foreign matter, 

and it is fairly resistant to breakage. During collection of the data presented in this report, only three 

parabolic sensors were broken. One was broken due 

to careless handling, and two were snapped off the 

sensor holders by large tree branches. 

Damage to hot-film sensors caused by colliding 
B4 TURBULENCE IN WATER 

sediment particles should be mentioned. The abrasion removes the quartz coating from the sensor after 

about 15 hours of continuous operation. Once this 

coating is removed and the platinum film is exposed, 

the sensor must be replaced. The quartz coating was 

worn off of three sensors during the data collection 

over the alluvial boundaries. 

SIGNAL-CONDITIONING EQUIPMENT 

The anemometer system has incorporated with it 

a certain amount of necessary signal-conditioning 

equipment. The most common additional electronic 

device is a voltmeter to measure the rms (root mean 

square) average of the output voltage of the anemometer. This output from the rms voltmeter and 

the unconditioned output of the anemometer were 

recorded on a dual-channel strip-chart recorder to 

give both a visual record and an analog record. The 

anemometer output and a reference signal from a 

standard signal generator of known frequency and 

amplitude were recorded on an FM (frequency modulated) magnetic tape recorder. The output of the 

anemometer as recorded on the FM tape recorder 

was monitored visually on an oscilloscope at all times. 

This allowed the operator to know when a recording 

was in progress and what was being recorded. This 

analog record from the FM tape recorder was later 

digitized, and a digital analysis was performed to obtain the desired statistical turbulence characteristics. 

For a more detailed description of the supporting 

electronic equipment and the statistical turbulence 

characteristics, refer to McQuivey ( 1973). 

MEAN-VELOCITY MEASURING EQUIPMENT 

Four different velocity measuring devices were 

used to obtain the local mean velocity in these studies. 

The local mean velocity in the 20-centimeter-, 2-foot-, 

and 4-foot-wide flumes was measured with a calibrated %-inch-diameter pitot tube, shown in figure 

4 at the right, along with the hot-film sensor. The 

differential pressure was measured by using a commercially available pressure transducer and transducer indicator. 

The local mean velocity taken in the 8-foot-wide 

flume and the Atrisco feeder canal and some of the 

velocity data in the Rio Grande conveyance channel 

were obtained with a small modified propeller meter. 

The propellers used were standard Ott minor propellers. The shaft had fastened to it a 30-toothed 

gear which produces 30 pulses per revolution of the 

shaft. The meter parts and propellers are shown in 

figure 5. The 1-3 propeller was used in these studies. 

A detailed description of the meter and the associated 

electronics was reported by Bennett (1968). The 

FIGURE 5. - Modified propeller meter used to obtain local 

mean velocity and turbulence intensity during the 8-footwide flume, Atrisco feeder canal, and Rio Grande conveyance channel studies. 

meter was also used to measure longitudinal turbulence intensities in the above-mentioned channels. 

A comparison of the turbulence intensities obtained with the meter and the hot-film anemometer 

system is found in table 12. 

In the Rio Grande conveyance channel, where the 

bed forms were changing fairly fast, a stack of 

standard Price current meters were used to obtain 

simultaneous local mean velocities at five points in 

a vertical profile. The velocities at each point were 

obtained with five of the current meters mounted on 

a single rod, as shown in figure 6. The impulses from 

the current meters were recorded by means of a multiple digital counter. Tests in a towing tank showed 

that the stacking of meters on a single rod did not 

appreciably affect the current-meter ratings. 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B5 

FIGURE 6. - Stack of current meters and digital counter used 

during the Rio Grande conveyance channel study. 

During the study on the Columbia River estuary, 

a large Ott propeller meter was used to obtain local 

mean velocities (fig. 7). Obtaining local mean-velocity profiles in an estuary can be fairly complicated 

and requires special equipment and data-reduction 

procedures. Prych, Hubbell, and Glenn (1967) described the instrumentation and the data-reduction 

procedure used in measuring the local mean velocity, 

direction of flow, and discharge. 

The standard Price current meter was used to 

obtain local mean velocities in the Missouri and MisFIGURE 7.- Large propeller meter used in obtaining local 

mean velocity during the Columbia River study. 

sissippi River studies. The arrangements of the 

sounding weight, current meter, and hot-film sensor 

are shown in figure 8. 

The hot-film sensor is about 8 inches in front of 

and about 8 inches above the sounding weight. The 

sounding weight and current meter did not influence 

the flow as it passed the hot-film sensor. 

In conjunction with measuring local mean velocities in the Mississippi River with a current meter 

(fig. 8B), the output of the current meter (one pulse 

per revolution of the shaft) was recorded on an oscillograph. This chart trace, or record, was later digitized and the longitudinal turbulence intensities 

calculated. A comparison of the turbulence intensities obtained with the current meter and the hot-film 

anemometer system is given in table 12. 
B6 TURBULENCE IN WATER 

B 

FIGURE 8. - Current meter and hot-film sensor arrangement 

for : A, Missouri River study; B, Mississippi River Study. 

SONIC DEPTH SOUNDERS 

Two commercially available sonic depth sounders 

were used extensively to determine the general bed 

configuration in the longitudinal direction throughout the distance studied in the 8-foot-wide flume and 

in the field studies. One sounder was used in depths 

of less than 6 feet, and the other in depths of more 

than 6 feet. This record of the bed configuration 

served a multitude of purposes. For example, the 

average depth could be computed very easily from 

the record. In the flume experiments the water surface and the bed slopes could be determined from the 

record. For most of the experiments the record was 

digitized, and a statistical analysis of the bed configuration was performed. The sounders were also 

used to locate the crests and troughs of dunes so that 

data could be collected in a consistent manner by 

following the desired features. 

BED· AND SUSPENDED-SEDIMENT SAMPLERS 

Bed-sediment samples were taken with a handoperated core sampler where the channel depths 

were less than about 5 feet. A standard US BM-54 

was used in rivers deeper than 5 feet. A representative sample was obtained by taking many samples 

throughout the flume or reach. 

Point suspended-sediment samples were taken in 

several different ways. Samples were obtained in the 

8-foot-wide flume by using a siphon sampler. The 

local mean velocity at a point was obtained from the 

small propeller meter. The siphon head was then set 

to siphon at the average local mean stream velocity. 

Gallon samples of sediment and water mixture were 

then collected. 

A DH-48 hand sampler was used in the Atrisco 

feeder canal and the first Rio Grande conveyance 

channel studies. A pumping point-type suspendedsediment sampler was tested on the last conveyance 

channel study. This system is still undergoing modifications and improvements, but basically it samples 

at stream velocity. Its electronics are capable of following the low-frequency (less than one cycle per 

second) changes in flow velocity. The sediment 

samples obtained with this device were probably the 

best collected, and the big advantage of this system 

is that samples can be obtained within about 0.05 

foot above the bed. Gallon samples of sediment and 

water mixture were collected. 

A pump-type sampler developed by the Omaha 

District, Corps of Engineers, was used to collect suspended-sediment samples on the Missouri River. The 

local mean velocity was determined from a standard 

Price current meter, and a variable-speed pump was 

set to pump at the local mean stream velocity. The 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B7 

B 

FIGURE 9. - Suspended-sediment sampler and equipment used 

during the Missouri River study: A, Pump; B, sampler. 

basic sampler was a standard US P-46 with a suction line from the nozzle to the pump. Gallon samples 

of sediment and water mixture were collected. The 

pump and sampler are shown in figure 9. 

A sampler developed by D. W. Hubbell's group, 

U.S. Geological Survey, was used to obtain suspended-sediment samples on the Columbia River 

estuary. The sampler is a vacuum system which lifts 

the sediment and water mixture up into 6-gallon containers in a boat (fig. 10). A large Ott meter is used 

to determine the local mean velocity at a point in the 

flow and then the vacuum system is set to pump the 

sample at mean stream velocity. The sampler was 

originally a US P-50. 

A standard US P-46 suspended-sediment sampler 

was used to collect suspended-sediment samples during the Mississippi River study. A crew on another 

FIGURE 10.- Suspended-sediment s amp) er used during the 

Columbia River study. 
BS TURBULENCE IN WATER 

boat moved to the same location to measure the turbulence and local mean velocities. This crew collected 

samples of sediment and water mixture in pint bottles, which are much too small to get a representative 

sample for such a large river. 

OPERATING PROCEDURE AND DATA 

REDUCTION 

The hot-film sensors were first calibrated in the 

20-centimeter-wide flume for mean flow velocities 

from about 0.3 to 7.0 feet per second and at several 

overheat ratios (from L10 to 1.06). This defined an 

adequate voltage/velocity relation for each sensor 

that accounted for the temperature range in the 

flume and in the field and the voltage drift, due to 

foreign contaminants that might collect on the 

sensor. These calibration curves were then used 

later in the data reduction process. (See McQuivey, 

1973.) 

The equipment was assembled at the study site. 

This included the anemometer, supporting electronic equipment, and the equipment necessary to 

collect the sediment data and the mean hydraulic 

parameters. 

An almost uniform procedure was used in 

collecting the data. The first step was to measure 

the local mean velocity in the flow at the desired 

point. This was obtained by a pitot tube, current 

meter, or propeller meter. The velocity was 

averaged at least every 3 minutes at each measuring point in the flow. The hot-film sensor was then 

moved to the same location that the local mean 

velocity was measured. The output voltage from 

the hot-film anemometer was recorded on FM 

magnetic tape for 3 minutes for the flume studies 

and for 4 minutes for the river studies. The output 

voltage from the anemometer and the rms voltmeter were also recorded on an analog strip-chart 

recorder. The signal that was recorded on the FM 

magnetic tape recorder was also observed visually 

on an oscilloscope. This informed the individual 

taking the data what was being recorded. 

Many times, while the local mean velocity and 

turbulence data were being collected, other crews 

were obtaining the sediment data and mean 

hydraulic parameters. 

The FM magnetic tapes were later digitized by 

employing a multiplexer and an analog to digital 

converter which was made available by the 

National Bureau of Standards at Boulder, Colo. 

The digital voltage output was stored on digital 

magnetic tape in a format compatible with the 

CDC-6400 computer system at Colorado State University. The mean and the root mean square of the 

fluctuations, the autocorrelation function, the 

space-time correlations, and the power spectra 

were obtained as computer printout. 

A similar independent analysis of the data was 

done by the General Electric Co. at the National 

Aeronautics and Space Administration's Mississippi Test Facility for the U.S. Geological Survey. 

The statistical evaluation system gave the values 

of the mean, standard deviation, and the skewness 

and flatness factor for each time series. 

This program has the option to calculate and 

plot the number of zero crossings; the probability 

density and empirical density; the autocorrelation; 

the cross correlation; the power spectral density; 

the cross-spectral density; and the phase angle for 

one or two time series. 

The software documentation was described by 

McQuivey (1973). 

Previous work had indicated that virtually all 

the power in the turbulence power spectrum is 

contained in frequencies of less than 100 cycles 

per second. This would dictate a digitizing 

sampling interval of 0.005 second. By playing the 

FM magnetic tapes into the digitizer at double the 

recording speed and digitizing at 1,000 samples 

per second, a real-time sample interval of 0.002 

second was obtained. The programed analysis was 

then set up to take only every fifth digitized point, 

or a sampling interval of 0.01 second. This gave a 

cutoff frequency, fc, of 50 cycles per second, an 

effective band width, Be, of 0.2 cycle per second, 

and 20 degrees of freedom. Thus, at 90-percent 

confidence level, the true power spectrum can be 

between 0.62 and 1.42 times the computed value. 

For more details refer·to McQuivey (1973). 

The intensity of turbulence was not obtained 

directly from the digital computer analysis because one calibration curve could not be used due 

to temperature variations and drift due to contamination buildup on the sensor. The local mean 

velocity at each measured point and the mean 

voltage were used to plot the velocity-voltage 

calibration. From this graph, an overheat ratio 

was determined. Then going to a plot of dE/dU 

versus velocity for various overheat ratios and 

knowing the mean velocity and the overheat ratio, 

a sensitivity, dE/dU, could be determined. Then 

the relation 

W=dEVU2 

dU (1) 

could be used to determine the intensity of turbulence, where W is the digitally obtained root 

mean square of the voltage fluctuations, dE/dU 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B9 

is the sensitivity, and 'W is the root mean square 

of the velocity fluctuations, where E is mean 

voltage, and U is local mean velocity. 

The yawed-film technique used to obtain the 

turbulent shear stress, and the vertical intensity 

of turbulence was employed only under the most 

ideal laboratory conditions. A complete description 

of this technique and its limitations was given by 

McQuivey (1973). 

The turbulence characteristics obtained from 

the data reduction are explained or defined in the 

following section. The hydraulic and sediment 

data collection and data-reduction procedures 

are discussed in the section on description of 

individual studies. The hydraulic and sediment 

parameters are explained and defined in the 

following section. 

DESCRIPTION OF EXPERIMENTAL VARIABLES 

AND PARAMETERS 

The following kinds of data are reported in 

tables 1-12 and are defined and described under 

four general areas, as follows: 

1. Basic hydraulic data 

Water surface and energy slopes 

Width of flumes and channels 

Water discharge 

Water temperature 

Depth at a vertical 

Average depth of a cross section 

Relative depth 

Mean velocity 

Velocity profile 

2. Turbulence characteristics 

Longitudinal turbulence intensity 

Vertical turbulence intensity 

Relative turbulence intensity 

Eulerian integral time scale 

Macroscale of turbulence 

Microscale of turbulence 

Measured turbulent shear stress 

Calculated turbulent shear stress 

Relative turbulent shear stress 

Energy spectra 

3. Sediment data 

Suspended-sediment concentration 

Size and gradation of sediment 

Fall velocity 

Total bed-material discharge 

4. Other parameters and observations 

Shear velocity 

Shear stress at the bed 

Kinematic viscosity 

Reynolds number 

Froude number 

Chezy discharge coefficient 

Bed configuration 

WATER SURFACE AND ENERGY SLOPES 

The water-surface slopes for flow in the 20-centimeter-wide flume were determined from a series 

of piezometer tubes. Piezometer taps were located 

at 1-meter intervals along the centerline of the 

flume bed. These taps were connected to the 

piezometer tubes with plastic tubing of equal 

lengths. The water levels in the tubes were a 

representation of the water-surface elevation 

along the flume. 

Water-surface slopes for the 2-foot-, 4-foot-, and 

8-foot-wide flumes were measured with a point 

gage and an engineer's level at 5-foot intervals 

along the centerline. The measured water-surface 

elevations and the corresponding stations of the 

flume for a working reach were used to compute 

a least-squares line of the water-surface slope. 

The mean water-surface slope of each run was 

determined by averaging the corresponding slopes 

of the least-squares lines. The least-squares line 

for the energy-grade line was computed from the 

values which were obtained by adding t,he local 

velocity head, Q2 /2g(WD) 2, to the corresponding 

water-surface elevations. The mean slope of the 

energy-grade line, called the energy slope, of each 

run was determined by averaging the corresponding slopes of the least-squares lines. 

Water-surface slopes in the field studies were 

determined by observing the water-surface elevation by employing surveying methods. This procedure and the accuracy varied somewhat from 

field study to field study, but the final results 

are presumed to be within acceptable limits. 

WIDTH OF FLUMES AND CHANNELS 

The flume widths were known, and the field 

channel widths were measured with a surveyor's 

chain in channels less than 100 feet wide. In the 

larger river systems, the channel width was determined by surveying methods, usually stadia. 

WATER DISCHARGE 

The water discharges in the flumes were determined in the return-flow lines of the recirculating 

flumes 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. 

Water discharge actually means the discharge 

of the water and sediment mixture. A concentration of 50,000 milligrams per liter of sediment 

means that about 5 percent of the water and 

sediment mixture is sediment by weight, and 

nearly 2 percent of the mixture is sediment by 

volume. 

The discharge during the Atrisco feeder canal 

study was obtained by the wading-current-meter 

method about every 2 hours. The discharge remained constant during the data-collection period. 

The Rio Grande conveyance channel discharge 
BIO TURBULENCE IN WATER 

was measured upstream from the study reach at 

the control structure. During both runs, the discharge changed considerably. The discharge was 

determined from the stage-discharge relation at 

the control structure at the time of each run. 

The discharge measurement during the Columbia River estuary study was made using the 

moving-boat method. This is described in detail 

in the "Techniques of Water-Resources Investigations of the United States Geological Survey," 

Book 3, Chapter All. 

The discharge of the Missouri River was measured by the U.S. Geological Survey at the Omaha 

bridge with a current meter. 

The discharge of the Mississippi River was measured from a boat with current meters. Because of 

the size of the river, many vertical sections were 

required, and each discharge measurement required 1 day. 

WATER TEMPERATURE 

The water temperatures, in degrees centigrade, 

were measured to the nearest one-tenth of a degree 

with a mercury thermometer. The temperature 

reported was based on an average of about 10 

readings obtained during data collection. For 

some of the river studies, there was a considerable 

change in temperature during the data-collection 

phase. 

DEPTH AT A VERTICAL 

The depth at a vertical was determined by measuring it with a sounding weight and reel system 

in the deep rivers, a wading rod in the shallow 

channels, and a point gage in the flumes, while 

obtaining the local mean velocities and turbulence 

data. In the places where the bed forms were 

moving, a sonic depth sounder was used to follow 

the desired features, such as the crests and 

troughs of dunes. 

For flow over the rigid boundaries, the depth of 

a vertical was determined by a volumetric 

approach. The roughness elements were considered solids and the rest of the volume to the 

tops of the roughness elements were considered 

voids. The depth at a vertical was then taken as 

the depth from the water surface to an imaginary 

bottom elevation, as if the roughness elements 

completely filled the bottom up to the imaginary 

bottom. 

AVERAGE DEPTH OF CROSS SECTION 

The average depth in the flumes over the rigid 

boundaries is the same as the total depth of a 

vertical. For flow over sand beds in the flumes and 

conveyance channels, the average depth of flow 

was determined by observing the difference in 

elevation between the water surface and the sand 

bed with a point gage or by using the sonic depth 

sounder down the entire centerline of the channel. 

As many intervals as desired could be averaged 

to obtain an average depth. For flow in the rivers, 

the average depth is the mean depth at a cross 

section obtained by a sounding weight. 

RELATIVE DEPTH 

The relative depth is the depth above the channel 

bottom divided by the total depth at the vertical 

of interest. 

CROSS-SECTIONAL AVERAGE VELOCITY 

The mean velocity reported was determined from 

the observed values of discharge (Q), average 

depth (D), and the width (W) by use of the continuity equation, 

(2) 

MEAN-VELOCITY PROFILE 

The mean-velocity profile data were obtained 

by a variety of instruments. In the 20-centimeter-, 

2-foot-, and 4-foot-wide flumes a pitot tube, pressure transducer, and transducer indicator were 

used. Standard current meters and the propeller 

meter were used for the other studies. The velocity 

profiles were taken primarily to aid in the turbulence-data reduction. In fact, in order to evaluate 

the turbulence data, the local mean velocity had 

to be measured at every point turbulence measurements were made. Generally, the local mean 

velocity was measured and then the hot-film 

sensor was moved to that same location and the 

turbulence data were taken. Some of the velocity 

profiles changed very fast as the bed forms moved 

downstream. For this reason, the stack of current 

meters were used to get an entire velocity profile 

at once. However, in most of the other velocity 

profiles, the bed configuration was not moving 

so fast, and an hour could be spent getting the 

necessary velocity and turbulence data. Most of 

the point velocities were averaged over 3 to 5 

minutes. 

LONGITUDINAL TURBULENCE INTENSITY 

One of the best physical pictures of turbulence 

is obtained by recording the longitudinal velocity 

fluctuations at various points in the section of a 

channel. The longitudinal intensity of turbulence 

is defined as the standard deviation of the fluctuations from the mean and is called the root-meansquared values of the fluctuating velocity in the 

streamwise direction, which can be expressed as 

follows: 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B11 

u=v7:2. {3) which can be expressed as: 

This component of turbulence is the easiest to 

measure. The hot-film sensor is oriented so that it 

senses the local mean velocity, U, and its fluctuating component, v7:2, to the first order. From a 

vector diagram of the mean velocity and the three 

fluctuating components, it is easy to see how v7:2 

can be obtained and why the other two components, (~ ~), become only of second-order 

importance. The fluctuating component v'U2 was 

also obtained in the 20-centimeter- and 2-footwide flumes from a yawed-film technique. The 

procedure has been explained in detail by 

McQuivey (1973). The values of viU2 obtained by 

orienting the hot-film sensor in the standard way 

and the yawed-film technique were within the 

expected accuracy of ±10 percent. 

This longitudinal component of the turbulence 

intensity is also obtained with the standard Price 

current and propeller meters. 

Note, too, that the turbulence measurements 

given in this report are probably only accurate to 

±10 percent of the expected values. This percentage of accuracy is not uncommon with all turbulence measurements reported. 

VERTICAL TURBULENCE INTENSITY 

The vertical turbulence intensity is defined as 

the standard deviation of the vertical fluctuations 

from the mean and is called the root-mean-squared 

value of the fluctuating velocity in the vertical 

direction-that is, 

y;;2 vV 

u* or u*. (6) 

EULERIAN INTEGRAL TIME SCALE 

The Eulerian integral time scale is defined as 

the area under the autocorrelation curve 

I; R(t')dt' = T E' (7) 

where R(t') is the autocorrelation function defined 

as 

u(t) u(t+ t') R(t'), (8) 

~VU2 

where (t) is time and (t') is the delay time. 

Physically, the output of the anemometer, u(t), is 

correlated with itself by delaying the time by an 

amount t'. Therefore, an autocorrelation curve is 

defined where R(t')=1 at time t'=O, and t' is increased until R(t')=O. The area under this curve 

is then the Eulerian integral time scale. This 

scale provides an estimate of the average eddy 

size associated with the flow. 

In some instances where R (t') did not reach zero, 

the data points were plotted on a curve of the 

log R(t') versus t'. Then a linear best-fit curve was 

established through the data points, and the area 

was obtained by integrating the equation of the 

line. This was done particularly for the Mississippi 

River data. 

MACROSCALE OF TURBULENCE 

v=vV. 

To get an indication of a mean eddy size in the 

{4) direction of the flow, the macroscale of turbulence 

This was defined as component of the turbulence was determined 

from the yawed-film technique. Measurements 

were made only in the 20-centimeter- and 2-footwide flumes where all the conditions were as ideal 

as possible. This component of turbulence is very 

difficult to measure in the field with present 

equipment and techniques. 

RELATIVE TURBULENCE INTENSITY 

The intensity, root-mean-squared value, or 

standard deviation of the velocity fluctuations is 

usually expressed as a ratio or percentage of the 

mean flow velocity or the local mean velocity, as 

follows: 

y;;2 ~ 

V or U. {5) 

Another useful way to express the relative intensity of turbulence is by nondimensionalizing the 

intensity with the shear velocity (defined later) 

Lx = U I; R(t') dt', (9) 

where U is the local mean velocity, and R(t') is the 

autocorrelation function. This scale, or mean eddy 

size definition, is a good approximation so long as 

the velocity is uniform-that is, dx= U dt. 

MICROSCALE OF TURBULENCE 

The microscale of turbulence is a measure of the 

smallest eddies that are responsible for the 

dissipation of energy. The microscale relation is 

developed from the cosine transform of the autocorrelation function, and is given by 

(lOa) 

where U is the local mean velocity, n is the frequency, and F(n) is the normalized energy spectrum function and will be discussed later. 
B12 TURBULENCE IN WATER 

The microscale may be calculated directly by 

assuming a normal and independent distribution 

for u from the following relation: 

_!__~ (Average number of zero 

Ax- U crossings of u per second). (lOb) 

It is known that the distribu~ion of u is closely a 

Gaussian one, even in turbulent shear flows. For 

the preliminary measurements of Ax reported 

presently, no corrections were applied for small 

deviations from the normal distribution. 

CALCULATED TURBULENT SHEAR STRESS 

Turbulent shear flows are described by the 

continuity equation, the Navier-Stokes equations 

of motion, and the energy equation, with additional 

terms in the velocity due to the turbulent fluctuations. The special case of fully developed turbulent 

open-channel flow, where the viscous and dynamic 

processes have reached a statistically stable state 

imposed by the rigid boundaries, was set up in the 

20-centimeter-wide flume. Considering these 

conditions and for flow of a two-dimensional 

nature, the mean N a vier-Stokes equation of 

motion in the x direction becomes 

-puv=yDS(l- Y/D)-IJ- ~~, (11) 

whei~e p uv is the Reynolds turbulent shear force, 

pis the water mass density, y is the specific weight 

of water, and IL is the dynamic viscosity. Knowing 

the slope, S, depth, D, and the velocity profile, the 

turbulent shear stress can be calculated. 

MEASURED TURBULENT SHEAR STRESS 

From the yawed-film technique the Reynolds 

stress, uv, was determined. This allowed a direct 

evaluation of the turbulent shear stress and does 

allow a direct comparison between the measured 

and calculated values. A detailed description of 

this measurement was given by McQuivey (1973). 

RELATIVE TURBULENT SHEAR STRESS 

The Reynolds stresses are sometimes expressed 

as a function or ratio of the local mean velocity, 

mean velocity, or the shear velocity: 

uv uv uv 

(U)2' or (V)2' or (U*)2" (12) 

ENERGY SPECTRA 

The energy spectrum provides information on 

how the energy is distributed in relation to the 

frequency. According to Kolmogoroff's theory, 

energy enters the spectrum through the larger 

eddies and is then transferred through the spectrum to the smaller eddies, where it is finally 

dissipated. In turbulent shear flows, it is not 

known how the one-dimensional function is related 

to the three-dimensional spectrum function. However, the one-dimensional spectrum function is 

still assumed to be an integral effect of the threedimensional spectrum function. Despite these and 

other experimental difficulties, the study of the 

energy spectra may lead to very interesting 

conclusions. 

The fractional energy content, F(n), is defined as 

I; F(n)dn=l, (13) 

where F(n) is a Fourier cosine transformation of 

R(t'): 

F(n)=4(\l~/ I; R(t')dt' cos2?Tnt'. (14) 

Power spectra were obtained at many points in 

the flow for all the different studies. These results 

were discussed and presented by McQuivey (1973). 

SUSPENDED-SEDIMENT CONCENTRATION 

Suspended-sediment concentration is defined as 

the ratio of the weight of solids to the weight of 

the water and sediment mixture. The samples 

were collected at local mean stream velocity. The 

samples, collected at various sites, varied in size 

(amount) from 6 gallons to 1 pint. The size of the 

samples is probably the most important consideration, so far as accuracy in testing is concerned. 

The suspended-sediment samples are probably 

as good as any that were taken. Concerted effort 

was made to collect each sample at mean stream 

velocity. The sampler, developed by the U.S. 

Geological Survey, adjusted the intake velocity 

for low-frequency changes and should therefore 

give very good results. 

SIZE AND GRADATION OF SEDIMENT 

The mean particle size and (or) the gradation 

distribution in terms of fall diameter of each suspended-sediment and bed-material discharge 

sample, and each bed-material sample was 

determined by drying the total sample, splitting 

it into a workable size where necessary, and then 

analyzing it in the visual-accumulation tube (U.S. 

Inter-Agency Committee on Water Resources, 

1957a). Each bed-material sample consisted of 

several samples taken at random from the beds of 

channels or flumes. In the studies where fine sediment was present, the fine sediment was washed 

out of the sample before the sample was dried, 

split, and analyzed. 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B13 

The gradation (u) was determined by the 

equation 

(15) 

in which d50 is the median size, and dt 6 and d84 are 

the respective sizes for which 16 and 84 percent of 

the sample is finer than the indicated size. 

FALL VELOCITY 

The fall velocity, as defined and discussed in 

Report 12 of the U.S. Inter-Agency Committee on 

Water Resources (1957b), is recorded in the tables 

for which suspended-sediment samples were collected. The fall velocity recorded is for the median 

size of the entire suspended-sediment sample 

collected at a point in the flow. It is recorded in 

feet per second, so that it can be compared later 

with the turbulence intensity, which is also recorded in feet per second. 

TOTAL BED-MATERIAL DISCHARGE 

The concentration of total sediment discharge 

was obtained with a width-depth integrating 

sampler located at the nappe, where the flow 

dropped from the 8-foot-wide flume into the tailbox. After uniform flow was established, more 

than 30 samples were taken at about 1-hour intervals. This gave a good statistical average of the 

total sediment discharge for each established 

flow condition. 

SHEAR VELOCITY 

Shear velocity is defined as Vi/iS", or v:;:JP, 

where g is the gravitational constant, R is the 

hydraulic radius, and S is the water-surface or 

energy slope. 

SHEAR STRESS AT THE BED 

The shear stress or tractive force at the bed 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=yDS, (16) 

where D is the depth at a particular vertical, S is 

the water-surface or energy slope, and 'Y is the 

specific weight of water. 

KINEMATIC VISCOSITY 

The kinematic viscosity of the water and sediment mixture was determined from the temperature of the water and appropriate standard tables. 

REYNOLDS NUMBER 

The Reynolds number is a ratio of the viscous 

forces to the total inertial forces in the channel. It 

is defined as 

R= VDp, or VD. (17) IL v 

It is commonly used as a measure of the effect of 

viscosity on the flow pattern. 

FROUDE NUMBER 

The effect of gravity on the flow pattern is 

commonly related to the Froude number, which is 

the ratio of the gravity force to the total inertial 

force. As commonly used and reported herein, 

v F=vgv· 

CHEZY DISCHARGE COEFFICIENT 

(18) 

Parameters related to average resistance to 

flow in channels are based on the variabl~s S, D, 

and V. The dimensionless Chezy discharge coefficient is defined as 

c v v 

-=- or--=== vg u*' ViDS. (19) 

Note that the discharge coefficient is the inverse 

of resistance, where the resistance coefficient is 

defined as 

f =8g_!!S 

(V)2 • 

BED CONFIGURATION 

(20) 

The general bed configurations were determined 

visually in the 20-centimeter-wide flume, and a 

sonic depth sounder was used extensively in the 

8-foot-wide flume and in the field. The sounder 

chart records were later digitized, and a statistical 

analysis was completed to determine the bed-form 

statistics. 

The general description, such as ripples, dunes, 

and flat bed, is given in the "Basic Data" section. 

DESCRIPTION OF INDIVIDUAL STUDIES 

This section of the report documents general observations of the flow field and operational procedures during the collection of the data. This includes 

a description of each study site, the roughness and 

bed configurations, the flow characteristics, operational procedures and techniques, and any variation 

in the data collection procedure between the various 

studies. A brief statement is included to explain the 

objective of each study. Many photographs are included to show the study sites, roughness or bed 

forms, and data collection. References and objectives 

are given in each section to relate the data to that 

taken in conjunction with other studies. 
B14 TURBULENCE IN WATER 

Manometer 

Piezometers 

mD 

motor 

FIGURE 11.- Schematic diagram of the 20-cent imeter-wide flume at Colorado State University. 

20-CENTIMETER-WIDE FLUME, RIGID BOUNDARY 

The experiments were performed in an open-surface recirculating flume made of Lucite. The channel 

was 10 meters long and had a cross section 20 centimeters wide by 20 centimeters deep. The slope of the 

channel could be varied from 0 to 0.085. An overall 

sketch of the flume is shown in figure 11. For a more 

detailed description of the flume refer to the report 

of Rathbun, Guy, and Richardson (1969). 

During the first study two boundary roughnesses 

were used. The Lucite floor of the channel provided 

a hydrodynamically smooth boundary. Sheets of aluminum coated with a layer of 0.173-inch-diameter 

lead shot packed at maximum density provided a 

hydrodynamically rough boundary. This roughness 

is shown in figure 12. 

The depth of flow over the lead shot was measured 

from a point slightly below the top of the lead shot. 

This mean bed elevation was determined by balancing the volume of the lead shot with the volume of 

the voids above the lead-shot centerline and to the 

top of the shot. The flow conditions were sufficient to 

provide fully developed turbulent flow at a test section 8.5 meters downstream from the headbox. The 

two-dimensionality of the flow at the test section was 

checked by a velocity survey taken with the small 

pitot tube. 

The data were then collected in the test section at 

the centerline of the flume. Cylindrical hot-film sensors were used to obtain most of the data; however, 

the wedge-shaped sensor was also used. The small 

pitot tube was used to obtain the local mean velocities. 

The primary experimental objective of this study 

FIGURE 12.- Lead-shot roughness used in the 20-centimeterwide flume study. 

was to develop the techniques and procedures involved in making turbulence measurements that 

could be reproduced in not only filtered systems (removing all foreign contaminants that might become 

attached to the hot-film sensor), but also sedimentladen channels. Therefore, a method was developed 

to measure turbulence in open channels that carried 

sediment and other types of foreign matter. 

The experimental objectives for flow over the 

rough and smooth boundaries were to measure the 

longitudinal and vertical components of the turbulence intensity, the turbulent shear stress, and to see 

if these measurements verified the two-dimensional 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B15 

equation of motion in open-channel flow. The yawedfilm technique was used to obtain these measurements. Estimates of the energy balance were also 

obtained. By measuring the production of energy 

and estimating the amount of energy dissipated, the 

amount of energy diffused could be calculated. Other 

turbulence characteristics obtained include the macroscale and microscale of turbulence, the Eulerian 

integral time scale, and energy spectra at various 

positions in the flow field. 

Several hot-film sensors were also used at this time 

to evaluate their performance and repeatability. A 

detailed description of the procedures and results 

can be found in a report by McQuivey (1967). 

The basic data collected over the two rigid boundaries for several different flow conditions along with 

the mean hydraulic parameters are reported in table 

1a and b. 

Table 1c ("Basic Data" section) summarizes the 

basic data collected in the 20-centimeter-wide flume 

over a % -inch rock roughness for nine different flow 

conditions. These data were collected in conjunction 

with a study of the reaeration process in open-channel flows. The reaeration process in a stream is 

characterized by its surface reaeration coefficient. 

Turbulence is a major factor in this mass-transfer 

phenomenon. The results of this study will be reported in other publications. 

20-CENTIMETER-WIDE FLUME, ALLUVIAL BOUNDARY 

The first turbulence measurements over an alluvial 

boundary were carried out in this flume. Two natural 

sand sizes were used; one with a d50 = 0.38 mm and 

a = 1.69, and another with a d5o = 0.19 mm and 

a = 1.42. The longitudinal and vertical intensities of 

turbulence were measured, as well as the turbulent 

shear stress over the sand beds at incipient motion, 

over ripples, and fiat bed with sediment moving. 

Flow in the flume over the ripple bed is shown in 

figure 13. 

The primary objective of these experiments was 

to study the turbulence characteristics for flow over 

alluvial boundaries, to verify the two-dimensional 

Navier-Stokes equation of motion in the x direction, 

to study the production, dissipation, and diffusion of 

the turbulent energy, and to compare the various 

scales of turbulence and the power spectra at various 

places in the flow. 

The data were collected in the test section at the 

centerline of the flow, where the flow was fully developed and two dimensional. The cylindrical hotfilm sensor was used to obtain all the turbulence 

data. The small pitot tube was used to obtain the 

local mean velocities. 

FIGURE 13. - Ripples formed in the 20-centimeter-wide flume. 

Sheets of aluminum were coated with liquid fiberglass resin, followed by a uniform thickness of the 

0.19 mm sand on one set and 0.38 mm sand on another set. The aluminum sheets were then placed in 

the flume on top of a %-inch layer of foam rubber. 

The flow conditions were set up to simulate a fiat-bed 

condition, with the appropriate slope, depth, and discharge. 

The turbulence characteristics were measured over 

the fixed roughnesses without sediment moving. Sediment of the same size as that attached to the aluminum 

sheets was then added to the flow, to the extent that 

it moved through the system at a maximum transport rate without deposition on the bed occurring. 

The same measurements were then repeated. 

The turbulence characteristics were also measured 

over both sand beds (natural) at the point of incipient motion and for natural flat beds. The natural 

flat-bed results could then be compared with the artificial flat bed results. 

The main objective of this study was to determine 

the effect of the moving sediment on the turbulence 

characteristics and the mean flow parameters. 

The turbulence characteristics and hydraulic parameters collected over the alluvial boundary for 

several different flow conditions are reported in 

table 2. 

2-FOOT-WIDE FLUME, BLOCK ROUGHNESS 

The flume used in this experiment was a recirculating flume 60 feet long, 2 feet wide, and 2.5 feet 
B16 TURBULENCE IN WATER 

a Pumping 

b Motor 

0 

unit Baffles and screens 

Rails 

c Center support k Instrument carriage 

d Orifice I Flume 

NOTE : NOT TO SCALE 

e Flexible connection m Tailgate 

Jacks n Tail box 

g Manifold diffuser 0 Manometer board 

h Head box 

FIGURE 14.- Schematic diagram of the 2-foot-wide flume at Colorado State University. 

deep. The side walls were made of 0.5-inch Lucite, 

and the floor was made of 0.25-inch stainless-steel 

plate. The discharge could be adjusted from 0 to 8 

cubic feet per second, and the slope from horizontal 

to 0.10. A schematic diagram of this flume is shown 

in figure 14. 

The turbulence data collected over the rigid boundary was taken in conjunction with a study of dispersion and diffusion. The roughness consisted of 

wooden blocks glued to the stainless-steel floor. Three 

different heights of blocks were used. The spacing 

of the blocks was the same for the three block 

heights. The size and spacing of the blocks are shown 

in figure 15. Figure 16 shows the blocks after they 

were placed in the flume. A standard swimming-pool 

filter and a set of screens were placed just downstream of the headbox to filter the flow, to remove 

all foreign contaminants, and to straighten out the 

flow, eliminating any irregular flow conditions caused 

by the entrance conditions. 

The turbulence data were collected 40 feet downstream from the headbox, where the flow was fully 

developed. The cylindrical hot-film sensor was used 

to collect all the turbulence data. The small pitot tube 

was used to obtain the local mean velocities. The data 

were collected at the channel centerline. 

The turbulence characteristics were obtained primarily to relate them with dispersion and diffusion 

characteristics. It was hoped that the percentage of 

dispersion and diffusion due to turbulence could be 

determined. 

The turbulence characteristics obtained included 

the longitudinal intensity of turbulence, the Eulerian 

integral time scale, the macroscale of turbulence, and 

space-time correlation relations in the x-, y-, and 

z-coordinate directions. These data along with the 

mean hydraulic parameters for nine flow conditions 

are given in table 3a. 

Additional data were later taken over the same 

roughness elements and at the approximate same 

flow conditions. The objectives of this study were to 

study the development of flow in a flume and to 

study more specifically the turbulence characteristics 

as the turbulent boundary layer developed. Turbulence data were collected at 5-foot intervals down the 

length of the flume at the channel centerline and 

between the centerline and the wall. Velocity profiles 

were taken at every 3-inch interval across the entire 

channel width and at every longitudinal measuring 

section. These data are summarized in table 3b. 

The yawed-film technique was used to obtain measurements of the vertical velocity fluctuations and 

the turbulent shear stress over the block roughnesses 

at various stations down the flume. These data along 

with the mean hydraulic parameters for six flow conditions are given in table 3c. 

4·FOOT·WIDE FLUME, ROCK ROUGHNESS 

The flume used in this experiment was a nonrecirculating flume 120 feet long, 4 feet wide, and 2 feet 

deep. The interior of the flume is surfaced with plywood coated with fiber glass, except for a 24-foot 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B17 

1" 

A 

2" 

B 

1" 

2" L ~ , I 1,, .. _[_;8 

~ _L I 

Tl· 

2" ·I 2"L 

I I 

t_ 

D 

c 

FIGURE 15.- Block roughnesses and spacing pattern used in 

the 2-foot-wide flume: A, '"h inch high; B, lh inch high; and 

C, 1 '"h inches high. 

section of the left sidewall which is of Lucite. The 

discharge could be regulated from zero flow up to 

the maximum capacity of the flume, which is about 

30 cubic feet per second. The slope could be adjusted 

from horizontal to about 0.03. A schematic diagram 

of this flume is shown in figure 17. 

The turbulence data collected in the 4-foot-wide 

flume were taken in conjunction with a study of 

thermal pollution, dispersion, and diffusion. The 

fiber-glass-plywood construction provided a hydrodynamically smooth boundary. The second boundary 

FIGURE 16.- Block roughness in the 2-foot-wide flume. 

was %-inch rock. The 3,4-inch rock was removed, 

and 11/2-inch rock provided the third roughness. The 

fourth roughness included the 11/2-inch roughness 

with 4- to 6-inch rock placed 6 to 8 inches apart. 

Two of these boundary conditions are shown in figure 18. The depth of the rock roughness placed was 

approximately that of the mean diameters. 

A series of four grids was placed just downstream 

from the headbox to straighten out the flow, eliminating any irregular flow conditions caused by the 

entrance conditions. A fifth grid was floated on the 

water surface to act as a wave suppressor. 

The turbulence data were collected 75 feet downstream from the headbox, where the flow was fully 

developed. The parabolic-shaped hot-film sensor was 

used to collect all the turbulence data. The small 

pitot tube was used to obtain the local mean velocities. The data were collected at the channel centerline and halfway between the centerline and the wall. 

The turbulence characteristics were obtained primarily to relate them with the dispersion and diffusion of a heated jet discharging into the flow. It was 

again hoped that the percentage of dispersion and 

diffusion due to turbulence could be determined. 

The turbulence characteristics obtained included 

the longitudinal intensity of turbulence, the Eulerian 

integral time scale, the microscale of turbulence, and 

space-time correlation relations in the x-, y-, and zcoordinate directions. These data along with the 

mean hydraulic parameters for 12 flow conditions 

are given in table 4. 

S·FOOT-WIDE FLUME, BLOCK ROUGHNESS 

These experiments were conducted in a 200-footlong recirculating flume with an 8-foot-wide by 

4-foot-deep rectangular cross section. The interior of 
B18 TURBULENCE IN WATER 

NOTE: NOT TO SCALE 

ADJUSTABLE 

JACKS 

TAILGATE 

RAILS 

INSTRUMENT 

CARRIAGE 

MANIFOLD 

DIFFUSER 

INFLOW FROM 

CONSTANT 

HEAD 

+- SOURCE 

VALVE 

FIGURE 17.- Schl!matic diagram of the 4-foot-wide flume at Colorado State University. 

A B 

FIGURE 18.- Boundary roughnesses in the 4-foot-wide flume: A, %-inch rock; B, riverbed. 

the flume is surfaced with aluminum, except for a 

72-foot section of the left sidewall, which is of Lucite. The pumping system consists of three pumps, 

30, 60, and 120 horsepower, with maximum discharge of 12, 28, and 40 cubic feet per second, respectively. The flume is mounted on adjustable screw 

jacks driven by syncronous motors with which the 

slope can be adjusted very easily and quickly from 

horizontal to 0.03. Figure 19 shows a schematic diagram of the flume. 

The turbulence data collected over the rigid boundary in the 8-foot-wide flume was taken in conjunction with the study of Jobson (1968) on vertical 

mass transfer in open-channel flow. The roughness 

consisted of wooden blocks glued to the aluminum 

floor. The size and spacing of the block are shown 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES Bl9 

ADJUSTABLE TAILGATE 

200' 

SIDE CONTRACTED 

ORIFICES 

LONGITUDINAL SECTION 

1-------8' -------~--1 NOTE : NOT TO SCALE 

f 

4' 

ADJUSTABLE 

SCREW JACKS 

CROSS SECTION 

FIGURE 19.- Schematic diagram of the 8-foot-wide flume at Colorado State University. 

FIGURE 20. - Block roughness and spacing pattern used in 

the 8-foot-wide flume. 

in figure 20. Figure 21 shows the blocks after they 

were placed in the flume and a honeycomb section 

was placed near the headbox to straighten out the 

flow and eliminate any irregular flow conditions 

caused by the entrance conditions. 

The turbulence measurements were taken for two 

reasons. First, it was hoped that the measurements· 

could be related to the vertical transfer coefficient, 

and, second, they were taken at frequent intervals 

along the channel to determine where the boundary 

layer became fully developed. The turbulence meaFIGURE 21.-Block roughness and honeycomb section installed 

near headbox of 8-foot-wide flume. 

surements were obtained with both the cylindricalshaped hot-film sensor and the parabolic-shaped 

sensor. The parabolic hot-film sensor was used to 

obtain most of the data. The turbulence characteristics obtained included the longitudinal intensity of 
B20 TURBULENCE IN WATER 

turbulence, the Eulerian integral time scale, the 

macroscale of turbulence, the velocity profiles, and 

the related mean hydraulic parameters. These data 

are given in table 5. 

Jobson ( 1968) investigated three flow conditions 

at a constant depth during his study. Data in the 

present report include two other flow conditions; 

one where the depth was one-half of his depth, and 

the other, twice the depth used by Jobson. 

The procedure was to measure the local mean velocity at a point with the small modified Ott meter and, 

then, to place the hot-film sensor at that same point 

and obtain the turbulence measurements. The data 

were taken 1.5 feet from the wall and along the channel centerline on a vertical line extending upward 

from the middle of a rectangular opening formed by 

four roughness elements. 

S·FOOT·WIDE FLUME, ALLUVIAL BOUNDARY 

The experiments on flow over an alluvial boundary 

in the big flume were started after the roughness 

elements were removed. The bed material used was 

a natural river sand from the Rio Grande conveyance channel near Bernardo, N.Mex. The average of 

20 samples analyzed, using the visual-accumulation 

tube, indicated that the median fall diameter, d50, 

was 0.25 mm, and the gradation, u, was 1.44. 

A series of 33 different flow conditions were 

studied. The average depth varied from about 1 to 

2.8 feet, and the discharge varied from about 15 to 

75 cubic feet per second. The mean velocity, Q/ A, 

ranged from about 1.8 to 6.5 feet per second. Turbul('nce data were only taken over a selected number 

of flow conditions. 

After operating the flume for several days at a 

particular depth and discharge, equilibrium was established for each run. Then, for at least 30 hours, 

the water-surface slope, the discharge of water and 

sediment mixture, the water temperature, a bed profile, the mean depth, and the total sediment discharge 

were recorded every hour to obtain a good statistical 

average of each variable. During this time the turbulence data, velocity profiles, and suspended-sediment data were being collected. Suspended-sediment 

samples were obtained with a %-inch siphon set to 

siphon at the local mean velocity. When data were desired over a crest or trough of a dune that was moving, the sonic depth sounder was used to position the 

data-collection equipment over the crest or trough 

as it migrated downstream. 

The general bed configurations over which turbulence data were collected are shown in the following 

photographs. Figure 22 shows a ripple-bed configuration. The turbulence data were taken about 120 

FIGURE 23. -Typical flat bed in the 8-foot-wide flume. 

feet downstream from the headbox and at the centerline of the flume. Figure 23 shows a flat-bed condition. For another flat-bed run, data were taken at 

several stations downstream from the headbox to see 

if the flow was fully developed. The velocity profiles, 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B21 

FIGURE 24.-Typical three-dimensional dune bed in the 8-footwide flume. 

turbulence intensity profiles and suspended sediment 

distributions indicated that down to as much as 100 

feet below the headbox the flow was not developed. 

Figure 24 shows a dune bed configuration. Turbulence data were collected over crests, troughs, and the 

backs of the dunes. Figure 25 shows that the bed 

configuration constitutes (a) three-dimensional 

dunes up near the headbox and (b) long two-dimensional dunes downstream. 

The turbulence characteristics, hydraulic parameters, and sediment data are recorded in table 6. 

A TRISCO FEEDER CANAL 

A reach of the Atrisco feeder canal near Bernalillo, N. Mex., about 15 miles north of Albuquerque, 

was selected as the first field experimental site. A 

location map of the study site is shown in figure 26. 

Several other studies have been completed in the 

reach, including a transverse and longitudinal mixing experiment and a fluorescent sediment tracer 

study. Extensive alluvial channel data have been collected there. The channel has a straight alinement 

for a distance of approximately 12,000 feet. The 

cross section shown in figure 27 (as viewed upstream) 

was several thousand feet from the inlet to the canal. 

The channel is about 58 feet wide, and the average 

depth was approximately 1. 70 feet. The bed forms 

were small three-dimensional dunes. 

B 

FIGURE 25. - Transitional bed in the 8-foot-wide fi·ume: A, 

Three-dimensional features near headbox; B, two-dimentional features near tailbox. 

The parabolic-shaped hot-film sensor was used to 

obtain the turbulence data. Figure 28 shows the hot-
B22 TURBULENCE IN WATER 

44 

N 

I 0 I MILE 

FIGURE 26.- Location of the Atrisco feeder canal. 

FIGURE 27.- Upstream view of the Atrisco feeder canal, 

photographed from the study section. 

film sensor used in obtaining the turbulence m~asurements in the field. Six verticals were taken in the 

cross section defining the distributions of mean velocity (obtained with the small propeller meter), 

FIGURE 28.- Hot-film sensor used during the Atrisco feeder 

canal study. 

longitudinal intensity of turbulence, Eulerian integral time scale, macroscale of turbulence, and 

suspended sediment. Bed-sediment samples were collected, and the bed configuration was observed. Turbulence measurements were also obtained with the 

small propeller meter. 

The primary objectives of this study were to obtain some turbulence characteristics in the field and 

to evaluate the hot-film anemometer as a field instrument. It was also hoped that the turbulence characteristics could be correlated with the hydraulic 

parameters and the sediment data to better understand the mechanics of the flow. 

The hydraulic, sediment-data, and turbulence characteristics obtained are given in table 7. 

RIO GRANDE CONVEYANCE CHANNEL 

The second experimental reach selected was the 

Rio Grande conveyance channel near Bernardo, 

N. Mex., about 70 miles south of Albuquerque. A 

location map of the study site is shown in figure 29. 

Extensive alluvial-channel data have been collected 

at this site. A basic-data report by Culbertson, Scott, 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B23 

CO NTROL STRUCTURE AND 

TOTAL- SEDIMENT SAMPLER 

DATA CO LL ECTED HE RE 

N 

NEW ME XICO l 0 

0 2 MILES 

FIGURE 29.- Location of the Rio Grande conveyance channel. 

and Bennett (1972) gives a detailed description of 

the channel and how it operates. 

Data were collected from the channel at two different times and at two different locations. The first 

data were collected in the spring of 1968 at station 

12.5. Figure 30 shows a downstream view of the 

channel. The channel has several sections of straight 

alinement, with a width of about 70 feet. The depth 

of flow varies with discharge and bed form. 

The bed form was rather large dunes during the 

first data-collection period. The parabolic hot-film 

sensor was used to obtain the turbulence data. Six 

verticals were taken in the cross section defining the 

distributions of mean velocity, longitudinal turbulence intensity, Eulerian integral time scale, macroscale of turbulence, and suspended sediment. 

The next day the above data were collected at one 

vertical in the flow as fast as possible (about every 

15 minutes) while the bed forms moved past the platform. Fifteen verticals were taken to define the variation in the various distributions in relation to time. 

The second data-collection period was in the spring 

of 1970. The test section was at station 16, as shown 

in figure 29. The test section is shown in figure 31 

(upstream view). The bed form was flat, and the 

suspended-sediment concentrations were fairly large. 

FIGURE 30. - Downstream view of the Rio Grande conveyance 

channel, as photographed from the 1968 data-collection site 

(station 12.5). 

FIGURE 31.- Upstream view of the Rio Grande conveyance 

channel, as photographed from the 1970 data-collection site 

(station-16). 

The same equipment was used, and the same basic 

data were collected. A new pumping point sampler 
B24 TURBULENCE IN WATER 

B 

FIGURE 32. - Data collection at the Rio Grande conveyance 

channel: A, Turbulence equipment; B, other supportive 

equipment. 

was used to obtain suspended-sediment samples. The 

data-collection equipment and the people involved 

are shown in figure 32. 

The objective of these experiments was to correlate the turbulence characteristics with the hydraulic 

parameters and the suspended-sediment data to gain 

greater insight into the mechanics of the flow. 

The hydraulic parameters, sediment data, and turbulence characteristics are reported in table 8. 

COLUMBIA RIVER ESTUARY 

The next experimental site was the mouth of the 

Columbia River at Astoria, Oreg., in the estuary. The 

cross section studied was a few hundred feet upstream from the bridge that goes across the estuary, 

as shown on the location map in figure 33 and in the 

photograph in figure 34. The channel is several miles 

wide at the cross section. The discharge varies with 

the tidal cycle, which complicates a data-collection 

program. These data were collected in conjunction 

with D. W. Hubbell's project. 

The procedures used in collecting the data were 

described by Hubbell and Glenn (1970). 

These were the first turbulence measurements 

made in depths up to 60 feet and where salinity might 

be a problem. A special probe cable and probe holder 

were used to make measurements in depths up to 125 

feet. 

Difficulties with electronic equipment used to obtain the direction of flow and the mean velocity 

plagued the data collection for 3 days. When all of 

Hubbell's equipment worked, the turbulence equipment failed to give good clean signals. A grounding 

problem was the main cause of the noisy signal. 

Once this problem was solved, one good profile of 

turbulence data was collected. 

Along with the turbulence data, salinity, temperature, and mean velocity data and suspended-sediment 

samples were collected. 

Salinity, large depths, and esturian flow did not 

seem to be a problem in getting good turbulence 

data. Turbulence measurements could be made but a 

great deal of thought and planning would have to go 

into a data collection program. Flow in estuaries is 

very complex, and it would be important to know all 

the variables of interest in order to correlate the turbulence measurements with the flow variables. 

The data collected are summarized in table 9. 

MISSOURI RIVER 

The next experimental reach was selected on the 

Missouri River, a few miles downstream from 

Omaha, Nebr. The cross section selected was in a 

7-mile study reach between Missouri River miles 609 

to 616, as shown in figure 35. The specific cross section where the turbulence measurements were obtained was at river-mile 612.51. Figure 36 shows the 

channel, viewed downstream from the cross section, 

and figure 37 shows the channel, as viewed upstream. 

The Omaha District of the Corps of Engineers has 

been collecting basic sediment and hydraulic data in 

the reach for 4 years. (For a summary of their results, see U.S. Army Corps of Engineers, 1968, 1969.) 

Data were collected at two different times. The 

first set of data was collected in September of 1968. 

The bed forms were long two-dimensional dunes. The 

equipment was assembled in a boat. The boat was 

positioned in the cross section by means of a stadia 

rod in the boat and a transit on the riverbank. The 

boat was then anchored in the river at the desired 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B25 

WASHINGTON 

PACIFIC 

OCEAN N 

1 

OREGON 

0 5 10 MILES 

FIGURE 33.- Location of the Columbia River estuary study. 

FIGURE 34. - Southward cross-section view of the Columbia 

River estuary. 

location. Five verticals were taken in the cross section. The parabolic hot-film sensor was used to obtain 

the turbulence measurements, and six data points 

were collected in a vertical. At each vertical, sufficient data were collected to define distributions of 

mean velocity, longitudinal turbulence intensity, Eulerian integral time scale, macroscale of turbulence, 

and suspended sediment. Bed-sediment samples, the 

bed configuration, and other hydraulic parameters 

were collected by Corps personnel. 

The second set of data was collected in November 

of that same year, when the bed was nearly flat. Data 

were taken at three verticals in the same cross section, and the same types of data were collected. 

The objective of this study was to correlate the 

sediment data and hydraulic parameters with the 

turbulence characteristics. The basic data are given 

in table 10. 

MISSISSIPPI RIVER 

The last field site was the Milliken Bend section of 

the Mississippi River, just upstream from Vicksburg, Miss. The section of the river in which data 

were collected is indicated in figure 38. The turbulence, local mean velocities, and suspended-sediment 

data were collected at river-miles 444.0, 443.2, 441.6, 

and 440.0. Two typical cross sections of the river are 

shown in figures 39 and 40. 

Four crews in four boats collected the data. One 

crew measured the discharge, one crew obtained bedand suspended-sediment samples, another crew obtained bed form information, and the other crew 

obtained the local mean velocities and the turbulence 

data. Anchoring the boats was an impossibility because of the large amount of barge traffic. Therefore, 

the position was held by the boat operator. Positioning of the boats was determined by surveying the 

distance between the boat and visible triangulation 

stations on the riverbank. 
B26 

\!\ 

TURBULENCE IN WATER 

AK-SAR-BEN HWY 

BRIDGE · 

NEBRASKA 

~f :l : -y 

6/3.99 w 

:~ W . IOWA 

DATA COLLECTED HERE 

611 .53 

NEBRASKA 

0 

IOWA 

OMAH 

DES• MOINES 

OUNCIL BLUFFS 

LINCOLN• r----

-c._____..ll MI LE 

FIGURE 35. - Loca tl. on of the Missouri River study. 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B27 

FIGURE 36. - Downstream view of the Missouri River, as 

photographed from the study section. 

FIGURE 37. - Upstream view of the Missouri River, as photographed from the study section. 

The turbulence measurements were obtained with 

the parabolic-shaped hot-film sensor. The local mean 

velocities were obtained with a standard Price current meter. Three vertical distributions of the local 

mean velocity, longitudinal turbulence intensity, suspended sediment, Eulerian integral time scale, and 

the macroscale of turbulence w~re obtained at each 

cross section. The turbulence data and local mean 

velocities were averaged over 4 minutes, which is 

probably not a long enough time in a river system of 

that size. The suspended-sediment samples were collected in 1-pint containers. The length of time used 

to collect a 1-pint container of water and sediment 

mixture was about 10 seconds, which is not a long 

enough time to collect a representative sample. In 

DAfA 

CCLLS.C TED 

HERE 

N 

1 

MISSISSIPPI 

ISSISSIPPI 

0 2 MILES 

FIGURE 38.- Location of the Mississippi River study. 

FIGURE 39. - Upstream view of the Mississippi River, from 

study section 444.0. 

some verticals the suspended-sediment data collection was repeated, and it's easy to see from the wide 

range in the data why these samples were not very 

meaningful. 

The objective of this study was to correlate the 

turbulence characteristics with the mean hydraulic 
B28 TURBULENCE IN WATER 

FIGURE 40.- Cross section of the Mississippi River at study 

section 441.6. 

parameters and the sediment data. The data are recorded in table 11. 

CURRENT METER RESULTS 

At the cross sections of the Atrisco feeder canal 

and the first data-collection site on the Rio Grande 

conveyance channel, the local mean velocities were 

obtained with the small modified propeller meter. 

The 1-3 Ott propeller was used. The digital output 

from the propeller meter was changed to an analog 

signal by a digital-to-analog converter. This output 

was recorded on the FM magnetic-tape recorder. 

These data were analyzed by digitizing the data as 

explained in the "Operating Procedure and Data Reduction" section, and from a computer analysis, the 

longitudinal turbulence intensity was obtained. A 

detailed description of the equipment and data-reduction procedure for the data collected with the 

small propeller meter is given by Bennett and McQuivey (1970). Table 12a and b summarizes the 

turbulence intensities obtained with the propeller 

meter and the hot-film anemometer at the Atrisco 

and Rio Grande conveyance sites. 

Table 12c summarizes the longitudinal turbulence 

intensity values obtained with the standard Price 

current meter used at sections 441.6 and 444.0 during the Mississippi River study, as well as the results 

obtained with the hot-film anemometer. The current 

meter impulses were recorded on an oscillograph for 

4 minutes at each point in the flow. This record was 

later digitized and the longitudinal intensity calculated. 

REFERENCES 

Bennett, J. P., 1968, Turbulence measurement with a propeller flowmeter: U.S. Geo!. Survey open-file report, 171 p. 

Bennett, J. P., and McQuivey, R. S., 1970, Comparison of a 

propeller flowmeter with a hot-film anemometer in measuring turbulence in movable-boundary open-channel 

flows: U.S. Geol. Survey Prof. Paper 700- B, p. B254-

B262. 

Culbertson, J. K., Scott, C. H., and Bennett, J. P., 1972, Summary of basic data, Rio Grande conveyance channel, New 

Mexico, 1965-69: U.S. Geol. Survey Prof. Paper 562-J, 

49 p. 

Hubbell, D. W., and Glenn, J. L., 1970, Distribution of radionuclides and sediments in the Columbia River estuary: 

U.S. Geol. Survey open-file report, 130 p. 

Jobson, H. E., 1968, Vertical mass transfer in open-channel 

flow: U.S. Geol. Survey open-file report, 204 p. 

McQuivey, R. S., 1967, Turbulence in a hydrodynamically 

rough and smooth open-channel flow: U .S. Geo!. Survey 

open-file report, 105 p. 

___ 1973, Principles and measuring techniques of turbulence characteristics in open-channel flows: U.S. Geol. 

Survey Prof. Paper 802-A, 82 p. 

Prych, E. A., Hubbell, D. W., and Glenn, J. L., 1967, New 

esturine measurement equipment and techniques: Am. 

Soc. Civil Engineers Proc., v. 93, no. WW2, p. 41-46. 

Rathbun, R. E., Guy, H. P., and Richardson, E. V., 1969, 

Response of a laboratory alluvial channel to changes of 

hydraulic and sediment-transport variables: U.S. Geol. 

Survey Prof. Paper 562-D, 32 p. 

U.S. Army Corps of Engineers, 19~8, Missouri River channel 

regime studies: M.R.D. Sediment Ser. 13A, U.S. Army 

Engineers District [Omaha], 53 p. 

___ 1969, Missouri River channel regime studies: M.R.D. 

Sediment Ser. 13B, U.S. Army Engineers District 

[Omaha], 76 p. 

U.S. Inter-Agency Committee on Water Resources, 1957a, The 

development and calibration of the visual-accumulation 

tube: Minneapolis, Minn., St. Anthony Falls Hydraulics 

Lab., Rept. 11, 109 p. 

___ 1957b, Some fundamentals of particle size analysis: 

Minneapolis, Minn., St. Anthony Falls Hydraulics Lab., 

Rept. 12, 55 p. 
BASIC DATA 

SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

Mean flow parameters 

and variables 

TABLE la. - 20-centimeter-wide flume, rigid boundary 

Mean flow parameters 

and variables 

B31 

Smooth boundary, channel centerline, cylindrical hot-film sensor Shot roughness, channel centerline, cylindrical hot-film sensor 

S = 0.89xl63 u* = o .046 fps 0. 786 1.010 0.0559 0.0554 1.215 

w = 0.~32 ft T = 0,0053 lb/ft2 .615 .980 .0660 .0674 1.435 

.445 .945 .0714 .0756 1.552 

Q = 0.054 cfs v = 0.920xl65 ft2/sec .359 .910 .0786 .0864 1. 709 

T = 21.2 •c R = 9,300 .274 . 860 .0821 .0955 1. 785 

.189 .807 .0921 .1141 2.002 

D = 0.096 ft F = o .506 .104 • 702 .1087 .1548 2.363 

V = 0.89 fps Cf/i= 19.35 .063 .625 .1195 .1912 2.598 

.041 .565 .1296 .2294 2.817 

0.810 1.090 0.0686 0.0629 1.024 

$ = 1.80Xl03 u* = o .0670 fps .647 1.040 .0790 .0760 1.179 

w = 0.632 ft T = 0.011 lb/ft2 .484 .970 .0932 .0961 1.391 

.320 .880 .1082 .1230 1.615 

Q = 0.062 cfs v = 1.00x1o5 ft2/sec .238 . 835 .1211 .14SO 1.808 

T = 23.9 •c R = 9,400 .167 . 735 .1303 .1773 1.945 

.121 .660 .1381 .2092 2.061 

D = 0.102 ft F = o .52 .075 .560 .1541 .2752 2.300 

V = 0.930 fps Cf/i= 13.85 .056 .500 .1623 .3246 2.422 

.026 .380 .2092 .5811 3.122 

$ = 1, 7QX1Q 3 u* = o .0648 fps .937 1.503 .0592 .0394 .914 

.775 1.462 .0656 .0449 1.012 

w = 0.632 ft T = 0,0106 lb/ft2 .614 1.418 .0752 .0530 1.160 

v = 0.920xU55 ft2/sec .452 1.354 .0878 .0648 1.355 Q = 0.087 cfs .372 1.310 .0987 .0753 1.523 

T = 21.2 •c R = 15,000 .290 1.253 .1110 .0886 1. 713 

D = 0.101 ft F = o. 76 .208 1.194 .1200 .1005 1.852 

.129 1.090 .1320 .1211 2.037 

V= 1.365 fps c;lg = 21.10 .071 .965 .1480 .1534 2.284 

.045 . 873 .1670 .1913 2.577 

S = 5 .07xl63 U * = 0 .111 fps .995 1.940 .1036 .0534 .935 

,828 1.870 .1183 .0633 1.068 

w = 0.632 ft T = 0.031 1b/ft2 .662 1. 790 .1237 .0691 1.113 

Q = 0.099 cfs v = 1.01x165 ft 2 /sec .491 1.680 .1357 .0808 1.222 

.331 1.530 .1603 .1048 1.444 

T=23.6"C R = 14,800 .245 1.420 .1836 .1293 1.654 

D = 0.099. ft F = o .86 .165 1.270 .2070 .1630 1.865' 

.083 1.010 .2430 .2406 2.189 

V = 1.58 fps C//g = 13.50 .056 • 860 .2741 ,. 3187 2.469 

.033 ,660 .3225 .4886 2.905 

S = 3.30x10"> u* = 0.089 fps .887 2.230 .0857 .0384 .963 

w = 0.632 ft T = 0.019 lb/ft2 .713 2.160 .1027 .0476 1.154 

Q = o .US cfs V = 0.9Q9Xl0 5 ft 2/sec .539 2,070 .ll40 .0551 1.281 

.364 1.930 .1266 .0656 1.422 

T = 21.8 •c R = 20,500 .278 1.830 .1391 .0760 1.563 

D = 0.094 ft F = 1.14 .191 1. 700 .1632 .0960 1.834 

.104 1.510 .1806 .ll96 2.029 

V = 1.98 fps c;lg = 22 .3o .055 1.400 .2121 .1515 2.383 

S = 9.52xl0"3 u * = 0. 153 fps . 755 2.570 .1418 .0552 .928 

T = 0.056 lb/ft2 .602 2.460 .1530 .0623 1.000 w = 0.632 ft .452 2.330 .1702 ,0731 1.113 

Q = 0.128 cfs v = 1.01x165 ft2/sec .301 2.120 .1940 .0915 1.268 

T = 23.3 •c: R = 19,500 .226 1.960. .2290 .1163 1.497 

.151 1. 760 .2570 .1460 1.680 

D = 0.101 ft F = 1.08 .076 1.420 .3170 .2232 2.072 

v = 1.99 fps C//g = 12.40 .035 1.220 • 3870 .3170 2.529 

.030 .960 .4250 .4427 2. 778 

Smooth boundary, channel centerline, wedge hot-film sensor Shot roughness, channel centerline, wedge hot-film sensor 

S = 0.87xl63 u* = o .0456 fps .811 1.005 .0470 .0370 1.031 

T = 0.0047 1b/ft2 .643 .976 .0520 .0430 1.140 w = 0.632 ft .475 .937 .0587 .0520 1.287 

Q = 0.054 cfs v = 1.01x1o5 ft 2 /sec .306 .888 .0688 .0660 1.509 

.222 . 781 .0775 .0770 l. 700 T = 23.3 •c R = 8,500 .138 . 730 .0874 .0900 1.917 

D = 0.097 ft F = o .so .054 .581 .1050 .1560 2.303 

V = 0.88 fps C//g= 19.35 .037 .525 .llOO .1760 2.412 

s= 1.80xl(f3 u* = 0.068 fps . 795 1.082 .0512 .0473 . 752 

T = 0,012 1b/ft2 .642 1.038 .0633 .0610 .930 w = 0.632 ft .490 .980 .0745 .0760 1.096 

Q = 0.065 cfs v = l.04xl65 ft 2/sec . 336 .902 .0873 .0968 1.284 

.260 .848 .0990 .1167 1.456 T= 24.4 •c R = 10,200 .183 ,774 .1130 .1460 1.662 

D = 0.107 ft F = 0 .so .107 .630 .lllO .1762 1.632 

C//g = 13.65 ,061 .545 .1480 .2716 2.176 v= 0.960 fps .052 .510 .1580 .3098 2. 324 

S = 1. 82xl63 U * = 0 . 0664 fps .885 1.483 .0506 .0260 . 762 

w = 0.632 ft T = 0.011 lb/ft2 . 719 1.447 .0611 .0330 .920 

.551 1.404 .0702 .0400 1.057 

Q = 0.085 cfs v = l.Olxl65 ft 2 /sec .386 1.322 .0782 .0480 1.178 

T= 23.3 •c R = 13,300 .302 1.277 .0850 .0550 1.295 

• 219 1. 208 .0952 .0656 1.434 

s= 5.60xlo-3 u* = 0.1193 fps .810 1.982 .0740 ,0370 .620 

T = 0.037 lb/ft2 .655 1.903 .0855 .0450 .716 w= 0.632 ft ,499 1.801 .1086 .0620 .910 

Q = 0.105 cfs v = l.04xl05 ft2/sec .343 1.658 .1319 .0800 1.105 

.265 1.573 .1458 .0930 1.222 T= 24.4 •c R = 16,600 .187 1.439 .1592 .1110 1.334 

D = 0.099 ft F = o. 76 .136 1.126 .1056 .0780 1.590 D = 0.105 ft F = o. 84 .109 1.183 .1843 .1560 1.545 

V = l. 36 fps C//g= 20.50 .053 ,947 .1370 .1250 2.063 

.033 .870 .1531 .1580 2.306 C/rg = 13.00 .062 1.030 .2202 .2140 1.846 v= 1.58 fps .053 .972 .2388 .2460 2.002 

S = 3. 3Qxl()3 u* = 0.0904 fps .902 2.158 .0572 .0270 .632 

.824 2.123 .0628 .0300 .694 

w = 0.632 ft T = 0.021 1b/ft2 .663 2.061 .0702 ,0340 .776 

Q = 0.121 cfs l.Olxl65 ft2/sec .502 1.974 .0849 .0430 .939 v = .341 1.856 .0997 .0540 1.103 

T= 23.3 •c R = 19,000 .260 1. 781 .1033 .0580 1.143 

D= 0.101 ft F = 1.05 .180 1.665 .ll95 .0680 1.322 

.100 1.498 .1522 .0850 1.684 

V = 1.90 fps C//g= 21.00 .052 1.298 .1787 .122 1.977 

.032 1.153 .1982 .163 2.192 

s= 8.44 x1()"3 u * = 0 .1444 fps .840 2.493 .0800 .0320 .554 

T = 0.053 lb/ft2 .677 2.401 .0960 .0400 .664 w= 0.632 ft .517 2.278 .1160 .0510 .803 

Q= 0.134 cfs v = l.04x105 ft 2 /sec .355 2.090 .1440 ,0690 .997 

.274 1.976 .1560 .0790 1.080 T= 24.4 •c R = 20,800 .194 1.824 .1860 .1020 1.288 

D= 0.101 ft F = 1.10 .113 1.506 .2120 .1410 1.468 

C//g= 13.85 .065 1. 391 .2880 .2070 1.994 v= 2.10 fps ,055 1.250 .3100 .2480 2.147 
B32 TURBULENCE IN WATER 

TABLE lb.- 20-centimeter-wide flume, rigid boundary, yawed-film results 

Mean flow parameters 

and variables 

s = 0.48><1()3 u. = 0.035 fps 

w = 0.632 ft T = 0.0031 lb/ft2 

Q = 0.044 cfs v = l.OOxl(f5 ft 2/sec T = 23.9 •c R=7,000 

D = 0.103 ft F = o .37 

V= 0.675 fps C//g= 19.3 

S = 1. 75xl(J3 u. = 0.0657 fps 

w = 0. 632 ft T = 0.0110 lb/ft2 

Q = 0.0874 cfs v = 0.920xl65 ft 2/sec 

T = 27.2 •c R = 15 ,ooo 

D = 0.1013 ft F = o. 75 

V = 1.36 fps C//(j = 20.7 

s = 3.3Ixlo3 U * = 0. 089 fps 

w = 0.632 ft T = 0.0194 lb/ft2 

Q = 0.1188 cfs v = 0.909xl65 ft2/sec 

T = 27.8 •c R = 20,600 

D = 0.094 ft F = 1.14 

V = 1.99 fps Cj/(j = 22.3 

S = 2.11xHP u. = 0.0743 fps w = 0. 632 ft T = 0.0144 lb/ft2 Q = 0.073 cfs v = 1. 07x 10-s ft2 I sec T = 21.4 •c R = 11,900 D = 0.109 ft F = 0.60 

V = 1.06 fps Cj/g = 14.3 

8 : 6.28Xl03 

w = 0.632 ft u; : ~:~!~ i~~ft2 I Q = 0.1205 cfs v = l.06xl65 ft 2/sec I T = 21.7 •c R = 17,400 

D = 0.1125 ft F = o. 85 

I V = 1. 70 fps Cj/g = 13.1 

s = 8.54xlo3 U* = 0.147 fps w = 0.632 ft T = 0.055 lb/ft2 Q = 0. 1307 cfs v = 1.01x165 ft2/sec T = 23.3 •c R = 21,300 D = 0.1037 ft F = 1.13 V = 2.01 fps C//(j =13.6 

0.564 0.683 

.450 .651 

.240 .607 

.083 .484 

. 775 1.460 

.452 1.350 

.290 1. 260 

. 208 1.190 

.129 1.090 

.071 .960 

.713 2.160 

.539 2.060 

.364 1.930 

. 278 1. 840 

.191 1. 710 

.104 1.510 

. 780 1.220 

.513 1.110 

• 336 1.020 

.225 .950 

.180 . 790 

.085 .630 

. 749 2.000 

. 461 1.840 

. 31R 1. 720 

. 212 1.600 

. 201 1.610 

.113 1.400 

I 

. 795 2.500 

.636 2.400 

.477 2.250 

.305 2.040 

.161 1. 720 

.083 1.490 

Smooth boundary, channel centerline 

0.0505 0.0739 1.443 o. 0346 0.0507 0.989 0.00088 0.00134 0.00097 

.0577 .0886 1.649 .0394 .0605 1.126 . 00120 • 00170 .00146 

.0705 .1161 2.014 .0486 .0801 1.389 .00164 .00234 .00229 

.0880 .1818 2.514 .0568 .1174 1.623 .00172 .00283 .00378 

.0760 .0520 1.157 .0523 .0358 . 796 .00206 .00249 .00050 

.0960 .0711 1.461 .0646 .0478 .983 .00487 .00606 . 00138 

.1110 .0881 1.690 .0760 .0603 1.157 .00637 .00785 .00207 

.1230 .1034 1.872 .0843 .0708 1.283 .00767 .00876 .00279 

.1340 .1229 2.040 .0897 .0823 1.365 .00784 .00964 .00340 

.1600 .1666 2.435 .1060 .1104 1.613 .00793 . 01028 .00444 

.1080 .0500 1.214 .0737 .0341 . 8281 .00450 . 00557 .00050 

.1200 .0583 1. 348 .0799 .0388 .8978 .00900 .00895 .00110 

.1410 .0731 1.584 .0939 .0487 1.0550 .01090 .01235 .00150 

.1560 .0848 1. 753 .1020 .0554 1.1460 .01270 . 01402 .00190 

.1650 .0965 1.854 .1050 .0614 1.1800 .01440 .01571 .00250 

.1940 .1285 2.180 .1290 .0854 1.4490 .01660 .01740 .00380 

Shot roughness, channel centerline 

.0837 .0686 1.126 .0564 .0462 . 7591 .00330 .00316 .00110 

.0917 .0826 1.234 .0595 .0536 .8008 .00580 .00699 .00300 

.1089 .1068 1.466 .0725 .0711 .9758 .00720 .00953 .00360 

.1240 .1305 1.669 .0816 .0859 1.0980 .00820 .01112 . 00470 

.1480 .1873 1.992 .0936 .1185 1. 2600 .00940 .Oll77 .00780 

.1712 .2717 2.304 .1125 .1786 1.5140 .01030 .01313 .01340 

.1330 .0665 1.023 .0830 .0415 .6385 . 01090 .01107 .00140 

.1620 .0870 1.246 .0970 .0527 • 7462 .01440 .02376 .00220 

.1760 .1023 1. 354 .1260 .0733 .9692 .01920 .03007 .00330 

.2020 .1263 1.554 .1370 .0856 1.0540 .02400 .03474 .00480 

.2120 .1317 1.631 .1460 .0907 1.1230 .02600 .03522 .00520 

.2470 .1764 1.900 .1610 .1150 1. 2380 .02850 .03910 .00750 

.1550 .0620 1.053 .0880 .0352 .5986 .01030 . 01133 . 00080 

.1660 .0693 1.130 .0934 .0389 .6354 .01680 . 02012 .00150 

.1880 .0836 1.280 .1190 .0529 .8095 . 02270 .02890 . 00230 

.2020 .0990 1.374 .1410 .0691 .9592 .02860 .03819 . 00350 

.2560 .1488 1. 742 .1660 .0965 1.1290 .03720 .04636 . 00650 

.3080 .2067 2.095 .1980 .1329 1. 3470 .03910 . 05067 .00910 

0. 3703 

.5049 

.6901 

• 7238 

.2460 

.5816 

• 7607 

.9159 

.9362 

.9470 

.2928 

.5857 

. 7093 

. 8265 

.9371 

1.0800 

.2290 

.4020 

.4996 

. 5680 

.6520 

. 7160 

,3325 

.4392 

.5856 

. 7320 

. 7930 

.8693 

.2457 

.4007 

.5415 

.6822 

.8874 

.9327 

TABLE lc.- 20-centimeter-wide flume, rigid boundary, %-inch rock roughness 

- r--

~tean Flow Parameters 0 ~ju. TE L 

X >. X 

and Variables Y/D u ~;u (fps) (fps) u? (sec) (ft) (ft) 

--

S = 2. 44X10- 3 u,.. = 0.0866 fps 0.118 0.400 0.171 0.428 1.971 0.081 0.032 0.0061 w = 0.656 ft T = 0. 0146 1b/ft2 .252 .620 .187 .302 2.160 .164 .102 .0081 Q = 0. 0742 cfs v = 0.967X1o-s ft2/sec • 386 • 730 .161 .220 1. 860 .192 .140 .0104 T=24.9°c R = 8,240 .555 .S50 .159 .1S7 l.S35 .22S .194 .011S D = 0.135 ft F = 0. 399 . 722 .940 .13S .147 1.593 .186 .175 .0126 

v= O.S33 fps C//g= 9.62 • S91 1.000 .121 .121 1.39S .115 .115 .013fi 

.975 1.020 .136 .133 1.565 .209 .213 .0197 

2cm Rt f .975 1.070 .117 .109 1.351 .157 .16S .0173 

4cm Rt {; .975 1.120 .096 .086 1.110 .137 .153 .0156 

6cm Rt f .975 1.000 .11S .118 1.362 .075 .075 .01S4 

Scm Rt f .975 • 760 .102 .134 1.176 .041 .031 .0124 

- S = S. 1SX1Q- 3 u,.. = 0.159 fps .060 . 390 .184 .472 1.157 .043 .017 .0033 

w = 0.656 ft T = 0.049 1b/£t2 .172 .77S .245 .316 1.530 .038 .030 .0062 

Q = 0.1363 cfs v = 0.967X10- ft 2/sec .302 .990 • 241 .252 1.515 .130 .129 .0076 

T = 24.9 °c R = 15,200 .474 1.240 .237 .191 1.490 .102 .126 .0095 

D = 0.136 ft F = 0. 730 .646 1.410 .223 .158 1.402 .090 .127 .0118 

V = 1. 530 fps C/fg = 9. 61 .844 1.650 .195 .118 1.226 .120 .198 .0131 

.957 1. 720 .192 .111 1.206 -- -- .0145 

2cin Rt f -957 1.820 .1S5 .102 1.163 .110 .200 .0170 

4cm Rt f .957 1.920 .155 .OS1 .975 .030 .05S .014S 

6cm Rt f • 957 1. 730 .153 .089 .963 .037 .064 .0140 

Scm Rt £ .957 1.320 .13S .105 .S68 .049 .065 .0128 

/.. X 

(ft) 

0.247 0.169 0.0187 

.263 .171 .0223 

.281 .170 .0196 

.253 .123 .0162 

.203 .287 .0101 

.159 .215 .0124 

.186 .234 .0116 

.184 .219 .0103 

.173 .189 .0082 

.177 .170 .0071 

.112 .242 .0086 

.136 .280 .0111 

.154 . 297 .0092 

.142 .261 .0103 

.157 . 268 .0077 

.147 .222 .0053 

.132 .161 .0119 

.157 .174 .0135 

.186 .190 .0128 

.177 .168 .0117 

.142 .ll2 .0086 

.lll .070 .0057 

.087 .175 .0115 

.103 .190 .0123 

.116 .200 .0117 

.114 .182 .0103 

.111 .179 .0096 

.108 .151 .0059 

.073 .183 .0109 

.095 .228 .0107 

.104 .234 .0105 

.112 .228 .0099 

.102 .175 .0087 

.091 .136 .0063 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B33 

TABLE lc.- 20-centimeter-wide flume, rigid boundary, %-inch rock roughness- Continued 

~lean Flow Parameters I 01 '?fr r;,~ju. TE L X A 

X 1/D u and Variables (fps) (fps) (sec) (ft) (ft) 

S = 15.6x10- 3 u,. = 0.219 fps .146 • S50 --~ -=-::.~ 

Fl.529 .147 .i2s~ ~ -.006S -- • 335 • 394 

w = 0.656 ft T = 0. 093 1b/ft 2 .244 1.190 • 347 .292 1.5S6 .137 .163 .OOS6 

Q = 0.1S36 cfs v = 0. 967X10- 5 ft 2 /sec • 366 1.650 • 350 .212 1.600 .190 .313 .0114 

T=24.9°C R = 20,500 • 529 2. 000 • 304 .152 1. 3S9 .097 .194 .0131 

D = 0.135 ft F = 0.993 .691 2. 2SO • 276 .121 1.260 .122 .27S .0152 

v= 2.070 fps C//g= 9.44 .S54 2.450 .217 .OS9 .992 .090 .221 .0164 

.S77 2.490 .20S .OS4 .951 .095 .236 .0176 

2cm Rt £ .S77 2.530 .230 .091 1.050 .090 .22S .0174 

4cm Rt £ .S77 2. 720 .176 .065 • S04 .056 .152 .0172 

6cm Rt f .S77 2.540 .164 .065 • 750 .100 .254 .0153 

Scm Rt £ .S77 2.140 .169 .079 .772 .100 • 214 .0119 

s • 1S. 5x10- 3 u,. = 0.214 fps .225 1.220 • 354 .290 1.654 .047 .057 .0076 

w = 0.656 ft T = 0.0S9 1b/ft2 .394 1.660 .32S .19S 1.533 .075 .124 .0094 

Q = 0.11S3 cfs v = 0.967X10-s ft 2 /sec .561 1.960 • 262 .134 1. 224 .044 .OS6 .0107 

T = 24.9 °C R = 14,250 .730 2.200 .235 .107 1.097 .OS5 .1S7 .0127 

D = 0.101 ft F = 0.992 .933 2. 3SO .1SS .079 .S7S .oso .190 .0143 

ii = 1. 790 fps C//g = S.36 

2cm Rt f .933 2.220 .217 .09S 1.015 .10S .240 .0142 

4cm Rt £ .921 2.290 .190 .OS3 .sss .077 .176 .014S 

6cm Rt £ .921 2.400 .152 .064 .713 .061 .146 .0136 

.921 1.900 .163 .OS6 • 764 .036 .06S .0110 Scm Rt £ 

s = S.13x1o- • u,. - 0.141 fps • 324 .725 .1S6 .257 1.320 .163 .11S .0061 

w = 0.656 ft T = 0.03S9 1b/ft2 .471 .975 .177 .1S1 1.253 .170 .165 .0073 

Q • 0. OS4S cfs v = 0. 967x10- 5 ft 2 /sec .61S 1.190 .161 .135 1.140 .144 .171 .0094 

T = 24.9 °C R = 10,220 • 765 1. 330 .149 .112 1.056 .111 .14S .0107 

D = 0.100 ft F = 0. 719 .961 1.490 .123 .OS3 .S73 .149 .222 .0132 

-v- 1. 290 fps C/li,= 9.13 

2cm Rt £ .961 1.470 .139 .094 .9S6 .149 .219 .0119 

4cm Rt £ .961 1.520 .123 .OS1 • S73 .090 .136 .012S 

6cm Rt £ .961 1.4SO .13S .093 .97S -- -- .0125 

Scm Rt £ .961 1.140 .127 .111 .902 -- -- .0103 

5 = 2. 53X10- 3 u,. = 0.079 fps 0.125 0.2SO .096 • 343 1.216 -- -- 0.0045 

w = 0.656 ft T = 0.0121 1b/ft 2 .312 .510 .099 • 194 1.253 -- -- .0070 

Q = 0. 0351 cfs v • 0.967x10- 5 ft 2 /sec .500 .650 .oso .123 1.012 .130 .OS5 .OOS9 

T = 24.9 °C R = 4,250 .6SS .710 .075 .106 .948 -- -- .0091 

D = 0.100 F = 0.29S .950 • 7S5 .066 

v= 0.535 fps C/lg= 6.76 .OS4 .S36 -- -- .009S 

2cm Rt £ .950 .775 .064 .OS3 .S12 .172 .133 .0106 

4cm Rt £ .950 • 790 .05S .074 • 735 .152 .120 .0114 

6cm Rt £ .950 • 770 .056 .073 • 708 -- -- .0106 

Scm Rt £ .950 .595 .070 .11S .SS6 .OS5 .051 .0097 ---

s~ 2.42x1o-· u,. = 0.065 fps .139 .130 .043 .330 .660 .120 .016 .0032 

w = 0.656 ft T = 0. 00S4 1b/ft2 .372 .300 .04S .160 • 740 .116 .035 .0064 Q = 0.0215 dfs v = 0. 967x10- 5 ft 2 /sec .605 .40S .065 .159 1.000 -- -- .0062 

T = 24.9 °C R = 2 ,S20 • S37 .455 .05S .127 .S93 -- -- .OOS4 

D = 0.066 ft h = 0.342 .954 .46S .060 .12S .922 -- -- .0106 V = 0.499 fps C/ g = 7.64 

2cm Rt t .954 .43S .045 .103 .694 -- -- .ooss 

4cm Rt .954 .495 .042 .OS5 .64S .172 .QS5 .0073 

6cm Rt f .954 .460 .042 .091 .64S .152 .070 .009S 

Scm Rt f .954 .41S .031 .074 .477 -- -- .OOS6 

5 • S.14X10- 3 u,. = 0.119 fps .270 .662 .175 .265 1.472 .OS5 .056 .OOS2 w = 0.656 ft T = 0.027S 1b/ft2 .461 .S20 .143 .174 1.201 .120 .09S .0074 Q • 0.0351 cfs v • 0.967x10- 5 ft 2 /sec .654 .940 .121 .129 1.018 .116 .109 .0102 

T • 24.9 °C R = 4,600 • S46 1.020 .118 .116 .992 -- .0116 

D = 0.066 ft F = 0. 559 .943 1.030 .11S .115 .992 .120 .124 .010S 

v= O.S14 fps C/1&= 6.S1 

2cm Rt £ .943 .960 .095 .099 . 79S .116 .111 .0101 

4cm Rt £ .943 1.060 .097 .092 .S15 .071 .075 .0099 

6cm Rt £ .943 1.020 .103 .101 .868 -- -- .0109 

Scm Rt £ • 943 .970 .099 .102 .S32 -- -- .0137 

5 = 1S.5XlQ 3 u,. = 0.1S1 fps .2S3 1.070 .253 .236 1.39S .072 .077 .0072 

w = 0.656 ft T = 0.0635 1b/ft 2 .472 1. 320 .248 .18S 1.370 .022 .028 .0074 

Q = 0. 043S cps v = 0.967X10- 5 ft 2 /sec .660 1.500 .212 .141 1.171 .036 .054 .OOS6 

T = 24.9 °C R = 5, 760 .S50 1.620 .18S .116 1.039 .021 .034 .0093 

D = 0.066 ft ,i; = 0.691 • 925 1. 650 .1S5 V = 1.010 fps C/ g = 5.56 .112 1.022 .036 .059 .0103 

2cm Rt £ .925 1.500 .167 .111 .924 .021 .032 .0099 

4cm Rt £ .925 1.600 .16S .105 • 93S .022 .035 .009S 

6cm Rt f • 925 1.620 .1SS .116 1.039 -- -- .0167 

Scm Rt f .925 1.570 .140 .090 .776 .022 .035 .0090 
B34 TURBULENCE IN WATER 

TABLE 2.- 20-centimeter-wide flume, alluvial boundary, yawed-film results 

Mean flow parameters 

and variables 

1

0.910 

.770 

.670 

.630 

.500 S = 0.471xl63 

w = 0.632 ft 

Q = 0.057 cfs 

T = 22.2 °C 

D = 0.133 ft 

V = 0.68 fps 

v50 = 0.196 mm~ 

S = 4.33xl(j3 

w = 0.632 ft 

Q = 0.212 cfs 

T = 22.2 °C 

D = 0.141 ft 

V = 2.38 fps v50 = 0.196 mm 

S = O.S7x1()3 

w = 0.632 ft 

Q = 0.062 cfs 

T = 30.0 oc D = 0.142 ft 

v = 0.720 ft 

Dso = 0.38 mm 

U* = 0.0377 fps 

T = 0. 00349 lb/ft2 

v = 0.942xl(j5 ft2/sec 

R = 10,700 

F = o .43 

C/vg = 18.04 

U* = 0.117 fps 

T = 0.038 lb/ft2 

v = 1.026xl(j5 ft2/sec 

R = 29,300 

F = 1.00 

c ;g = 20.34 

u. = 0.041 fps 

T = 0.0004 lb/ft2 

v = 0.868xl<f5 ft 2/sec 

R = 9,600 

F = o .37 

c /g = 17.56 

S = 9.10xllf3 U* = 0.171 fps 

W = 0.632 ft T = 0.0823 lb/ft2 

Q = 0.243 cfs v = 0.868x1()5 ft2/sec 

T = 30.0 °C R = 46,300 

D = 0. 145 cfs F = 1. 28 

V = 2.66 fps C lg = 15.56 

Dso = 0.38 mm 

S = 4.86xi03 

w = 0.632 ft 

Q = 0. 209 cfs 

T = 26.1 °C 

D = 0.137 ft 

V = 2.39 fps 

Dso = 0.196 mm 

S = 4. 86xliP 

w = 0.632 ft 

Q = 0.181 cfs 

T = 26.1 °C 

D = 0.133 ft 

V = 2.15 fps 

Dso = 0.196 mm 

S = 8.97x1()3 

w = 0.632 ft 

Q = 0.255 cfs 

T=26.1°C 

D = 0.138 ft 

V = 2.92 fps 

D50 = 0.38 mm 

u. = 0.122 fps 

T = 0.0415 lb/ft2 

v = 0.942x1()5 ft2/sec 

R = 30 ,ooo F = 0.98 

c ;g = 19.59 

u. = 0.121 fps 

T = 0.0403 lb/ft2 

v = 0.942xl(i5 ft2/sec 

R = 27,400 

F = 0.94 

C/vg= 17.76 

U* = 0.167 fps 

T = 0.0772 lb/ft2 

v = 0.942x1()5 ft 2/sec 

R=37,200 

F = 1. 20 

C//i= 17.48 

.480 

.390 

.350 

.220 

.170 

.100 

.080 

.030 

0.810 

. 700 

.580 

.460 

. 340 

.230 

.170 

.110 

.050 

~.941 

. 795 

.653 

.508 

.392 

.293 

.220 

.161 

.119 

.075 

.046 

~- 762 

.643 

.524 

.405 

.310 

.226 

.167 

.119 

.083 

~).950 

.830 

.710 

.590 

.470 

.350 

.230 

.170 

.120 

.080 

.060 

.040 

0.910 

• 790 

.670 

.540 

.420 

.300 

.170 

.110 

.080 

.040 

0. 767 

.588 

.492 

.396 

.277 

.158 

.098 

.067 

.038 

o. 790 

. 750 

.730 

.720 

. 700 

.690 

.660 

.640 

.610 

.580 

.520 

.490 

.400 

2.570 

2.520 

2.440 

2.340 

2.220 

2.040 

1.920 

1. 730 

1.400 

0.800 

.803 

. 782 

• 752 

.723 

. 701 

.666 

.624 

.580 

.548 

.482 

3.310 

3.220 

3.160 

3.030 

2.910 

2.680 

2.490 

2.150 

1.960 

0.0477 

.0483 

.0496 

.0524 

.0583 

.0588 

.0630 

.0672 

.0759 

.0781 

.0870 

.0860 

.0899 

0.1240 

.1390 

.1480 

.1700 

.1830 

.1960 

.2070 

.2230 

.1920 

0.0453 

.0491 

.0536 

.0561 

.0588 

.0685 

.0766 

.0824 

.0895 

.0929 

.0999 

0.1880 

.2340 

.2570 

.2880 

.3220 

.3490 

.3600 

.3740 

.4080 

Flume Centerline, Incipient Motion 

0.061 

.065 

.068 

.073 

.084 

.085 

.096 

.lOS 

.124 

.135 

.167 

.175 

.224 

1.265 

1.280 

1.316 

1.391 

1.545 

1.560 

1.673 

1. 775 

2.013 

2.074 

2.308 

2.281 

2.381 

0.0355 0.0486 0.9416 0.00113 

.0396 .0574 1.0500 .00166 

.0440 .0688 1.1670 .00219 

.0454 .0783 1.2040 .00274 

.0442 .0902 1.1720 .00306 

Flume Centerline, Natural Flatbed 

0.048 

.056 

.061 

.073 

.084 

.097 

.108 

.129 

.138 

1.060 

1.188 

1.265 

1.453 

1.581 

1.675 

1. 769 

1.906 

1.641 

0.1080 0.0429 0.9230 0.01080 

.1150 . 0491 . 9829 . 01610 

.1240 .0559 1.0598 .01850 

.1480 . 077~ 1. 2650 . 02790 

Flume Centerline, Incipient Motion 

0.057 1.102 ------ ------ ------ ------- .061 1.197 0.0327 0.0410 0.8020 0.00890 

.068 1.306 ------ ------ ------ ------- .074 1.369 .0379 .OSlO .9260 .01920 

.081 1.435 .0417 .0580 1. 0170 .02140 

.098 1.667 .0457 .0650 1.1140 .02660 

.115 1.868 .0490 .0730 1.1930 . 03020 

.132 2.011 ------ ------ ------ ------- .154 2.178 .0544 .0940 1. 3230 .03650 

.169 2.267 .0595 .1086 1.4500 .03450 

.207 2.440 ------ ------ ------ -------

Flwne Centerline, Natural Flatbed 

0.056 

.072 

.081 

.095 

.111 

.130 

.144 

.173 

.208 

1.101 

1.370 

1.501 

1.682 

1.884 

2.042 

2.109 

2.186 

2.385 

0.1360 0.0410 0. 7950 0.01950 

.1870 .0592 1.0920 .03350 

.2700 .0926 1.5761 .04540 

• 2820 .1130 1. 6480 . OS 700 

.2970 .1514 1. 7380 .06500 

0. 00035 

. 00090 

.00129 

.00145 

.00195 

. 00203 

.00238 

.00254 

.00305 

.00324 

. 00352 

.00360 

.00379 

0.00724 

. 01140 

.01600 

.02060 

.02510 

.02930 

.03160 

.03390 

.03620 

0.00030 

.00104 

.00175 

.00248 

• 00307 

.00357 

.00394 

. 00424 

• 00445 

.00467 

. 00482 

0.01960 

. 02940 

.03920 

.04900 

.05680 

.06370 

. 06860 

.07250 

.07550 

Flwne Centerline, Artificial Flatbed With Sediment Motion 

2.580 

2.530 

2.470 

2.400 

2.310 

2.200 

2.050 

1.930 

1. 770 

1.650 

1.440 

1.340 

2.440 

2.380 

2.280 

2.120 

2.020 

1.890 

1. 780 

1.670 

1.470 

1.320 

3.190 

3.070 

2.960 

2.860 

2.670 

2.380 

2.140 

1.940 

1.650 

0.1020 

.1100 

.1300 

.1380 

.1430 

.1540 

.1770 

.1980 

.2060 

.2220 

.2310 

.2570 

0.040 

;043 

.053 

.057 

.062 

.070 

.086 

.103 

.116 

.135 

.160 

.192 

0.835 

.904 

1.066 

1.130 

1.172 

1.263 

1.449 

1.622 

1.689 

1.820 

1.890 

2.108 

0. 0980 0. 0400 0. S040 0. 01030 

.1020 . 0440 . 8350 • 01480 

.1220 .0590 1.0000 .02020 

.1420 . 0800 1. 1630 • 02430 

.1600 .1111 1.3110 .03160 

0.00208 

.00706 

.01200 

.01700 

• 02200 

.02700 

.03200 

.03450 

. 03660 

.03820 

.03910 

.03990 

Flume Centerline, Artificial Flatbed Without Sediment Motion 

0.0940 

.1090 

.1160 

.1290 

.1520 

.1790 

.2020 

.2040 

.2290 

.2590 

0.0390 

.0460 

.OSlO 

.0610 

.0750 

.0950 

.1130 

.1220 

.1560 

.1970 

0. 776 

.900 

.958 

1.066 

1.256 

1.477 

1.672 

1.690 . 

1.894 

2.140 

0.0890 0.0370 0.7350 0.00980 

• 0960 • 0450 . 7940 . 01720 

.1370 . 0730 1.1350 . 02400 

.1440 .0860 1.1900 .02810 

Flwne Centerline, Artificial Flatbed With Sediment Motion 

0. 2330 

.2700 

.2840 

.2920 

.3060 

.3120 

.3250 

.3470 

.3690 

0.0730 

.0880 

.0960 

.1020 

.1140 

.1310 

.1520 

.1790 

.2240 

1.170 

1.350 

1.420 

1.460 

1.530 

1.560 

1.947 

2.081 

2.202 

0.1230 0.0390 o. 7350 0.01760 

.1260 .0410 .7540 .02930 

. 1620 • 0600 • 9680 . 03860 

.1860 . 0780 1.1120 . 05020 

.1950 .1005 1.1680 . 06100 

0.00363 

.00847 

.01330 

.01860 

.02340 

.02820 

.03350 

.03590 

.03710 

.03870 

0.01800 

. 03180 

.03920 

.04670 

.05580 

.06500 

. 06970 

.07210 

.07430 

0. 00109 0. 4098 

.00180 .6020 

. 00276 . 7943 

• 00420 . 9937 

• 00657 1.1098 

0.00088 0.4067 

.00152 .6063 

.00194 .6966 

.00390 1.0506 

------- ------ 0.00071 o. 2700 

------- ------ .00175 .5870 

.00213 .6560 

.00279 .8170 

.00350 .9250 

------- ------ .00560 1.1120 

.00593 1.0560 

------- ------

0. 00092 0. 3437 

.00173 .5905 

. 00276 • 8003 

.00474 1.0048 

• 00872 1. 1460 

0.00087. 0.3567 

. 00143 • 5125 

• 00248 • 6996 

• 00400 • 8416 

• 00786 1. 0940 

0. 00089 0. 3450 

• 00197 . 6056 

. 00346 • 8450 

.00519 • 9893 

0. 00089 0. 3253 

. 00172 .5414 

• 00279 . 7134 

.00457 • 9278 

• 00835 1.1270 

;>. X 

(ft) 

0.295 0.221 0.0209 

• 315 • 220 . 0204 

.335 .205 .0174 

0.145 0.365 0.0076 

.140 . 311 • 0066 

. 205 • 355 . 0038 

----- ----- ------ 0.261 0.210 0.0170 

----- ----- ------ .283 .213 .0210 

.280 .202 .0230 

.247 .173 .0180 

.301 .200 .0200 

----- ----- ------ .268 .156 .0190 

.254 • l39 .0160 

----- ----- ------

0. 075 0. 093 0. 0081 

.085 .116 .0073 

.105 .104 .0088 

.130 .107 .0077 

• 080 • 087 • 0065 

0.127 0. 314 0. 0073 

.143 . 330 . 0077 

.138 • 283 • 0081 

.1461 - .258 .0067 

~~~~~ 1 ~~~~~ . 0051 

0.123 0.293 0.0083 

.147 .312 .0086 

.136 .257 .0079 

• 122 • 204 • 0065 

0.130 0.415 0.0083 

.145 . 415 • 0077 

. 140 • 333 . 0069 

.105 .173 .0037 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

TABLE 2.- 20-centimeter-wide flume, alluvial boundary, yawed-film results- Continued 

Mean flow parameters 

and variables 

Flume Centerline, Artificial Flatbed Without Sediment Motion 

S = 8.97xl(j3 

w = 0.632 ft 

Q = 0. 253 cfs 

T = 26.1 °C 

D = 0.140 ft 

V = 2. 86 fps 

Dso = 0.38 mm 

s = 1. 75xlo 3 

w = 0.632 ft 

Q ., 0.072 cfs 

T = 22.2 °C 

D = 0.196 ft 

V = 0.728 fps 

Dso = 0.38 mm 

5 = 1. 75Xl(j3 

w = 0.632 ft 

Q = 0.072 cfs 

T = 22.2 °C 

D = 0.120 ft 

V = 0. 728 fps 

Dso = 0.38 mm 

0. 741 3.200 0.1460 0.0460 0.868 0.1060 0.0330 0.0632 0.01890 

v. = 0.168 fps .565 3.040 .1680 .0550 1.000 .1210 .0400 . 7200 . 03120 

T = 0.0783 lb/ft2 .389 2.820 .1850 .0660 1.100 

y = 0.942xl<f5 ft 3/sec . 272 2.610 .2120 .0810 1.261 .1600 .0610 .9530 .05000 

R = 35,400 .155 2.280 .2500 .1100 1.487 .1780 .0780 1.0600 .06050 

F = 1.12 .096 1.980 .2910 .1470 1. 735 .1900 ,0960 1.1320 .06600 

C//g = 17.02 .054 1.650 .3200 .1940 1.905 

.038 1.440 .3670 .2550 2.186 

Flume Center line, Dune Trough 

v. = 0.077 fps 0.863 0.920 0.0984 0.1070 0.937 0.0635 0.0690 0. 8247 0.01800 T = 0.0214 lb/ft2 .728 .870 .1110 .1280 1.057 .0792 .0910 1.0290 .03500 v = 1.026xl(f5 ft2/sec .552 . 780 .1370 .1760 1.305 .0983 .1260 1. 2770 .04500 R = 13,100 .381 .580 . 2160 .3720 2.057 .1180 .2034 1.5320 .05600 F = o. 27 .289 .350 .1000 .2870 .952 .0684 .1954 .8883 .06700 C//g = 9.45 .223 .140 .0330 .2360 .314 ,0200 .1429 . 2597 .07900 

v = o.l57 ft I 

Flume Centerline, Dune Crest 

v. = 0.077 fps 0.817 1.000 0.1180 0.1180 1.436 

T = 0.0131 lb/ft2 .680 .960 .1210 .1260 1.472 

v = 1.026xl(Y5 ft 2/sec .542 .940 .1260 .1340 1.533 

R = 8,000 .405 .890 .1310 .1470 1.594 

F = o. 35 .268 .870 .1380 .1590 1.679 

C//g = 9.45 .131 .840 .1460 .1740 1. 776 

v = o.l57 ft 

TABLE 3a.- 2-foot-wide flume, rigid boundary 

Mean Flow ParaJReters 

and Variables 

1/8-lnch Block Roughness, Channel Centerline 

0.900 1.170 0.106 0.091 1.072 

S = l.04xlo'3 . 800 1.170 .136 .106 1.378 v. = 0.0989 fps 

w . 700 1.120 .142 .126 1.436 = l. 96 ft T = 0.0189 lb/ft2 .600 1.100 .151 .137 1.529 Q = 0.815 cfs v = 0,930xH)5 ft2/sec .500 1.020 .150 .147 1. 518 T = 26.5 °C R = 44,600 .400 .970 .156 .161 1.580 D = 0.415 ft F = 0.274 . 300 .900 .161 .178 1.630 V = 1.00 fps C/fi = 10.14 .200 .880 .169 .192 1.711 .100 .710 .178 .251 1. 806 

l/8-Inch Block Roughness Channel Centerline 

0.900 2. 200 0.171 0.07& 0.982 

.800 2.100 .173 .082 .996 S = 3.10xlo'3 v. = 0.174 fps • 700 2.030 .186 .091 1.071 w = 1.96 ft T = 0.0562 lb/ft2 .600 1.970 .207 .105 1.189 Q = 1.42 cfs v = 0,930xl05 ft2/sec .500 l. 890 .205 .108 1.178 T=26.5°C R=77,900 .400 1. 730 .217 .125 1.246 D = 0.415 ft F = 0.449 .300 1.680 .231 .137 1.324 V = 1. 75 fps c;fi = 10.23 .200 1.520 . 245 .161 1.410 

.100 1.340 .289 .216 1.662 

l/8-Inch Block Roughness, Channel Centerline 

0. 800 3. 210 0.257 0.080 0.996 

S = 7 .20x10° U * = 0. 258 fps . 700 3.110 .264 .085 1.023 w = 1.96 ft T = 0,128 lb/ft2 .600 3.000 .288 .096 1.117 Q = 2.14 cfs v = 0 .930x1()5 ft2/sec .500 2. 860 .287 .095 1.112 T = 26,5 °C R = 117,700 .400 2. 700 .324 .120 1.258 D = 0.410 ft F = 0.734 .300 2.610 .360 .138 1.396 V = 2.67 fps C//g = 10.21 .200 2.410 .395 .164 1.534 

.100 2.030 .380 .187 1.471 

1/2-Inch Block Roughness, Channel Centerline 

0.900 1.160 0.174 0.149 0.979 S = 3.40xl03 v. = 0.1775 fps . 800 1.140 .188 .165 1.101 w = 1.96 ft T = 0.0611 lb/ft2 . 700 1.110 .202 .183 1.138 Q = 0. 815 cfs v = 0.930xll)5 ft 2/sec .600 1.060 ',204 .193 1.150 T = 26.5 °C R = 44,800 .500 1.090 . 230 .211 1.296 D = 0.409 ft F = o. 282 .400 1.020 .248 .243 1.396 V = 1.02 fps c;lg = 6.17 ,300 1.000 .240 .240 1.354 

.200 .800 .248 .310 1.396 

0.660 

.720 

.800 

. 780 

. 760 

.800 

. 750 

.610 

.840 

0.380 

.530 

.640 

. 260 

.280 

.400 

.330 

.500 

.540 

0.095 

.410 

.390 

.330 

.440 

.420 

. 380 

.360 

0.510 

.540 

.470 

.680 

• 290 

.510 

.480 

. 370 

0.02030 

. 03410 

,04790 

.05700 

. 06620 

.07080 

.07410 

.07540 

0,00293 

• 00582 

.00959 

.01320 

.01520 

.01660 

0.00240 

.00419 

.00600 

. 00780 

.00959 

.01140 

0.00095 

. 00174 

.00378 

• 00600 

.00868 

0.01100 

X 

:r: 

(ft) 

.02390 

. 03810 

.08580 

. 28190 

.20780 

0. 770 0.0160 

.840 .0153 

.890 .0144 

.860 .0131 

.770 .0126 

.770 .0097 

.680 .0103 

.540 .0083 

.600 ------

0.840 Q.0196 

1.110 .0183 

1.'300 .0161 

.510 .0165 

.530 .0143 

.690 .0147 

.550 .0128 

. 760 .0122 

.720 .0101 

0.310 0.0226 

1.270 ,0213 

1.170 .0209 

.940 ,0216 

1.180 .0193 

1.100 • 0185 

.910 .0169 

. 730 .0122 

0.580 ----- .610 ----- .520 ----- .720 ----- .320 ----- .520 ----- .480 ----- • 300 -----

0. 3452 

.5698 

.9132 

1.1049 

1.2050 

0. 1570 

.3050 

.3910 

.4870 

.5830 

.6870 

0.130 0.416 

.125 .353 

.165 .327 

.180 .259 

0.115 0.106 

----- ----- .145 .113 

.170 .099 

----- ----- .115 .016 

.095 ,095 

.135 .120 

.145 .122 

B35 

>. :r: 

(ft) 

0.0081 

.0078 

.0061 

.0042 

0.0076 

------

,0081 

.0072 

------

.0051 

.0091 

.0088 

.0064 
B36 TURBULENCE IN WATER 

TABLE 3a. - 2-foot-wide flume, rigid boundary- Continued 

Mean Flow Parameters 

and Variables 

1/2-Inch Block Roughness, Channel Centerline 

0.900 2.420 0.256 0.106 0.958 

.800 2.420 .262 .109 .983 

s = 7 .63xHP u* = 0.267 fps . 700 2.330 .264 .113 .990 

w = 1.96 ft T = 0,138 lb/ft2 .600 2.260 .281 .125 1.052 

Q = 1.42 cfs v = o. 930xlos ft2/sec .500 2.090 .285 .136 1.067 

T = 26.5 °C R = 77,900 .400 1.940 .296 .153 1.110 

D = 0.414 ft F = 0.481 .3aO 1.830 .308 .168 1.152 

V = 1. 75 fps ctli= 6.65 .2aO 1.600 .342 .214 1.281 

.100 . 730 .313 .428 1.176 

1/2-Inch Block Roughness, Channel Centerline 

0.900 3.110 0.303 0.097 0.834 

S = 14,00xl63 u* = 0.364 fps .800 3.030 .318 .lOS .875 

w = 1.96 ft T = 0.256 lb/ft2 . 700 2.920 .318 .109 .875 

Q = 2.14 cfs v = 0.930xl65 ft2/sec .600 2. 780 .355 .128 .975 

T = 26.5 °C R = 117,200 .sao 2.600 .381 .147 1.050 

D = a.433 ft F = 0.676 .400 2.3SO .386 .164 l.06a 

V = 2.52 fps C//g= 6.94 .3aO 2.050 .399 .194 1.09S 

.200 1.670 .352 .217 .969 

.100 1.080 .372 .344 1.020 

1 1/8-Inch Block Roughness, Channel Centerline 

S = 4.89xlo3 u* = 0.212 fps 0.900 1.4la 0 .22a 0.156 1.043 

w = 1.96 ft T = 0,087 lb/ft2 .800 1.330 .222 .168 1.062 

Q = 0.815 cfs v = 0.930xl(j5 ft2/sec . 700 1.220 .227 .186 1.070 

T = 26.5 °C R = 46 ,ooo .6aO 1.150 .228 .198 1.086 

D = 0.417 ft F = 0.279 .500 1.040 .228 .219 1.086 

V = 1.03 fps c;lg = 4. 83 .400 .920 .228 .249 1.086 

.300 .890 .213 ,250 1.006 

1 1/8-Inch Block Roughness, Channel Centerline 

s = lS .aOxHP u* = o .380 fps 0.900 2.640 0.390 0.148 l.a2S 

w = 1.96 ft T = 0,271 lb/ft2 .800 2.400 .389 .163 1.020 

Q = 1.42 cfs v = 0.930xl65 ft 2/sec . 7aO 2.1Sa .414 .193 1.090 

T = 26.S °C R = 77,900 .600 1.990 .432 .217 1.138 

D = 0.414 ft F = 0.479 .sao 1.870 .422 .226 1.110 

v= 1.7S fps c;lg = 4.66 .400 1.660 .410 .247 1.078 

.3aa 1.42a .39S .278 l.a4a 

1 1/8-Inch Block Roughness, Channel Centerline 

S = 29 ,6xl()3 u* = o.s3S fps .8aO 3.880 0.623 0.161 1.16S 

w = 1.96 ft T = 0.552 lb/ft2 . 7aO 3. 780 .64a .17a 1.195 

Q = 2.14 cfs v = 0.93axl65 ft2/sec .6aO 3.52a .67S .192 1.26a 

T = 26.5 °C R = 117 ,3oa .sao 3.330 .678 .2a4 1.26a 

D = a.430 ft F = 0,683 .4aa 3.010 .719 .239 1.345 

V = 2.54 fps C//g= 4.76 .3aa 2.670 . 705 .265 1.32a 

0.470 1.140 

.510 1.230 

. 760 1. 77a 

.600 1.38a 

.620 1.290 

.450 . 870 

.540 .990 

.380 .6la 

.470 .340 

0.330 1.030 

.500 l.Sla 

.530 l.ssa 

.550 1.530 

.630 1,640 

.37a .870 

.200 .4la 

.38a .630 

.240 .260 

a.460 0.650 

.520 .68a 

.5oa .610 

.450 .520 

.440 .460 

.47a .430 

.370 .330 

0.26a 0.690 

.1sa .360 

.460 .98a 

.310 .620 

.360 .670 

.27a .4Sa 

.3la .44a 

0.22a a.8SO 

.24a .9la 

.37a 1.3la 

.44a 1.46a 

.370 1.11a 

.18a .48a 

TABLE 3b.- 2-foot-wide flume, rigid boundary, developing flow 

Mean Flow Parameters 

and Variables 

1 1/8-Inch Block Roughness, Channel Centerline, Station 5 

S = S.a4xlQ3 U * = 0. 216 fps a.898 1.445 a.l74 0.120 0.8a6 0.124 

w = 1.96 ft T = 0.128 lb/ft2 • 796 1.445 .175 .121 .8la .126 

Q = a.78 cfs v = 1.a68x165 ft2/sec .694 1.415 .181 .128 .838 .14a 

T = 21 °C R = 37,247 .592 1.4aa .177 .126 .819 .128 

g_ = 0.4a8 ft F = a. 269 .49a 1.34a .197 .147 .912 .142 

V = 0.975 fps c;lg = 4.514 .388 1.17a .217 .185 l.Oas .135 

.286 .960 .199 .2a7 .921 .16a 

1 1/8-Inch Block Roughness, 6 Inches From wall, Station 5 

S = 5 .a4xl63 u* = a.216 fps a.898 l.sao 0.167 0.111 o. 773 a.l31 

w = 1.96 ft T = a.l28 lb/ft2 • 796 1.485 .165 .111 . 764 .135 

Q = a.78 cfs v = 1.068xlo5 ft 2/sec .694 1.39a .163 .117 . 755 .132 

T = 21 °C R=37,247 .592 1.33a .178 .134 .824 .142 

D = 0.4a8 ft F = o .269 .49a 1.285 .242 .188 1.12a .125 

V = a.975 fps c;lg = 4.514 .388 1.19S .223 .187 1.032 .132 

.286 .99a .232 .234 l.a74 .138 

1 1/8-Inch Block Roughness, Channel Centerline Station 1a 

S = 5.04xl63 V* = a.217 fps a.898 1.195 0.12a a.tao a.553 0.126 

w = 1.96 ft T = a .130 lb/ft2 • 796 1.195 .136 .114 .627 .117 

Q = 0. 78 cfs v = 1.068xl65 ft2/sec .694 1.125 .142 .126 .654 .142 

T = 21.1 °C R = 37,278 .592 l.a9a .171 .157 • 788 .154 

D = a.413 ft F = o .264 .49a l.a7o .167 .156 .770 .137 

V = a.964 fps C//g= 4.442 .388 .940 .175 .186 .8a6 .119 .286 .9aa .212 .236 .977 .130 

a.l79 

.182 

.198 

.179 

.19a 

.1S8 

.153 

a.l96 

.2aO 

.184 

.189 

.161 

.158 

.137 

0.151 

.14Q 

.160 

.168 

.147 

.112 

.117 

l. 

:r: 

(ft) 

-----

-----

-----

-----

-----

-----

-----

-----

-----

,----- -----

I -----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

>. :r: 

(ft) 

0. aa86 

.0092 

.oa83 

.a081 

.a085 

.aa79 

.aa63 

0. a074 

.aa76 

.a071 

.oan 

.0087 

.Oa81 

.oa7s 

0.0102 

.0109 

.0094 

.0112 

.0094 

.0081 

.0067 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

TABLE 3b.- 2-/oot-wide fiu'tne, rigid boundary, developing flow- Continued 

Mean Flow Par11111eters 

and Variables 

1 1/8-Inch Block Roughness 6 Inches From Wall Station 10 

S = 5.04xl63 u. = 0.217 fps 0. 898 1.620 0.205 0.127 0.945 0.147 0.238 

w = 1.96 ft T = 0.130 lb/ft2 . 796 1.620 .239 .148 1.101 .148 . 240 

Q = 0. 78 cfs v = 1.068xl05 ft 3 /sec .694 1.580 .259 .164 1.194 .120 .190 

T = 21.1 •c R = 37,278 .592 1.420 .23S .165 1.083 .130 .184 

D = 0.413 ft F = 0.264 .490 1.340 .253 .189 1.166 .134 .180 

V = 0.964 fps c;lg = 4.442 .388 1.140 .262 .230 1.207 .133 .152 

.286 .900 .212 .236 .977 .137 .123 

1 1/8-Inch Block Roughness, Channel Centerline Station 15 

s = 5. 04x163 u. = 0.217 fps 0.898 1.240 0.126 0.102 0.581 0.242 0.300 

w = 1.96 ft T = 0.130 lb/ft2 . 796 1. 235 .157 .127 . 724 .205 .253 

Q = 0. 78 cfs v = 1.068xl0 5 ft 2/sec .694 1.190 .169 .142 .779 .362 .430 

T = 21.1 •c R=37,265 .592 1.190 .192 .161 .885 .317 .377 

D = 0.412 ft F = 0. 265 .490 1.100 .188 .171 .866 .361 .398 

V = 0.966 fps C//g = 4.452 .388 .990 .2ll .213 .972 .265 .262 

.286 .880 .181 .206 .834 .299 .263 

1 1/8-Inch Block Roughness 6 Inches From Wall Station 15 

S = 5.04xl63 u. = 0.217 fps 0.898 1.570 0.199 0.127 0.917 0.398 0.625 

w = 1. 96 ft T = 0,130 lb/ft2 . 796 1.570 .208 .132 .959 .378 .594 

Q = 0. 78 cfs v = 1.068xH)5 ft 2/sec .694 1.560 .232 .149 1.069 .347 . 542 

T=2l.l"C R=37,265 .592 1.500 .213 .142 .982 .264 .396 

D = 0.412 ft F = 0.265 .490 1. 400 .242 .173 1.115 .329 .461 

V = 0.966 fps c;lg = 4.452 .388 1.205 .214 .178 .986 .516 .622 

.286 1.010 .197 .195 .908 .403 .407 

1 1/8-Inch Block Roughness Chinnel Centerline Station 20 

S = 5.40xl()3 u. = 0.216 fps 0.898 1.300 0.157 0.121 0. 727 0.383 0.498 

w = 1. 96 ft T = 0.128 lb/ft2 . 796 1.270 .178 .140 .824 .417 .530 

Q = 0.78 cfs v = 1.068xl65 ft2/sec .694 1.230 .175 .142 .810 .537 .660 

T = 21.1 •c R = 37,270 .592 1.230 .198 .161 .917 .412 .506 

D = 0.407 ft F = 0.270 .490 1.140 .205 .180 .949 .214 .244 

V = 0.978 fps C/fg= 4.528 .388 1.010 • 203 • 201 .940 .492 .497 

.286 .770 .161 .209 • 745 . 751 .578 

1 1/8-lnch Block Roughness 6 Inches From Wall Station 20 

S = 5.04xliP u. = 0.216 fps 0.898 1.600 0.209 0.131 0.968 0.437 0.701 

w = 1. 96 ft T = 0.128 lb/ft2 . 796 1.595 .234 .147 1.083 .304 .486 

Q = 0. 78 cfs v = 1.068xHi5 ft 2/sec .694 1.590 .253 .159 1.171 .411 .652 

T=2l.l"C R = 37,270 .592 1.540 .275 .178 1.273 • 726 1.117 

D = 0.407 ft F = 0.270 .490 1.400 .256 .183 1.185 .390 .545 

V= 0.978 fps C/fg = 4.528 .388 1.270 .242 .191 1.120 • 271 • 344 

.286 1.100 . 238 .216 1.102 .340 .374 

1 1/8-lnch Block Roughness, .:hanne1 Centerline, Station 25 

S = 5.04x163 u. = 0.214 fps 0.898 1. 380 0.195 0.141 0.9ll 0.392 0.541 

w = 1.96 ft T = 0.125 lb/ft2 . 796 1.350 .220 .163 1.028 .355 .480 

Q = 0. 78 cfs v = 1.068xl65 ft2/sec .694 1.310 .212 .162 .991 .486 .636 

T = 21.1 •c R=37,266 .592 1.250 .236 .189 1.103 .395 .493 

!2. = 0_,398 ft F = 0.279 .490 1.180 .235 .199 1.098 .413 .488 

V = 1.000 fps c;lg = 4.673 .388 1.120 .253 .226 1.182 .512 .572 .286 .930 .239 .257 1.117 .404 .376 

1 1/8-Inch Block Roughness 6 Inches From Wall Station 25 

S = 5.04xl63 u. = 0.214 fps 0.898 1.640 0.192 O.ll7 0.897 0.224 0,368 

w = 1.96 ft T = 0,125 lb/ft2 • 796 1.690 .219 .130 1.023 • 655 1.107 

Q = 0.78 cfs v = l.068xl65 ft2/sec .694 1.695 .221 .130 1.033 .367 .623 

T = 21.1 •c R=37,266 .592 1.600 .268 .168 1.252 .695 1.111 

!2. = 0.398 ft F = 0.279 .490 1.520 .275 .181 1.285 .327 .496 

V = 1.000 fps c;lg = 4.673 .388 1.345 .272 .202 1.271 .410 .552 

.286 1.000 .239 .239 1.117 .158 .158 

1 1/8-Inch Block Roughness Channel Centerline Station 30 

S = 5 .04xl(j3 u. = 0.215 fps 0.898 1.380 0.207 0.150 0.963 0.429 o. 592 

w = 1.96 ft T = 0.126 lb/ft2 • 796 1.330 .229 .172 1.065 .684 .911 

Q = 0. 78 cfs v = 1.068xlo-s ft 2/sec .694 1.300 .238 .183 1.107 .676 .880 

T=21.1"C R=37,264 .592 1.270 .276 .217 1.284 .306 .388 

!2. = 0.402 ft F = 0.275 .490 1.130 .238 .211 1.107 .218 .246 

V = 0.990 fps c;lg = 4.605 .388 1.050 .253 .241 1.177 .658 .692 .286 .770 ----- ----- ----- .348 • 268 

1 1/8-Inch Block Roughness 6 Inches From Wall Station 30 

S = 5. 04xl63 u. = 0. 215 fps 0.898 1.630 0.188 0.115 0.874 0.468 o. 764 

w = 1.96 ft T = 0.126 lb/ft2 • 796 1.650 .214 .130 .995 .388 .640 

Q = 0. 78 cfs v = 1.068xlo-s ft2/sec .694 1.635 .225 .138 1.047 • 501 .819 

T = 21.1 •c R=37,264 .592 1.540 .230 .149 1.070 . 382 .589 

!2. = 0.402 ft F = o .275 .490 1.395 .226 .162 1.051 .355 .496 

v = 0.990 fps. c;lg = 4.605 . 388 1. 240 .238 .192 1.107 .416 .516 .286 1.010 ----- ----- ----- .393 .396 

1 1/8-Inch Block Roughness Channel Centerline Station 35 

S = 5.04xl63 u. = 0.216 fps 0.898 1.380 0.217 0.157 1.005 , .• , I , .• ,. w = 1.96 ft T = 0.128 lb/ft2 . 796 1.330 .249 .187 1.153 . 34-4 .458 

Q = 0. 78 cfs v = 1.068xl65 ft 2/sec .894 1.335 .245 .184 1.134 . 374 .448 

T = 21.1 •c R = 37,270 .592 1.170 .227 .194 1.051 .601 .703 

D = 0.407 ft F = 0.270 .490 1.110 .235 .212 1.088 .321 I .356 

V = 0.978 fps C/fg= 4.528 .388 1.000 .239 .239 1.106 .538 .538 

.286 • 700 .170 .243 • 787 .457 ,326 

). 

::: (ft) 

0.0098 

.0105 

.0097 

.0094 

.0087 

.007!l 

.0066 

0. 0101 

.0097 

.0098 

.0106 

.0096 

.0084 

.0075 

o. 0135 

.0119 

.0120 

.0119 

.0131 

.0092 

.0081 

0.0101 

.0122 

.0102 

.0104 

.0088 

.0088 

.0072 

0.0123 

.0133 

.0153 

.0138 

.0117 

.0100 

.0091 

0.0115 

.0101 

.0122 

.0104 

.0087 

.0084 

.0074 

0.0133 

.0139 

.0142 

.0126 

.0116 

.0104 

.0098 

0.0126 

.0117 

• 0123 

.0109 

.0096 

.0085 

.0079 

0.0127 

.0134 

.0143 

.0124 

.0117 

.0108 

.0101 

0.0132 

.0109 

.0125 

.0121 

.0096 

.0092 

.0084 

B37 
B38 TURBULENCE IN WATER 

TABLE 3b.- 2-foot-wide flume, rigid boundary, developing flow- Continued 

Mean Flow Parameters 

and Variables 

1 1/8-Inch Block Roughness 6 Inches From Wall Stati on 35 

s = 5.o4xHP 

w = 1. 96 ft 

Q = 0.78 cfs 

T=2l.l°C 

!!..= 0.407 ft 

V = 0.978 fps 

S = 5.04xHJ3 

w = 1. 96 ft 

Q = 0. 78 cfs 

T = 21.1 •c 

D = 0.408 ft 

V = 0.975 fps 

S = 5 .04xl63 

w = 1.96 ft 

Q = 0. 78 cfs T = 21.1 •c-

!!.. = 0.408 ft 

V = 0.975 fps 

S = 5.04xHP 

w = 1. 96 ft 

Q = 0.78 cfs 

T=2l.r•c 

D = 0.412 ft 

V = 0.966 fps 

S = 5.04xJ63 

w = 1.96 ft 

Q = 0.78 cfs T = 21.1 •c 

D = 0.412 ft 

V = 0.966 fps 

s = 13. 25xJo3 

w = 1.96 ft 

Q = 1.21 cfs 

T=2Lr•c 

D = 0.405 ft 

V. = 1.524 fps 

S = 13. 25xJ(j3 

w = 1.96 ft 

Q = 1.21 cfs 

T = 21.1 •c 

D = 0.405 ft 

V = 1.524 fps 

S = 13.25x}()3 

w = 1. 96 ft 

Q = 1.21 cfs 

T=2l.l°C 

D = 0.410 ft 

V = 1.506 £ps 

S = 13.25xl03 

w =· 1.96 ft 

Q = 1. 21 cfs 

T = 21.1 'r· 

D = 0.410 ft 

V = 1.506 fps 

S = 13.2SxJQ3 

w = 1.96 ft 

Q = 1.21 cfs 

T = 21.1 •c 

D = 0.415 ft 

V = 1.488 fps 

u. = 0.216 fps 0.898 1.550 0.178 O.ll5 0.824 

T = 0.128 Jb/ft2 . 796 1.610 .190 .ll8 .880 

v = 1.068xJ65 ft 2/sec .694 1.620 .217 .134 1.005 

R = 37,270 .592 1.580 .229 .145 1.060 

F = o .270 .490 1.480 .230 .155 1.065 

c;/g= 4.528 .388 1.280 .251 .196 1.162 

.286 1.030 .228 .221 1.056 

1 1/8-Inch Block Roughness Channel Center!' 1ne, St a t 1on · 40 

u. = 0.216 fps 0.898 1.350 0.204 0.151 0.944 

T = 0,128 Jb/ft2 . 796 1.260 .204 .162 .944 

v = 1.068xJ()5 ft2/sec .694 1.205 .221 .183 1.023 

R = 37,247 .592 1.060 .215 .203 .995 

F = o. 269 .490 1.030 .214 .208 .991 

C//g= 4.514 .388 .900 .200 .222 .926 

.286 .770 .192 .249 . 889 

1 1/8-Inch Block Roughness 6 Inches From Wall Station 40 

u. = 0.216 fps 0.898 1.560 0.192 0.123 0.889 

T = 0.128 lb/ft2 . 796 1.580 .204 .129 .944 

v = 1.068xlQS ft2/sec .694 1.580 .218 .138 1 009 

R = 37,247 .592 1.540 .220' .143 1.019 

F = o .269 .490 1.460 .237 .162 1.097 

C//g= 4.514 .388 1.280 .252 .197 1.167 

.286 1.050 .206 .196 .954 

1 1/8-Inch Block Roughness Channel Centerline Station 45 

u. = 0.217 fps 0.898 1.295 0.198 0.153 0.912 

T = 0.130 lb/ft2 . 796 1.280 .215 .168 .991 

v = 1.068xl65 ft2/sec .694 1.160 .217 .187 1.000 

R = 37,265 .592 1.030 .189 .183 .871 

F = o .265 .490 .990 .183 .185 .843 

c;lg = 4.452 .388 .960 .220 .229 1.014 

.286 . 790 .192 .243 .885 

1 1/8-Inch Block Roughness 6 Inches From Wall Station 45 

u. = 0.217 .fps 0.898 1.520 0.175 O.ll5 0.806 

T = 0,130 Jb/ft2 . 796 1.550 .199 .128 .917 

v = 1. 068xl05 ft 21 sec .694 1.560 .195 .125 .899 

R = 37,265 .592 1.550 .217 .140 1.000 

F = o .265 .490 1.475 .233 .158 1.074 

c;lg = 4.452 .388 1.270 .255 .201 1.175 

.286 .930 .209 .225 .963 

1 1/8-Inch Block Roughness Channel Centerline Station 5 

u. = 0.350 fps 0.898 2.360 0.258 0.109 o. 737 

T = 0 ,335 lb/ft2 • 796 2.300 0.267 O.ll6 0. 763 

v = 1. 068xHf5 ft2 /sec .694 2.200 0.245 O.ll3 0. 700 

R = 57,792 .592 2.100 0.247 O.ll8 0. 706 

F = 0.422 .490 1.870 0.238 0.127 0.680 

c;lg = 4.354 .388 1.590 .247 .155 • 706 

.286 1.300 .223 .172 .637 

1 1/8-Inch Block Roughness 6 Inches From Wall Station 5 

u. = 0.350 fps 0.898 2.330 0.263 O.ll3 0. 751 

T = 0,335 lb/ft2 • 796 2.380 .310 .130 .886 

v = 1.068xJ05 ft2/sec .694 2.400 .350 .146 1.000 

R = 57,792 .592 2.400 .446 .186 1.274 

F = o .422 .490 2.310 .500 .216 1.429 

c;lg = 4.354 .388 2.100 .509 .242 1.454 

.286 1.680 .382 .227 1.091 

1 1/8-Inch Block Roughness, Channel Centerline, Station 10 

u. = 0.351 fps 

T = 0.339 lb/ft2 

v_ = 1.068xi05 ft2/sec 

R=S7,815 

F = 0.414 

c;lg = 4.291 

0.898 

. 796 

.694 

.592 

.490 

.388 

.286 

2.200 

2.030 

1.960 

1.805 

1.650 

1.500 

1.300 

0.287 

.212 

.271 

.241 

.260 

.269 

.313 

0.130 

.104 

.138 

.134 

.158 

.179 

.241 

0.818 

.604 

.772 

.686 

. 741 

. 766 

.892 

1 1/8-Inch Block Roughness, 6 Inches From Wall, Station 10 

u. = 0.351 fps 

T = 0.339 lb/ft2 

v = 1.068xJ6 5 ft 2/sec 

R = 57,815 

F = 0.414 

C//g= 4.291 

0.898 

• 796 

.694 

.592 

.490 

.388 

.286 

2.280 

2.310 

2.320 

2.320 

2.205 

1.905 

1.470 

0.224 

.300 

.412 

.440 

.415 

.462 

.4ll 

0.098 

.130 

.178 

.190 

.188 

.243 

.280 

0.638 

.855 

1.174 

1. 254 

1.182 

1.316 

1.171 

1 1/8-Inch Block Roughness, Channel Centerline, Station 15 

u. = 0.353 fps 

T = 0.343 lb/ft2 

v = 1.068xi05 ft2/sec 

R = 57,820 

F = 0.407 

C//g = 4.215 

0.898 

. 796 

.694 

.592 

.490 

.388 

.286 

2.200 

2.080 

2.030 

1.950 

1. 770 

1.500 

1.305 

0.295 

.309 

.325 

.313 

.299 

.285 

.293 

0.134 

.149 

.160 

.161 

.169 

.190 

.225 

0.836 

.875 

.921 

.887 

.847 

.807 

.830 

0.267 

.333 

.646 

.255 

.567 

.579 

.304 

0.504 

• 343 

.356 

.342 

.494 

. 283 

.243 

0.253 

.268 

.3ll 

. 347 

. 337 

.618 

.516 

o. 233 

.375 

.270 

.367 

.474 

.289 

.541 

0.463 

. 289 

.495 

.300 

.269 

.431 

.384 

0.157 

.136 

.147 

.126 

.299 

.151 

.160 

0. 204 

.169 

.152 

.146 

.185 

.171 

. 217 

0.414 

.536 

1.043 

.403 

.837 

. 741 

. 313 

0.680 I .432 

.429 

. 363 

.508 

,;254 

.187 

0.394 

.423 

.491 

.534 

.492 

• 791 

.542 

0.320 

.480 

.313 

.378 

.468 

.2_77 

.4_27 

o. 705 

.447 

• 772 

.465 

.397 

.547 

.357 

0.371 

. 313 

.323 

.264 

.559 

• 240 

.208 

0.475 

.402 

.365 

.351 

.427 

.359 

.365 

A 

:r: 

(ft) 

o. 0142 

.0127 

.0163 

,0123 

.0132 

.0121 

.0107 

0.0125 

.0108 

.0123 

.Olll 

.0124 

.0086 

.0077 

0. 0125 

.0121 

.Oll7 

. 0113 

.0108 

.0097 

.0089 

0.0119 

.0123 

,0121 

.0116 

.0108 

.0093 

.0081 

0.0137 

.0136 

.0138 

.0131 

.0126 

.0114 

.0105 

0.0133 

.0127 

.0136 

.0129 

.0102 

.0092 

.O,!J84 

0.0133 

.0136 

.0131 

.0142 

.0131 

.0126 

.0113 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

TABLE 3b.- 2-foot-wide flume, rigid boundary, developing flow- Continued 

Mean Flow Parameters 

and Variables 

1 1/8-Inch Bloc;k Roughness, 6 Inches From Wall, Station 15 

S = 13.25xl()3 u. = 0.353 fps 0.898 2.360 0.269 O.ll4 o. 762 

w = 1.96 ft T = 0. 343 lb/ft2 . 796 2.380 .265 .lll . 751 

Q = 1. 21 cfs v = 1. 068xlQ5 ft 2/sec .694 2.400 .350 .146 .992 

T = 21.1 °C R=57,820 .592 2.380 .384 .161 1.088 

D = 0.415 ft F = 0.407 .490 2.240 .444 .198 1.258 

V = 1. 488 fps C/lg = 4. 215 .388 1.900 .420 .188 1.190 

.286 1.560 .415 .266 1.176 

1 1/8-Inch Block Roughness Channel Centerline Station 20 

s· = 13. 25xl()3 U * = 0. 352 fps 0.898 1.920 0.245 0.128 0.696 0.319 

w = l. 96 ft T = 0. 341 lb/ft2 . 796 1.810 .236 .130 .670 . 296 

Q = 1.21 cfs v = 1.068xl05 ft 2/sec .694 1.680 .259 .154 . 736 .505 

T = 21.1 °C R=57,788 .592 1.580 .255 .161 .724 .281 

D = 0.412 ft F = 0.411 .490 1.510 .271 .179 .770 .198 

V = 1.498 fps C/ g = 4.256 .388 1.360 .288 .212 .818 • 203 

.286 1.030 .220 .214 .625 .427 

1 1/8-Inch Block Roughness 6 Inches From Wall Station 20 

s = 13.2Sxlo3 u. = 0.352 fps 0.898 2.500 0.289 O.ll6 0.821 0.218 

w = 1.96 ft T = 0.341 lb/ft2 • 796 2.530 .337 .133 .957 .209 

Q = 1.21 cfs v = 1.068xH}5 ft 2/sec .694 2.540 .376 .148 1.068 .249 

T = 21.1 °C R = 57,788 .592 2.500 .431 .172 1.224 . 293 

D = 0.412 ft F = 0.4ll .490 2.405 .469 .195 1. 332 • 343 

V = 1.498 fps C/lg = 4.256 .388 2.170 .493 .227 1.401 .433 

.286 1. 735 .417 .240 1.185 .185 

1 1/8-Inch Block Roughness, Channel Centerline, Station 25 

s = 13. 25xlo3 u. = 0.348 fps o. 898 2.100 o. 318 0.151 0.914 0.256 

w = 1.96 ft T = 0. 329 lb/ft2 . 796 1.995 .316 .158 .908 .245 

Q = 1.21 cfs v = l.068xl05 ft 2/sec .694 1.905 .308 .162 .885 .237 

T = 21.1 °C R = 57,799 .592 1.820 .323 .177 .928 .395 

D = 0.398 ft F = 0.433 .490 1. 750 .358 .205 1.029 .313 

V = 1.551 fps c;lg = 4.457 .388 1.580 .368 .233 1.057 . 264 

.286 1.400 ----- ----- ----- .418 

1 1/8-Inch Block Roughness, 6 Inches From Wall, Station 25 

s = 13. 25xlo3 u. = 0.348 fps 0.898 2.600 0.288 O.lll 0.828 o. 214 

w = l. 96 ft T = 0. 329 "lb/ft2 . 796 2.660 .370 .139 1.063 .409 

Q = 1.21 cfs v = l.068xHi5 ft 2/sec .694 2.680 .425 .159 1.221 • 264 

T = 21.1 °C R = 57,799 .592 2.600 .447 .172 1.284 .243 

D = 0.398 cfs F = 0.433 .490 2.430 .489 .201 1.405 .187 

V = 1.551 fps C/lg = 4.457 .388 2.120 .506 .239 1.454 .261 

.286 1.610 ----- ----- ----- • 322 

1 1/8-Inch Block Roughness, Channel Centerline, Station 30 

s = 13. 25xlo3 u. = 0.351 fps 0.898 2.ll0 0.302 0.143 0.860 

w = 1.96 ft T = 0.338 lb/ft2 • 796 2.060 .330 .160 .940 

Q = 1.21 cfs v = l.068xl65 ft2/sec .694 1.940 .332 .171 .946 

T = 21.1 °C R = 57,788 .592 1.840 .308 .167 .877 

!!. = 0.409 ft F = 0.416 .490 l. 720 .365 .212 1.040 

V = 1.509 fps C//i= 4.299 .388 1.560 .392 .251 1.117 

.286 1.200 

1 1/8-Inch Block Roughness, 6 Inches From Wall, Station 30 

s = 13. 25xlo3 u. = 0.351 fps 0.898 2.570 0.308 0.120 0.877 

w = l. 96 ft T = 0. 338 lb/ft2 • 796 2.640 .353 .134 1.006 

Q = 1.21 cfs v = l.068xl05 ft2/sec .694 2.620 .409 .156 1.165 

T = 21.1 °C R = 57,788 .592 2.500 .424 .170 1.208 

D = 0.409 ft F = 0.416 .490 2.310 .531 .230 1.513 

V = 1.509 fps C//i= 4.299 .388 2.000 .536 .268 1.527 

.286 1. 720 

1 l/8=Inch Block Roughness, Channel Centerline, Station 35 

s = 13.25xlo3 U * = 0 • 350 fps 0.898 2.ll0 0.318 0.151 0.909 

w = 1.96 ft T = 0.337 lb/ft2 . 796 2.030 .337 .166 .963 

Q = l. 21 cfs v .= 1.068xl05 ft2/sec .694 1.940 .362 .187 1.034 

T = 21.1 °C R = 57,811 .592 1. 790 .373 .208 1.066 

D = 0.407 ft F = 0.416 .490 1.630 .360 .221 1.029 

V = 1.517 fps c;lg = 4.334 .388 1.520 .405 .266 1.157 

.286 1.205 .327 .271 .934 

1 1/8-Inch Block Roughness, 6 Inches From Wall, Station 35 

S = .13.25xl()3 u. = 0.350 fps 0.898 2.520 0.303 0.120 0.866 

w = 1.96 ft T = 0. 337 lb/ft2 .796 2.580 .369 .143 1.054 

Q = 1.21 cfs v = 1.068xto5 ft 2/sec .694 2.600 .395 .152 1.129 

T=2l.l°C R = 57,811 .592 2.560 .448 .175 1.280 

D = 0.407 ft F = 0.416 .490 2.400 .484 .202 1.383 

V = 1.517 fps C/lg = 4.334 .388 2.100 .533 . 254 1.523 

.286 1.660 .soo .301 1.429 

1 1/8-Inch Block Roughness, Channel Centerline, Station 40 

s = 13. 2Sxt63 u. = 0.351 fps 0.898 2 .ObO 0.315 0.153 0.897 0.403 

w = 1. 96 ft T = 0.337 lb/ft2 . 796 2.030 .360 .177 1.026 .243 

Q = 1. 21 cfs v = l.068xl65 ft 2/sec .694 1.930 .386 .200 1.100 . 300 

T = 21.1 °C R = 57,800 .592 1. 790 .397 .222 1.131 .370 

D = 0.408 ft F = 0.417 .490 1.680 .421 .251 1.199 .571 

V = 1.513 fps C//(j = 4.311 .388 1.500 .407 .271 1.160 .568 

.286 1.230 .356 .289 1.014 . 262 

0.613 

.536 

.848 

.444 

. 299 

. 276 

.439 

0.545 

. 529 

.633 

• 733 

.826 

.940 

.321 

0.538 

.489 

.451 

.718 

.548 

.417 

.586 

0.556 

1.088 

• 708 

.632 

.455 

.553 

.518 

0.830 

.494 

.579 

.663 

.960 

.853 

. 322 

X 

:r: 

(ft) 

0.0131 

.0137 

. 0135 

.0123 

.0127 

.0106 

.0109 

o. 0176 

.0168 

.0153 

.0144 

.0137 

.0119 

.0123 

0.0151 

.0141 

.0145 

.0126 

.0131 

.0109 

.0122 

0.0178 

.0181 

.0166 

.0153 

.0148 

.0134 

.0126 

0.0150 

.0147 

.0142 

.0138 

• 0144 

.0132 

.0127 

B39 
B40 TURBULENCE IN WATER 

TABLE 3b.- 2-foot-wide flume, rigid boundary, developing flow- Continued 

Mean Flow Parueters 

and Variables 

S = 13.25x1()3 

w = 1. 96 ft 

Q = 1. 21 cfs 

T = 21.1 •c D = 0.408 ft 

V = 1.513 fps 

S = 13. 25xl!P 

W a 1.96 ft 

Q = 1.21 cfs 

T = 21.1 •c 

D = 0.406 ft 

V = 1.520 fps 

S = 13.25xl(J3 

w = 1.96 ft 

Q = 1.21 cfs T = 21.1 •c D = 0.406 ft 

V = 1.520 fps 

S = 20. 54xl(j3 

w = 1.96 ft 

Q = 1.56 cfs 

T = 21.1 •c D = 0.413 ft 

V = 1.927 fps 

s = 20. 54xHP 

w = 1.96 ft 

Q = 1. 56 cfs 

T = 21.1 •c D = 0.413 ft 

V = 1.927 fps 

S = 20.54xl()3 

w = 1.96 ft 

Q = 1.56 cfs 

T = 21.1 •c iJ = o.4o7 ft 

V = 1.956 fps 

s = 20.54xto3 

w = 1.96 ft 

Q = 1. 56 cfs 

T=2Lt•c 

D = 0.407 ft 

V = 1.956 fps 

s = 20 .54xlo3 

w = 1.96 ft 

Q = 1.56 cfs T = 21.1 •c D = 0.413 ft 

V = 1.927 fps 

S = -20. 54xlQ3 

w = 1.96 ft 

Q = 1.56 cfs 

T = 2r.1 •c D = 0.413 ft 

V = 1.927 fps 

S = 20.54xl03 

w = 1.96 ft 

Q = 1.56 cfs T = 21.1 •c D = 0.412 ft 

V = 1.932 fps 

1 1/8-Inch Block Roughness, b Inches From Wall, Station 40 

u* = 0.351 fps 0.898 2.450 0.333 0.136 0.949 

T = 0, 337 lb/ft2 . 796 2.500 .344 .138 .980 

v = 1.068xlO-s ft2/sec .694 2.500 .394 .158 1.123 

R = 57,800 .592 2.440 .417 .171 1.188 

F = 0.417 .490 2.305 .474 .206 1.350 

c;lg = 4.311 .388 2.030 .516 •f54 1.470 

.286 1.660 .480 .289 1.368 

1 1/8-Inch Block Roughness Channel Centerline Station 45 

U* = 0.350 fps 0.898 2.040 0.328 0.161 0.937 

T = 0.336 lb/ft2 . 796 2.000 .367 .184 1.049 

v = 1.068xl05 ft 2/sec .694 1.940 .395 .204 1.129 

R = 57,783 .592 1.820 .396 .218 1.131 

F = o .420 .490 1.690 .400 .237 1.143 

c;lg = 4.343 .388 1.560 .415 .266 1.186 

.286 1.270 .352 .277 1.006 

1 1/8-Inch Block Roughness 6 Inches From Wall Station 45 

u* = 0.350 fps 0.898 2.330 0.304 0.130 0.869 

T = 0.336 lb/ft2 . 796 2.420 .353 .146 1.009 

v = l.068x165 ft2/sec .694 2.450 .374 .153 1.069 

R = 57,783 .592 2.430 .404 .166 1.154 

F = 0.420 .492 2.305 .465 .202 1.329 

C//g= 4.343 .388 2.030 .464 .229 1.326 

.286 1.470 .400 .272 1.143 

1 1/8-Inch Block Roughness, Channel Centerline, Station 5 

u. = 0.438 fps 

T = 0.529 lb/ft2 

v = 1.068xH)5 ft2/sec 

R = 74,518 

F = o .528 

c;lg = 4.4oo 

0.898 

. 796 

.694 

.592 

.490 

.388 

.286 

3.180 

3.270 

3.205 

3.030 

2.800 

2.450 

1.960 

0.349 

.400 

.436 

.518 

.657 

.718 

.593 

0.110 

.122 

.136 

.171 

.235 

.293 

.303 

0. 797 

.913 

.995 

1.183 

1.500 

1.639 

1.354 

1 1/8-Inch Block Roughness, 6 Inches From Wall, Station 5 

u. = 0.438 fps 

T = 0.529 lb/ft2 

v = 1.068xl05 ft2/sec 

R = 74,518 

F = o .528 

C//g= 4.400 

0.898 

. 796 

.694 

.592 

.490 

.388 

.286 

3.140 

3.350 

3.405 

3.340 

3.130 

2. 700 

2.200 

0.333 

.351 

·.370 

.451 

.475 

.527 

.511 

0.106 

.105 

.109 

.135 

.152 

.195 

.232 

0. 760 

.801 

,845 

1.030 

1.084 

1.203 

1.16.7 

1 1/8-Inch Block Roughness, Channel Centerline, Station 10 

u. = 0.436 fps 

T = 0.522 lb/ft2 

v = 1.068xl65 ft 2/sec 

R = 74,540 

F = 0.540 

C//g= 4.486 

0.898 

. 796 

.694 

.592 

.490 

.388 

.286 

3.300 

3.160 

2.890 

2. 740 

2.510 

2.200 

1.880 

0.581 

.640 

.677 

.717 

. 755 

. 739 

.690 

0.176 

.202 

.234 

.262 

.301 

.336 

.367 

1.333 

1.468 

1.553 

1.644 

1. 732 

1.695 

1.583 

1 1/8-Inch Block Roughness, 6 Inches From Wall, Station 10 

u. = 0.436 fps 

T = 0.522 lb/ft2 

v = 1.068xl05 ft2/sec 

R = 74,540 

F = o .540 

c;lg = 4.486 

0.898 

. 796 

.694 

.592 

.490 

.388 

.286 

3.370 

3.380 

3.350 

3.260 

3.110 

2.840 

2.220 

0.454 

.422 

.417 

.435 

.492 

.610 

.485 

0.135 

.125 

.124 

.133 

.158 

.215 

.218 

1.041 

.968 

.956 

.998 

1.128 

1.399 

1.112 

1 1/8-Inch Block Roughness, Channel Centerline, Station 15 

u* = o ,438 fps 

T = 0,529 lb/ft2 

v -= 1.068xlQS ft2/sec 

R = 7.4,518 

F = 0.528 

c;lg = 4 .4oo 

0.898 

. 796 

.694 

.592 

.490 

.388 

.286 

2.930 

2.800 

2.605 

2.310 

2.080 

1.840 

1.500 

0.590 

.624 

.682 

.656 

.614 

.491 

0.201 

.223 

.262 

.284 

.295 

.267 

1.347 

1.425 

1.557 

1.498 

1.402 

1.121 

1 1/8-Inch Block Roughness, 6 Inches From Wall, Station 15 

u* = o .438 fps 

T = 0, 529 lb/ft2 

v = l.068x105 ft2/sec 

R = 74,518 

F = 0.528 

c;lg = 4.400 

0.898 

. 796 

.694 

.592 

.490 

.388 

.286 

3.270 

3.285 

3.290 

3.240 

3.100 

2.860 

2.250 

0.400 

.341 

.387 

.429 

.483 

.614 

.626 

0.122 

.104 

.118 

.132 

.156 

.215 

.278 

0.913 

.779 

.884 

,979 

1.103 

1.402 

1.429 

1 1/8-Inch Block Roughness, Channel Centerline, Station 20 

u. = 0.438 fps 

T = 0.528 lb/ft2 

v = 1.068xl65 ft2/sec 

R = 74,530 

F = 0.530 

c;lg = 4.411 

0.898 

. 796 

.694 

.592 

.490 

.388 

.286 

2. 700 

2.610 

2.450 

2.250 

2.000 

1. 780 

1.400 

0.489 

.573 

.615 

.585 

.550 

.624 

0.181 

.220 

.251 

.260 

.275 

.351 

1.116 

1.308 

1.404 

1.336 

1.256 

1.425 

0. 329 0.806 

.411 1.028 

. 337 .843 

.320 .781 

.534 1. 234 

.469 .960 

.369 .613 

0.468 0.955 

. 282 .564 

.406 . 786 

.270 .491 

.398 .672 

.408 .637 

.421 '.535 

0.315 0.734 

. 21Z .513 

.249 .610 

.377 .916 

.312 .720 

.251 .509 

.247 .363 

A 

:r: 

(ft) 

0. 0181 

.0184 

.0182 

.0176 

.0152 

.0121 

.0108 

0.0142 

.0139 

.0136 

.0124 

.0115 

.0102 

.0096 

0.0164 

.0166 

.0157 

~0153 

.0127 

.0109 

.0085 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

TABLE 3b.- 2-foot-wide flume, rigid boundary, developing flow- Continued 

Mean Flow Paraaeters X 

:r: 

and Variables (ft) 

1 1/8-Inch Block Roughness, 6 Inches From Wall, Station 20 

s = 20.54xlo3 u* = 0.438 fps 0.898 3.280 0.378 O.ll5 0.863 

w = 1.96 ft T = 0,528 1b/ft2 • 796 3.255 . 376 .ll6 .858 

Q = 1. 56 cfs v = 1.068x165 ft2/sec .694 3.230 .365 .ll3 .833 

T=2l.l°C R = 74,530 .592 3.200 .410 .128 .936 

D = 0.412 ft F = 0.530 .490 3.130 .505 .161 1.153 

V = 1.932 fps ctli = 4.411 .388 2.830 .617 .218 1.409 

.286 2.400 .592 .247 1.352 

1 1/8-Inch Block Roughness, Channel Centerline, Station 25 

S = 20, 54x163 u* = o .433 fps 0.898 2.800 0.536 0.191 1.238 

w = 1.96 ft T = 0.510 lb/ft2 • 796 2.600 .480 .185 1.109 

Q = 1.56 cfs v = 1.068xl<f5 ft2/sec .694 2.430 .494 ,203 1.141 

T = 21.1 •c R = 74,532 .592 2.280 .540 .237 1.247 

D = 0.398 ft F = o .559 .490 2.070 .508 .245 1.173 

V = 2.000 fps c;lg = 4.619 .388 1.860 .537 .289 1.240 

.286 1.600 .458 .286 1.058 

1 1/8-Inch Block Roughness, 6 Inches From Wall, Station 25 

S = 20.54x1()3 u* = o .433 fps 0.898 3.430 0.374 0.109 0.864 

w = 1.96 ft T = 0.510 lb/ft2 • 796 3.430 • 386 .ll3 .891 

Q = 1.56 cfs v = 1.068x165 ft2/sec .694 3.420 .389 .114 .898 

T = 21.1 •c R = 74,532 .592 3.360 .432 .129 .998 

D = 0. 398 ft F = o .559 .490 3.200 .557 .174 1.286 

V = 2.000 fps ctli = 4.619 .388 2.895 .338 .117 . 781 

.286 2.320 

1 1/8-Inch Block Roughness, Channel Centerline, Station 30 

S = 20. 54x1()3 u* = o .432 fps 0. 898 2. 770 0.543 0.196 1.257 

w = 1.96 ft T = 0.515 lb/ft2 • 796 2.540 .532 .209 1.231 

Q = 1. 56 cfs v = 1.068x165 ft2/sec .694 2.320 .520 .224 1.204 

T = 21.1 •c R = 74,528 .592 2.140 .510 .238 1.181 

D = 0.402 ft F = o .550 .490 1.920 .443 .231 1.025 

V = 1.980 fps c;lg = 4.583 .388 1.640 .405 .247 .938 

. 286 1. 270 

1 1/8-Inch Block Roughness, 6 Inches From Wall, Station 30 

S = 20.54x1()3 u* = o .432 fps 0.898 3.500 0.357 0.102 0.826 

w = 1. 96 ft T = 0.515 lb/ft2 . 796 3.510 .403 .115 .933 

Q = 1. 56 cfs v = 1.068xJ65 ft 2/sec .694 3.480 .419 .120 .970 

T=21.1•c R = 74,528 .592 3.360 .495 .147 1.146 

D = 0.402 ft F = o .550 .490 3.100 .620 .200 1.435 

V = ;.980 fps c;lg = 4.583 .388 2. 710 .663 .245 1.535 

.286 2.220 

1 1/8-Inch Block Roughness Channel Centerline Station 35 

s = 20 .54x1()3 u* = o .438 fps 0.898 2. 740 0.518 0.189 1.183 0.328 0.865 0.0168 

w = 1.96 ft T = 0.527 lb/ft2 . 796 2.560 .515 .201 1.176 .325 .832 -----

Q = 1.56 cfs \1 = 1. 068xl65 ft 2/sec .694 2.350 .558 .237 1.274 .233 .548 -----

T = 21.1 •c R = 74,542 .592 2.180 .516 .237 1.178 • 201 .438 -----

D = 0.411 ft F = 0.532 .490 1.980 .557 .281 1.272 • 285 .564 -----

V= 1.937 fps ctli = 4.422 .388 1. 700 .594 .349 1.356 .493 .840 .0113 

,286 1.350 ----- ----- ----- ----- ----- -----

1 1/8-Inch Block Roughness 6 Inches From Wall Station 35 

S = 20.54x1()3 u* = 0.438 fps 0.898 3.400 0.384 0.113 0.877 0.161 I 0.547 0.0190 

w = 1.96 ft T = 0.527 lb/ft2 . 796 3.410 .400 .117 .913 .158 .538 -----

Q = 1.56 cfs v = 1.068xl65 ft2/sec .694 3.380 .403 .119 .920 .185 1 .625 -----

T = 21.1 •c R = 74,542 .592 3.300 .471 .143 1.075 .157 ' . 518 -----

D = 0.411 ft F = 0.532 .490 3.120 .563 .180 ..," L~L . ,, _____ .388 2. 750 .693 .252 1.58~ .192 .528 ----- V = 1.937 fps ctli = 4.422 ,286 2.200 .668 .304 1.525- .343 -.7551 .0134 ~ 

1 1/8-Inch Block Roughness, Channel Centerline, Station 40 

S = 20. 54xJ(j3 u* = o .437 fps 0.898 2. 730 0.480 0.176 1.098 0.241 0.658 0.0167 

w = 1.96 ft T = 0.525 lb/ft2 . 796 2.630 .553 .210 1.265 .190 .500 .0161 

Q = 1.56 cfs v = 1.068xJ65 ft2/sec .694 2.410 .541 .224 1.238 . 259 .629 .0153 

T = 21.1 •c R = 74,514 .592 2.220 .519 .234 1.188 .181 .403 .0128 

D = 0.410 ft F = 0.534 .490 2.000 .592 .296 1.355 .178 .356 .0136 

V = 1.941 fps ctli= 4.442 .388 1.680 .525 .313 1.201 .322 .541 .0117 

.286 1.540 .484 .314 1.108 .150 • 231 .0102 

1 1/8-Inch Block Roughness, 6 Inches From Wall Station 40 

S = 20. 54xliP u* = o .437 fps 0.898 3.310 0.424 0.128 0.970 0.150 0.496 0.0195 

w = 1. 96 ft T = 0.525 lb/ft2 • 796 3.330 .408 .123 .934 .138 .460 .0186 

Q = 1.56 cfs v = 1.068xl65 ft2/sec .694 3.310 .427 .129 .977 .177 .585 .0189 

T = 21.1 •c R = 74,514 .592 3.230 .485 .150 1.110 .159 .514 .0171 

D = 0.410 ft F = 0.534 .490 3.090 .555 .180 1.270 .201 .620 .0158 

V = 1.941 fps ctli= 4.442 .388 2. 780 .648 . 233 1.483 .174 .484 . 0138 

.286 2.195 . 778 .354 1. 780 .236 .517 .0160 

1 1/8-Inch Block Roughness, Channel Centerline, Station 45 

S = 20.54x1()3 u* = 0.437 fps 0.898 2.810 0.520 0.185 1.190 

w = 1. 96 ft T = 0.524 lb/ft2 . 796 2.600 .544 • 209 1. 245 

Q = 1.56 cfs v = 1.068xl65 ft2/sec .694 2.450 .596 .243 1.364 

T = 21.1 •c R = 74,524 .592 2.230 .555 .249 1.270 

D = 0.409 ft F = 0.536 .490 2.040 . 595 .292 1. 362 

V = 1.946 fps c;lg = 4.453 .388 1.880 .572 .304 1.309 

.286 1.640 .665 .405 1.522 

B41 
B42 TURBULENCE IN WATER 

TABLE 3b.- 2-/oot-wide flume, rigid boundary, developing flow- Continued 

Mean Flow Parmeters ;\. 

:r: 

and Variables (ft) 

1 1/8-Inch Block Roughness, 6 Inches From Wall, Station 45 

S = 20 .54xliJ3 v. = 0.437 fps 0.898 3.200 0.389 0.122 0.890 

. 796 3.240 .395 .122 .904 w = 1. 96 ft T = 0.524 lb/ft2 .694 3.260 .413 .127 .945 Q = 1.56 cfs v = 1.068xl65 ft2/sec 

T = 21.1 •c R = 74.524 .592 3.200 .455 .142 1.041 

D = 0.409 ft F = 0.536 .490 3.030 .555 .183 1.270 

V ~ 1.946 fps C//g = 4.453 .388 2.640 .666 .252 1.524 

.286 2.050 .519 .253 1.188 

1/2 -Inch Block Roughness, Channel Centerline, Station 5 

0.899 1.260 O.ll8 0.094 o. 707 

S = 2.95xliJ3 v. = 0.167 fps . 798 1.185 .ll8 .100 . 707 

w = 1. 96 ft T = 0.077 lb/ft .697 1.090 .107 .098 .641 

Q = 0.88 cfs v = 1.068xl05 ft2/sec .596 1.020 .092 .090 .551 

T = 21.1 •c R = 42,028 .495 .938 .086 .092 .515 

D = 0.416 ft F = o. 295 .394 .878 .084 .096 .503 

V = 1.079 fps C//g= 6.461 .293 .823 .084 .102 .503 

.192 . 760 .ll2 .147 .671 

1/2 -Inch Block Roughness, 6 Inches From Wall, Station 5 

0.899 1.370 0.163 O.ll9 0.976 

S = 2.95xl()3 v. = 0.167 fps . 798 1.420 .179 .126 1.072 

w = 1.96 ft T = 0.077 lb/ft2 .697 1.440 .200 .139 1.198 

Q = 0.88 cfs v = 1.068xl65 ft2/sec .596 1.450 .216 .149 1.293 

T = 21.1 •c R = 42,028 .495 1.400 .224 .160 1.341 

D = 0.416 ft F = o. 295 .394 1.300 .192 .148 1.150 

V = 1.079 fps C//g= 6.461 .293 1.150 .183 .159 1.096 

.192 .980 .152 .155 .910 

1/2-Inch Block Roughness, Channel Centerline, Station 10 

0.899 1.130 0.062 0.055 0.371 

S = 2.95xl03 v. = 0.167 fps • 798 1.070 .056 .052 .335 

w = 1.96 ft T = 0.077 lb/ft2 .697 .995 .054 .054 .323 

Q = 0.88 cfs v = 1.068xl{)5 ft 2/sec .596 .950 .058 .061 .347 

T=21.1°C R = 42,057 .495 .900 .062 .069 .371 

D = 0.419 ft F = 0.292 .394 .800 .078 .098 .467 

V = 1.072 fps c;lg = 6.419 .293 . 743 .091 .122 .545 

.192 .690 .ll2 .162 .671 

1/2-Inch Block Roughness, 6 Ilfches From Wall, Station 10 

0.899 1.440 0.124 0.086 0. 743 s = 2.95xlo- 3 v. = 0.167 fps • 798 1.465 .149 .102 .892 

w = 1.96 ft T = 0.077 lb/ft2 .697 1.485 .178 .120 1.066 

Q = 0.88 cfs v = 1. 068x 105 ft 2 /sec .596 1.470 .209 .142 1.251 

T = 21.1 •c R = 42,057 .495 1.420 .214 .151 1.281 

D = 0.419 ft F = o. 292 .394 1.330 .216 .162 1.293 

V = 1.072 fps c;lg = 6.419 .293 1.160 .191 .165 1.144 

.192 .900 .171 .190 1.024 

1/2-Inch Block Roughness, Channel Centerline, Station 15 

0.899 1.060 0.056 0.053 0.337 

S = 2. 95xl03 v. = 0.166 fps . 798 .990 .050 .051 .301 

w = 1.96 ft T = 0. 076 lb/ft2 .697 .940 .049 .052 .295 

Q = 0. 88 cfs v = 1.068xl<f5 ft2/sec .596 .900 .055 .061 .331 

T = 21.1. •c R = 42,020 .495 .840 .057 .068 .343 

D = 0.414 ft F = 0.297 .394 • 765 .066 .086 .398 

V = 1.084 fps c;lg = 6.530 .293 .710 .085 .120 .512 

.192 .640 .087 .136 .524 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 15 

0.899 1.370 0.143 0.104 0.861 

s = 2.95xlo3 U * = 0 .166 fps • 798 1.395 .160 .ll5 .964 

w = 1.96 ft T = 0 .076 lb/ft2 .697 1.420 .185 .130 l.ll4 

Q = 0.88 cfs v = 1.068xl05 ft2/sec .596 1.430 .207 .145 1.247 

T = 21.1 •c R = 42,020 .495 1.420 .227 .160 1.367 

D = 0.414 ft F = 0.297 .394 1.380 .252 .183 1.518 

V = 1.084 fps c;lg = 6.530 .293 1.230 .241 .196 1.452 

.192 1.130 .237 .210 1.427 

1/2-Inch Block Roughness, Channel Centerline, Station 20 

0.899 1.120 0.062 0.055 0.373 

S = 2.95xl03 u. = o .166 fps • 798 1.060 .061 .058 .367 

w = 1.96 ft T = 0.075 lb/ft2 .697 1.060 .061 .058 .367 

Q = 0.88 cfs v = 1.068xl<i5 ft 2/sec .596 1.025 .065 .063 .392 

T=2l.l°C R = 42,037 .495 .990 .076 .077 .458 

D = 0.410 ft F = o. 301 .394 .960 .089 .093 .536 

V = 1.095 fps c;lg = 6.596 .293 .920 .ll8 .128 • 711 

.192 .800 .147 .184 .886 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 20 

0.899 1.350 0.109 0.081 0.657 

S = 2.95xl0 3 u. = 0.164 fps . 798 1.380 .140 .101 .843 

w = 1.96 ft T = 0.073 lb/ft2 .697 1.395 .152 .109 .916 

Q = 0.88 cfs v = 1. 068xl0 5 ft2 /sec .596 1.405 .170 .121 1.024 

T = 21.1 •c R = 42,037 .495 1.400 .196 .140 1.181 

D = 0. 399 ft F = 0.314 .394 1.335 .206 .154 1.241 

V= 1.125 fps c;lg = 6.860 .293 1.220 .201 .165 1.211 

.192 1.015 .184 .181 1.108 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B43 

TABLE 3b.- 2-foot-wide flume, rigid boundary, developing flow- Continued 

Mean Flow Para11eters 1. ~ 

and Variables (ft) 

1/2-lnch Block Roughness, Channel Centerline, Station 25 

0.899 1.205 0.058 0.048 0.354 S = 2.95xl()3 u* = 0.164 fps . 798 1.180 .059 .050 .360 

w = 1.96 ft ' = 0.073 lb/ft2 .697 1.140 .063 .055 .384 

Q = 0. 88 cfs v = 1.068xl65 ft2/sec .596 1.100 .068 .062 .410 

T=2l.l 0C: R = 42,029 .495 1.050 .085 .081 .518 

D = 0. 399 ft F = 0.314 .394 1.025 .103 .100 .628 

V= 1.125 fps c;lg = 6.860 .293 .970 .143 .147 .872 

.192 .850 .157 .185 .957 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 25 

0.899 1.390 0.107 0.077 0.652 

S = 2. 95xliJ3 u* = 0.164 fps . 798 1.430 .132 .092 .805 

w = 1.96 ft ' = 0.073 lb/ft2 .697 1.445 .170 .us 1.037 

Q = 0.88 cfs v = 1.068xl05 ft2/sec .596 1.420 .180 .127 . 1.098 

T = 2. 21 •c R = 42,029 .495 1.370 .173 .126 1.055 

D = 0.399 ft F = 0.314 .394 1.270 .171 .135 1.043 

V = 1.125 fps c;lg = 6 .s6o .293 1.090 .167 .153 1.018 

.192 .692 .124 .179 . 756 

1/2-Inch Block Roughness, Channel Centerline, Station 30 

0.899 1.215 0.055 0.045 0.333 S = 2.95xl()3 u* = 0.165 fps . 798 1.170 .061 .052 .370 

w = 1.96 ft ' = 0.074 lb/ft2 .697 l.llO .065 .059 .394 

Q = 0. 88 cfs v = 1.068xl65 ft2/sec .596 1.085 .066 .061 .400 

T = 21.1 •c R = 42,044 .495 1.040 .085 .082 .515 

D = 0.402 ft F = 0.310 .394 .960 .106 .llO .642 

V = l.ll7 fps c;lg = 6. 770 .293 .900 .148 .164 .897 

.192 .860 .185 .215 1.121 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 30 

0.899 1.420 O.ll7 0.082 0. 709 S = 2.95xlQ3 u* = 0.165 fps . 798 1.460 .124 .085 . 752 

w = 1.96 ft ' = 0.074 lb/ft2 .697 1.480 .172 .ll6 1.042 

Q = 0.88 cfs v = 1.068xl65 ft 2/sec .596 1.450 .186 .128 1.127 T = 21.1 •c R = 42,044 .495 1.390 .189 .136 1.145 

D = 0.402 ft F = o .310 .394 1.280 .216 .169 1.309 

V = l.ll7 fps c;lg = 6. 770 .293 1.080 .177 .164 1.073 

.192 .720 .127 .176 .770 

1/2-Inch Block Roughness, Channel Centerline, Station 35 

0.899 1.195 0.069 0.058 0.416 

s = 2.95xlo3 U * = 0 .166 fps . 798 1.160 .076 .066 .458 

w = 1.96 ft ' = 0.075 lb/ft2 .697 1.150 .078 .068 .470 

Q = 0.88 cfs v = 1.068xl05 ft 2/sec .596 1.105 .083 .075 .500 

T = 21.1 •c R = 42,037 .495 1.030 .091 .088 .548 

D = 0.410 ft F = 0.301 .394 1.005 .104 .103 .627 

v = 1.095 fps c;lg = 6.596 .293 .940 .129 .137 . 777 

.192 .885 .180 .203 1.084 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 35 

0.899 1.350 O.ll9 0.088 o. 717 

s = 2.95xlo3 U * = o .166 fps . 798 1. 390 .135 .097 . 813 

w = 1.96 ft ' = 0.075 lb/ft2 .697 1.410 .143 .101 .861 

Q = 0.88 cfs v = 1.068xl65 ft 2/sec .596 1.420 .168 .ll8 1.012 

T = 21.1 •c R = 42,037 .495 1.400 .198 .141 1.193 

D = 0.410 ft F = 0.301 .394 1.325 .196 .148 1.181 

V = 1.095 fps c;lg = 6.596 .293 1.160 .190 .164 1.145 

.192 .935 .162 .173 .976 

1/2-Inch Block Roughness, Channel Centerline, Station 40 

0.899 1.165 0.078 0.067 0.404 S = 2.95xlQ3 u* = 0.166 fps . 798 1.150 .081 .070 .422 

w = 1.96 ft ' = 0.076 lb/ft2 .697 1.140 .084 .074 .446 

Q = 0.88 cfs v = 1.068xHf5 ft 2/sec .596 1.105 .094 .085 .512 T = 21.1 •c R = 42,020 .495 1.080 .102 .094 .566 

D = 0.414 ft F = 0.297 . 394 1.035 .120 .ll6 .699 

V = 1.084 fps C//g = 6.530 .293 1.020 .129 .126 . 759 

.192 . 860 .122 .142 .855 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 40 

0.899 1.300 O.ll6 0.089 0.699 S = 2 .95xlQ3 U * = 0 .166 fps . 798 1.335 .133 .100 .801 

w = 1.96 ft ' = 0.076 lb/ft2 .697 1.350 .146 .108 .880 

Q = 0. 88 cfs v = 1.068xl65 ft2 /sec .596 1.340 .154 .ll5 .928 

T = 21.1 •c R = 42,020 .495 1.302 .153 .ll8 .922 

D = 0.414 ft F = 0.297 .394 1.235 .170 .138 1.024 

V = 1.084 fps C//g= 6.530 .293 1.095 .164 .150 .988 

.192 .900 .181 .201 1.090 

1/2-Inch Block Roughness, Channel Centerline, Station 45 

0.899 1.150 0.071 0.062 0.425 

S = 2.95xl63 u* = 0.167 fps . 798 1.120 .075 .067 .449 

w = 1. 96 ft ' = 0.077 lb/ft2 .697 1.095 .075 .068 .449 

Q = 0. 88 cfs v = 1.068xl65 ft2/sec .596 1.085 .077 .071 .461 T = 21.1 •c R = 42,035 .495 1.100 .097 .088 .581 

D = 0.418 ft F = 0.293 .394 1.090 .ll5 .106 .689 

V = 1.074 fps C//g= 6.431 .293 1.025 .122 .119 . 731 

.192 .900 .131 .146 . 784 
B44 TURBULENCE IN WATER 

TABLE 3b.- 2-foot-wide flume, rigid boundary, developing fiow- Continued 

Mean Flow Parueters 

and Variables 

1/2-Incn Bloc!< Koughness, 6 Inches From Wall, Station 45 

0.899 1.290 0.107 0.083 0.641 

S = 2.95xl!J3 u* = 0.167 fps . 798 1.310 .121 .092 .725 

w = 1.96 ft T = 0. 077 lb/ft2 .697 1.315 .131 .100 . 784 

Q = 0.88 cfs v = 1.068xl65 ft2/sec .596 1.300 .142 .109 .850 T = 21.1 •c R = 42,035 .495 1.270 .152 .120 .910 

D = 0.418 ft F = 0.293 .394 1.220 .150 .123 .898 

V = 1.074 fps c;lg = 6.431 .293 l.ll5 .172 .154 1.030 

.192 .970 .176 .181 1.054 

1/2-Inch Block Roughness, Channel Centerline, Station 5 

0.899 2.130 0.267 0.125 0.985 

s = 7 .80xlo3 u* = 0.271 fps . 798 2.145 .272 .127 1.004 

w = 1.96 ft T = 0.202 1b/ft2 .697 2.170 .277 .128 1.022 

Q = 1.53 cfs v = 1.068xl65 ·ft2/sec .596 2.150 .263 .122 .970 

T = 21.1 •c R = 73.073 .495 2.150 .260 .121 .959 

D = 0.416 ft F = 0.513 .394 2.080 .280 :135 1.033 

V = 1.876 fps c;lg = 6.923 .293 2.000 .341 .171 1.258 

.192 1.630 .342 .210 1.262 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 5 

0.899 2.230 0.273 0.122 1.007 ----- s = 7.80xl63 u. = 0.271 fps . 798 2.320 .301 .130 1.111 ----- w = 1.96 ft T = 0.202 lb/ft2 .697 2.400 .346 .144 1.277 ----- Q = 1.53 cfs v = 1. 068xlO-s ft 2/sec .596 2.470 .380 .154 1.402 ----- T = 21.1 •c R = 73,073 .495 2.50!> .450 .180 1.661 ----- D = 0.416 ft F = 0.513 .394 2.370 .514 .228 1.897 ----- V= 1.876 fps c;lg = 6.923 .293 2.070 .470 .227 1. 734 ----- .192 1.695 .408 .241 1.506 -----

1/2-Inch Block Roughness, Channel Centerline, Station 10 

0.899 2.600 0.150 0.058 0.551 

S = 7. 80xl63 u. = 0.272 fps . 798 2.575 .167 .065 .614 

w = 1.96 ft T = 0. 204 lb/ft2 .697 2.480 .173 .070 .636 

Q = 1.53 cfs v = 1.068xl65 ft2/sec .596 2.405 .2ll .088 .776 

T = 21.1 •c R = 73,107 .495 2.300 .251 .109 .923 

D = 0.420 ft F = o .506 .394 2.180 .262 .120 .963 

V = 1.859 fps c;lg = 6. 835 .293 1.960 .300 .153 1.103 

.192 1. 780 .342 .192 1.257 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 10 

0.899 2.405 0.294 0.122 1.081 

S = 7.80xl()3 u. = 0.272 fps . 798 2.380 .323 .136 1.188 

w = 1. 96 ft T = 0. 204 lb/ft2 .·697 2.320 .351 .151 1.290 

Q = 1. 53 cfs v = 1.068xl05 ft2/sec .596 2.230 .362 .162 1.331 

T = 21.1 •c R = 73,107 .495 2.105 . 370 .176 1.360 

D = 0.420 ft F = o .506 .394 2.020 .386 .191 1.419 

V = 1. 859 fps c;lg = 6. 835 .293 1.900 .367 .193 1.349 

.192 1. 700 .343 .202 1.261 ----- \ 

1/2-Inch Block Roughness, Channel Centerline, Station 15 

0.899 2.410 0.235 0.098 0.864 ----- s = 7. 80x163 u. = 0.272 fps . 798 2.395 .277 .ll6 1.018 ----- w = 1.96 ft T =. 0.205 1b/ft2 .697 2.370 .307 .130 1.129 ----- Q = 1.53 cfs v = 1.068xl05 ft 2/sec .596 2.320 .320 .138 1.176 ----- T = 21.1 •c R = 73,084 .495 2.270 .349 .154 1.283 ----- D = 0.421 ft F 0.504 .394 2.160 .376 .174 1.382 ----- V= 1.854 fps c;lg = 6.816 .293 2.050 .4ll .200 1.511 ----- .192 1. 740 .474 .272 1. 743 -----

1/2-Inch Block Roughness, 6 Inches From Wall, Station 15 

0.899 2.510 0.289 0.115 1.063 S = 7 .80xl(j3 u* = 0.272 fps . 798 2.520 .348 .138 1.279 w = 1.96 ft T = 0. 205 lb/ft2 .697 2.510 .360 .143 1.324 Q = 1.53 cfs v = 1.068xl65 £t2/sec .596 2.470 .377 .153 1.386 T = 21.1 •c R = 73,084 .495 2.410 .362 .150 1.331 D = 0.421 ft; F = 0.504 .394 2.350 .373 .159 1.371 V = 1.854 fps c;lg = 6.816 .293 2.250 .382 .170 1.404 

.192 1.990 .462 .232 1.699 

1/2-Inch Block Roughness, Channel Centerline, Station 20 

S = 7.80xl0- 3 0.899 2.405 0.208 0.086 o. 768 u. = 0.271 fps . 798 2.340 .287 .123 1.059 w = 1.96 ft T = 0.202 lb/ft2 .697 2.250 .269 .120 .993 Q = 1. 53 cfs v = 1.068xl0-s ft 2/sec .596 2.160 .311 .144 1.148 T = 21.1 •c R = 73,073 .495 2.020 .284 .141 1.048 D = 0.416 ft F = 0.513 .394 1.910 .323 .169 1.192 V = 1.876 fps c;lg = 6.923 .293 1.800 .348 .193 1.284 

.192 1.630 .395 .2'212 1.458 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 20 

S = 7 .80xl0- 3 0.899 2.415 0.170 0.070 0.627 

U* = 0.271 fps . 798 2.520 .223 .088 .823 w = 1.96 ft T = 0. 202 lb/ft2 .697 2.610 .286 .110 1.055 Q = 1. 53 cfs v = l.068x10-5 ft2/sec .596 2.645 .344 .130 1.269 T = 21.1 •c R = 73,073 .495 2.600 .351 .135 1.295 D = 0.416 ft F = 0.513 .394 2.450 .383 .156 1.413 V = 1.876 fps c;lg = 6.923 .293 2.250 .388 .172 1.432 

.192 1.980 .493 .249 1.819 

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:z: (ft) 

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SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

TABLE 3b.- 2-foot-wide flume, rigid boundary, developing flow- Continued 

Mean Flow Parameters 

and Variables 

1/2-lnch Block Roughness, Channel Centerline, Station 25 

0.899 2.495 0.207 0.083 o. 772 

S = 7 .80xl0- 3 u. = 0.268 fps . 798 2.410 .262 .109 .978 

w = 1.96 ft T = 0.196 lb/ft2 .697 2.280 .296 .130 1.104 

Q = 1.53 cfs v = 1.068xl05 ft 2/sec .596 2.180 .323 .148 1.205 

T = 21.1 •c R = 73,098 .495 2.030 .321 .158 1.198 

D = 0.402 ft F = 0.540 .394 1.860 .317 .170 1.183 

V = 1.942 fps c;l{j = 7.246 .293 1. 710 .314 .184 1.172 

.192 1.410 .263 .187 .981 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 25 

0.899 2.495 0.167 0.067 0.623 

S=7.80xl0- 3 u. = 0.268 fps . 798 2.570 .228 .089 . 851 

w = 1.96 ft T = 0.196 lb/ft2 .697 2.640 .228 .086 .851 

Q = 1. 53 cfs v = l.068xl0-s ft 2/sec .596 2.660 .257 .097 .959 

T = 21.1 •c R = 73,098 .495 2.595 .268 .103 1.000 

D = 0.402 ft F = o .540 .394 2.390 .375 .157 1.399 

V = 1.942 fps C//{j= 7.246 .293 2.050 .389 .190 1.451 

.192 1.530 .390 . 255 1.455 

1/2-lnch Block Roughness, Channel Centerline, Station 30 

S = 7. 80xl0- 3 0.899 2.310 0.290 0.126 1.082 

u. = 0.268 fps . 798 2.215 .315 .142 1.175 

w = 1.96 ft T = 0.197 lb/ft2 .697 2.100 .330 .157 1.231 

Q = 1.53 cfs v = l. 068xlO- 5 ft2/sec .596 1.950 .328 .168 1.224 

T=2l.l"C R = 73,083 .495 1.810 .348 .192 1.299 

D = 0.404 ft F = 0.536 .394 1.690 .322 .191 1.201 

V = 1.932 fps c;l{j = 7.209 .293 1.500 .305 .203 1.138 

.192 1.390 .327 .235 1.220 

1/2-lnch Block Roughness, 6 Inches From Wall, Station 30 

0.899 2.495 0.167 0.067 0.623 

S = 7 .80x1o- 3 u. = 0.268 fps . 798 2.590 .161 .062 .601 

w = 1.96 ft T = 0.197 lb/ft2 .697 2.640 .214 .081 . 799 

Q = 1. 53 cfs v = 1.068xl0- 5 ft 2/sec .596 2.630 .214 .081 . 799 

T=2l.l"C R = 73,083 .495 2.530 .277 .llO 1.034 

D = 0.404 ft F = 0.536 .394 2.330 .341 .146 1.272 

V = 1.932 fps c;l{j = 7.209 .293 2.060 .398 .193 1.485 

.192 1.615 .391 .242 1.459 

1/2-Inch Block Roughness, Channel Centerline, Station 35 

S = 7.80x]..0- 3 0.899 2.250 0.271 0.120 1.007 

u. = 0.269 fps . 798 2.125 .304 .143 • .. 130 

w = 1.96 ft T = 0.199 lb/ft2 .697 2.000 .313 .157 1.164 

Q = 1.53 c~~ v = l.068xl0- 5 ft 2/sec .596 1.860 .270 .145 1.004 

T = 21.1 •c R = 73,081 .495 1. 750 .315 .180 1.171 

D = 0.408 ft F = 0.528 .394 1.600 .283 .177 1.052 

V = 1.913 fps C//{j= 7.112 .293 1.400 .255 .182 .948 

.192 1.260 .269 .213 1.000 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 35 

0.899 2.405 0.219 0.091 0.814 S=7.80xl0- 3 u. = 0.269 fps . 798 2.520 .222 .088 .825 w = 1.96 ft T = 0.199 lb/ft2 .697 2.600 .230 .088 .855 Q = 1.53 cfs v = 1. 068xlO- 5 ft2 /sec .596 2.630 .235 .089 .874 

T = 21.1 •c R = 73,081 .495 2.590 .273 .105 1.015 

D = 0.408 ft F = 0.528 .394 2.410 .335 .139 1.245 

V = 1.913 fps C//{j= 7.112 .293 2.220 .404 .182 1.502 

.192 1.830 .431 .236 1.602 

1/2-Inch Block Roughness, Channel Centerline, Station 40 

0.899 2.150 0.268 0.125 0.992 S = 7 .80xl0- 3 u. = 0.270 fps . 798 2.100 .304 .145 1.126 

w = 1.96 ft T = 0. 201 1b/ft2 .697 2.020 .313 .155 1:159 

Q = 1.53 cfs v = 1.068x10- 5 ft2/sec .596 1.950 .335 .172 1.241 T = 21.1 •c R = 73,087 .495 1.870 .336 .180 1.244 

D = 0.413 ft F = 0.518 .394 1. 755 .348 .198 1.289 

V = 1.890 fps c;l{j = 7 .ooo .293 1.660 .344 .207 1.274 

.192 1.500 .345 .230 1.278 

1/2-Inch Block Roughness 6 Inches From Wall Station 40 

0.899 2.405 0.274 0.114 1.015 S = 7.80xl0- 3 u. = 0.270 fps . 798 2.480 .301 .121 1.115 

w = 1.96 ft T = 0.201 lb/ft2 .697 2.510 .3ll .124 1.152 

Q = 1.53 cfs v = 1.068xlO-s ft 2/sec .596 2.520 .3ll .124 1.152 T=21.1"C R = 73,087 .495 2.455 .366 .127 1.356 

D = 0.413 ft F = o .518 .394 2.300 . 373 .162 1. 381 

V = 1.890 fps C//{j = 7.000 .293 1.990 .390 .196 1.444 

.192 1.480 .383 .259 1.419 

1/2-Inch Block Roughness, Channel Centerline, Station 45 

0.899 2.285 0.190 0.083 0. 701 

S = 7.80x10- 3 u. = 0.271 fps . 798 2.250 .216 .096 . 797 

w = 1.96 ft T = 0. 203 lb/ft2 .697 2.150 .225 .105 .830 

Q = 1.53 cfs v = 1.068x10-s ft2/sec .596 2.100 .228 .109 .841 

T = 21.1 •c R = 73,092 .495 2.000 .237 .119 .875 

D = 0.417 ft F = 0.5ll .394 1.910 .252 .132 .930 

V = 1.872 fps c;l{j = 6.908 .293 1.815 .290 .160 1.070 

.192 1.640 .342 .209 1.262 

0.320 0.688 

.361 • 758 

.262 .529 

.267 .520 

.318 .595 

.314 .552 

.262 .435 

.358 .537 

0.209 0.503 

.254 .630 

.156 .392 

.151 .380 .183 .449 

.297 .683 

.198 .394 

.192 .284 

0.348 o. '795 

.208 .468 

.427 .918 

.212 .445 

.348 .696 

.290 .554 

.136 .247 

.144 .236 

A 

X 

(ft) 

0.015 

.014 

.013 

.012 

.012 

.011 

.010 

.008 

0.017 

.016 

.016 

.015 

.014 

.012 

.009 

.008 

0.01 53 

41 

46 

38 

.01 

.01 

.01 

.013 

.012 

5 

7 

1 

6 

.013 

.011 

B45 
B46 TURBULENCE IN WATER 

TABLE 3b.- 2-foot-wide flume, rigid boundary, developing flow- Continued 

Mean Flow Paraaeters 

and Variables 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 45 

0.899 2.300 0.256 O.lll 0.945 0.175 S = 7.80xl0-3 v. = 0.271 fps .698 2.420 .275 .ll4 1.015 .173 

w = 1. 96 ft T = 0. 203 lb/ft2 .697 2.480 .285 .ll5 1.052 .226 

Q = 1.53 cfs v = 1.068x 10- 5 ft2/sec .596 2.480 .298 .120 1.100 .198 

T = 21.1 •c R = 73,092 .495 2.420 .325 .134 1.199 .187 

D = 0.417 ft F = 0.5ll .394 2.300 .342 .149 1.262 .202 

V = 1.872 fps Cl/i= 6.908 .293 1.990 .353 .177 1.303 .176 

.192 1.530 .417 .273 1.539 .200 

1/2-Inch Block Roughness, Channel Centerline, Station 5 

0.899 3.000 0.377 0.126 1.019 0-.148 

s = 14.57xHP u* = 0.370 fps . 798 3. 090 .408 .132 1.103 .214 

w = 1. 96 ft T = 0.376 lb/ft2 .697 3.105 .387 .125 1.046 .194 

Q = 2.10 cfs v = 1.068xl(j5 ft2/sec .596 3.140 .405 .129 1.095 .193 

T=21.1•c R = 100,321 .495 3.050 .416 .136 1.124 .158 

D = 0.414 ft F = o. 709 .394 2.840 .450 .158 1.216 .172 

V = 2. 588 fps C//i= 6.995 .293 2.480 .464 .187 1. 254 .151 

.192 2.050 .528 .258 1.427 .160 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 5 

0.899 3. 310 0.425 0.128 1.149 0.187 

s = 14.57 163 u* = 0. 370 fps . 798 3.480 .433 .124 1.170 .160 

w = 1. 96 ft T = 0. 376 lb/ft2 .697 3.530 .465 .132 1.257 .161 

Q = 2.10 cfs v = 1. 068xl65 ft 2/sec .596 3.480 .508 .146 1.373 .205 

T = 21.1 °L R = 100.,321 .495 3.295 .527 .160 1.424 .354 

D = 0.414 ft F = o. 709 .394 2.930 .569 .194 1.538 . 273 

V= 2. 588 fps C/lg = 6.995 .293 2. 580 .591 .229 1.597 .136 

.192 2.140 . 547 .256 1.478 .189 

1/2-Inch Block Roughness, Channel Centerline, Station 10 

0.899 3.515 0. 300 0. 085 0.813 0.246 

8 = 14.57XJQ3 u* = 0.369 fps . 798 3.320 . 375 .113 1.016 .161 

w = 1. 96 ft T = 0.374 lb/ft2 .697 3.130 .422 .135 1.144 .140 

Q = 2.10 cfs v = 1.068xlo5 ft 2/sec .596 2.810 .465 .165 1.260 .133 

T=21.1•c R = 100,326 .495 2.600 .494 .190 1.339 .153 

D = 0.411 ft f=0.717 .394 2.310 .485 . 210 1.314 .167 

V = 2.607 fps C//i = 7.065 .293 2.000 .470 . 235 1.274 .238 

.-192 1.605 . 399 . 249 1.081 . 213 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 10 

0.899 3.200 0.189 0.059 0.512 0.185 

S = 14. 57xl03 U * = 0. 369 fps . 798 3.180 .226 .071 . 721 .222 

w = 1.96 ft T = 0.374 lb/ft2 .697 3.150 .278 .088 . 753 .159 

Q = 2.10 cfs v = l.068xl65 ft 2/sec .596 3.120 .304 .097 .824 .205 

T = 21.1 •c R = 100,326 .495 3.060 .332 .108 .900 .215 

D = 0.411 ft F = o. 717 .394 2.990 .359 .120 .973 ,210 

V = 2.607 fps c;;g = 7.065 .293 2.840 .405 .143 1.098 .247 

.192 2.530 .489 .193 1.325 . 262 

1/2-Inch Block Roughness, Channel Centerline, Station 15 

0.899 3.110 0.421 0.135 1.132 

s = 14. S7xl63 U * = 0. 372 fps • 798 3.000 .519 .173 1. 395 

w = l. 96 ft T = 0.384 lb/ft2 .697 2.850 .550 .193 1.478 

Q = 2.10 cfs v = l.068xl65 ft 2/sec .596 2.640 .581 .196 1.562 

T = 21.1 •c R = 100,324 .495 2.450 .574 .234 1.543 

D = 0.422 ft F = 0.689 . 394 2.180 .568 .261 1.527 

V = 2.539 fps C//i= 6.825 .293 2.040 .563 .276 1.513 

.192 1.415 .380 .269 1.022 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 15 

0.899 3.380 0.164 0.049 0.441 

s = 14. 57Xl03 u* = 0.372 fps . 798 3.400 .169 .050 .454 

w = l. 96 ft T = 0.384 lb/ft2 .697 3.390 .194 .057 .522 

Q = 2.10 ft v = l. 068xl05 ft 2/sec .596 3.330 .200 .060 .538 

T = 21.1 •c R = 100,324 .495 3.220 . 270 .084 .726 

D = 0.422 ft F = 0.689 .394 3.130 .337 .108 .906 

V = 2. 539 fps C//g = 6.825 .293 2.935 .456 .159 1.226 

.19? 2. 700 .381 .141 1.024 

1/2-Inch Block Roughness, Channel Centerline, Station 20 

0.899 3.010 0.389 0.129 1.049 S = 14.57xlQ3 u* = 0.371 fps • 798 2.805 .422 .150 1.137 

w = 1.96 ft T = 0.380 lb/ft2 .697 2.600 .445 .171 1.199 

Q = 2.10 cfs v = 1.068xl05 ft2/sec .596 2.360 .440 .186 1.186 

T = 21.1 •c R = 100,312 .495 2.100 .402 .191 1.084 

D = 0.418 ft F = 0.699 .394 1.910 .388 .203 1.046 

V = 2.563 fps C!/i= 6.908 .293 1. 720 .337 .196 .908 

.192 1.400 .336 .240 .906 

). 

:c (ft) 

0.403 0.0165 

.418 .0148 

.560 .0152 

.491 .0144 

.453 .0131 

.465 .0129 

.350 .0109 

.236 .0101 

0.444 0.0200 

.661 .0201 

.603 .0186 

.606 .0189 

.492 .0166 

.488 .0154 

.374 .0143 

.328 .0136 

0.618 o. 0226 

.556 .0217 .568 .0229 

.714 .0206 

1.164 .0213 

.800 .0184 

.352 .0169 

.405 .0146 

0.867" 0.0306 

.535 .0273 

.438 .0222 

.374 .0197 

.398 :0173 

.386 .0154 

.476 .0133 

.342 .Oll9 

0.592 0.0277 .706 .• 0268 

.sao .0252 

,640 .0261 

,657 .0247 

,625 .0233 

.701 .0223 

,663 .0219 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B47 

TABLE 3b.- 2-foot-wide flume, rigid boundary, developing flow- Continued 

Mean Flow Parameters J.. :c 

and Variables (ft) 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 20 

0.899 3. 400 0. 278 0.082 o. 749 S = 14.57xl()3 u. = 0.371 fps • 798 3.530 .242 .068 .652 

w = 1.96 ft T = 0.380 lb/ft2 .697 3.570 .247 .069 .666 

Q = 2.10 cfs v = 1.068xll)5 ft 2/sec .596 3.560 .245 .069 .660 T = 21.1 •c R = 100,312 .495 3.490 .283 . 081 • 763 

D = 0.418 ft F = o .699 .394 3.270 . 368 .ll3 .992 

V = 2.563 fps C//g = 6.908 .293 2.850 .463 .162 1. 248 

.192 2.390 .598 .250 1.612 

1/2-Inr.h Block Roughness, Channel Centerline, Station 25 

0.899 2.860 0.344 0.120 0.937 

S = 14 .57xl63 u. = 0.367 fps • 798 2. 780 .390 .140 1.063 

w = 1.96 ft T = 0.370 lb/ft2 .697 2.675 .437 .163 1.191 

Q = 2.10 cfo v = 1.068xll)5 ft2/sec .596 2.600 .489 .188 1.332 T=2l.l"C R = 101' 483 .495 2.470 .472 .191 1.286 

D = 0.407 ft F = 0.736 .394 2.260 .4ll .182 1.120 

V = 2.633 fps c;lg = 7.256 . 293 2.020 .433 .214 1.180 

.192 1.580 .325 .206 .886 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 25 

0.899 3.390 0.194 0.057 0.529 

S = 14.57xlo"3 u. = 0.367 fps • 798 3.490 .206 .059 .561 

w = 1.96 ft T = 0.370 lb/ft2 .697 3.520 .203 .058 .553 

Q = 2.10 cfs v = 1.068xl65 ft 2/sec .596 3.480 .208 .060 .567 

T=2l.l°C R = 101,483 .495 3.370 .310 .092 .845 

D = 0.407 ft F = 0.736 .394 3.090 .421 .136 1.147 

V = 2.633 fps C//g= 7.256 .293 2.615 .513 .196 1.398 

.192 1.680 .452 .269 1.232 

1/2-Inch Block Roughness, Channel Centerline, Station 30 

0.899 2.910 0.390 0.134 1.057 

S = 14.57xl63 u. = 0.369 fps . 798 2.850 .428 .150 1.160 

w = 1.96 ft 1 = 0.375 lb/ft2 .697 2. 700 .462 .171 1.252 

Q = 2.10 cfs v = 1.068xl()S ft2/sec .596 2.530 .455 .180 1.233 

T=2l.l"C R = 100,338 .495 2.370 .453 .191 1.228 

D = 0.412 ft F = 0.714 . 394 2.220 .506 .228 1.371 

V = 2.601 fps c;lg = 7.049 .293 1.950 .476 .244 1.290 

.192 1.680 . 442 . 263 1.198 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 30 

0.899 3.520 0.206 0.059 0.558 

S = 14.57xl()3 u. = 0.369 fps . 798 3.650 .203 .056 .550 

w = 1.96 ft 1 = 0. 375 lb/ft2 .697 3.690 .209 .057 .566 

Q = 2.10 cfs v = 1.068xl65 ft 2/sec .596 3.640 .244 .067 .661 

T = 21.1 •c R = 100,338 .495 3.475 .366 .105 .992 

D = 0.412 ft F = o. 714 .394 3.ll0 .492 .158 1.333 

V= 2.601 fps C//g = 7.049 .293 2. 700 .570 .2ll 1.545 

.192 1.820 .454 .249 1.230 

1/2-Inch Block Roughness, Channel Centerline, Station 35 

0.899 3.020 0.405 0.135 1.098 0.275 0.830 1 0.0236 

S = 14.57xl63 U • = 0 . 369 fps . 798 2.905 .447 .154 1.2ll .297 • 865 .0232 

w = 1.96 ft T = 0.375 lb/ft2 .697 2. 750 .424 .154 1.149 . 320 .880 .0227 

Q = 2.10 cfs v = 1.068xl65 ft2/sec .596 2.610 .481 .182 1.304 .403 .836 .0209 

T = 21.1 •c R = 100,338 . 495 2.470 .462 .187 1.252 .266 .656 .0184 

D = 0.412 ft F = 0. 714 . 394 2.270 .476 .210 1.290 .161 .366 .0158 

V = 2.601 fps C//g = 7.049 . 293 2.050 .459 .224 1.244 .258 .529 .0134 

.192 1.820 .505 .277 1.369 .276 .503 .0123 

1/2- Inch Block Roughness, 6 Inches From Wall, Station 35 

0.899 3.370 0.311 0.092 0.843 0.301 1.013 0. 0294 

S = 14 .57xl()3 u. = 0.369 fps . 798 3.540 .309 .087 . 837 .1-71 .606 .0306 

w = 1.96 ft T = 0.375 lb/ft2 .697 3.600 .290 .081 . 786 .286 1-.030 .0283 

Q = 2.10 cfs v = 1.068xl65 ft2/sec .596 3.600 .284 .079 .770 .190 .684 .0266 

T = 21.1 °L R = 100,338 .495 3.500 .341 .097 .924 .322 1.126 .0242 

D = 0.412 ft F = 0.714 .394 3.250 .422 .130 1.144 .235 . 764 . 0209 

V = 2.601 fps C//g = 7.049 .293 2.810 .515 .183 1.396 . 223 .627 .0198 

.192 2.200 .58/ .267 1.591 .249 .548 . 0192 

1/2-Inch Block Roughness, Channel Centerline, Station 40 

0.899 3.020 0.397 0.131 1.076 1 o. 238 0. 719 o. 0230 

S = 14 .57xl()3 u. = 0.369 fps . 798 2.900 .410 .141 l.lll .388 1.125 .0244 

w = 1.96 ft T = 0.375 lb/ft2 .697 2.830 .428 .151 1.160 .274 . 776 .0217 

Q = 2.10 cfs \) = 1.068xl65 ft2/sec .596 2. 700 .451 .167 1.222 . 327 .883 .0194 

T = 21.1 •c R = 100,338 .495 2.610 .478 .183 1.295 . 318 .830 .0168 

D = 0.412 ft F = 0.714 • 394 2.470 .490 .198 1.328 .316 . 780 .0151 

V = 2.601 fps C//g = 7.049 .293 2.300 .487 .212 1.320 .230 .529 .0137 

.192 1.825 . 457 . 250 1.238 .318 . 580 .0120 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 40 

0.899 3.390 0.271 0.080 0. 734 o. 341 1.157 0.0314 

S = 14.57xl63 u. = 0.369 fps . 798 3.500 .255 .073 .691 . 254 .888 .0327 

w = 1.96 ft T = 0,375 lb/ft2 .697 3.530 .259 .073 . 702 .183 .646 .0294 

Q = 2. 10 cfs v = 1.068xl65 ft2/sec .596 3.500 .278 .079 . 753 .314 1.099 .0285 

T=2l.l"C R = 100,338 .495 3.400 .356 .105 .965 . 298 1. 018 . 0276 

D = 0.412 ft F = o. 714 .394 3.100 .445 .144 1.206 .246 . 762 .0241 

V = 2.601 fps C//g = 7.049 .293 2.670 .520 .195 1.409 . 294 • 785 . 0198 

.192 2.320 • 750 .323 2.033 . 388 .900 .0177 
B48 TURBULENCE IN WATER 

TABLE 3b.- 2-foot-wide flume, rigid boundary, developing flow- Continued 

Mean Flow Parameters 

and Variables 

1/2-Inch Block Roughness, Channel Centerline, Station 45 

0.899 3.030 0.342 0.113 0.924 

S = 14.57xl()3 u* = 0.370 fps . 798 3.010 .395 .132 1.068 

w = 1.96 ft ' = 0. 378 lb/ft· .697 2.910 .400 .137 1.081 

Q = 2.10 cfs v = 1.068x165 ft2/sec .596 2.800 .407 .145 1.100 

T = 21.1 •c R = 100,338 .495 2. 710 .442 .163 1.195 

D = 0.416 ft F = o. 704 .394 2.570 .442 .172 1.195 

V= 2.576 fps C//i = 6.962 .293 2.420 .430 .178 1.162 

.192 2.280 .490 .215 1.324 

1/2-Inch Block Roughness, 6 Inches From Wall, Station 45 

0.899 3.260 0.268 0.082 0. 724 

S = 14 .57xl03 u* = 0.370 fps . 798 3.405 .275 .081 . 743 

w = 1.96 ft ' = 0.378 lb/ft2 .697 3.450 .271 .079 . 732 

Q = 2.10 cfs v = 1.068xl65 ft2/sec .596 3.415 .297 .087 .803 

T = 21.1 •c R = 100,338 .495 3.300 .351 .106 .949 

D = 0.416 ft F = o. 704 .394 3.050 .400 .131 1.081 

V= 2.576 fps C//i = 6.962 .293 2.620 .460 .176 1.243 

.192 2.020 .475 .235 1.284 

A 

:r: (ft) 

0.369 1.118 0.0252 

.451 1.356 . 0255 

.255 . 743 .0226 

.218 .610 .0241 

.l25 .881 .0192 

.377 .970 .0180 

. 301 .729 .0172 

.372 .849 .0164 

0.313 1.020 o. 0302 

.225 . 766 .0320 

.405 1.397 .0308 

.440 1.500 .0277 

.467 1.584 .0233 

.464 1.413 .0206 

.SOl 1. 311 .0183 

. 245 .495 .0148 

TABLE 3c.- 2-foot-wide flume, rigid boundary, yawed-film results 

Mean flow parameters 

and variables 

S a 5.04x10- 3 U* = 0. 216 fps 

w = 1. 96 ft 't = 0.128 lb/ft2 

~ : ~i~~ ~~s v • 1. 068x10- 5 ft 2 /sec R= 37,250 

D = 0.408 ft F = 0.269 

V- 0.975 fps etrg • 4.51 

s = 5.o4xlo-• U* • 0. 216 fps 

w = 1. 96 ft 't = 0.128 lb/ft 2 

Q • 0. 78 cfs V • 1.068x10- 5 ft 2 /sec 

T • 21.1 De R= 37,250 

D • 0.408 ft F • 0.269 

V • 0.975 fps e//i, = 4.51 

S • 13.25X10- U* = U, J:>U fps 

w - 1. 96 ft 't = o. 335 lb/ft2 

Q = 1.21 cfs v = 1.068x10- 5 ft 2 /sec 

T = 21.1 De R = 57,800 

D = 0.405 ft F = 0.422 

v• 1.524 fps e{/i,= 4.35 

S - 13.25Xl0- u* = 0. 350 fps 

w - 1. 96 ft 't = o. 335 lb/ft 2 

Q • 1.21 cfs v = 1.068xlo- 5 ft 2 /sec 

T•21.1De R= 57,800 

D • 0.405 ft F- 0.422 

v = 1. 524 fps ef/i, = 4. 35 

S = 20.54Xl0- 3 U* = 0. 438 fps 

w - 1. 96 ft 't - o. 527 lb/ft 2 

Q • 1.56 cfs v • 1.068X10- 5 ft 2 /sec T • 21.1 De R • 74,540 

D = 0.411 ft F = 0.532 

v • 1.937 fps e/-/g = 4. 42 

0.900 1.550 0.170 

.800 1.530 .170 

. 700 1.520 .171 

.600 1.450 .178 

.500 1.380 .220 

.400 1.260 .221 

• 340 1.190 .219 

.280 1.120 .217 

. 220 1.040 .237 

.900 1.520 .165 

.800 1.480 .182 

• 700 1.450 .199 

.600 1.430 .204 

.500 1.400 .216 

.400 1.250 .213 

.340 1.170 .196 

.280 1.040 .188 

.220 .880 .193 

.900 2. 390 .260 

. 800 2.300 .282 

. 700 2.200 . 301 

.600 2.030 . 347 

.500 1.800 . 370 

.400 1.590 .383 

. 340 1.430 .377 

.280 1.230 . 319 

.220 1.010 . 307 

.900 2.400 .281 

.800 2. 340 .283 

. 700 2.290 • 337 

.600 2.210 .348 

.500 2.110 .421 

.400 2.030 .352 

.340 1.950 . 374 

.280 1.880 .339 

.220 1. 790 .326 

.800 2.880 • 336 

• 700 2. 740 .371 

.600 2.600 .404 

.500 2.400 .483 

.400 2.000 .566 

.340 1. 720 .613 

.280 1.360 .587 

.220 .980 .553 

Note: Scales of turbulence are given in table 3b. 

Station 6 feet - 3 inches right of centerline 

0.110 o. 790 0.136 0.088 0.630 0. 0103 .0128 .111 . 790 .132 .086 .612 .0274 .0246 

.113 .800 .139 .091 .644 .0338 .0384 

.123 .820 .143 .099 .663 .0417 .0512 

.160 1.020 .177 .128 .818 .0621 .0641 

.175 1.020 .168 .133 .778 .0645 .0768 

.184 1.010 .174 .146 .806 .0672 .0842 

.193 1.008 .171 .152 . 792 .0508 .0919 

.227 1.094 .181 .174 .840 .0293 .0996 

Station 15 feet - 3 inches right of centerline 

.108 . 764 .127 .084 .590 .0335 .0128 

.123 .843 .139 .094 .645 .0399 .0246 

.137 .922 .161 .111 • 746 .0477 .0384 

.143 .945 .158 .101 . 732 .0596 .0512 

.154 1.000 .173 .124 .801 .0704 .0641 

.170 .986 .166 .132 • 768 .0761 .0768 

.167 .908 .170 .145 . 788 .0734 .0842 

.181 .872 .155 .149 .718 .0762 .0919 

.219 .894 .149 .170 .691 .0583 .0996 

Station 6 feet - 3 inches right of centerline 

.108 • 744 .196 .082 .560 .Ul!S!S .0335 

.123 .805 .231 .101 .659 .0470 .0670 

.136 .860 .246 .112 . 703 .0935 .1005 

.171 .992 .268 .132 • 766 .1334 .1340 

.205 1.056 .302 .167 . 863 .1440 .1675 

.241 1.093 .297 .186 .848 .1458 .2001 

.263 1.079 .304 .212 . 870 .1386 .2171 

.259 .913 .273 .222 • 780 .0953 .2370 

.304 .877 .255 .253 • 730 .0616 .2568 

Station 15 feet - 3 inches right of centerline 

.11'7 .803 .232 .097 .663 .U'+YU .0335 

.121 .809 .226 .097 .645 .0622 .0670 

.147 .964 .263 .115 • 751 .0873 .1005 

.158 .995 .278 .126 • 795 .1337 .1340 

.200 1.121 .324 .153 .925 .1408 .1675 

.173 1.005 .298 .147 .853 .1423 .2001 

.192 1.070 .305 .156 .873 .1481 .2171 

.180 .970 .286 .153 .816 .1415 .2370 

.183 .933 .253 .141 .724 .1189 .2568 

Station 6 feet - 3 inches right of centerline 

.116 • 766 .247 .086 .5U4 .1025 .1054 

.135 • 848 .303 .ll5 .6?3 .1454 .1580 

.155 .922 . 331 .127 • 755 .1827 .2108 

.201 1.112 .387 .161 . 883 .2364 .2637 

.283 1.291 .472 .235 1.078 .3116 • 3161 

.356 1.400 .496 .288 1.132 .2849 • 3489 

.432 1. 340 .458 .337 1.050 .2017 . 3820 

.564 1.262 .419 .427 .956 .1523 .4133 

0.002 0.114 .006 .302 

.008 .373 

.010 .461 

.017 .686 

.021 .712 

.024 .742 

.021 .561 

.014 .324 

0.007 0.370 

.009 .441 

.012 .527 

.015 .658 

.019 .778 

.025 .841 

.028 .811 

.036 .842 

.039 .644 

0.003 0.121 

.005 .198 

.010 .393 

.017 .561 

.023 .606 

.030 .614 

.035 .583 

.033 .401 

.031 .259 

0.004 0.206 

.007 .262 

.009 .367 

.014 .562 

.016 .592 

.018 .599 

.020 .623 

.021 .595 

.019 .500 

0.006 0.275 

.010 .425 

.014 .491 

.021 .635 

.040 .837 

.050 • 766 

.056 .542 

.082 .409 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

TABLE 3c.- 2-foot-wide flume, rigid boundary, yawed-film results- Continued 

Mean flow parameters 

and variables 

S c 20.54Xl0-! U* = 0. 438 fps 

w = 1. 96 ft 1: s o. 527 lb/ft 2 

Q = 1. 56 cfs v = 1.068x1Q- 5 ft 2 /sec 

T = 21.1 De R s 74,540 

D • 0.411 ft F = 0.532 

v = 1.937 fps etlg = 4.42 

S = 2.95XlQ-! U* = 0.164 fps 

w = 1.96 ft 1: = 0.073 lb/ft 2 

Q • 0.88 cfs v • 1. 068x1Q- 5 ft 2 /sec 

T • 21.1 De R = 42,030 

D • 0.399 ft F = 0. 314 

v • 1.125 fps e/.Tg = 6, 86 

S = 2.95Xl0- 3 U* • 0. 164 fps 

w = 1.96 ft 1: = 0.073 lb/ft 2 

Q • 0.88 cfs v = 1.068Xl0- 5 ft 2 tsec 

T=21.1De R= 42,030 

D • 0.399 ft F • 0. 314 

V = 1.125 fps e/lg = 6.86 

S = 7.80Xl0- 3 U* • 0. 272 fps 

w = 1. 96 ft 1: - o. 205 lb/ft 2 

Q • 1.53 cfs v • 1.068Xl0-s ft 2 /se 

T • 21.1 De R = 73,084 

D s 0. 421 ft F = 0.504 

;;- 1. 854 fps etli, = 6. 82 

S • 7.80xl0- 3 U* = 0.272 fps 

w = 1.96 ft 1: = o. 205 lb/ft 2 

Q = 1.53 cfs v = 1.068><1.0- 5 ft 2 /sec 

T • 21.1 De R = 73,084 

D = 0.421 ft F = 0.504 

-v= 1. 854 fps er/i, = 6. 82 

S = 14.57X10- 3 U* = 0.371 fps 

w - 1. 96 ft 1: - 0. 380 lb/ft 2 

Q = 2.10 cfs v = 1.068xl0- 5 ft 2 /sec 

T • 21.1 De R = 100,310 

D = 0.418 ft F= 0.699 

v = 2 .563fps e!li • 6. 91 

S- 14.57x10- 3 U* = 0.371 fps 

w = 1.96 ft 1: = 0.380 1b/ft 2 

Q = 2.10 cfs v • 1.068x1Q-s ft 2 /sec 

T=21.1°e R = 100,310 

D = 0.418 ft F = 0.699 

V = 2.563 fps cJii = 6.91 

.900 2.930 

.800 2.840 

• 700 2. 700 

.600 2.660 

.500 2.550 

.400 2.360 

. 340 2.220 

.280 2.090 

.900 1.370 

.800 1.420 

• 700 1.440 

.600 1.450 

.500 1.400 

.400 1.300 

. 340 1.240 

.280 1.130 

.220 1.002 

.900 1.370 

.800 1. 390 

. 700 1.420 

.600 1.430 

.500 1.420 

.400 1. 380 

.340 1.340 

.280 1.240 

. 220 1.150 

0.900 2.230 

.800 2.320 • 700 2.400 

.600 2.470 

.500 2.500 

.400 2.370 

.340 2. 200 

.280 2.010 

.220 1. 770 

.900 2.510 

.800 2. 520 

. 700 2.510 

.600 2.470 

.500 2.410 

.400 2.350 

. 340 2.270 

.280 2.180 

.220 2.060 

.800 3.480 

. 700 3. 530 

.600 3.480 

.500 3.295 

.400 2.930 

.340 2. 710 

.280 2.480 

.220 2.190 

.900 ). 380 

.800 3.400 

. 700 3.390 

.600 3.330 

.500 3.220 

.400 3.130 

. 340 2.950 

.280 2.870 

. 220 2. 740 

Station 15 feet - l inches right of centerline 

.545 .186 1.244 .441 .150 1.004 .0422 

• 495 .175 1.130 . 398 .140 • 907 .0941 

.536 .198 1.222 .426 .158 .973 .1311 

.539 .203 1.227 .444 .166 1.012 .1910 

.597 .234 1. 360 .473 .186 1.080 .2365 

.614 .260 1.400 .502 .212 1.142 .2880 

.609 .274 1. 386 . 486 .219 1.109 .2722 

.626 .300 1.430 .477 .228 1.088 .2708 

Station 6 feet - 6 inches right of centerline 

.163 .119 .994 .131 .096 • 798 .0101 

.179 .126 1.091 .147 .103 .897 .0160 

.200 .139 1.220 .165 .114 1.004 .0258 

.216 .149 1.316 .172 .119 1.048 .0394 

.224 .160 1. 365 .184 .131 1.121 .0478 

.192 .148 1.172 .176 .136 1.073 .0403 

.187 .151 1.141 .163 .131 .993 .0389 

.183 .162 1.118 .144 .128 .878 .0275 

.152 .152 .928 .118 .108 .721 .0172 

Station 15 feet - 6 inches right of centerline 

.143 .104 .872 .107 .078 .654 .0088 

.160 .115 .976 .119 .086 .726 .0154 

.185 .130 1.126 .148 .104 .903 .0263 

.207 .144 1.261 .173 .121 1.054 .0316 

.226 .159 1.378 .179 .126 1.092 .0405 

.252 .182 1.540 .193 .140 1.177 .0437 

.248 .185 1.511 .196 .146 1.195 .0419 

.241 .195 1.468 .188 .152 1.147 .0398 

.237 .206 1. 445 .175 .152 1.067 .0366 

Station 6 feet - 6 inches right of centerline 

Q.273 o.122 1.003 0.194 Q.087 a. 713 .0196 . 301 .130 1.104 .227 .098 .835 .0383 . 346 .144 1.272 .273 .114 1.003 

.380 .154 1.396 .306 .124 1.125 .0429 

.450 .180 1.650 .344 .138 1.266 .0637 

.0738 .514 .216 1.900 • 398 .168 1.464 .1061 .497 .226 1.825 .402 .183 1.478 .1446 .470 .234 1. 724 • 383 .191 1.409 .1145 .408 .230 1.503 .327 .185 1.203 ·1047 

Station 15 feet - 6 inches right of centerline 

.289 .115 1.062 .235 .093 .866 .0201 

.348 .138 1.278 .266 .105 .978 .0332 

.360 .143 1.323 .292 .116 1.074 .0598 

. 377 .153 1.386 .301 .122 1.107 .0665 

.362 .150 1.330 .291 .121 1.071 .0862 

.373 .158 1.371 .307 .131 1.128 .1121 

.377 .166 1. 386 . 304 .134 1.123 .1088 

.382 .175 1.404 .316 .145 1.161 .14'5''4 .442 .214 1.623 .363 .176 1. 336 .1575 

Station 6 feet - 6 inches right of centerline 

0.433 0.124 1.169 0.358 0.103 0.963 .0380 

.465 .132 1.253 . 364 .103 .978 .0658 

.508 .146 1.372 .407 .117 1.096 .0827 

.527 .160 1.420 .413 .125 1.110 .1366 

.569 .194 1.532 .466 .159 1.255 .1822 

.580 .214 1.562 .448 .165 1.204 .1829 

.591 .238 1.591 .471 .190 1.269 .1871 

.547 .250 1.473 .435 .198 1.170 .154"1 

Station 15 feet - 6 inches right of centerline 

.164 .048 .442 .153 .045 .413 .0325 

.169 .050 .456 .137 .040 .370 .0721 

.194 .057 .523 .166 .049 .448 .1163 

.200 .060 .540 .174 .052 .468 .1428 

.270 .084 .727 .233 .072 .628 .1799 

. 337 .107 .908 .284 .091 . 766 .2064 

. 386 .131 1.041 .325 .110 .876 .2181 

.456 .162 1.231 .372 .130 1.~~! .2316 

.381 1 n?~ . 328 . 120 . l<lnll 

Note: Scales of turbulence are given in table 3b. 

.0527 0.003 

.1054 .006 

.1580 .009 

.2108 .014 

.2637 .019 

.3161 .027 

.3489 .028 

.3820 .032 

.0074 0.004 

.0147 .004 

.0221 .006 

.0294 .010 

.0368 .013 

.0431 .012 

.0486 .013 

.0537 .011 

.0580 .009 

.0074 0,002 

.0147 .004 

.0221 .007 

.0294 .008 

.0368 .010 

.0431 .012 

.0486 .012 

.0537 .013 

.0580 .014 

.0380 0.002 

.0760 .004 

.1140 .004 

.1520 .005 

.1900 .006 

.2280 .010 

.2496 .015 

.2731 .015 

.2952 .017 

.0184 0.002 

.0760 .003 

.1140 .005 

.1520 .006 

.1900 .008 

.2280 .010 

.2496 .011 

.2731 ,016 

.• 2952 .019 

.0411 0.002 

.0616 .003 

.0822 .004 

.1026 .007 

.1231 .011 

.1332 .013 

.1454 .016 

.1575 .017 

.0206 0.002 

.0332 .003 

.0598 .005 

.0822 .007 

.1026 .009 

.1231 .011 

.1332 .013 .1454 .015 

.1575 .013 

0.113 

.253 

.352 

.513 

.635 

.774 

• 731 

.728 

0.194 

.307 

.495 

• 755 

.916 

.773 

• 746 

.527 

.330 

0.169 

.295 

.504 

.606 

.776 

.838 

.803 

.763 

.701 

0.137 

.267 

.299 

.444 

.514 

.739 

1.007 

• 798 

.729 

0.140 

.231 

.417 

.463 

.601 

• 781 

.758 

1.013 

1.097 

0.142 

.246 

.310 

.512 

.682 

.685 

• 701 

.578 

0.122 

.270 

.436 

.535 

.674 

• 773 

.817 

.867 

.715 

B49 
B50 TURBULENCE IN WATER 

TABLE 4.- 1,.-foot-wide flume, rigid boundary 

Mean Flow Parameters 

and Variables 

Smooth Boundary, Channel Centerline 

0.963 1. 096 0.027 0.025 0.613 

.908 1.090 . 024 .022 .546 

. 854 1. 091 .023 .021 .520 

. 799 1.102 .022 .020 .500 

S = 0. 0928xl6 3 u* = o. 044 fps . 744 l.llO .023 . 021 .520 

.690 1.110 .024 .022 .546 

w = 3. 87 ft T = 0.0036 lb/ft2 . 635 1.108 .026 .023 .593 

.580 1. 095 .029 .026 .661 

Q = 3.67 cfs " = 1.62x10- 5 ft 2/sec . 526 1.077 .033 .031 • 750 

.471 1.055 .037 . 035 .840 

T=S.2°C R = 58,500 .416 1.001 .040 .040 .910 

.362 .970 .044 .045 1.000 

D = 0.915 ft F = 0.191 . 307 . 938 . 046 .049 1.045 

.252 .907 . 053 . 059 1.211 

v= 1. 036 fps clfi = 22.6 .198 .879 .057 .065 1.300 

.143 .845 .061 .072 1.388 

.089 . 797 .069 .087 1.570 

.034 . 700 . 088 .125 2.000 

.025 .647 .099 .153 2.250 

. 017 . 615 .110 .179 2.500 

Smooth Boundary, Between Channel Centerline and Wall 

0.963 1. 007, 0.026 0.026 0. 592 

.908 1. 012 .026 . 026 .592 

.854 1.042 .026 .025 . 568 

. 799 1.077 . 025 . 023 .524 

. 744 1.105 . 023 .021 .477 

s = 0.0928xl6 3 u* = 0. 044 fps . 690 1.110 .025 .023 . 524 

.635 1.107 .027 . 025 . 568 

w = 3. 87 ft T = 0.0036 lb/ft2 .580 1.094 . 029 . 026 .592 

.526 1.075 . 032 . 030 .683 

Q = 3.67 cfs " = 1.62x10- 5 ft 2/sec .471 1. 046 .034 .033 . 749 

.416 1.001 .037 .037 .843 

T = 5. 2 °C R = 58,500 .362 .970 .039 .040 .910 

.307 .938 .046 .049 1.045 

D = 0.915 ft F = 0.191 . 252 .908 .054 .060 1. 228 

.198 . 880 .063 .072 1.436 

V= 1. 036 fps c;fi = 22.6 .143 .846 .067 .079 1. 522 

. 089 . 797 . 071 . 089 1.612 

.034 . 700 .083 .119 1.886 

.025 .671 .096 .143 2.181 

.016 .610 .lOS .172 2.386 

. 009 .541 .123 . 228 2.800 

3/4-Inch Rock Roughness, Channel Centerline 

0.943 1.132 0.048 0.042 0.593 

.890 1.123 .051 .045 .630 

. 836 1.120 .051 .046 .630 

S = 0.324xl()3 u* = o. 081 fps . 782 1 .124 .054 .048 .667 

. 729 1.126 .057 .051 . 704 

w = 3. 87 ft T = 0. 0128 1b/ft2 .675 1.124 .061 .054 • 754 

.622 1.120 .062 .055 . 767 

Q = 3.071 cfs v = 1. 72x1o-s ft2/sec .568 1.120 .064 .057 . 781 

.514 1.101 .067 .061 .828 

T = 2. 7 °C R = 46,100 .461 1. 067 . 072 .068 .888 

.407 1.012 .073 .072 .903 

D = 0. 933 ft F = 0.155 . 354 .954 .077 .081 1.000 

.300 .900 .083 .092 1.025 

V = 0.849 fps c;fi = 1o.so . 247 .847 . 085 .100 1.050 

.193 . 785 .089 .113 1. 098 

.139 .695 . 097 .140 1.198 

. 086 .570 .119 .209 1.470 

. 032 .340 .136 .400 1.679 

3/4-Inch Rock Roughness, Between Channel Centerline and Wall 

0.943 0.867 0.043 0.050 0.531 

.890 .870 .045 .052 .554 

.836 . 879 .047 .053 .581 

s = 0.324xHP u* = 0.081 fps . 782 .886 .051 .058 .630 

.728 .889 .054 .061 .667 

w = 3. 87 ft T = 0.0128 1b/ft 2 .675 .889 .055 .062 .679 

.622 .880 .058 .066 .716 

Q = 3.071 cfs " = 1. 72xl()5 ft 2/sec .568 .865 .062 .072 . 765 

2. 7 °C . 514 .842 . 065 .077 .803 

T = R = 46,100 .461 .829 .071 .086 .876 

.407 .827 .068 .082 .840 

D = 0.933 ft F = o.1ss . 354 .838 .074 .088 .913 

.300 .842 .077 .092 .951 

V= 0.849 fps C//g = 10.50 . 274 . 830 .082 .099 1. 012 

.193 . 719 . 086 .119 1.061 

.139 .661 . 094 .142 1.160 

.086 .567 .111 .195 1.370 

.032 .334 .129 .385 1.592 

2. 342 

1.566 

1.405 

1.432 

2.043 

1.373 

1.422 

1. 516 

1.995 

1.620 

1.581 

2. 724 

1 ;504 

2.565 

1.853 

1. 575 

1.558 

2. 064 

1.525 

1.002 

1.335 

1.431 

1.433 

1.450 

1.523 

1.355 

1.333 

1.426 

1.283 

1.640 

2.337 

1. 351 

1.504 

1.412 

1.821 

1.492 

2.133 

1.324 

1.247 

1. 201 

.943 

p.824 

.214 

. 747 

.690 

. 716 

. 349 

.647 

.821 

. 769 

. 763 

.656 

.095 

.654 

. 765 

.696 

.061 

.679 

.445 

1.255 

.835 

.629 

. 783 

.665 

. 734 

. 755 

1.349 

.813 

.498 

.949 

. 766 

.913 

.831 

.841 

1.042 

.644 

.473 

2. 566 

1. 706 

1.532 

1.578 

2.267 

1.920 

1.575 

1. 660 

2.148 

1. 709 

1.582 

2.642 

1.410 

2. 326 

1.628 

1.565 

1.265 

1.444 

.986 

.616 

1.344 

.448 

1.493 

.561 

1.682 

1.504 

1.475 

.560 

.379 

1. 715 

~.339 

.310 

.410 

.282 

1.602 

. 262 

. 700 

.926 

.836 

. 732 

.510 

.932 

~- 363 

.836 

. 775 

. 806 

.516 

.724 

.919 

. 846 

. 814 

.669 

.044 

. 588 

.647 

.546 

. 716 

.387 

.153 

1.088 

.726 

.525 

.693 

.591 

.652 

.664 

.166 

.684 

.412 

. 784 

.641 

. 768 

.689 

.585 

.688 

. 365 

.157 

;, 

:r: 

(ft) 

0.022 

-----

.018 

-----

.020 

-----

.025 

-----

.034 

-----

.033 

-----

.030 

-----

.026 

-----

.021 

-----

.018 

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0.018 

-----

.020 

-----

.020 

-----

.021 

-----

. 020 

-----

.018 

-----

.016 

-----

.016 

-----

.014 

.009 

-----

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------
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

TABLE 4.- 4-foot-wide flume, rigid boundary- Continued 

Mean Flow Parueters 

and Variables 

Riverbed Roughness, Channel Centerline 

0.934 1.219 0.089 0.073 

.885 1.210 .090 .074 

.835 1.200 . 091 .076 

• 785 1.190 .093 .078 

s = 0.443xl(j3 u* = 0.1045 fps . 736 1.172 .094 .080 

.686 1.155 .096 .083 

w = 3. 87 ft T = 0.0212 lb/ft2 .636 1.130 .099 .088 

.586 1.100 .102 .093 

Q = 3. 205 cfs v = 1. 73xl65 ft 2/sec .537 1.066 .lOS .098 

2. 65 °C 

.487 1.022 .107 .104 

T = R = 47' 800 .437 1.012 .110 .108 

.388 .919 .113 .123 

D = 0.945 ft F = 0.158 .338 .851 .118 .139 

. 288 . 798 .127 .159 

V= 0.875 fps C//g = 8.4 .239 . 730 .133 .182 

.189 .649 .139 .214 

.139 .548 .152 .277 

.089 .410 .173 .422 

. 040 . 282 .197 .699 

0.851 0.833 .015 

.862 .942 .139 

.872 .922 .106 

.890 . 734 • 873 

.900 .692 .811 

.918 . 742 .857 

.947 . 739 .835 

.976 .889 .977 

1. 004 . 610 .650 

1.025 .689 . 704 

1.053 .633 .640 

1.081 1.080 .992 

1.129 .,SOl .681 

1. 215 .676 .539 

1.273 .614 .448 

1.330 .854 . 554 

1.456 1.016 .556 

1.654 .861 .353 

1.884 .420 .118 

Riverbed Roughness, Between Channel Centerline and Wall 

S = 0.443xuj3 

w = 3.87 ft 

Q = 3. 205 cfs 

T = 2.65 °C 

D = 0.945 ft 

v= 0.875 fps 

S = 0.1427xl(f3 

W=3.87ft 

Q = 1.643 cfs 

T = 8.3 °C 

D = 0.528 ft 

V = 0.852 fps 

S = 0.162xl63 

w = 3. 87 ft 

Q = 3. 888 cfs 

T = 8. 3 °C 

D = 0.924 ft 

v= 1. 098 fps 

S = J. 3939xl()3 

w = 3.87 ft 

Q = 1. 302 cfs 

T = 8.3 °C 

D = 0.469 ft 

V = 0. 72 fps 

S = 0.3667xl63 

w = 3. 87 ft 

Q = 3. 450 cfs 

T = 8. 3 °C 

D = 0.892 ft 

V = 0.956 fps 

0.947 1.049 0.089 0.084 

.894 1.049 .086 .081 

.841 1.065 .087 .081 

u* = 0.1045 fps • 788 1.095 .090 .082 

• 735 1.115 .093 .083 

T = 0.0212 lb/ft2 .683 1.099 .097 .088 

.598 1.072 .101 .094 

v = 1. 73xU)5 ft 2/sec .545 1.071 .107 .099 

.492 1.028 .106 .103 

R=47,800 .439 .977 .113 .115 

.386 .914 .116 .118 

F = 0.158 .333 .843 .121 .143 

.280 . 788 .129 .163 

Cf/i = 8.4 . 228 .714 .134 .187 

.175 .621 .141 .227 

.122 .502 .156 .310 

. 069 .362 .181 . 500 

.016 .168 .233 1.386 

Smooth Boundary, Channel Centerline 

u* = 0.0415 fps 0.928 0.97 0.031 0.032 

T = 0.0037 lb/ft2 .833 .96 .034 .035 

v = 1. 778xlos ft2/sec . 739 .95 .036 .038 

R = 25,300 .644 .94 .039 .041 

F = 0.206 .549 .92 .044 .048 

C//g = 20.5 .455 .90 .049 .054 

.360 .88 .051 .058 

Smooth Boundary, Channel Centerline 

0.924 1.16 0.028 0.024 

.816 1.17 .026 .022 

u* = o.0482 fps • 762 1.17 .026 . 022 

T = 0. 0066 lb/ft2 .654 1.16 .029 .025 

v = 1. 778xHJ5 ft 2/sec .545 1.15 .032 .028 

R = 57,100 .437 1.13 .036 .032 

F = 0.201 .329 1.09 .043 .040 

C!/i = 22.8 . 221 1. 04 . 052 .050 

.113 .94 .068 .072 

.040 . 78 .093 .119 

1 1/2-Inch Rock Roughness, Channel Centerline 

0.951 0.86 0.064 0.074 

.898 . 85 .067 .079 

u* = 0.0694 fps . 791 .83 .071 .086 

T = 0.0093 lb/ft2 .684 .81 .077 .095 

v = 1. 778xl65 ft2/sec .578 . 79 .082 .104 

R = 17,200 .471 . 74 .084 .113 

F = o. 185 . 365 . 68 .088 .129 

c;lg = 10.4 .258 .62 .097 .156 

.151 .51 .114 .224 

.087 .42 .119 .284 

1 1/2-lnch Rock Roughness, Channel Centerline 

u* = o. 085 fps 

T = 0. 0141 lb/ft2 

v = 1. 778xl65 ft2/sec 

R = 48,000 

F = 0.178 

C!/i = 11.2 

0.900 1.16 

.676 1.09 

.452 .98 

.228 .83 

.037 .51 

0.067 

.079 

.084 

.103 

.137 

0.058 

.072 

.086 

.124 

. 268 

0.851 0.861 p.903 

.823 . 816 . 855 

.832 . 737 • 784 

.861 1.348 .476 

.890 .837 .933 

.928 1.291 .418 

. 965 .913 . 978 

1.024 . 763 .817 

1.013 .671 .689 

1.081 .693 .677 

1.110 .814 . 743 

1.158 . 843 .710 

1. 236 .613 .483 

1.282 • 734 .524 

1.350 .947 .588 

1.493 .614 .308 

1. 731 .812 . 293 

2.228 . 737 .123 

0. 748 1.594 1.546 

.821 1.858 1. 782 

.916 1.346 1.278 

.988 1.639 1.539 

1.156 1.594 1.467 

1.300 2. 099 1. 885 

1.399 1.519 1.334 

0.583 1.519 1. 762 

.540 1.673 1.960 

. 540 1.998 2. 331 

.602 1.467 1. 703 

.665 2.021 2. 320 

.-748 1.462 1.648 

.894 1.329 1.447 

1. 081 • 865 .902 

1.411 1.480 1.392 

1.934 1. 283 1.000 

0.922 0. 757 0.650 

.965 .803 .682 

1.022 .919 . 763 

1.110 • 732 .582 

1.183 .845 .667 

1.210 . 787 .583 

1.267 . 781 .532 

1. 398 .880 .545 

1.643 . 713 .366 

1. 716 .686 . 288 

o. 788 0. 873 1. 012 

• 929 . 944 1. 029 

.988 . 737 • 723 

1.212 .829 .687 

1.613 .668 .342 

~ :z: (ft) 

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0.018 

-----

.019 

-----

.019 

-----

.020 

-----

.018 

-----

.021 

-----

.011 

-----

.006 

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B51 
B52 TURBULENCE IN WATER 

TABLE 4.- 4-foot-wide flume, rigid boundary- Continued 

Mean Flow Paraaeters 

and Variables 

Riverbed Roughness, Channel Centerline 

0.960 0.94 0.098 0.104 

s = 0.7439xl()3 u. = 0. 0996 fps .866 .93 .080 .086 

w = 3. 87 ft T = 0.192 1b/ft2 . 771 .91 .086 .095 

Q = 1.591 cfs v = l. 778xU)5 ft2/sec .676 .89 .104 .117 

T = 8.3 °C R = 18,700 .581 .86 .110 .128 

D = 0. 528 ft F.=0.189 .487 .83 .124 .149 

V= 0. 780 fps C//g = 7.8 . 392 .77 .143 .186' 

. 297 • 70 .162 .231 

.203 .60 .164 .274 

Riverbed Roughness, Channel Centerline 

S = 0. 473xl()3 u. = 0.0948 fps 0.906 1.20 0.076 0.063 

W= 3.87 ft T = 0.0174 lb/ft2 . 730 1.18 .082 .069 

Q = 3.205 cfs v = 1. 778x105 ft 2/sec .. 553 1.12 .094 .083 

T = 8. 3 °C R = 41,900 .377 1.01 .099 .098 

D = 0.851 ft F = 0.167 .260 .89 .117 .132 

V= 0.876 fps c;lg = 9.2 

0.984 0.981 

.804 . 706 

.865 .817 

1.043 .722 

1.105 .697 

1. 246 . 741 

1.436 .811 

1.628 .871 

1.647 • 711 

0.803 p.813 

.866 1.219 

.993 • 761 

1.047 .868 

1.236 .829 

TABLE 5.- 8-foot-wide flume, rigid boundary 

Mean Flow Paraaeters 

and Variables 

Flume Centerline, Station 5 Feet - Parabolic Sensor 

0.900 1. 220 0.037 0.030 0. 2891 

.800 1.150 .035 .030 .2734 

S = 0.50Sxl(j3 u. = 0.128 fps • 700 1.170 .038 .032 .2969 

w = 8.0 ft T = 0. 042 lb/ft2 .600 1.160 .042 .036 .3281 

Q = 10.23 cfs v = 1.12xl65 ft 2/sec .500 1.130 .050 .044 .3906 

T = 18.9 °C R = 123,000 .400 1.090 .067 .061 .5234 

D = 1. 335 ft F = 0.146 .300 .990 .130 .131 1.0160 

V = 0.964 fps c;lg = 7.53 .200 • 760 .166 .218 1. 2970 

.100 .390 .157 .402 1. 2270 

.050 .190 .031 .163 .2422 

Flume Centerline, Station 10 Feet - Parabolic Sensor 

0.900 1.270 0.029 0.023 0. 2266 

.800 1.220 .028 .023 .2188 

s = 0.5osxuP u. = 0.128 fps . 700 1.210 .034 .028 .2656 

w = 8.0 ft T = 0.042 lb/ft2 .600 1.190 .048 .040 .3750 

Q = 10.23 cfs v = 1.12xU)5 ft 2/sec .500 1.130 .081 .072 .6328 

T=l8.9°C R = 123,000 .400 1.050 .108 .103 .8438 

D = 1. 335 ft F = 0.146 .300 .890 .161 .181 1.2580 

V = 0.964 fps c lg = 7.53 .200 .720 .183 .254 1.4300 

.100 .350 .164 .469 1.2810 

.050 .180 .024 .133 .1875 

Flume Centerline, Station 15 Feet - Parabolic Sensor 

0.900 1.310 0.032 0.024 0. 2500 

.800 1.270 .034 .027 .2656 

s = o. 505xuP u. = 0.128 fps • 700 1.230 .047 .038 .3672 

w = 8.0 ft T = 0.042 lb/ft2 .600 1.170 .067 .055 .5234 

Q = 10.23 cfs v = 1.12x105 ft 2/sec .500 1.100 .094 .085 • 7344 

T = 18.9 °C R = 123,000 .400 1.040 .105 .101 .8203 

D = 1. 335 ft F = 0.146 .300 .880 .ll8 .134 .9219 

V = 0.964 fps c;lg = 7.53 .200 .690 ; 140 .203 1.0940 

.100 .490 .123 .251 .9609 

.050 . 270 .062 .230 .4844 

Flume Centerline, Station 25 Feet - Parabolic Sensor 

0.900 1.340 0.051 0.038 0.3984 

.800 1.310 .059 .045 .4609 

S = 0. SOSxl03 u* = 0.128 fps • 700 1.240 .072 .058 .5625 

w = 8. 0 ft T = 0.042 1b/ft2 .600 1.160 .086 .074 .6719 

Q = 10.23 cfs v = 1.12xlos ft2/sec .500 1.100 .098 .089 • 7656 

T = 18.9 °C R = 123,000 .400 1.020 .115 .113 .8984 

D = 1.335 ft F = 0.146 .300 .930 .143 .154 1.1170 

V = 0.964 fps c;lg = 7.53 .200 . 780 .170 .218 1. 3280 

.100 .470 .131 .279 1. 0230 

.050 .260 .072 .277 .5625 

0.921 

.656 

. 744 

.642 

.600 

.615 

.624 

.610 

.427 

0.975 

1.434 

.853 

.876 

• 737 

A 

:r (ft) 

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A 

:r 

(ft) 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES B53 

TABLE 5. - 8-foot-wide flume, rigid boundary- Continued 

). Mean Flow Parameters X 

and Variables (ft) 

Flume Centerline, Station 35 Feet - Parabolic Sensor 

0.900 1.330 0.077 0.058 .6016 

.800 1.290 .085 .066 .6641 S = 0. SOSxHP u. = 0.128 fps . 700 1.220 .086 .070 .6719 w = 8.0 ft T = 0.042 1b/ft2 .600 1.180 .089 .075 .6953 Q = 10.23 cfs v = 1.12xH)5 ft 2/sec .500 1.170 .102 . 087 . 7969 T = 18.9 °C R = 123,000 .400 1.080 .120 .111 .9375 D = 1. 335 ft F = o .146 . 300 1.000 .145 .145 1.1330 V = 0.964 fps C//g = 7.53 .200 .840 .168 .200 1.3120 

.100 .580 .169 .291 1. 3200 

.050 .330 .102 .309 . 7969 

Flume Centerline, Station 50 Feet - Parabolic Sensor 

0.900 1.320 0.075 0.057 .5859 

.800 1. 270 .081 .064 .6328 

S = O.SOSxl0- 3 u. = 0.128 fps . 700 1.220 .087 .071 .6797 

w = 8. 0 ft T = 0.042 lb/ft2 .600 1.180 .097 .082 . 7578 

Q = 10.23 cfs v = 1.12xlo-5 ft 5/sec .500 1.180 .108 .092 .8438 

T = 18.9 °C R = 123,000 .400 1.140 .123 .108 .9609 

D = l. 335 ft F = 0.146 .300 1.020 .155 .152 1.2110 

V = 0.964 fps C//g = 7.53 .200 . 790 .169 .214 l. 3200 

.100 .550 .161 .293 1. 2580 

.050 .320 .102 . 319 . 7969 

Flume Centerline, Station 75 Feet - Parabolic Sensor 

0.900 1.230 0.073 0.059 .5703 

.800 1.210 .077 .064 .6016 

s = o.sosxlo-3 u. = 0.128 fps . 700 1.190 .086 .072 .6719 

W=8.0ft T = 0.042 lb/ft2 .600 1.170 .092 .079 . 7188 

Q = 10.23 cfs v = l.12xlo- 5 ft 2/sec .500 1.150 .103 .090 .8047 

T = 18.9 °C R = 123,000 .400 1.120 .122 .109 .9531 

D = l. 335 ft F = 0.146 .300 .960 .149 .155 1.1640 

V = 0.964 fps C//g= 7.53 .200 .800 .177 .221 1.3830 

.100 .500 .151 .302 1.1800 

.050 .280 .106 .379 .8281 

Flume Centerline, Station 100 Feet - Parabolic Sensor 

0.875 1.375 0.078 0.0567 0.5571 0.640 0,880 -----

0.6lxl0- 3 . 750 1.320 .085 .0644 .6071 • 740 .977 ----- s = u. = 0.140 fps .625 1.250 .101 .0808 . 7214 ----- ----- ----- w = 8.0 ft T = 0.50 lb/ft2 .500 1.180 .116 .0983 .8286 .840 .991 ----- Q = 11.52 cfs v = l.04xl0- 5 ft 2/sec .375 1.080 .128 .1185 .9143 .730 . 788 ----- T = 22.2 °C R = 138,500 .250 .932 .164 .1760 1.1710 .770 . 718 ----- D = 1 •• 312 ft F = 0.17 .125 . 704 .194 .2756 1.3860 .510 .359 ----- v= 1. 098 fps C//g = 7.83 .108 .650 .201 .3092 1. 4360 .490 .319 ----- .063 .446 .180 .4036 1. 2860 ----- ----- ----- .031 .279 .116 .4158 .8286 ----- ----- -----

Flume Centerline, Station 100 Feet - Cylindrical Sensor 

0.900 1.420 0.076 0.054 0.535 

.800 1.390 .083 .060 .586 S = 0.473xlo-3 u. = 0.141 fps • 700 1.370 .088 .064 .627 

w = 8.0 ft T = 0. 039 lb/ft2 .600 1.310 .lOS .080 . 746 

Q = 11.52 cfs v = l.04xlo-5 ft2/sec .500 1.220 .116 .095 .818 

T = 22. 2°c R = 137,600 .400 1.160 .128 .110 .905 

D = 1.312 ft F = 0.17 .300 1.030 .154 .150 1.089 

V = 1.091 fps C//g=7.72 .200 .900 .173 .192 1.227 

.100 .800 .208 .260 1.475 

.050 .630 .142 .226 1.009 

Flume Centerline, Station 5 Feet - Parabolic Sensor 

0.900 2.390 0.084 0.035 .3443 

.800 2.300 .090 .039 .3689 S = l.84xlo- 3 u. = 0. 244 fps . 700 2.250 .088 .039 .3607 

w = 8.0 ft T = 0.153 lb/ft2 .600 2.210 .090 .041 .3689 

Q = 20.15 cfs v- = l. 03xlo- 5 ft2/sec .500 2.160 .lOS .049 .4303 

T = 22.6 °C R = 237 ,ooo .400 2.060 .147 .071 .6025 

D = l. 333 ft F = 0.287 .300 1.820 .248 .136 1.0160 

v = 1.88 fps C//g= 7.72 .250 1.640 .264 .161 1.0820 

.200 1.420 .314 .221 1.2870 

.150 1.150 .325 .283 1. 3320 

.100 . 750 .258 .344 1. 0570 

Flume Centerline, Station 10 Feet - Parabolic Sensor 

0.900 2.580 0.092 0.036 0. 3770 

. 800 2.480 .078 .031 . 3197 

. 700 ?..370 .094 .040 .3852 

S = 1. 84xl()3 u. = 0. 244 fps .600 2.280 .126 .055 .5164 

w = 8.0 ft T = 0.153 lb/ft2 .500 2.130 .168 .079 .6885 

~ : ~~: ~s ~fs v = 1. 03xl()5 ft 2/sec .400 1.920 .213 .111 .8730 

R = 237 ,ooo .300 1.670 .251 .150 1.0290 

D = 1. 333 ft F = 0.287 .250 1. 500 . 252 .168 1.0330 

V = l. 88 fps C//g=7.72 .200 1. 300 . 280 .215 1.1480 

.150 1.050 .275 .262 1.1270 

.100 .680 .222 . 326 .9098 
B54 TURBULENCE IN WATER 

TABLE 5.- 8-foot-wide flume, rigid boundary- Continued 

). 

Mean Flow Parameters X 

and Variables (ft) 

Flume Centerline, Station 15 Feet - Parabolic Sensor 

0.900 2.690 0.097 0.036 0. 3975 

s = 1. 84xUP u* = 0.244 fps .800 2. 560 .105 .041 .4303 

. 700 2. 420 .140 .058 . 5738 

w = 8. 0 ft T = 0.153 lb/ft2 .600 2. 260 .169 .075 . 6926 

. 500 2.080 .198 .095 . 8ll5 

Q = 20.15 cfs v = l.03xlos ft 2/sec .400 1. 890 .225 .119 .9221 

. 300 1.660 .256 .154 1.0490 

T = 22 .6 °C R = 237,000 . 250 1. 510 .250 .166 1. 0250 

. 200 1. 340 . 273 .204 l.ll90 

D = 1. 333 ft F = o. 287 .150 1.100 .278 .253 1.1390 

.100 . 780 .235 .301 .9631 

V= 1. 88 fps C//g=7.72 .050 .120 .123 1.025 .5041 

Flume Centerline, Station 25 Feet - Parabolic Sensor 

0.900 2. 760 0.161 0.058 0.6598 

8: 1.84XlQ3 u* = 0.244 fps . 800 2. 590 .190 .073 . 7787 

. 700 2.410 .218 .090 .8934 

w = 8. 0 ft T = 0,153 lb/ft2 .600 2. 240 .229 .102 .9385 

.500 2. 070 .256 .124 1. 0490 

Q = 20.15 cfs v = 1. 03x165 ft 2 /sec .400 1.890 .259 .137 1. 0610 

T = 22.6 °C 

.300 1.680 . 287 .171 1.1760 

R = 237,000 .250 1.540 .284 .184 1.1640 

.200 1.370 .298 .218 1. 2210 

D = 1. 333 ft F = 0.287 .150 1.150 .308 .268 1.2620 

.100 .840 .340 .405 1. 3930 

V= 1. 88 fps C//g=7.72 .050 .310 .158 .510 .6475 

Flume Centerline, Station 45 Feet, Parabolic Sensor 

s = 1.84x1o3 u* = 0.244 fps 0.900 2.520 0.202 0.080 .8279 

.800 2.440 .192 .079 . 7869 

w = 8. 0 ft T = 0.153 1b/ft2 . 700 2.350 . 205 .087 .8402 

.600 2.240 . 233 .104 .9549 

Q = 20.15 cfs v = 1. 03xH)5 ft 2/sec .500 2.110 . 216 .102 .8852 

.400 1.960 .248 .126 1. 0160 

T = 22.6 °C R = 237 ,ooo .300 1. 760 . 279 .158 1.1430 

. 200 1.480 .305 .206 1. 2500 

D = 1. 333 ft F = 0.287 .150 1.280 .370 .289 1. 5160 

.100 1.000 .398 .398 1. 6310 

V= 1. 88 fps C//g = 7. 72 .050 . 520 .260 .500 1. 0660 

Flume Centerline, Station 75 Feet - Parabolic Sensor 

0.900 2.450 0.198 0.081 0.8ll5 

s = 1. 84x11J3 u* = 0.244 fps .800 2.440 .201 .082 .8238 

. 700 2.340 . 205 .088 .8402 

w = 8.0 ft T = 0,153 1b/ft2 .600 2.270 .234 .103 .9590 

.500 2.130 . 239 .112 .9795 

Q = 20.15 cfs v = 1.03xl65 ft2/sec .400 1.940 .251 .129 1.0290 

.300 1. 750 .283 .16211.1600 T = 22.6 °C R = 237 ,ooo .250 1.630 .298 .183 1. 2210 

.200 1.480 . 316 . 214 1. 2950 

D = 1. 33 ft F = 0.287 .150 1.260 . 371 .294 1. 5200 

.100 .980 .407 .415 1.6680 

V = 1.88 fps C//g=7.72 .050 .510 .253 . 496 11. 0370 

Flume Centerline, Station 100 Feet - Parabolic Sensor 

0.900 2.590 0.164 0, 0633 0.5816 0.430 1.114 ----- s = 1. 88xUP u* = 0.282 fps .800 2.500 .180 . 0720 .6383 ----- ---- ----- . 750 2.460 .198 .0805 . 7021 .660 1.624 ----- w = 8.0 ft T = 0.156 lb/ft2 . 700 2.410 . 212 .0880 . 7518 ----- ---- ----- .600 2. 290 .229 .1000 .8121 .460 1.053 ----- Q = 22.06 cfs \) = 1. 03xl65 ft2/sec .500 2.180 .233 .1069 .8262 . 760 1.657 ,.. ____ 

.400 2.020 .250 .1238 .8865 .460 .929 ----- T = 22.6 °C R = 267,900 .300 1.810 .286 .1581 1. 0140 ----- ---- ----- .250 1.670 .335 .2006 1. 1880 .540 .902 ----- D = 1.331 ft F = 0.31 . 200 1.520 .357 . 2349 1. 2660 ----- ----- .,.. ____ 

.150 1.140 .383 . 3360 1.3580 ----· ----- ___ .... _ 

V= 2.073 fps C//g = 8.4 .100 .840 .421 .5012 1.4930 .480 1.403 ----- . 050 .530 .280 .5283 .9929 . 560 . 297 -----

Flume Centerline, Station 75 Feet - Parabolic Sensor 

0.900 4.050 0.264 0.065 0.6804 

S = 4.63xl03 u* = o. 3R8 fps .800 4.100 .270 .066 .6959 

. 700 4.010 .285 .071 . 7345 

W=8.0ft T = 0.380 lb/ft 2 .600 3. 770 .316 .084 .8144 

.500 3.670 .386 .lOS .9948 

Q = 30.53 cfs 1. 04xl65 ft2/sec .400 3.530 .436 .124 1.1240 

.300 3.070 .480 .156 1.2370 

T = 22.2 °C R = 369,000 . 250 2.840 .500 .176 1. 2890 

. 200 2.480 .520 .210 1. 3400 

D = 1.316 ft F = 0.446 .150 2. 290 .604 .264 1.5570 

.100 1. 710 .675 .395 1. 7400 

v = 2.903 fps c;lg = 7.50 .050 .920 .497 .540 1.2810 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

TABLE 5. - 8-foot-wide flume, rigid boundary - Continued 

Mean Flow Parameters 

and Variables 

18 Inches Off Flume Centerline, Station 100 Feet - Parabolic Sensor 

s = 4.63xHP U * = 0 . 388 fps 

w = 8. 0 ft T = 0.380 lb/ft2 

Q = 30.53 cfs v = 1. 04xl(j5 ft2/sec 

T = 22.2 °C R = 369 ,ooo 

D = 1.316 ft F = 0.446 

v = 2.903 fps C!/i = 7.50 

Flume Centerline, 

S = 4.63xl()3 U * = 0. 388 fps 

w = 8.0 ft T = 0. 381 lb/ft2 

Q = 30.S3 cfs v = 1. 04xl65 ft2/sec 

T = 22.2 °C R = 436,000 

D = 1. 32 ft F = 0.446 

V = 2.903 fps C//g= 7.SO 

Flume Centerline, 

S = 1.101x163 u* = 0.234 fps 

w = 8.0 ft T = 0.172 lb/ft2 

Q = 46.6 cfs v = 1.12xl65 ft 2/sec 

T = 18.9 °C R = 463,000 

D = 2. SO ft F = o. 23 

V = 2. 34 fps c/lg = 10.0 

Flume Centerline, 

S " 1.101x103 u* = 0.234 fps w = 8.0 ft T = 0.172 lb/ft2 

Q = 46.6 cfs v = 1.12x165 ft 2/sec 

T=l8.9°C R = 463,000· 

D = 2.Sl ft F = o. 23 

V = 2.34 fps C//i = 10.0 

Flume Centerline, 

S = 1.10lxl03 u* = 0.234 fps 

W=8.0ft T = 0,172 lb/ft2 

Q = 46.6 cfs v = 1.12xl()5 ft2/sec 

T = 18.9°C R = 463,000 

D = 2. 52 ft F = o. 23 

V = 2.34 fps C//g = 10.0 

Flume Centerline, 

S = 10.S4xl()3 u* = 0.447 fps 

W=8.0ft T = 0,452 lb/ft2 

Q = 14.09 cfs v = 1. 06x165 ft 2/sec 

T = 21.1 °C R = 141,900 

D = 0. 687 ft F = o. 46 

V = 2.S6 fps C//g = S.60 

Flume Centerline, 

s = 10.54x163 u* = 0.447 fps 

W'= 8.0 ft T = 0.452 lb/ft2 

Q = 14.09 cfs v = 1.06xl65 ft2/sec 

T = 21.1 °C R = 146,300 

D = 0.687 ft F = 0.48 

V = 2.S6 fps C//g = 5.60 

0.900 3.900 0.266 0.068 0 .68S6 

.800 3.890 .2SO .064 .644! 

. 700 3. 770 .302 .080 . 7784 

.600 3. 770 .316 .084 .8144 

.soo 3.620 .376 .104 .9691 

.400 3.430 .438 .128 1.1290 

. 300 3.ll0 .479 .1S4 1.23SO 

. 250 2.920 .S20 .178 1. 3400 

. 200 2.660 .S72 .215 1. 4740 

.lSO 2. 2-so .608 . 270 1. 5670 

.100 1. 740 .636 .36S 1.6390 

.oso .980 .SS6 .567 1. 4330 

Station 100 Feet - Parabolic Sensor 

0.900 3.960 r.267 o. 0674 0.6881 

.800 3.940 .266 .067S .68S6 

• 7SO 3.910 .282 .0721 . 7268 

. 700 3.880 .298 .0768 . 7680 

.600 3. 760 .319 .0848 .8222 

.soo 3.600 .366 .1017 .9433 

.400 3.390 .413 .1218 1. 0640 

.3SO 3. 260 .446 .1368 1.1490 

.300 3.ll0 .486 .1S63 1.2S30 

.2SO 2.940 .522 .1776 1. 34SO 

• 200 2.680 .S46 .2037 1.4070 

.126 2.3SO .6ll .2600 1. 57 SO 

.100 1. 750 .639 .36Sl 1. 6470 

.080 1.380 .561 .4065 1. 4460 

Station SO Feet - Parabolic Sensor 

0.900 2. 790 0.154 o.oss 0.658 

.800 2.840 .150 .053 .640 

. 700 2.810 .176 .063 • 7S2 

.600 2.650 .195 .074 .833 

.soo 2.470 .222 .090 .948 

.400 2.140 .249 .116 1.062 

.300 1.8SO .276 .149 1.179 

.200 1.520 .306 .201 1.307 

.100 1.140 • 348 • 303 1.488 

.oso .660 .375 .568 1.602 

Station 7S Feet - Parabolic Sensor 

0.900 2.910 0.172 0.058 o. 74S 

.800 2. 820 .184 .065 • 781 

. 700 2.670 .202 .076 .863 

.600 2.Sl0 .224 .089 .956 

.500 2.290 .2S4 .111 1.084 

.400 2.0SO .269 .131 1.1S2 

. 300 1. 840 .287 .1S6 1.226 

. 200 1. 570 .316 .201 1.352 

.100 1.130 .3S4 .316 1.514 

.050 .680 .388 .S62 1.661 

Station 100 Feet - Parabolic Sensor 

0.900 2.660 p.l78 0.067 o. 761 

.800 2. 710 .184 .068 • 786 

. 700 2. 590 .204 .079 .872 

.600 2.490 .226 .091 .966 

.soo 2.400 .2S4 .106 1.087 

.400 2.290 .264 .11S 1.129 

.300 1.940 .285 .147 1.218 

.200 1. 760 .312 .177 1.334 

.100 1.330 .369 .278 1.577 

.050 .820 .390 .475 1.668 

Station SO Feet - Parabolic Sensor 

0,900 3.200 0.316 0.099 o. 708 

.800 3.040 .362 .ll9 . 811 

. 700 2.890 .400 .138 .896 

.600 2.6SO .441 .166 .989 

. 500 2.420 .487 . 201 1.091 

.400 2.010 .530 .264 1.188 

. 300 1. 530 .S47 . 358 1. 224 

.200 1.130 .517 .4S8 1.1S7 

.100 .900 .4SS .S06 1.020 

Station 7S Feet - Parabolic Sensor 

0.900 

.800 

. 700 

.600 

.soo 

.400 

• 300 

. 200 

.100 

3.210 0.348 

3.130 .373 

2. 910 . 392 

2.710 .448 

2.440 .513 

2. 090 . 580 

1. 640 .590 

1. 220 .543 

.970 .463 

0.108 

.ll9 

.135 

.165 

. 210 

.278 

. 360 

.445 

.447 

0. 780 

.834 

.879 

l.OOS 

1.148 

1. 298 

1.322 

1. 216 

1. 038 

O.S30 

.480 

.S40 

.320 

.380 

.330 

.3SO 

2.099 

1.877 

2.030 

1.1S2 

1.288 

.970 

.613 

). 

:r 

(ft) 

B55 
B56 TURBULENCE IN WATER 

TABLE 5.- 8-foot-wide flume, rigid boundary- Continued 

Mean How Parameters 

and Variables 

Flume Centerline, Station 100 Feet - Parabolic Sensor 

0.900 3.270 0.338 0.103 0. 758 

S = 10. 54x11P U • = 0. 44 7 fps .800 3.140 . 395 .126 . 884 

w = 8. 0 ft T = 0.452 lb/ft 2 . 700 2.970 .413 .139 .924 

Q = 14.09 cfs v = l.06xl65 ft2/sec .600 2. 740 .470 .172 1.052 

T = 21.1 °C R = 149,100 .500 2.450 . 533 .218 1.195 

D = 0.687 ft F = o. 49 .400 2.140 .608 . 318 1.363 

V = 2. 56 fps C//g = 5.60 .300 1.690 .608 .402 1. 363 

.200 1.290 .562 .436 1.258 

.100 1. 020 .438 .429 .983 

Flume Centerline, Station 140 Feet - Parabolic Sensor 

S = 10.54xl63 u. = 0.447 fps 

W = 8.0 ft T = 0.452 lb/ft2 

Q = 14.09 cfs v = l.06xHJ5 ft 2 /sec 

T = 21.1 °C R = 150,000 

D = 0.687 ft F = 0.49 

v = 2.56 fps C//g = 5.6 

0.900 3.240 0.361 

. 800 3.110 . 382 

• 700 2.930 .388 

.600 2. 700 .477 

. 500 2.460 . 502 

.400 2.150 . 558 

. 300 1. 790 . 614 

. 200 1. 350 . 577 

.100 1.070 .485 

0.111 

.123 

.132 

.177 

.204 

. 260 

.343 

.427 

.453 

0.807 

. 846 

.870 

1.068 

1.122 

1. 250 

1.375 

1.296 

1.086 

TABLE 6.- 8-foot-wide flume, alluvial boundary 

Mean Flow Parameters 

and Variables 

Flume Centerline, Station 120 Feet - Ripples 

0.90 1.45 0.063 0.044 0.677 1.11 1.610 

s = 0. 320lxliJ3 dso = 0.121 mm .80 1.44 .074 .051 . 796 .92 1.325 

w = 8.0 ft v. = 0.093 fps . 70 1.41 .084 .059 .903 .97 1.368 

Q = 9.94 cfs T = 0.0209 lb/ft2 .60 1.37 .093 .068 1.000 1.01 1.384 

T =22.7"C v = l.027X1QS ft 2/sec .so 1.31 .lOS .080 1.129 .94 1.231 

!!. = 1.046 ft R = 124,300 .40 1.23 .104 .084 1.118 .92 1.132 

v = 1.19 fps F = 0.210 .30 1.12 .107 .095 1.151 .94 1.053 St = 0.813 gpl C//(j = 12.80 .20 .95 .110 .116 1.183 . 78 • 741 

D = 1.046 ft Dso = 0.26 mm .10 .66 .114 .173 1.226 .65 .429 

Flume Centerline, Station 120 Feet - Ripples 

0.90 1.85 0.088 0.047 o. 779 0.97 1. 795 

s = 0.4743xl()3 dso = 0.141 mm .80 1.84 .123 .067 1.088 .80 1.472 w = 8.0 ft v. = 0.113 fps . 70 1.80 .142 .079 1.257 . 79 1.422 

Q = 15.07 cfs T = 0.0311 1b/ft2 .60 l. 75 .149 .085 1.319 . 78 1.365 T = 21.7 •c v = 1.044xl65 ft 2/sec .so 1.67 .183 .110 1.619 • 75 1.253 

!!. = 1.052 ft R = 160,:.100 .40 1.59 .195 .123 1. 726 .67 1.065 v = 1. 79 fps F = 0.273 .30 1.47 .152 .137 1.345 . 70 1.029 

St= 73.0 gp1 C//g = 15.80 .20 1.32 .162 .153 1.434 .66 .871 

D = 1.052 ft Dso = 0.26 mm .10 1.07 .131 .177 1.159 .54 .578 

Flume Centerline, Station 120 Feet - Dune Trough 

0.92 2. 74 0.238 0.087 1.400 

.83 2. 78 .240 .086 1.412 

s = l.l07x 1ij3 dso = 0.179 mm . 75 2.68 .309 .115 1.818 

w = 8.0 ft V * = 0 . 170 fps .67 2.36 .345 .145 2.029 

Q = 19.66 cfs T = 0.0905 lb/ft2 .59 2.17 .339 .156 1.994 

T = 20.6 •c v = l.07Sxl65 ft 2/sec .so 2.10 .354 .168 2.082 

!!. = 1. 31 ft R = 251,600 .42 1.96 .398 .203 2.341 

v = 2.42 fps F = 0.313 .34 1.93 .492 .245 2.894 

E.t = 996.4 gpl C//g= 14.30 .26 1. 70 .532 .314 3.129 

.19 1.46 .392 .268 2.306 D = l. 012 ft Dso = 0.26 mm .15 1.36 .361 .266 2.124 

.08 1.13 .468 .287 2. 753 

Flume Centerline, Station 95 Feet - Dune Crest 

0.88 3.56 0.185 0.0520 1 088 s = 1.107x1(j3 dso = 0.179 mm • 76 3.50 .199 .0569 1.171 w = 8.0 ft v. = 0.170 fps .64 3.43 .219 .0638 1.288 Q = 19.66 cfs T = 0.0580 lb/ft2 .52 3.25 .251 .0772 1.476 T = 2o.6 •c v = 1.075x165 ft 2/sec .40 3.07 .269 .0876 1.582 

!!. = 0. 84 ft R = 214,100 .29 2.84 .283 .0996 1.665 v = 2.42 fps F = o. 527 .25 2.29 .241 .1052 1.418 !::.t = 996.4 gp1 C//(j = 14.30 .17 1.62 .208 .1284 1.224 

D = 1.012 ft Dso = 0.26 mm .09 1.07 .167 .1561 .982 

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

-----

A 

X 

(ft) 

(fps) 

-- ---- ---- ------ 8 0.11 1.36 .0361 

-- ---- ---- ------ 10 .12 1.41 .0387 

12 .12 1.37 .0387 

-- ---- ---- ------ 21 .13 1.38 .0427 

56 .14 1.37 .0483 

81 .16 1.36 .0565 

-- ---- ---- ------ 7 .12 1.42 .0387 

-- ---- ---- ------ 9 .13 1.37 .0427 

-- ---- ---- ------ 18 .16 1.46 .0565 

-- ---- ---- ------ 76 .19 1.38 .0722 

139 .20 1.37 .0791 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

TABLE 6.- 8-foot-wide flume, alluvial boundary- Continued 

Mean Flow Parameters 

and Variables 

s = 1.1073xlQ3 dso = 0.179 nun 

w = 8.0 ft u. = 0.170 fps 

Q = 19.66 cfs T = 0.0988 lb/ft2 

T = 20.6 •c v = 1.07Sxl05 ft 2/sec 

p_ = 1.43 ft R = 228,800 

v = 2.42 fps F 0.253 

Et = 996.4 gpl c;lg = 14.30 

D = 1.012 ft Dso = 0. 26 nun 

s = l.l07xl63 dso = 0.179 nun 

w = 8.0 ft u. = 0.170 fps 

Q = 19.66 cfs T = 0. 0642 lb/ft2 

T = 20.6 •c v = 1.07Sxl05 ft 2/sec 

p_ = 0.93 ft R = 177,300 

v = 2.42 fps F = 0.375 

c = 996.4 gpl c;lg = 14.30 -t 

D = 1.012 ft Dso = 0.26 nun 

s = 0. 887x!6 3 dso = 0.183 mm 

w- = 8.0 ft u. = 0.155 fps 

Q = 24.72 cfs T = 0.0591 lb/ft2 

T = 21.3 •c v = 1.054xl65 ft 2/sec 

D = 1.068 ft R = 247,200 

v = 2.89 fps F = o .416 

Et = 872.8 gpl c;lg = 18.68 

D = 1.068 ft Dso = 0. 26 nun 

s = 1. 219Xl(j3 dso = a. 205 nun 

w = 8.0 ft u* = 0.184 fps 

Q = 35.98 cfs T = 0.0822 lb/ft2 

T = 21.8 •c v = 1.046xl()5 ft2/sec 

p_ = 1.081 ft R = 450,600 

v = 4.15 fps F = o. 739 

c = 1719.2 gpl C/fg = 22.55 11= 1.081 ft Dso = 0.26 m 

s = 1.023x163 dso = 0. 206 nun 

w = 8.0 ft u. = 0.167 fps 

Q = 17.02 cfs T = 0.0842 lb/ft2 

T = 20.8 •c v = 1. 82xl65 ft 2 /sec 

!2. = 1.32 ft R = 225,600 

v = 1.97 fps F = 0.279 

s,= 350.8 gpl c;lg = 11.77 

D = 1.079 ft Dso = 0.26 m 

s = 1. 023xlO 3 dso = 0. 206 nun 

w = 8.0 ft u, = 0.167 fps 

Q = 17.02 cfs T = 0.0575 lb/ft2 

T = 20.8 •c v = 1.06Sxl65 ft 2/sec 

D = 0.90 ft R = 182,500 

v = 1.97 fps F = 0.401 

c = 350.8 gpl C/vg = 11.77 _t 

D = 1.079 ft Dso = 0.26 mm 

Flume Centerll.11e, ~tat:1on lOS Feet - Dune 1rough 

0.93 2.57 0.139 0.054 o. 818 0.51 1.311 ----- --- .86 2 .so .159 .063 .935 .54 1.350 ----- --- .80 2.45 .185 .076 1.088 .55 1.348 ----- 241 

. 73 2.22 .211 .095 1.241 .44 .977 ----- --- .65 2.21 .256 .116 1.506 .58 1.282 ----- --- .58 2.16 .246 .114 1.447 .53 1.145 ----- 422 

.52 2.07 .310 .150 1.824 .57 1.180 ----- --- .45 1.94 .339 .175 1.994 .54 1.048 ----- --- .38 1. 79 .396 .221 2.329 .59 1.056 ----- 583 

.31 .85 .208 .245 1.224 .61 .519 ----- --- .24 .84 .202 .241 1.188 .53 .445 ----- 191 

.14 .83 .200 .241 1.176 .48 .398 ----- --- .08 .82 .191 .233 1.124 .47 .385 ----- 101 

.07 .80 .177 .216 1.041 .48 .384 ----- ---

Flume Centerline, Station 100 Feet - Dune Crest 

0.88 2.40 0.143 0.059 0.841 0.48 1.152 ----- --- . 79 2.32 .145 .063 .853 .64 1.485 ----- --- .68 2.22 .147 .066 .865 .46 1.021 ----- 337 

.58 2.18 .173 .079 1.018 .so 1.090 ----- --- .46 2.16 .180 .083 1.059 .53 1.145 ----- 447 

.38 2.15 .204 .095 1.200 .54 1.161 ----- --- .24 2.11 .217 .103 1.276 .48 1.013 ----- 554 

.16 2.10 .264 .126 1.553 .so 1.050 ----- --- .08 1.91 .282 .148 1.659 .48 .917 ----- 1670 

.04 .92 .176 .191 1.035 .46 .423 ----- 3030 

Flume Centerline, Station 120 Feet - Transition 

0.90 2.81 0.181 0.0644 1.168 0.54 1.517 ----- --- .80 2. 73 .185 .0678 1.194 .46 1.256 ----- --- . 70 2.64 . .205 .0776 1.323 .so 1.320 ----- 134 

.60 2.59 .224 .0865 1.445 .57 1.476 ----- --- .so 2.54 .229 .0902 1.477 .56 1.422 ----- 256 

.40 2.39 .228 .0954 1.471 . 52 1. 243 ----- --- .30 2.30 .244 .1061 1.574 .46 1.058 ----- 449 

.20 2.20 .269 .1223 1. 735 .42 .924 ----- 885 

.10 1.90 .291 .1532 1.877 . 38 .722 ----- 2220 

Flume Centerline, Station 120 Feet - Flatbed 

0.90 4.86 0.242 0.050 1.316 0.48 2.333 ----- --- .80 4.82 .256 .053 1.391 .57 2. 747 ----- 270 

• 70 4.64 .265 .058 1.441 .54 2.506 ----- --- .60 4.62 .291 .063 1.580 .69 3.188 ----- 425 

.so 4.49 .314 .070 1. 702 ,63 2.829 ----- --- .40 4.43 .349 .079 1.895 .65 2.880 ----- 665 

.30 4.31 .402 .093 2.180 .66 2.845 ----- 918 

.20 3. 92 .419 .107 2.276 .61 2.391 ----- 1220 

.10 3.18 .426 .134 2.317 .48 1.526 ----- 2950 

Flume Centerline, Station 110 Feet - Dune Trough 

0.93 2.35 0 '177 0.076 1.060 0.41 0.964 ----- 46 

.85 2.24 .206 .092 1.234 .67 1.501 ----- 122 

.77 2.19 .296 .135 1. 772 .52 1.139 ----- 301 

.68 2.20 .293 .133 1. 754 .49 1.078 ----- 788 

.61 2.22 .300 .135 1. 796 .53 1.177 ----- 343 

.52 2.06 .260 .126 1.557 .44 .906 ----- 225 

.45 2.13 .297 .140 1. 778 .56 1.193 ----- 236 

.38 1.95 .329 .168 1.970 .46 .897 ----- 231 

.31 1.63 .442 .270 2.647 .54 .880 ----- 305 

.28 1.66 .507 ,306 3.036 .49 .813 ----- 475 

.16 1.27 .327 .257 1.958 .54 .686 ----- 221 

.08 1.17 .361 .309 2.162 .43 .503 ----- 501 

Flume Centerline, Station 100 Feet - Dune Crest 

0.89 2.23 0.161 0.072 0.964 0.57 1.271 ----- 66 

. 78 2.18 .159 .073 .952 .62 1.352 ----- 67 

.66 2.20 .178 .081 1.066 .48 1.056 ----- 130 

.ss 2.19 .186 .085 1:114 .53 1.161 ----- 96 

.44 2.17 .202 .093 1.210 .47 1.020 ----- 109 

.33 2.14 .208 .097 1.246 .61 1. 305 ----- 117 

.24 2.17 .230 .106 1.377 .63 1.367 ----- 175 

.10 2.15 .297 .138 1. 778 .51 1.097 ----- 290 

.01 2.00 ,510 .255 3.054 .72 1.440 ----- 9085 

(fps) 

---- ---- ------ ---- ---- ------ 0.14 1.36 0.0460 

---- ---- ------ ---- ---- ------ .16 1.41 .0559 

---- ---- ------ ---- ---- ------ .19 1.34 .0717 

---- ---- ------ .19 1.46 .0717 

---- ---- ------ .18 1.43 .0614 

---- ---- ------

---- ---- ------ ---- ---- ------ .15 1.38 0.0512 

---- ---- ------ .16 1.42 .0559 

---- ---- ------ .16 1.37 .0559 

---- ---- ------ .18 1.40 .0614 

.18 1.43 .0614 

---- ---- ------ ---- ---- ------ 0.13 1.33 0.0427 

---- ---- ------ .14 1.35 .0460 

---- ---- ------ .15 1.37 .0512 

.16 1.36 .0559 

.18 1.38 .0614 

----- ---- ------ 0.123 1.41 0.0387 

----- ---- ------ .128 1.46 .0417 

----- ---- ------ .131 1.44 .0429 

.140 1.52 .0460 

.144 1.50 .0480 

.152 1.56 .0518 

----- ---- ------ 0.147 1.33 0.0536 

----- ---- ------ ----- ---- ------ ----- ---- ------ ----- ---- ------ .164 1. 35 0. 0635 

----- ---- ------ ----- ---- ------ .171 1.37 .0665 

----- ---- ------ .172 1.33 .0680 

0.138 1.43 o. 0482 

----- ---- ------ .142 1.36 .0517 

----- ---- ------ ----- ---- ------ .148 1.25 .0551 

----- ---- ------ .164 1.40 .0636 

----- ---- ------

B57 
B58 TURBULENCE IN WATER 

TABLE 6.- 8-foot-wide fiume, alluvial boundary- Continued 

Mean Flow -Parameters 

and Variables 

s = l. 79lxl6 3 dso = 0.200 mm w = 8.0 ft u. = 0.264 fps 

Q = 73.33 cfs T = 0.194 1b/ft2 

T = 21.0 °C \1 = 1.057xl0° ft 2/sec 

!2. = 1. 732 ft R = 834,000 v = 5. 30 fps F = o. 682 

c = 1796.9 gpl c;lg = 20.48 -t D = 1. 732 ft Dso = 0.26 mm 

s = 1.056xi6 3 dso = 0.183 mm w = 8.0 ft u. = 0.210 fps 

Q = 48.65 cfs T = 0.111 1b/ft2 

T = 21.0 oc \1 = l.OS4x105 ft 2/sec 

!2. = 1.68 ft R = 573,800 v = 3.16 fps F = o. 489 

c = 778.1 gpl C//g = 15.03 -t 

D = 1.920 ft Dso = 0.26 mm 

s = 1.056xl0 3 dso = 0.183 mm w = 8.0 ft u. = 0.210 fps 

Q = 48.65 cfs T = 0.186 lb/ft2 

T = 21.0 oc \1 = 1.054xi05 ft 2/sec 

!2. = 2.82 ft R = 671,600 v = 3.16 fps F = 0.263 

E.t = 778.1 gpl c;lg = 15.03 

D = 1.920 ft Dso = 0.26 mm 

s = 1. 056xi63 dso = 0.183 mm w = 8.0 ft u. = 0.210 fps 

Q = 48.65 cfs T = 0.115 lb/ft2 

T = 21.0 •c v = 1. 054xl65 ft 2/sec 

Q = 1. 75 ft R = 564,500 

v = 3.16 fps F = 0.453 

c = 778.1 gpl C//g = 15.03 -t 

D = l. 920 ft Dso = 0.26 mm 

s = l.22lxl03 dso = 0.206 mm 

w = 8.0 ft u. = 0.185 fps 

Q = 25.lll cfs T = 0.0843 lb/ft2 

T = 20.7 •c \1 = 1.049x165 ft 2/sec 

Q = 1.107 ft R = 296,500 

v = 2.92 fps F = 0.469 c 826,8 gp1 c;lg = 15.80 

If= 1.107 ft Dso = 0.26 mm 

s = 1. 221x103 dso = 0. 206 mm 

w = 8.0 ft u. = 0.185 fps 

Q = 25.81 cfs T = 0.0843 lb/ft2 

T = 20.7 oc \1 = 1.049x105 ft 2/sec 

!2. = 1.107 ft R = 350,400 

v = 2.92 fps F = 0.556 

c = 826.8 gpl c;lg = 15.80 -t 

D = 1.107 ft Dso = 0.26 mm 

s = l. 221x103 dso = 0.206 mm 

w = 8.0 ft u. = 0.185 fps 

Q = 25.81 cfs T = 0.0843 lb/ft2 

T = 20.7 oc \1 = l. 049xl05 ft 2/sec 

Q = 1.107 ft R = 340,900 

v = 2.92 fps F = 0.541 

c = 826.8 gpl c;lg = 15.80 -t 

D = 1.107 ft Dso = 0.26 mm 

0.94 s. 71 0.325 0.057 1.231 0. 76 4.340 0.023 185 .89 5.62 .326 .058 l. 235 .68 3.822 .022 161 .83 5.69 .341 .060 1.292 .83 4. 723 .024 221 .72 5.43 .353 .065 1.337 • 78 4.235 .023 351 .67 5.55 .411 .074 1.557 • 75 4.163 .022 352 .61 5·.43 .440 .081 1.666 .86 4.670 .023 512 .so 5.42 .461 .085 1. 746 .80 4.336 .024 697 .45 5. 38 .490 .091 1.856 .71 3.820 .023 685 .39 5.39 .550 .102 2.083 .63 3.396 .024 940 .28 5.13 .533 .104 2.019 . 75 3.848 .025 1399 .22 4.88 .522 .107 1.977 .68 3.318 .024 1650 .17 4.67 .579 .124 2.193 .68 3.176 .023 2103 .11 4.35 .592 .136 2.242 .62 2.697 .022 2673 .07 3.92 .592 .151 2.242 .66 2.587 .020 6477 .06 3. 74 .587 .157 2.223 .58 2.169 .012 6732 

1'1ume Centerlme, Statlon 105 Feet - Dune Crest 

0.94 3.85 0.262 0.068 1.248 0.43 1.656 0.034 118 .82 3.90 .285 .073 1.357 .57 2.223 .033 149 .69 3.93 .322 .082 1.533 .63 2.476 .036 176 

.57 3.87 .329 .085 1.566 . 76 2.941 .028 197 .45 3.80 .365 .096 l. 738 .59 2.242 .028 262 .36 3.52 .348 .099 1.657 .71 2.499 .027 256 .24 3.42 .338 .099 1.609 .80 2. 736 .025 345 .13 3.53 .431 .122 2.052 .59 2.083 .026 449 .09 3.30 .469 .142 2.•233 .62 2.046 .025 551 .03 2.86 .603 .211 2.871 .56 1.602 .024 ---

Flume Centerhne, Statwn 95 Feet - Dune Trough 

0.96 3.80 0.236 0.062 1.124 0.54 2.052 ----- 83 .89 3. 75 .244 .065 1.162 .72 2. 700 ----- 162 .81 3. 76 .271 .072 1.290 .69 2.594 ----- 229 

. 74 3. 70 .296 .080 1.410 .58 2.146 ----- 246 .68 3.58 .286 .080 1.362 .64 2.291 0.041 332 .61 3.60 .306 .085 1.457 .61 2.196 .034 418 .53 3.55 .330 .093 1.571 .68 2.414 .031 458 .47 3.23 .400 .124 1.905 .62 2.003 .034 1110 .40 3.32 .647 .195 3.081 .58 1.926 .034 2304 .33 1.27 .485 .382 2.310 .66 .838 .035 1554 .26 .47 .186 .397 .886 .67 .315 .038 2022 .18 .47 .173 .368 .824 .65 .306 .028 ---- .11 .34 .110 .323 .524 .68 .231 .023 ---- .04 .32 .092 .287 .438 . 74 .237 .012 ----

Flume Centerhne Statlon 105 Feet - Dune Back 

0.94 3.64 0.266 0.073 1.267 0,42 1.529 ----- 104 

.83 3.56 .281 .079 1.338 .58 2.065 ----- 389 

.71 3.43 .394 .115 1.876 .60 2.058 ----- 296 

.60 3.40 .401 .118 1.910 .53 1.802 ----- 391 

.49 3.35 .402 .120 1.914 .54 1.809 ----- 374 

,37 3.34 .431 .129 2.052 ,64 2.138 ----- 513 

.26 3.31 .447 .135 2.129 • 80 2.648 ----- 592 

.14 3.27 .477 .146 2. 271 .62 2.027 ----- 569 

.03 3.22 .505 .157 2.405 .51 1.642 ----- 763 

Flume Centerhne, Stat1on 20 Feet - Flatbed 

0.91 2.93 0.196 0.067 1.059 0.48 1.406 ----- 186 

.82 2.92 .196 .067 1.059 .64 1.869 ----- 254 

• 73 2.86 .212 .074 1.146 .53 1.516 ----- 289 

.64 2.86 .226 .079 1.222 .58 1.659 ----- 349 

.55 2.87 .247 .086 1.335 .56 1.607 ----- 401 

.46 2.80 .263 .094 1.422 .64 1. 792 ----- 474 

.37 2. 79 .265 .095 1.432 .68 1.897 ----- 519 

.28 2. 72 .261 .096 1.411 .57 1.550 ----- 571 

.19 2. 74 .266 .097 1.438 .61 1.671 ----- 714 

.09 2.66 .295 .lll 1.595 .54 1.436 ----- 1203 

.04 2.63 .329 .125 1. 778 .63 1.657 ----- ----

Flwne Centerhne, Stahon 60 Feet - Flatbed 

0.92 3.67 0.257 0.070 l. 389 0,54 1.982 ----- 59 

.83 3.58 .265 .074 1.432 .56 2.005 ----- 60 

• 75 3.54 .297 .084 1.605 .52 1.841 ----- 39 

.67 3.51 .305 ,087 1.649 .55 1.931 ----- 81 

.58 3.48 .310 .089 1.676 .54 1.879 ----- 147 

.so 3.37 .347 .103 1.876 .62 2.089 ----- 328 

.42 3.36 .380 .113 2.054 .54 1.814 ----- 257 

.33 3.22 .399 .124 2.157 .68 2.190 ----- 272 

.25 3.17 .412 .130 2.227 .60 1.902 ----- 279 

.17 2.96 .462 .156 2.497 .54 1.598 ----- 369 

.08 2.62 .524 .200 2.832 .49 1.284 ----- 618 

Flume Centerline, Station 90 Feet - Flatbed 

0.89 3.68 0.217 0.059 1.173 0.62 2.282 ----- 25 

• 79 3.67 .235 .064 1.270 .56 2.055 ----- 24 

.68 3.64 .240 .065 1.297 .52 1.893 ----- 39 

.57 3.62 .246 .068 1. 330 .58 2.100 ----- 78 

.47 3.50 .290 .082 1.568 .68 2. 380 ----- 129 

.36 3.27 .307 .093 1.659 .65 2.126 ----- 218 

.25 3.15 ,335 .106 1.811 .52 1.638 ----- 434 

.15 2.86 .377 .131 2.038 .51 1.459 ----- 974 

.OS 2.12 .367 .173 1.984 .46 ,975 ----- 5383 

(fps) 

----- ---- ------ ----- ---- ------ ----- ---- ------ ----- ---- ------ ----- ---- ----- 0.122 1.64 0.0413 

----- ---- ------ ----- ---- ------ .136 1.39 .0478 

----- ---- ------ ----- ---- ------ .152 1.69 .0577 

----- ---- ------ .183 1.71 .0742 

----- ---- ------

----- ---- ------ ----- ---- ------ 0.127 1.46 0.0436 

----- ---- ------ ----- ---- ------ .137 1.50 .0485 

.139 1.48 .0500 

----- ---- ------ .145 1.45 .0544 

----- ---- ------

----- ---- ------ ----- ---- ------ ----- ---- ------ 0.129 1.41 0.0446 

----- ---- ------ ----- ---- ------ .139 1.44 .0500 

----- ---- ------ .158 1.40 .0594 

.164 1.39 .0636 

.187 1.44 .0755 

----- ---- ------ ----- ---- ------ ----- ---- ------

----- ---- ------ ----- ---- ------ ----- ---- ------ 0.149 1,41 0,0552 

----- ---- ------ .156 1,57 .0647 

----- ---- ------ .147 1.45 .0547 

.151 1.46 .0564 

0.153 1.45 0.0584 

----- ---- ------ ----- ---- ------ ----- ---- ------ .178 1.42 .0702 

----- ---- ------ ----- ---- ------ .187 1.40 .0754 

----- ---- ------ .192 1.39 .0780 

----- ---- ------

0.130 1.37 0.0456 

----- ---- ------ ----- ---- ------ ----- ---- ------ ----- ---- ------ 0.156 1.47 0.0581 

----- ---- ------ ----- ---- ~-----

.143 1.39 ,0524 

----- ---- ------ .147 1.32 ,0544 

0.117 1.39 o. 0388 

----- ---- ------ .119 1. 36 .0394 

----- ---- ------ ----- ---- ------ .134 1.33 .0472 

----- ---- ------ .172 1.43 .0675 

----- ---- ------
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

Mean Flow Parameters 

and Variables 

S = 0.57xtfi 3 

w = 56 ft 

Q = 203 cfs 

T = 11.4 •c 

D = 1.66 ft 

V= 2.13 fps 

fi = t. 10 ft 

S = 0.57X1Q3 

w = 56 ft 

Q = 203 cfs 

T = 12.2 •c 

D = 1. 77 ft 

V = 2.13 fps 

fi = t. 10 ft 

S = 0.57xl(j3 

w = 56 ft 

Q = 203 cfs 

T = 14.7 •c 

D = 1.87 ft 

V= 2.13 fps 

fi = t. 10 ft 

S = 0. 57xl(j3 

w = 56 ft 

Q = 203 cfs 

T = to.o •c 

D = 1.91 ft 

V= 2.13 fps 

fi = 1. 70 ft 

s = o.570xto3 

w = 56 ft 

Q = 203 cfs 

T = to.s •c 

D = 1. 86 ft 

V = 2.13 fps 

fi = t. 7o ft 

S = 0.570xtfi3 

w = 56 ft 

Q = 203 cfs 

T=l3.3•c 

D = 1.39 ft 

V=2.13fps 

fi = 1. 70 ft 

u* = 0.171 fps 

' = 0.059 lb/ft2 

v = 1.36xt()5 ft 2/sec 

R = 250,200 

F = o. 28 

c;!g = 12.45 

Dso = 0.235 mm 

u* = 0.171 fps 

T = ().063 lb/ft2 

v = 1.33xto-s ft2/sec 

R = 212~900 

F = 0.13 

c;!g = 12.45 

Dso = 0.235 mm 

u* = 0.171 fps 

' = 0.066 lb/ft2 

v = 1.22x105 ft2/sec 

R = 326,500 

F = o .27 

c;!g = 12.45 

Dso = 0.235 mm 

u* = 0.171 fps 

' = 0.0679 lb/ft2 

v = 1. 41xto·s ft 2/sec 

R = 270,900 

F = 0.306 

c;!g = 12.45 

D5o = 0.235 mm 

u* = 0.171 fps 

T = 0.0662 lb/ft2 

v = l. 38xto5 ft 2/sec 

R = 281,700 

F = 0.270 

c;!g = 12.45 

Dso = 0.235 mm 

u* = 0.171 fps 

T = 0.0494 lb/ft2 

v = 1.29xt()5 ft2/sec 

R = 227,400 

F = o .'315 

c;lg = 12.45 

Dso = 0.235 mm 

TABLE 7.- Atrisco feede·r canal 

0.98 

.86 

• 75 

.49 

. 37 

. 36 

.27 

.22 

.17 

.13 

0.92 

.81 

• 70 

.60 

.49 

.36 

.22 

.11 

0.97 

.86 

. 76 

.65 

.45 

.29 

.19 

.08 

0.95 

.85 

. 73 

.64 

.52 

.41 

.31 

.23 

.13 

0.95 

.84 

• 74 

.64 

.54 

.43 

.35 

.28 

.16 

0.90 

. 77 

.58 

.48 

.34 

.19 

44 Feet From Left Bank - Dunes 

2.07 0.127 0.061 0. 742 

2.06 .135 .065 • 791 

2.05 .145 .071 .847 

2.07 .168 .081 .982 

2.05 .187 .091 1.092 

2.05 .194 .095 1.133 

2.05 .219 .107 1.280 

2.04 .228 .112 1.334 

2.04 .240 .118 1.403 

2.03 .268 .132 1.567 

44 Feet From Left Bank - Dunes 

1.67 0.126 0.075 o. 737 

1.64 .138 .083 .808 

1.64 .148 .090 .865 

1.62 .157 .097 .918 

1.58 .171 .108 1.000 

1.57 .191 .121 1.117 

1.56 .217 .138 1.269 

1.41 .251 .178 1.469 

44 Feet From Left Bank - Dunes 

2.39 0.124 0.052 0. 725 

2.36 .142 .060 .830 

2.33 .224 .096 1.310 

2.31 .229 .099 1.339 

2.29 .247 .108 1.444 

2.14 .280 .130 1.637 

1.91 .302 .158 1. 766 

1.35 .305 .226 1. 784 

44 Feet i'rom Left Bank - Dunes 

2. 78 

2. 76 

2.66 

2.55 

2.59 

2.06 

2.12 

2.10 

2.00 

0.145 

.164 

.177 

.188 

.196 

.186 

.200 

.232 

.270 

0.052 

.059 

.067 

.074 

.076 

.090 

.095 

.110 

.135 

0.!!48 

.959 

1.035 

1.099 

1.146 

1.088 

1.170 

1.357 

1.579 

28 Feet From Left Bank - Dunes 

2.54 0.151 0.060 0.883 2. 43 .189 .078 1.105 

2. 35 .194 .084 1.134 

2. 30 . 207 .090 1.211 

2.02 .202 .100 1.181 

2.06 .227 .110 1. 327 

1.86 .234 .126 1.368 

1. 75 .268 .153 l. 567 

1.55 .318 .205 1.860 

12 Feet From Left Bank - Dunes 

2.30 

2.27 

2.27 

2.12 

2.01 

1. 70 

0.146 

.158 

.180 

.198 

.217 

.248 

0.064 

.070 

.080 

.094 

.108 

.146 

0.854 

.924 

1.053 

1.158 

1.269 

1.452 

0.69 

.80 

. 78 

.72 

.88 

.88 

.80 

. 76 

0.65 

.85 

.77 

.85 

.82 

. 89 

• 79 

.87 

.77 

(fps) 

0.550 ---- 60 0.12 1.42 0.0364 

.448 ---- 73 .12 1.46 .0364 

.466 ---- 90 .12 1.43 .0364 

.554 ---- 116 .13 1.47 .0412 

.412 ---- 294 .14 1.44 .0457 

.599 ---- 320 .14 1.42 .0457 

.573 ---- 409 .15 1.39 .0513 

.351 ---- 816 .16 1.46 .0565 

1.651 ---- 69 0.11 1.33 0. 0325 2.066 ---- 76 .12 1.36 .0364 

1.810 ---- 94 .12 1.42 .0364 

1.955 ---- 127 .13 1.32 .0412 

1.656 ---- 249 .14 1.41 .0457 

1.833 ---- 339 .14 1.38 .0457 

1.469 ---- 428 .15 1. 34 .0513 

1.523 ---- 644 .16 1.47 .0565 

1.194 ---- 876 .17 1.43 .0614 

B59 
B60 

Mean Flow Parameters 

and Variables 

S = 0. 55x1(J3 

w = 68 ft 

Q = 510 cfs 

T = 15.6 •c 

D=3.18ft 

V = 2.68 fps 

v = 2.80 ft 

S = 0. 55x1iP 

w = 68 ft 

Q = 510 cfs 

T = 17.2 •c 

D = 3.07 ft 

V = 2.68 fps 

v = 2.8o ft 

S = 0.55xliJ3 

w = 68 ft 

Q = 510 cfs 

T = 17.8 •c 

D = 3.31 ft 

I= 2.68 fps 

D=2.80ft 

S = 0.550xHJ3 

w = 68 ft 

Q = 550 cfs 

T = 13.3 •c 

D = 3.23 ft E = 2.88 fps 

D = 2.80 ft 

S = 0. 550x1iP 

w = 68 ft 

Q = 550 cfs 

T=13.3•c 

D = 3. 33 ft X= 2.88 fps D = 2.80 ft 

s = o. 5SOxlii3 

w = 68 ft 

Q = 545 cfs 

T = 13.6 •c 

D = 3. 47 ft K = 2.86 fps 

D = 2. 80 ft 

S = 0.5SOxl03 

W=68.0ft 

Q = 540 cfs 

T =·13.6 •c 

D = 3. 34 ft E = 2.84 fps 

D = 2.80 ft 

u. = 0.214 fps 

T = 0.109 1b/ft2 

v = 1.217x105 ft2/sec 

R = 444,200 

F = 0.168 

c;lg = 12.53 

v50 = 0.240 uun 

u. = 0.214 fps 

T = 0.105 1b/ft2 

v = 1.16x11JS ft2/sec 

R = 674,900 

F = o. 256 

C//i = 12.53 

v50 = 0.240 mm 

u. = 0.214 fps 

T = 0.114 lb/ft2 

v = 1.. 45xHJ5 ft 2 /sec 

R = 685,100 

F = 0.230 

C//i= 12.53 

Dso = 0.240 mm 

u. = 0.214 fps 

T = 0.111 1b/ft2 

v = 1.29x1o5 ft 2/sec R = 691,100 

F = 0.271 

c;lg = 13.42 

D50 = o .240 uun 

u. = 0. 214 fps 

T = 0.114 lb/ft2 

v = 1.29xlos ft 2/sec 

R = 614,400 

F = 0.230 

C//i = 13.42 1 

Dso = 0.240 mm 

U* = 0.214 fps 

T = 0.119 lb/ft2 

v = 1. 28x165 ft2 /sec 

R = 574,700 

F = 0.201 

C//i = 13.35 

v50 s 0.240 mm 

v. = 0.214 fps 

T = 0.115 lb/ft2 

v = 1.28xl65 ft 2/sec 

R = 493,200 

F = 0.182 

C/lg = 13.25 

D50 = 0.240 mm 

TURBULENCE IN WATER 

TABLE 8.- Rio Grande conveyance channel 

52 Feet From Left Bank - Dunes 

0.96 

.86 

0 78 

.68 

.58 

.49 

.40 

0 30 

.18 

.09 

.08 

1.53 

1. 78 

1.94 

1.81 

2.16 

1.82 

1.58 

1.50 

1.53 

1.53 

1.46 

0.139 

.185 

.322 

.348 

.488 

.480 

.426 

.474 

.496 

.468 

.153 

0.091 

.104 

.166 

.192 

.266 

.264 

.270 

.316 

.324 

.306 

.105 

0.650 

0 864 

1.505 

1.626 

2.280 

2.243 

1.991 

2.215 

2. 318 

2.187 

.715 

34 Feet From Left Bank - Dunes 

0.96 2.83 0.125 0.044 0.584 

.86 2.86 .154 .054 .720 

0 76 2.85 .191 .067 .893 

.66 2. 73' .202 .074 .944 

.57 2. 70 .232 .086 1.084 

.47 2.62 .259 .099 1.210 

.36 2.52 .242 .096 1.131 

.25 2.21 .256 .116 1.196 

.18 2.11 .279 .132 1.304 

.12 2.02 .323 .160 1.509 

16 Feet From Left Bank - Dunes 

0.94 2.59 0.140 0.054 0.654 

.84 2.47 .158 .064 0 738 

0 76 2.44 .151 .061 0 706 

.66 2.66 .173 .065 .808 

.58 2 0 75 .215 .078 1.005 

.47 2.64 .241 .091 1.126 

.37 2.50 .260 .104 1.215 

.28 2.36 .277 .117 1.294 

.18 2.17 .306 .141 1.430 

.11 1.86 .293 .157 1.369 

.09 1.67 .284 .170 1.327 

34 Feet From Left Bank - Dunes 

0.95 3.09 0.167 0.055 0. 780 

.86 3.05 .235 .077 1.098 

.77 3.16 .275 .087 1.285 

.67 3.08 .342 .111 1.598 

.58 2.97 .404 .136 1.888 

.49 2.83 .416 .147 1.944 

.41 2.67 .433 .162 2.02.3 

.30 2.48 .439 .177 2.051 

.22 2.28 .431 .189 2.014 

.15 2.30 0 361 .157 1.687 

.09 2.40 .415 .173 1.939 

34 Feet From Left Bank - Dunes 

0.96 2.54 0.107 0.042 0.500 

.86 2.59 .111 .043 .519 

.77 2.64 .166 .063 • 766 

.69 2. 72 .245 .090 1.145 

.58 2. 70 .351 .130 1.640 

.so 2.62 .443 .169 2.070 

.42 2.50 .455 .182 2.126 

0 32 2.29 .472 .206 2.206 

.24 2.00 .490 .245 2.290 

.16 1.88 .451 .240 2.107 

.09 1. 73 .303 .175 1.416 

34 Feet From Left Bank - Dunes 

0.98 2.86 0.123 0.043 0.575 

.92 2.94 .138 .047 .645 

.86 2.98 .176 .059 .822 

.72 2.94 .223 .076 1.042 

.63 2.82 .288 .102 1. 346 

.55 2.48 .407 .164 1.902 

.46 2.12 .409 .193 1.911 

.37 1. 71 .3£13 .230 1. 836 

.31 1.40 .294 .210 1. 374 

.22 1.09 .251 .230 1.173 

.15 1.07 .209 .195 .977 

.09 1.10 .248 .225 1.159 

34 Feet From Left Bank - Dunes 

0.95 2. 78 0.170 0.061 o. 794 

.86 2. 70 .181 .067 .846 

.77 2. 75 .179 .065 .836 

.68 2.90 .203 .070 .949 

.60 2.66 .210 .079 .981 

0 51 2.23 .256 .115 1.196 

.42 1.77 .381 .215 1. 780 

.34 1.22 .373 .306 1. 743 

.23 1.06 .264 .249 1.234 

.16 .90 .178 .198 0 836 

.12 .90 .169 .188 0 790 

.08 0 80 .137 .171 .640 

1.08 3.056 

.82 2.345 

1.28 3.648 

1.03 2.812 

1.06 2.862 

1.31 3.432 

1.19 2.999 

1.01 2.232 

1.03 2.173 

.89 1. 798 

(fps) 

----- 283 0.132 1.32 0.0432 

----- 346 .135 1.37 .0444 

----- 483 .137 1.43 .0458 

----- 530 .138 1.51 .0463 

----- 594 .141 1.42 .0479 

----- 673 .145 1.46 .0494 

----- 612 .148 1.41 .0519 

----- 882 .163 1.51 .0584 

----- 1039 .171 1.44 .0623 

----- 1221 .183 1.46 .0692 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

TABLE 8. -Rio Grande conveyance channel- Continued 

Mean Flow Parameters 

and Variables 

s = o.550xl63 

w = 68.0 ft 

Q = 540 cfs 

T = 13.9 •c D = 2.94 ft 

V = 2.84 fps 

v = 2.80 ft 

s = o. 550Xl03 

w = 68.0 ft 

Q = 530 cfs 

T = 14.4 •c D = 2.40 ft 

V = 2.78 fps 

v = 2.8o ft 

s = o. 55ox1iP 

w = 68.0 ft 

Q = 530 cfs 

T = 14.4 •c D = 2.46 ft 

V = 2. 78 fps 

v = 2.8o ft 

s = 0. 550xlo3 

w = 68.0 ft 

Q = 520 cfs 

T = 14.1 •c D = 2.67 ft 

V = 2.74 fps 

D= 2.8o ft 

s = o.ssoxuP 

w = 68.0 ft 

Q = 520 cfs 

T = 1s.o •c D = 2.67 ft 

V = 2.74 fps 

v = 2.8o ft 

S = 0. 550xl()3 

w = 68.0 ft 

Q = 510 cfs 

T = 1s. o •c D = 2.63 ft ! = 2.68 fps 

D = 2.80 ft 

s = o.5SOxi63 

w = 68.0 ft 

Q = 510 cfs 

T = 15.6 •c D = 2.66 ft !:.: = 2.68 fps 

D = 2.80 ft 

U * = 0. 214 fps 

T = 0.101 lb/ft2 

v = 1. 27xl65 ft 2 /sec 

R = 578,700 

F = 0.257 

c;lg = 13.25 

D50 = 0.240 mm 

U * = 0. 214 fps 

T = 0.0824 3b/ft2 

v = 1. 2Sxi6 ft 2 /sec 

R = 562,600 

F = 0.333 

c;lg = 12.98 

Dso = 0.250 mm 

U * = 0. 214 fps 

T = 0,0844 lb/ft2 

v = 1. 2Sxi65 ft 2/sec 

R = 558,900 

F = o. 319 

C//i= 12.98 

D50 = 0.240 mm 

u* = 0.214 fps T = 0,0916 lb/ft2 

v = 1. 24xl05 ft 2/sec 

R = 480,200 

F = 0.241 

c;lg = 12.80 

Dso = 0.240 mm 

u* = 0.214 fps 

T = 0.0916 lb/ft2 

v = l. 23xi05 ft 2/sec 

R = 494,900 

F = 0.246 

C//i= 12.80 

Dso = 0.240 mm 

u* = 0.214 fps 

T = 0.0903 lb/ft2 

v = 1. 23x165 ft 2 /sec 

R = 472,500 

F = 0.240 

c;lg = 12.53 

Dso = 0.240 mm 

u* = 0.214 fps 

T = 0.0913 lb/ft2 

v = 1. 217xlos ft 2 /sec 

R = 478,700 

F = o .237 

c;lg = 12.53 

Dso = 0.240 mm 

0.95 

.86 

• 77 

.67 

.56 

.45 

.33 

.20 

.08 

0.94 

.85 

.77 

.69 

.60 

.52 

.44 

. 36 

.28 

.19 

.12 

0.94 

.85 

. 76 

.67 

.59 

.51 

.42 

.39 

• 31 

.23 

.15 

.12 

0.94 

.83 

.72 

.60 

.so 

.39 

.28 

.16 

.11 

0.94 

.83 

.71 

.61 

.so 

.38 

.28 

.17 

.13 

0.94 

.83 

• 71 

.60 

.48 

.38 

.27 

.16 

.11 

0.95 

.84 

• 75 

.64 

.52 

.39 

. 30 

.19 

.11 

34 Feet From Left Bank - Dunes 

2.42 0.165 0.068 0. 771 

2.49 .184 .074 .860 

2.65 .191 .072 .893 

2. 75 .198 .072 .925 

2.89 .280 .097 1.308 

2.83 .293 .104 1.369 

2.83 . 351 .124 1.640 

2. 78 .487 .175 2.276 

0.86 .170 .198 . 794 

34 Feet From Left Bank - Dunes 

2.69 0.202 0.075 0.944 

2.86 • 260 .091 1. 215 

2.96 .299 .101 1.397 

2.86 .332 .116 1.551 

2. 79 . 379 .136 1.771 

2.86 .332 .116 1.551 

2.96 . 326 .110 1.523 

3.06 .397 .130 1.855 

3.13 .385 .123 1. 799 

3.03 . 373 .123 1. 743 

2.98 .374 .126 1. 748 

34 Feet From Left Bank - Dunes 

2.86 0.223 0.078 1.042 

2.96 .243 .082 1.136 

3.03 .294 .097 1.374 

2.96 .302 .102 1.411 

2.86 .323 .113 1.509 

2.82 .327 .116 1.528 

2. 76 .351 .127 1.640 

2. 76 .364 .132 1. 701 

2.82 . 361 .128 1.687 

2.96 .429 .145 2.005 

2.98 .401 .135 1.874 

2.86 .486 .170 2.271 

34 Feet From Left Bank - Dunes 

2.50 0.215 0.086 1.005 

2.41 .251 .104 1.173 

2.30 .269 .117 1.257 

2.12 . 267 .126 1.248 

2.06 .280 .136 1.308 

2.02 .295 .146 1.379 

2.11 .312 .148 1.458 

2.30 .313 .136 1.463 

2.26 . 389 .172 1.818 

34 Feet From Left Bank - Dunes 

2.58 0.196 0.076 0.916 0.26 0.671 0,028 

2.68 .263 .098 1.229 .22 .590 .031 

2.55 .293 .115 1. 369 .17 .434 .033 

2.40 .338 .141 1.579 .21 .504 .029 

2.28 .415 .182 1.939 .23 .524 .027 

2.10 .372 .177 1. 738 .24 .504 .030 

2.00 .366 .183 1. 710 .19 .380 .028 

1.95 .343 .176 1.603 .20 .390 .026 

1.97 .299 .152 1. 397 .18 . 355 • 027 

34 Feet From Left Bank - Dunes 

3.08 0.129 0.042 0.603 

2.92 .178 .061 .832 

2. 77 .255 .092 1.192 

2.54 .272 .107 1.271 

2.37 .313 .132 1.463 

2.07 .277 .134 1.294 

1.83 .258 .141 1.206 

1.64 .246 .150 1.150 

1.65 .261 .158 1.220 

34 Feet From Left Bank - Dunes 

2. 74 0.156 0.057 0. 729 

2. 77 .249 .090 1.164 

2.60 .341 .131 1.593 

2.42 .351 .145 1.640 

2.15 .357 .166 1.668 

2.03 .309 .152 1.444 

1.82 .348 .191 1.626 

1.66 .400 .241 1.869 

1.55 .375 .242 1. 752 

(fps) 

426 0.126 1.46 0.0394 

497 .125 1.42 .0388 

545 .127 1.47 .0408 

489 .127 1. 38 .0408 

526 .128 1.40 .0418 

525 .131 1.46 .0440 

998 .145 1.54 .0498 

1112 .159 1.50 .0564 

1311 .169 1.48 .0623 

B61 
B62 TURBULENCE IN WATER 

TABLE 8. -Rio Grande conveyance channel- Continued 

Mean Flow Parameters 

and Variables 

s = 0.550xHP 

w = 68.0 ft 

Q = S10 cfs 

T = 15.6 •c D = 2. 31 ft 

JZ: = 2.68 fps D = 2.31 ft 

S = 0.550xl03 

w = 68.0 ft 

Q = 510 cfs 

T = IS .6 •c D = 2.54 ft 

V = 2.68 fps 

v = 2 .8o ft 

S = O.S7xl63 

W=73.0ft 

Q = 930.0 cfs 

T = l2 1,C "C 

D = 3.00 ft 

V = 4.60 fps 

[}=3.00ft 

S = 0. S7xl(j3 

w = 73.0 ft 

Q = 815.0 cfs 

T = 12.0 •c D = 2.90 ft 

V = 3.85 fps 

v = 2.90 ft 

u. = 0.214 fps 

T = 0.0793 lb/ft 2 

v = 1.217xl()5 ft 2 /sec 

R = 525 ,soo 

F = 0.321 

C//i = 12.53 

Ds 0 = 0.240 m 

u. = 0.214 fps 

T = 0.0872 lb/ft2 

v = 1.217x1()5 ft 2 /sec 

R = 690 ,soo 

F = 0.366 

C//i = 12.53 

Dso = 0.240 mm 

u. = -0.226 fps 

T = 0.103 lb/ft2 

v = 1. 34x165 ft2/sec 

R = 1,021,500 

F = o'.48B 

C//i= 20.40 

Dso = 0.200 mm 

u. = 0.224 fps 

T = 0.107 1b/ft2 

v = 1.34xl65 ft 2/sec 

R = 866,400 

F = 0. 394 

C//i = 17.2 

Dso - 0.202 mm 

0.94 

.83 

.71 

.58 

.45 

.27 

.13 

0.94 

.86 

• 74 

.63 

.42 

.31 

.20 

.10 

0.90 

. 79 

. 79 

.69 

.59 

.48 

.48 

.38 

.28 

.28 

.17 

.07 

.04 

0.87 

• 73 

.60 

.47 

.33 

.20 

.07 

34 Feet From Left Bank - Dunes 

2.95 0.156 0.053 0. 729 

3.00 .183 .061 .855 

3.00 .204 .068 .953 

2.97 .223 .075 1.042 

3.05 .262 .086 1.224 

2. 70 .338 .125 1.579 

1. 70 .380 .223 1.776 

34 Feet From Left Bank - Dunes 

3.32 

3.34 

3.31 

3.29 

3.28 

3.26 

3.27 

3.40 

0.173 

.200 

.225 

.273 

• 302 

.346 

.405 

.517 

0.052 

.060 

.068 

.088 

.092 

.106 

.124 

.152 

0.808 

.935 

1.051 

1.276 

1.411 

1.617 

1.893 

2.416 

36 Feet From Left Bank - Flatbed 

5.<13 0.261 0.048 1.155 

5.32 .289 .054 1.279 

5.30 .314 .059 1.388 

5.23 .341 .066 1.510 

5.12 .384 .075 1. 700 

5.01 .391 .078 1. 726 

4.97 .398 .080 1. 761 

4.82 .442 .092 1.951 

4.56 .452 .099 1.993 

4.61 .456 .101 2.020 

4.19 .518 .124 2.282 

3.58 .548 .153 2.430 

3.29 .624 .190 2. 763 

36 Feet From Left Bank - Flatbed 

4.14 0.228 0.055 1.018 

4.13 .248 .060 1.107 

4.11 .279 .068 1.246 

4.07 .334 .082 1.491 

3.93 .424 .108 1.893 

3.69 .435 .118 1.942 

3.12 .543 .174 2.424 

0. 73 2.15 

.68 2.04 

.81 2.43 

1.33 3.95 

.84 2.56 

.92 2.48 

.89 1.51 

1.54 8.36 

1.53 8.14 

1.51 8.00 

1.24 6.48 

1.03 5.27 

1.32 6.61 

1.43 7.11 

1.08 5.21 

1.26 s. 75 

1.17 5.39 

1.44 6.03 

1.51 5.41 

.94 3.09 

1.04 4.31 

1.16 4. 79 

1.57 6.45 

1.56 6.35 

1.34 5.27 

1.29 4. 76 

1.23 3.84 

TABLE 9.- Columbia River estua'ry 

Mean Flow Parameters T Y/D u 1;2 1:2/u 1:2/u. and Variables (fps) (fps) 

19.2 0.98 4. 73 ----- _,. ___ ----- 18.0 .83 4.03 0.387 0.196 -----

v = 1. 88 fps R = 93,271 15.8 .68 4. 34 1.128 .260 ----- 12.4 .51 .61 .171 .280 ----- v = 1.29x1o-s ft 2 /sec F = 0.041 11.2 .36 .37 .119 .321 ----- 10.7 .20 .27 .104 .386 ----- 10.5 .04 .37 ----- ----- ----- 10.3 .01 .35 .152 .435 -----

0.026 368 0.134 

.031 414 .136 

.028 487 .139 

.025 544 .142 

.029 527 .147 

.027 987 .167 

.024 1518 .182 

0.037 413 0.163 

,038 476 .167 

.041 476 ----- ,039 544 .174 

.043 661 .179 

.038 777 .185 

.036 777 ----- .040 1162 .189 

.039 1479 .196 

,042 1479 ----- .038 2423 .217 

.034 6084 .237 

.031 15800 .263 

0.042 397 0.156 

.037 526 .164 

.039 764 .172 

.041 916 .185 

.036 1031 .192 

.032 1426 .209 

.035 4116 .252 

TE L 

X cs (sec) (ft) (gpl) 

2.34 11 ;070 ----- 1. 78 7.173 ----- 2.28 9.895 100 

• 74 .451 180 

1.53 .566 173 

3.32 .896 116 

2.07 • 766 260 

1.49 . 522 321 

(fps) 

1.43 0.0434 

1.41 .0442 

1.35 .0454 

1.38 .0471 

1.45 .0497 

1.42 .0585 

1.51 .0676 

1.32 0.0574 

1.33 .0590 

---- ------ 1.35 .0612 

1.36 .0638 

1. 36 .0662 

---- ------ 1.41 .0683 

1.43 .0722 

---- ------ 1.44 .0813 

1.45 .0893 

1.51 .1032 

1.36 0.0522 

1.38 .0566 

1.37 .0598 

1.41 .0658 

1.43 .0690 

1.44 .0787 

1.47 .1015 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

Mean Flow Parameters 

and Variables 

S = 0. 150xl()3 

w = 697.6 ft 

Q = 31,400 cfs 

T = zo. o •c D = 14.4 ft 

V = 4.44 fps 

v = 10.1s ft 

S = 0 .150xl63 

w = 697.6 ft 

Q = 31,400 cfs 

T = 20 .o •c D = 15.6 ft 

£ = 4.44 fps 

D = 10.15 ft 

S = 0 .150xlfi3 

w = 697.6 ft 

Q = 31 ,400 cfs 

T = 20 .o •c D = 13.6 ft 

V = 4.44 fps 

Yf= 10.1s ft 

S = 0 .150xlfi3 

w = 697.6 ft 

Q = 31,400 cfs 

T = zo. o •c D = 11.3 ft 

V = 4.44 fps 

v = 10.1s ft 

S = 0 .150xlfi3 

w = 697.6 ft 

Q = 31 ,400 cfs 

T = 20 .o •c D = 6. 4 ft 

I= 4.44 fps 

D = 10.15 ft 

S = 0.15Sx163 

w = 645.4 ft 

Q = 32,500 cfs 

T = 2. 8 •c D = 16.3 ft 

r= 5.21 fps 

D=9.67ft 

S = 0.15Sx163 

w = 645.4 ft 

Q = 32,500 cfs 

T = 2. 8 •c D = 14.3 ft 

~ = 5.21 fps 

D=9.67ft 

S = 0 .15Sxl63 

w = 645.4 ft 

Q = 32,500 cfs 

T = 2. 8 •c D = 10.8 ft 

V= 5.21 fps 

v = 9.67 ft 

u. = 0.263 fps 

T = 0,135 lb/ft2 

v = 1.09lxt65 ft 2/se<: 

R = 5,675,500 

F = o. 200 

C//g = 19.20 

v50 = 0.203 mm 

u. = 0.274 fps 

T = 0.146 lb/ft2 

v = l.09lxl6 5 ft2/sec 

R = 8,420,000 

F = 0,263 

C//g = 19.20 

v50 = 0.237 mm 

u. = 0.256 fps 

T = 0.0849 1b/ 

v = 1.091x16 5 ft 2 /sec 

R = 8,102,700 

F = 0.311 

C//g= 19.20 

v50 = 0.252 mm 

u. = 0.234 fps 

T = 0,0705 lb/ft2 

v = 1.091x165 ft 2/sec 

R = 6, 183,400 

F = 0.266 

C//g= 19.20 

D50 = 0.283 mm 

u. = 0.187 fps 

T = 0,0399 1b/ft2 

v = 1.091xt65 ft 2/sec 

R = 2,974,200 

F = 0.353 

C/lg= 19.20 

D50 = o. 302 mm 

u. = 0.285 fps 

T = 0.119 1b/ft2 

v = 1.764x165 ft2/sec 

R = 5,645,900 

F = 0.266 

cf/g = 23.01 

D50 = 0.217 mm 

u. = 0.267 fps 

T = 0.104 1b/ft2 

v = 1. 764x1fi 5 ft2/sec 

R = 5,431,400 

F = 0.312 

C/lg = 23,01 

v50 = o. 232 mm 

u. = 0.232 fps 

T = 0,0788 lb/ft2 

v = 1. 764x165 ft 2/sec 

R = 3,673,400 

F = 0.322 

C/lg = 23.01 

Dso = 0.135 mm 

TABLE 10.- Missouri R-iver 

580 Feet From Left Bank at River Mile 612.51 - Dunes 

p.81 4. 70 0. 235 0.050 0.890 2.93 13.77 ----- .55 4.33 . 282 .065 1.071 3.32 14.38 ----- .34 3.98 .295 .074 1.120 4.06 15.91 ----- .23 3.92 .343 .088 1. 303 4.12 16.15 ----- .17 3.90 .378 .097 1.438 2.98 11.62 ----- .12 3. 82 .393 .104 1.501 2.61 9.97 ----- I 

I 497 Feet From Left Bank at River Mile 612.51 -Dunes 

0.80 6.49 0. 305 0.047 1.112 3.42 22.20 0.061 

.54 6.16 .357 .058 1.302 5.88 36.22 .062 

.33 5.44 .359 .066 1.311 4.16 22.63 .056 

• 21 5.18 .378 .073 1.380 3.81 16.47 .057 .15 5.05 .408 .081 1.493 3.24 16.36 ,058 

.11 4.96 .500 .102 1.828 2.90 14.38 .048 

l I . J===.=b 

440 Feet From Left Bank at River Mile 612.51 - Dunes 

~.81 6.81 0.318 0.047 1.243 2.94 

.55 6.61 .349 .053 1.366 3.87 

.35 6.42 .371 .058 1.450 4.04 

. 24 6.13 .406 .067 1.591 3.08 

.17 5.82 .441 .076 1. 724 3.84 

.13 s. 52 .486 ..089 1.902 2. 75 

I I I I i 373 Feet From Left Bank at River Mile 612.51 - Dunes 

p.82 6.59 0.309 0.047 1. 320 3.68 

.55 6.26 .346 .056 1.476 3. 23 

. 34 5.90 .384 .066 1.643 4.04 

.22 5.61 .413 .074 1. 764 3.26 

.16 5. 36 .474 .089 2.023 2.82 

I ! ! 226 Feet From Left Bank at River Mile 612.51 - Dunes 

0.91 5.38 0.228 0.043 1.222 2. 76 

.66 5.30 .281 .050 1.396 3.49 

.45 5.13 .297 .058 1. 589 '3.16 

.34 4.99 .324 .065 1. 781 3.03 

.28 4. 88 .374 .071 2.004 2.45 

I I I 540 Feet From Left Bank at River Mile 612.51 - Flat Bed 

p. 77 6.82 0.294 0.044 1.032 4.08 

.51 6.36 .308 . 049 1.081 5.19 

.30 5.63 .369 .066 1.296 3.18 

.18 5.45 .444 .082 1.555 3. 74 

.12 4.62 .466 .101 1.637 2.66 

.10 4.64 .472 .102 1.660 2.95 

481 Feet From Left Bank at River Mile 612.51 - Flat Bed 

p. 77 7.46 0. 322 0.044 1.205 3.22 

.so 7.04 .362 .052 1.356 3.92 

.22 6.46 .441 .068 1.650 4.17 

.17 6.09 .463 .076 1. 734 4.06 

.10 s. 36 .472 .088 1. 766 3.07 

.06 5.36 .488 .092 1.832 2.84 

I 340 Feet From Left Bank at River Mile 612.51 - Flat Bed 

.77 

.so 

.29 

.17 

.10 

6. 86 

6.46 

5.81 

5.27 

5.08 

0.305 0.045 

. 372 . 058 

.433 .075 

.448 .085 

.491 .097 

1.310 

1.595 

1.860 

1.925 

2.108 

3.23 

3. 78 

4.06 

3. 26 

2. 73 

20.02 

25.58 

25.94 

18.88 

22.35 

15.18 

24.25 

20.22 

23.84 

18.29 

15.12 

14.85 

18.50 

16.21 

15.12 

11.96 

27.83 

33.01 

17.87 

20.38 

12.29 

13.69 

24.02 

27,60 

26.94 

24.74 

16.46 

15.22 

22.16 

24.42 

23.59 

17.18 

13.87 

I 

-----

-----

-----

__ .., __ 

-----

-----

0.067 

.062 

.057 

.063 

.052 

-----

-----

-----

-----

-----

0.060 

.055 

.047 

.053 

.036 

.032 

-----

-----

-----

-----

-----

-----

(fps) 

37 0.097 1.34 0.0285 

109 .102 1.35 .0311 

132 .104 1. 36 .0322 

215 .107 1.40 .0334 

256 .109 1.42 .0341 

286 .112 1.44 .0360 

I I 

117 0.110 1. 26 0.0358 

285 .121 1.28 .0410 

409 .125 1.27 . 0426 

238 .119 1.29 .0394 

341 .127 1.31 .0437 

826 .129 i.33 .0450 

151 0.125 1.28 0.0426 

295 .133 1.30 .0466 

510 .137 1. 34 .0479 

656 .139 1.33 .0497 

1190 .141 1.39 .0512 

1989 .145 1.41 .0531 

I 

238 0.136 1. 35 0. 0476 

161 .138 1. 32 .0488 

391 .143 1.36 .0521 

666 .147 1.34 .0541 

802 .151 1.37 .0561 

I I 

162 0.154 1.31 0.0578 

262 .162 1.33 .0616 

292 .166 1. 37 .0640 

588 .175 1.41 .0694 

1062 .188 1.43 .0748 

I I I 

199 0.117 1.29 0.0272 

322 .125 1.33 .0308 

607 .128 1. 34 .0314 

980 .138 1.36 .0361 

1280 .146 1.39 .0390 

2518 . 181 1.40 .0546 

I I I 

220 0.135 1.31 o. 0345 

459 .137 1.33 .0357 

821 .135 1. 35 .0345 

1250 .139 1. 37 .0371 

1807 .140 1.38 .0377 

3603 .188 1.40 .0588 

I 

182 0.135 1.30 0.0345 

382 .141 1.32 .0377 

672 .160 1.35 .0459 

1159 .155 1. 38 .0434 

1756 .160 1.41 .0459 

B63 
B64 

Mean Flow Parameters 

and Variables 

S = 0.0236xl0- 3 

w = 2910 ft 

Q = 325,000 cfs 

T = 18.3 •c 

D = 25.5 ft 

V = 2.52 fps 

v = 44.4 ft 

S = 0.0236Xl0-3 

w = 2910 ft 

Q = 325,000 cfs 

T=l8.3•c 

D = 55.0 ft 

v = 2.52 fps 

v = 44.4 ft 

s = 0.0236xlo-3 

w = 2910 ft 

Q = 325,000 cfs 

T = 18.3 •c 

D = 110.0 ft 

V = 2.52 fps 

v = 44.4 ft 

S = 0.018lx10- 3 

w = 1880 ft 

Q = 325,000 cfs 

T = 11.1 •c 

D=22.5ft 

V = 3.23 fps 

v = 53.5 ft 

S = 0.0181Xl0-g 

w = 1880 ft 

Q = 325 ,000 cfs 

T = 11.1 •c 

D = 72.5 ft 

}: = 3.23 fps 

D = 53.5 ft 

S = O.Ol8lx10-3 

w = 1880 ft 

Q = 325,000 cfs 

T= 16.7 •c 

D = 104.0 ft 

}: = 3.23 fps 

D = 53.5 ft 

s = 0.0241Xl0-3 

w = 2000 ft 

Q = 325,000 cfs 

T = 11.2 •c 

D = 60.0 ft ! = 3.20 fps 

D = 50.9 ft 

S = 0,0241Xl0-3 

w = 2000 ft 

Q = 325,000 cfs 

T = 11.2 •c !!.. = 65 .o ft 

! = 3.20 fps 

D = 50.9 ft 

u* = 0.139 fps 

' = 0.0375 lb/ft2 

v = 1.13xl(j5 ft 2/sec 

R = 4,896,900 

F = 0.0757 

c;lg = 13.12 

Dso = 0.38 nun 

u* = 0.208 fps 

' = 0.0810 lb/ft2 

v = 1.13xl05 ft 2/sec 

R = 18,349,600 

F = o .0896 

c;lg = 13.72 

Dso = 0.38 nun 

u* = 0.289 fps 

T = 0,1620 lb/ft2 

v = 1.13x165 ft2/sec 

R = 33,876,100 

F = 0.0585 

C//g = 13.72 

Dso = 0.38 nun 

u* = 0.115 fps 

T = 0. 0254 lb/ft2 

v = 1.18xl05 ft 2/sec 

R = 3,,489,,400 

F = 0.068 

C!/Ci = 18.30 

D50 = 9.37 nun 

u* = 0.206 fps 

T = 0.0818 1b/ft2 

v = 1.18xl05 ft 2/sec 

R = 19,108,100 

F = 0.0644 

C/r'g = 18.30 

Dso = 0.37 mm 

u* = 0.246 fps T = 0.1173 lb/ft2 

v = 1.18x165 ft 2/sec 

R = 35,871,200 

F = 0.0703 

c;lg = 18.30 

Dso = 0~37 mm 

u* = o .216 fps 

T = 0.0901 lb/ft2 

v = 1.16xl65 ft 2/sec 

R = 21 ,982,800 

F = 0.0967 

c;lg = 16.11 

Dso = 0.43 nun 

u* = 0.225 fps 

T = 0,0976 1b/ft2 

v = 1.16xl(J5 ft 2 /sec 

R = 20,172,400 

F = 0.0787 

C/r'g= 16.11 

Dso = 0.43 nun 

TURBULENCE IN WATER 

TABLE 11.- Mississippi River 

550 Feet From Left Bank at River Mile 444.0 - Dunes 

0.86 

.66 

.46 

.26 

.06 

2.51 

2.37 

2.24 

2.06 

1.66 

0.138 0.055 

.152 .064 

.181 .081 

.208 .101 

.251 .153 

0.994 

1.093 

1.302 

1.495 

1.804 

5.02 

4.89 

6.95 

6.10 

5.51 

1150 Feet From Left Bank at River Mile 444.0 - Dunes 

0.88 4.65 0.244 0.052 1.172 7.34 

.68 4.28 .268 .063 1.288 8.53 

.48 3.42 .294 .086 1.413 4.97 

.28 3.67 .391 .107 1.880 6.49 

.08 2.84 .412 .145 1.982 6.23 

1600 Feet From Left Bank at River Mile 444.0 - Dunes 

0.89 4.30 0.284 0.066 0.984 8. 78 

.69 3.94 .324 .082 1.121 6.45 

.49 3.30 .365 .110 1.263 11.38 

.29 3.52 .426 .121 1.475 8.23 

.09 2.36 .486 .206 1.683 6.09 

650 Feet From Left Bank at River Mile 443.2 - Dunes 

0.86 2.14 0.132 0.061 1.147 5.18 

.64 2.05 .167 .081 1.453 6.53 

.46 2.00 .176 .088 1.530 8.06 

.25 1. 79 .187 .105 1.626 5.98 

.06 1.15 .202 .175 1. 756 4.75 

1050 Feet From Left Bank at River Mile 443.2 - Dunes 

0.88 3.00 0.202 0.067 0.983 8. 09 

.68 3.06 .242 .079 1.176 11.50 

.48 3.56 .278 .078 1.347 9. 23 

.28 3.07 .365 .119 1. 772 8.58 .08 2.88 .429 .149 2.081 6.93 

1650 Feet From Left Bank at River Mile 443.2 - Dunes 

0.89 4.28 0.265 0.062 1.077 7.15 .69 3.96 .301 .076 1.223 10.16 .49 4.14 .352 .085 1.431 10.73 .29 4.35 .470 .108 1.910 6.93 .09 3.55 .482 .136 1.956 5.18 

1155 Feet From Left Bank at River Mile 441. 6 - Dunes 

0.88 4.43 0.221 0.050 1.023 8.50 

.68 4.87 .336 .069 1.554 4. 94 .48 4. 74 .393 .083 1.817 7.31 .28 4.15 .486 .117 2.250 8.53 

.08 3.58 .523 .146 2.418 5. 74 

1755 Feet From Left Bank at River Mile 441.6 - Dunes 

0.88 4.08 0.236 0.058 1.049 6.28 .68 4.18 .297 .071 1.318 8.40 .48 3. 71 .319 .086 1.416 10.03 .28 3.52 .384 .109 1. 705 7.14 .08 2.51 .364 .145 1.619 4.34 

12.57 

11.80 

15.55 

12.53 

9.14 

34.13 

36.51 

17 .oo 

23.82 

17.70 

37.75 

25.41 

37.55 

28.97 

14.37 

11.08 

13.38 

16.12 

10.70 

5.46 

24.27 

35.19 

32.86 

26.34 

19.96 

30.60 

40.24 

44.42 

30.15 

18.40 

37.66 

24.06 

34.65 

35.40 

20.55 

25.62 

35.11 

37.21 

25.14 

10.90 

! 

24 

18 

18 

32 

34 

0.103 35 

.114 60 

.097 74 

.095 76 

.086 115 

23 

25 

39 

23 

17 

23 

17 

10 

123 

41 

67 

62 

126 

293 

33 

45 

105 

32 

115 

0.118 14 

.119 -- .094 226 

.073 73 

.052 504 

14 

12 

15 

14 

464 

(fps) 

0.143 1.54 0. 0492 

.148 2.26 .0541 

.103 2. 72 .0308 

.116 1. 71 .0377 

.112 1. 70 .0361 

0.130 1. 77 0.0446 

.148 1.56 .0541 

.141 1.58 .0499 

.146 1.64 .0525 

.157 1.53 .0581 

0.124 1.69 0.0413 

.121 1.54 .0394 

.140 1. 76 .0492 

.135 2.10 .0472 

.116 1. 70 .0377 

0.207 1.87 0.0820 

.127 2.04 .0413 

.149 2.16 .0525 

.108 1.58 .0322 

0.120 1.59 0.0731 

.123 1.67 .0384 

.160 1. 74 .0577 

.154 1.40 .0545 

.214 2.10 .0843 

0.134 2.56 0.0440 

.098 2.33 .0269 

.122 1.68 .0384 

.117 1.95 .0355 

.154 2.08 .0551 

0.121 1. 71 0.0387 

----- ---- ------ .203 1.58 .0804 

.137 1.41 .0469 

.188 1.37 .0728 

0.117 2.23 0.0374 

.102 1.85 .0295 

.103 1.93 .0299 

.110 1.33 .0335 

.182 1.25 .0692 
SUMMARY, DATA FROM RIVERS, CONVEYANCE CHANNELS, AND LABORATORY FLUMES 

Mean Flow Parameters 

and Variables 

S = 0 .0486xlO" U * = 0 .195 fps 

w = 2690 ft ~ = 0.0736 lblft2 

Q = 280,000 cfs v = 1.16x 105 ft2 I sec 

T = 17.2 "C R = 13,862,100 

D=24.3ft F = 0.112 

V = 4.27 fps Cl/i = 21.90 

li = 24.3 ft D50 = 0.41 mm 

S = 0.0486xlii3 u* = 0.234 fps w = 2690 ft ~ = 0.1062 lblft2 

Q = 280,000 cfs v = 1.16xl65 ft21sec 

T = 17.2 "C R = 12,129,300 

D = 35.0 ft F = o .120 

"!:: = 4.27 fps Cl/g = 21.90 

D = 24.3 ft D50 = 0.41 mm 

S = 0.0486xl()3 u* =0.181 fps w = 2690 ft ~ = 0.0637 lblft2 

Q = 280 ,oao cfs v = 1.16x 105 ft2 I sec 

T = 17.2 "C R = 7,856,900 

D = 21.0 ft F = 0.167 K = 4.27 fps Cl/i = 21.90 

D = 24.3 ft D50 = 0.41 mm 

TABLE 11.- Mississippi River- Continued 

770 Feet From Left Bank at River Mile 440 0 - Dunes 

0.88 4.82 0.323 0.067 1.146 6.00 28.92 0.096 28 

.68 4.54 . 368 .081 1. 374 6.36 28.87 .090 30 

.48 3.95 .356 .090 1.671 5.27 20.82 .091 86 

. 28 3.87 .406 .105 1.980 4.64 17.96 .094 144 

.08 2.93 .419 .143 2.143 3.24 9. 50 .093 118 

1370 Feet From Left Bank at River Mile 440.0 - Dunes 

0.87 4. 70 0.254 0.054 1.087 4.90 23.03 0.093 22 

.67 4.48 .296 .066 1.263 5.70 25.54 .087 77 

.47 4.06 .349 .086 1.490 5.14 20.87 .077 8 

.27 3.79 .379 .100 1.620 6.46 24.48 .083 143 

.07 3.08 .456 ;148 1.948 3.72 11.46 .065 95 

1970 Feet From Left Bank at River Mile 440.0 - Dunes 

0.84 4.63 0.239 0.052 1.320 5.14 23.80 0.088 11 

.60 4.48 .327 .073 1.804 7.40 33.15 .089 293 

.36 4.42 .385 .087 2.119 4.92 21.74 .084 405 

.12 3.83 .486 .127 2.690 3.48 13.36 .076 524 

i 

TABLE 12a.- Current meter results, Atrisco feeder canal 

Hot-Film Current Meter 

Mean flow parameter fj and variables YID (z)lg/fi (f~:) ro\ ,r;:f/U (fps) 

Atrisco Feeder Canal, 44 Feet From Left Bank - Dunes 

0.92 1.67 0.126 0.073 0.057 0.034 

S = O.S7xl()3 u* = 0.180 fps .81 1.64 .138 .083 .049 .030 

w = 56.0 ft "[ = 0.063 lblft2 . 70 1.64 .148 .090 .065 .043 

Q = 203 cfs v = 1. 700,.10-s ft21sec .60 1.62 .157 .097 .059 .036 

T = 12.2 "C R = 212,900 .49 1.58 .171 .108 • 065 .043 

D = 1. 77 ft F = 0.132 .36 1.57 .191 .121 .098 .060 

V = 1.60 fps Cl/i = 8.89 . 22 1.56 .217 .138 .090 .058 

.11 1.41 .251 .178 .065 .039 

Atrisco Feeder Canal, 28 Feet From Left Bank - Dunes 

0.95 2.54 0.151 0.060 0.009 0.004 

S = O.S7xl03 u* = 0.185 fps .84 2.43 .189 .078 .OO!i .004 

w = 56.0 ft "[ = 0.066 1blft2 • 74 2.35 .194 .084 .010 .004 

Q = 203 cfs v = 1. 714x1o-s ft21sec .64 2.30 .207 .090 .014 .006 

T = 10.8 •c R = 281,700 .54 2.02 .202 .100 .043 .020 

D = 1. 86 ft F = 0.207 .43 2.06 .227 .110 .069 .032 

v = 2.09 fps Cl/g= 11.30 .35 1.86 .234 .126 .139 .078 

.28 1. 75 .268 .153 .117 .067 

.16 1.55 .318 .205 .137 .098 

Atrisco Feeder Canal, 12 Feet From Left Bank - DlUles 

0.91 2.31 0.126 0.054 0.061 0.026 

S = O.S7x10° u* := 0.160 fps .80 2.25 .135 .060 .046 .020 

w = 56.0 ft "[ = 0.049 1blft2 .71 2.28 .143 .063 .036 .016 

Q = 203 cfs 11 = 1.682xlo-s ft21sec .59 2.28 .161 .070 .045 .020 

T = 13.3 •c R = 227,400 .48 2.11 .168 . 079 .059 .028 

D = 1. 39 ft F = 0.315 .41 2.12 .174 .082 .065 .031 

V = 2.11 fps Cl/g= 13.19 • 30 1.96 .179 .091 .084 .043 

.21 1.72 .198 .114 .087 .051 

.10 1. 37 .214 .156 .087 .064 

(fps) 

0.117 1.63 0.0377 

.130 1.60 .0427 

.184 1. 74 .0709 

.192 1.66 .0738 

.166 1.44 .0620 

0.121 1.47 0.0387 

.171 2.25 .0971 

.263 4.05 .1106 

.182 2.68 .0696 

.263 2. 73 .1106 

o. 248 2. 37 0.1043 

.108 1.59 .0328 

.272 1. 74 .1158 

.228 1.64 .0945 

B65 
B66 TURBULENCE IN WATER 

TABLE 12b.- Current meter results, Rio Grande conveyance channel 

Hot-Film Current Meter 

Mean flow parameter 

and variables Y/D u Q ja/u a l aj- (fps) (fps) u 2 (~ps) ,;2 u 

Rio Grande Conveyance Channel, 34 Feet From Left Bank - Dunes 

0.96 2.83 0.125 0.044 0.017 0.006 

.86 2.86 .154 .054 .028 .010 

S = 0,55xl<i3 u. = 0.214 fps • 76 2.85 .191 .067 .048 .017 

w = 68.0 ft T = 0 .105 lb/ft2 .66 2. 73 .202 .074 .127 .046 

Q = 510 cfs v = l.635xlO- 5ft2/sec .57 2. 70 .232 .086 .143 .053 

T = 17.2 •c R = 674,900 .47 2.62 .259 .099 .120 .044 

D = 3.07 ft F = 0.256 .36 2.52 .242 .096 .141 .056 

V = 2.68 fps c;lg = 12.53 .25 2.21 .256 .116 .159 .072 

.18 2.11 .279 .132 .136 .066 

.12 2.02 .323 .160 .158 .086 

Rio Grande Conveyance Channe 1, 16 Feet From Left Bank - Dunes 

0.94 2.59 0.140 0.054 0.051 0.020 

.84 2.47 .158 .064 .059 .024 

S = 0.55x103 u. = 0.214 fps • 76 2.44 .151 .062 .107 .042 

w = 68.0 ft T " 0.114 lb/ft2 .66 2.66 .173 .065 .171 .062 

Q = 510 cfs v = l.664xio-Sft2/sec .58 2. 75 .215 .078 ----- ----- T = 11. s •c R = 685,,100 .47 2.64 .201 .076 .194 .073 

D = 3. 31 ft F = 0.230 .37 2.50 .200 .080 .121 .048 

V = 2.68 fps c;li = 12.53 .28 2.36 .217 .092 .100 .043 

.18 2.17 .206 .095 .106 .048 

.11 1.86 .193 .104 ----- ----- .09 1.67 .184 .uo .211 .129 

Rio Grande Conveyance Channel, 52 Feet From Left Bank - Dunes 

0.96 1.53 0.139 0.091 0.435 0.271 

.86 l. 78 .185 .104 ----- ----- s = o.ssx1<i 3 u. = 0.214 fps • 78 1.94 .322 .166 .392 .202 

W= 63.0 ft T = 0.109 lb/ft2 .68 1.81 .348 .192 . 375 .206 

Q = 510 cfs \1 = 1.6Sx10- 5 ft2/sec .58 2.16 ,488 .226 .679 . 314 

T = 15.6 •c R = 444,200 .49 1.82 .480 .264 .469 .261 

D = 3.18 ft F = 0.168 .40 1.58 .426 .270 ----- -----

V = 2.68 fps c;lg = 12.53 .30 1.50 .474 . 316 .292 .194 

.18 1.53 .496 .324 ----- -----

.09 1.53 .468 • 306 .312 .202 

.08 1.46 .153 .lOS ----- -----

TABLE 12c.- Current meter results, Mississippi River 

Hot-Film Current Meter 

Mean flow parameter Y/D u t:f la;u ~I G/U and variables (fps) (fps) u2 (fpsJ u2 

Mississippi River, 770 Feet From Left Bank, River Mile 440.0 - Dunes 

S = 0.0486xJ{j3 u. = 0.195 fps 0.88 4.82 0.223 0.047 0.512 w = 2690 ft T = 0,0736 lb/ft2 .~8 4.54 .268 .059 .342 Q = 280,000 cfs v = 1.63Sxl0- 5ft2/sec .48 3.95 .326 .083 .576 T = 11.2 •c R = 13,862,100 .28 3.87 .386 .100 .441 D = 40.0 ft F = 0,112 .08 V = 4.27 fps C//g = 21.90 

2.93 .419 .143 .541 

Mississippi River, 1370 Feet From Left Bank, River Mile 440.0 - Dunes 

S = 0. 0486xi<i3 u. = 0.234 fps 0.87 4. 70 0.254 0.054 o. 383 

w = 2690 ft T = 0,1062 lb/ft2 .67 4.48 .296 .066 .575 

Q = 280,000 cfs v = l.63Sxlo- 5ft2 /sec .47 4.06 .349 .086 .514 T = '17.2 •c R = lt,l29,300 .27 3. 79 . 379 .100 . 757 

D = 35.0 ft F = 0.120 .07 3.08 .456 .148 .545 

V = 4.27 fps c;lg = 21.90 

Mississippi River, 1970 Feet From Left Bank, River Mile 440.0 - Dunes 

S = 0.0486xl63 

w = 2690 ft 

Q = 280,000 cfs 

T = 11.2 •c D = 21.0 ft 

V = 4.27 fps 

u. = 0.181 fps 

T = 0,0637 lb/ft2 

v = 1.63Sx10- Sft2/sec 

R = 7 ,556;900 

F = 0.167 

c;lg = 21.90 

0.84 

.60 

.36 

.12 

4.63 

4.48 

4.42 

3.83 

0.199 0.043 

. 327 .073 

.385 .087 

.486 .127 

0.518 

.637 

.830 

.888 

Mississippi River, 1055 Feet From Left Bank, River Miles 441.6 - Dunes 

0.103 

.073 

.132 

.Ill 

.180 

0.078 

.131 

.117 

.192 

.168 

0.109 

.135 

.188 

.243 

S = 0.0241X10- 3 u. = 0.216 fps 0.88 4.43 0.221 0.050 0.293 

Q 

w 

= 

= 

325,000 

2000 ft 

cfs v 

T = 

= 

0,0901 

1.63x1o-s 

1b/ft2 

ft2/sec .48 

.68 

4. 

4.87 

73 .393 

.336 .069 

,083 

.813 .168 

.494 I·~ D 

T = 

= 50.9 

17.2 "C 

ft 

R 

F = 

= 

0.097 

21,982,800 .28 

.08 3.58 

4.15 .486 .117 

.523 .146 

1.156 

. 734 I :g~ .209 V = 3.20 fps c;lg = 11.61 

Mississippi River, 1755 Feet From Left Bank, River Mile 441.6 - Dunes 

S = 0.0241X10-3 u. = 0.225 fps 0.88 4.08 0.216 0.058 0.647 0.140 

w = 2000 ft T = 0,0976 1b/ft2 .68 4.18 .297 .071 • 701 .163 

Q = 325,000 cfs v = 1. 63Sxlo- 5ft2 /sec .48 3. 71 .319 .086 .634 .149 

T = 17.2 •c R = 20,172,400 .28 3.52 .384 .109 .427 .110 

D = 65.0 ft F = 0.079 .08 2.51 .344 .137 .571 .181 

V = 3.20 fps c;lg = 16.11 

-tr u.s. GOVERNMENT PRINTING OFFICE: 1973 o-543--579/26