Velocity-Head 

Coefficients in 

Open Channels

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1869-C

Prepared in cooperation with the 

California Department offf^ater 

Resources t <, / ' L

WVelocity- Head 

Coefficients in 

Open Channels

By HARRY HULSING, WINCHELL SMITH, and ERNEST D. COBB

RIVER HYDRAULICS

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1869-C

Prepared in cooperation with the 

California Department of Water 

Resources

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

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

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

Washington, D.G. 20402 - Price 25 cents (paper cover)
CONTENTS

Page

Symbols_____________________________________________________ iv

Abstract_____________________________________________________ Cl

Introduction._______________________________________________ 1

Purpose and scope ________________________ 1

Acknowledgments. ________________________________________ 2

Definition of kinetic-energy coefficient_____________________________ 2

Sources of velocity data._____________________________ 3

Two-point (0.2d/0.8<f) velocity method. _ ________________ 3

One-point (0.6<£) velocity method____ _ __ _ ___ _____ _ __ 3

Multiple-point velocity method______________________________ 3

Computation procedures_________________________________________ 4

Arithmetic method__________________________________________ 4

Graphic method_______________________________________________ 4

Computer program.___________________________________________ 4

Comparison of alpha determined graphically and arithmetically _____ 7

Types of cross sections.________________________________ 8

Discharge measurements used_______________________________________ 8

Multiple-point velocity measurements_________________________ 8

Two-point (0.2d/0.8cO velocity measurements _______ ___ ________ 9

One-point (0.6d) velocity measurements__________________ 9

Analysis of variations of alpha...______________________ 9

Range of alpha________________________________ 9

Relation of alpha computed from multiple-point velocity measurements to alpha computed from two-point (0.2d/0.8d) velocity

measurements_________________________________ 11

Relation of alpha computed from multiple-point velocity measurements to alpha computed from one-point (0.6<£) measurements. ... 12

Correlation of alpha with roughness coefficient..______________ 12

Other correlations studied...______________________ 12

Recommendations for determining alpha...._______________ 15

Trapezoidal channels___________________________ 15

Channels with overflow sections.____________________ 15

Comparison with present method of computation__ _______ _ 17

Summary and conclusions..__________________________. 18

Selected references______________________._______ 20

Basic data__________________..._______________________ 21

ILLUSTRATIONS

Psee

FIGURE 1. Sketch illustrating computation of alpha by arithmetic integration_ __ . ._ C5 

2. Graph showing alpha values computed graphically compared

with alpha values computed by arithmetic integration.... 8

m
IV CONTENTS

Page 

FIGURE 3. Typical complex cross sections, Pit River near Bieber, Calif__ ClO

4. Graph showing relation of alpha computed from multiplepoint velocity observations (a) to alpha computed from 

0.2d/Q.8d velocity observations (a0 .2d/o.8d)----------------- 11

5. Graph showing relation of alpha computed from multiplepoint velocity observations (a) to alpha computed from 0.6d 

velocity observations (ao.ed)___________________________ 13

6. Graph showing correlation between alpha and Manning's

roughness coefficient (n)_______________________________ 14

7. Graph showing comparison of alpha computed from multiplepoint velocity discharge measurements in complex cross 

sections compared with alpha computed from equation 5, 

assuming the alpha value to be 1.00 in each subsection.... 18

8. Graph showing comparison of alpha computed from multiplepoint velocity measurements of discharge in complex cross 

sections with alpha computed from equation 5, in which 

alpha in each subsection has been computed from table 3__ 19

TABLES

Page 

TABLE 1. Coefficients for standard vertical-velocity curve_______. C7

2. Summary of alpha coefficients for various types of cross sections.... ____________________________________________ 10

3. Alpha coefficients, as based on n values___________.____ 14

4. Multiple-point velocity discharge-measurement data.________ 22

5. Two-point (0.2d/0.8d) velocity discharge-measurement data_ 27

SYMBOLS

A Cross-sectional area, in square feet.

AA Incremental cross-sectional area.

D Depth of water at point of observation, in feet.

d Distance from water surface to point of observation.

F Froude number.

g Gravitational acceleration=32.16 feet per second per second.

K Conveyance 486

n

n Manning's roughness coefficient. 

P Wetted perimeter, in feet. 

Q Discharge, in cubic feet per second. 

R Hydraulic radius, in feet. 

V Mean velocity in a section, in feet per second. 

v Point velocity. 

w_ _ Unit weight of water.

X, Y Coordinates of the centroid of flow relative to water's edge and water 

surface, respectively.
W- - C

Subscripts

0.2d/0.8d

CONTENTS

Denotes the mean in a cross section.

Maximum value.

Denotes that figure was derived from measurements based on multiplepoint velocity observations.

Denotes velocities or computations based on velocities observed at 

points 0.2 and 0.8 of the stream depth below the water surface.

Denotes velocities or computations based on velocities observed at 

points 0.6 of the stream depth below the water surface.

RIVER HYDRAULICS

VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS

By HARRY HULSING, WINCHELL SMITH, and ERNEST D. COBB

ABSTRACT

This report presents the results of a detailed study of the velocity-head coefficient, alpha, in natural channels. It is based upon an analysis of point velocities 

obtained from discharge measurements made by the multiple-point method or 

by the two-point (0.2d/0.8<£) method.

Computed values of alpha ranged from 1.03 to 4.70; the median value for 

trapezoidal channels was 1.40. Variation in the horizontal distribution of 

velocity is shown to have a greater effect on the value of alpha than variation in 

the vertical.

For channels without overbank flow, a significant correlation is shown between 

alpha and channel roughness, as expressed by Manning's n; no significant correlations were established with other channel or flow parameters. For channels 

with overbank flow, a rational method of estimating alpha is presented, based on 

Manning's n and on channel conveyance, K.

INTRODUCTION

PURPOSE AND SCOPE

Measurement of discharge in open channels is performed routinely 

by use of a current meter, but during flood periods, discharge frequently must be determined by such indirect methods as slope area, 

flow through culverts or bridges, and flow over dams. The hydraulic 

formulas used in these methods require an evaluation of the kinetic 

energy (velocity head) of the flowing water. This evaluation is based 

on the mean velocity of flow. Use of the mean velocity, however, 

will always result in a computed value for kinetic energy that is too 

low; to determine the true kinetic energy, a coefficient must be applied. 

The derivation of the kinetic-energy coefficient, alpha, is explained 

hi the section "Definition of Kinetic-Energy Coefficient."

The purpose of this study is to provide a means whereby the 

kinetic-energy coefficient can be evaluated on the basis of channel 

cross-section parameters. The results presented herein are based on 

an analysis of point velocities obtained from current-meter measurements of discharge in streams and canals. The measured discharges 

ranged from 1.1 cfs (cubic feet per second) to 636,000 cfs.

Cl
C2 RIVER HYDRAULICS

ACKNOWLEDGMENTS

The study described in this report was done under a cooperative 

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

Department of Water Resources. Work was performed under the 

general direction of Walter Hofmann, district chief, Water Resources 

Division, U.S. Geological Survey, Menlo Park, Calif.

Programing assistance furnished by Mr. W. L. Isherwood, U.S. 

Geological Survey, Washington, D.C., was invaluable, as was technical assistance given by Mr. S. E. Rantz, U.S. Geological Survey, 

Menlo Park, Calif. The cooperation of many district offices of the 

U.S. Geological Survey in furnishing multiple-point velocity measurements of discharge and other pertinent data is also gratefully 

acknowledged.

DEFINITION OF KINETIC-ENERGY COEFFICIENT

Streambed roughness, irregularity of channel-bank and bed configuration, curved channel alinement, upstream obstructions, and 

perhaps other factors cause the velocity in a given cross section of 

a stream to vary from point to point. Because of this variation in 

velocity, the velocity head, or the kinetic energy per pound of water,

V2 

is greater than the value computed from the expression, ^ > where V

^9

is the mean velocity in the cross section. This is true because the 

square of the average velocity is less than the weighted average of 

the squares of the point velocities. The true velocity head may be

V2 

expressed as ^~ > where alpha is the energy-head coefficient, or ^9 

Coriolis coefficient, so named in honor of G. Coriolis, who first proposed

it in 1836.

The derivation of kinetic-energy coefficients is described in most 

standard hydraulics texts. The following explanation is quoted from 

Chow (1959, p. 28):

Let AA be an elementary area in a cross section A, and w the unit weight of 

water; then the weight of water passing AA per unit time with a velocity v is

AA wvAA. The kinetic energy of water passing AA per unit time is wiP -* This ^9

v2 

is equivalent to the product of the weight wvAA and the velocity head jj The *g 

AA total kinetic energy for the whole area is equal to Suw8 -~ ^9

Now, taking the whole area as A, the mean velocity as V, and the corrected

 572 ys

velocity head for the whole area as a K-> the total kinetic energy is aAw 5 "Q "Q 

AA Equating this quantity with Zwv3 -^- and reducing:
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C3

(1)

SOURCES OF VELOCITY DATA

The basic data for this study consisted of point velocities obtained 

from measurements of discharge in streams and canals throughout 

the conterminous United States. In making a discharge measurement, a cross section of the stream is first divided into about 25 

subsections. The mean velocity in a vertical line in the center of 

each subsection then is obtained, after which, the discharge in each 

subsection is computed by multiplying each mean velocity by the area 

of its respective subsection. The total discharge of the stream is then 

obtained by summing these incremental discharges. The measurements of width and depth required to obtain the area of a subsection 

are straightforward. The mean velocity in each vertical can be 

determined by several methods. Generally, either the two-point or 

the one-point method is used; but if more precise definition is desired, 

the multiple-point velocity method is used.

TWO-POINT (0.2ef/0.8ef) VELOCITY METHOD

The method most commonly used for determining mean velocity 

in a vertical section is the two-point (Q.2d/Q.8d) method, which 

requires that point velocities be obtained at points 0.2 and at 0.8 of 

the stream depth below the water surface in each vertical. Distribution of the velocity in a vertical is usually parabolic and such that 

the average of the velocities,, measured at these two points, yields 

the mean velocity in the vertical. A complete two-point discharge 

measurement will include about 50 observations of point velocity.

ONE-POINT (0.6ef) VELOCITY METHOD

In this method only one point velocity at 0.6 of the depth is obtained 

at each vertical. Experience and theory demonstrate the velocity 

at 0.6 depth is, on the average, a good measure of the mean velocity 

in the vertical. This method will include about 25 point-velocity 

observations in each discharge measurement.

MULTIPLE-POINT VELOCITY METHOD

In the multiple-point velocity method a series of velocity observations at points fairly evenly distributed between the water surface

223-866 66 2
C4 RIVER HYDRAULICS

and the streambed is made in each vertical. This generally entails 

point-velocity observations at each 0.1 of the depth, but if the stream 

is deep enough, additional readings at the 0.05 and 0.95 depths are 

obtained. Depth is a factor because the current meter, when suspended on a cable above a sounding weight, can be placed no closer 

to the streambed than the distance from the meter to the bottom of 

the sounding weight. Furthermore, velocity observations are never 

made with the meter placed within a few tenths of a foot of either the 

water surface or streambed because the characteristics of the meter 

are such that it does not measure point velocities accurately in those 

circumstances. The mean velocity in the vertical is computed by 

weighting each observed velocity in proportion to the vertical increment which it represents. A discharge measurement made by this 

method will include about 250 point-velocity readings in the river 

cross section.

COMPUTATION PROCEDURES

ARITHMETIC METHOD

The alpha coefficient can be computed by arithmetic integration of 

equation 1. All that is needed is several point-velocity readings and 

their respective incremental areas.

Each velocity is assumed to be applicable to the incremental area 

surrounding it that is, the area enclosed by boundaries one-half the 

distance to the point velocity above and below it and to the right and 

left of it (fig. 1). Accuracy of the computation increases correspondingly with the number of point-velocity observations in the measurement.

GRAPHIC METHOD

In the graphic method, point velocities are plotted on a diagram of 

the stream cross section. Lines of equal velocity (isovels) are drawn, 

and the area enclosed by adjacent isovels is determined. Alpha is 

computed by applying equation 1, using the area between isovels 

for AA, and the average of adjacent isovels for v.

The reliability of the graphic method is subjectively affected by the 

manner in which isovels are drawn and by the magnitude of the selected 

difference between adjacent isovels.

COMPUTER PROGRAM

Both the arithmetic-integration and graphic methods were tried, 

using conventional office equipment. The graphic method proved to 

be extremely slow and costly. More than 2 man-days per computation were required. The arithmetic method, using a desk calculator, 

reduced this time by half; but with the quantity of data that needed 

processing, even this method was too slow. The obvious approach
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C5

\ V V

1

,-L,-.

' d i

\

<r-L2 ->

} 1> V /

AA-

 point-velocity 

observation

and a =

AA

where A = S A A

FIGURE 1. Computation of alpha by arithmetic integration.

was to program the arithmetic-integration method on an electronic 

computer. This was done for the Burroughs 220 computer.

The computer program was written so that alpha coefficients were 

computed by use of point velocities and related incremental areas. 

This resulted in the following computational procedures each of which 

was dependent on the number of point observations made in the 

vertical:

1. Eleven velocity observations in each vertical (multiple-point 

velocity measurement).

2. Two velocity observations in each vertical (0.2d/0.8d measurement).

3. One velocity observation in each vertical (O.Qd measurement).

From multiple-point velocity measurements three independent 

alpha coefficients could be obtained, because such measurements 

included observations at the 0.2d, Q.Qd, and Q.Sd. This is an important feature that will be discussed later in this report.

The decision was made to use an electronic computer, and the 

project was consequently expanded to include not only the computation 

of alpha coefficients but also the determination of various other 

parameters that might be used in correlation and peripheral studies 

of velocity distribution in natural channels. The computer was 

programmed to determine the following items:

A Cross-sectional area.

a Alpha coefficient, based on multiple-point velocity observations. 

Alpha coefficient, based on velocity observations made at 

0.2/0.8 depths in each subsection.

«o.2d/0.8d
C6 RIVER HYDRAULICS

o0 M Alpha coefficient, based on velocity observations made at

0.6 depth in each subsection. 

B Stream width. 

COM Co.Kd Velocity-profile coefficients; subscript indicates ratio of

observation depth to total depth, measured from the

water surface.

P Wetted perimeter. 

Qn, Vn Discharge and mean velocity, based on multiple-point

velocity observations. 

Qo.2d/o.sd>Vo.M/o.sd Discharge and mean velocity, based on velocity observations

made at 0.2 and 0.8 depths in each subsection. 

QO.MI VOM Discharge and mean velocity, based on velocity observations

made at 0.6 depth in each subsection. 

R Hydraulic radius. 

"X, Y Coordinates of the centroid of flow, as measured from the

water surface and one bank.

Discharge measurements are very often made under conditions 

where the flow is not perpendicular to the selected cross section. 

To get the correct discharge, a horizontal-angle correction is applied 

to the velocity at each vertical. This is satisfactory for discharge 

computations, but where energy considerations are involved, the 

application of the horizontal-angle correction results in an erroneous 

evaluation of kinetic energy. For example, the kinetic energy for a 

flow at some given stage and discharge in a uniformly shaped channel 

has a unique value. Different values of mean velocity and alpha 

would be computed if measurement cross sections at various angles 

to the current were used, and if horizontal angle coefficients were 

applied to the velocities. Because of the complications associated 

with angularity of the current where variable horizontal angles are 

present, discharge measurements that included skewed currents in 

more than 10 percent of the subsections were excluded from this 

study.

The computation procedure used with data obtained from multiplepoint velocity measurements of discharge required complete data for 

every vertical in the cross section. The inclusion of routines to fill 

gaps in the array of velocity data was consequently a major factor in 

the computer program.

The following procedure was used. Data for each vertical were 

examined by the computer to determine whether all 11 velocity values 

w^ere present. If fewer than 11 values in the array were known, 

the missing items were supplied by the computer, which used a 

selected routine that was dependent on the actual number of observed 

point velocities. A primary requirement was that the data had to 

include, as a minimum, VQ .M or VQ.M, and v0£d.

Two general computation processes were used. If three, or fewer, 

velocity observations were made in a vertical, the arithmetic mean 

was computed from the available data; all other points in the vertical 

were computed as the product of this mean and the standard vertical-
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C7

velocity curve coefficient included in the program. These coefficients were derived from 48 multiple-point velocity measurements 

that were complete in every detail. The vertical-velocity curve 

coefficients derived from these data are given hi table 1.

TABLE 1. Coefficients for standard vertical-velocity curve

Ratio of observation depth 

to depth of water

0.05 __________

.1 __ ____________

.2 _______________

.3____________.__

.4 ____ _________

.5 _______________

.6 ________ _ _

.7 ___ __ ___ -__

.8 ____ _____ __

.9____-___.______

.95 _____ _______

Ratio of point 

velocity to mean 

velocity in the 

vertical

1.160

1.160

1.149

1.130

1.108

1.067

1.020

.953

.871

.746

.648

If more than three observations were made, each item was examined and those values missing from the array were inserted by a 

process of interpolation whereby the observed velocities were weighted 

in accordance with an average velocity distribution. The reliability 

of the computed value of alpha is, to some degree, dependent on the 

completeness of data supplied. Most multiple-point velocity measurements were complete, however, except for those shallow subsections 

where limitations of the measuring equipment precluded precise 

definition of the vertical distribution of velocity. Probably very 

little bias resulted from using these procedures in completing the 

array of point velocities in the vertical.

COMPARISON OF ALPHA DETERMINED GRAPHICALLY AND 

ARITHMETICALLY

Arithmetic accuracy of the computer program was verified by 

manual computation of simplified measurements. The results obtained by graphic procedures were compared with those obtained 

by arithmetic integration performed by desk calculator or by the 

computer (fig. 2).

The results agree closely, although the coefficients computed by 

the graphic method averaged about 1.5 percent higher than those 

computed by the machine, probably owing to the difference in treatment given to the bottom velocities in each vertical and to the subjectivity involved in the graphic procedure. In figure 2 the departures 

shown are within an allowable tolerance, verifying the assumption 

that equivalent computations can be made by either method.
C8 RIVER HYDRAULICS

2.0

-'

(3

5 1.6

I

1.4

1.2

/ 

/

/

r

/ 

1.0 1.2 1.4 1.6 1.8 2.0 

ALPHA (a), COMPUTED GRAPHICALLY

FIGURE 2. Alpha values computed graphically compared with alpha values 

computed by arithmetic integration.

TYPES OF CROSS SECTIONS

The cross sections and channels represented by the measurements 

(given in "Basic Data" section) were classified into five types.

1. Type A: A natural trapezoidal-shaped channel without overbank 

flow and no bridge piers or other manmade obstructions.

2. Type B: A natural channel with bridge piers, abutments or manmade obstructions which may affect the flow pattern.

3. Type C: A canal or manmade channel without overbank flow.

4. Type D: Same as type A, but with overbank-flow sections.

5. Type E: Same as type C, but with overbank-flow sections.

DISCHARGE MEASUREMENTS USED

MULTIPLE-POINT VELOCITY MEASUREMENTS

A large group of multiple-point velocity measurements was available from an Operations Research project conducted by the Washing-
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C9

ton, D.C., office of the U.S. Geological Survey in 1959. These 

measurements were augmented by additional data from various other 

projects. Alpha coefficients were computed for 173 of these multiplepoint velocity measurements. Computed discharge ranged from 1.1 

cfs to 636,000 cfs, and mean velocity ranged from 0.41 to 10.44 fps 

(feet per second). Table 4 gives the station name and location and 

pertinent data for each measurement; the type of cross section is 

also indicated.

Plan views of the measuring sites and roughness coefficients (Manning's ri), selected in the field, were obtained for each measurement 

through the cooperation of personnel responsible for the measurements. 

From the plan views, the length of tangent from the first upstream 

bend and the degree of curvature of this bend were determined.

TWO-POINT (0.2d/0.8d) VELOCITY MEASUREMENTS

In addition to the multiple-point velocity measurements, alpha 

coefficients were computed for 721 discharge measurements made by 

the usual Q.2d/Q.Sd-depth method. These measurements were 

selected to represent a wide variation in channel characteristics and 

in discharge at each site. Comparision of alpha with variations in 

roughness, discharge, velocity, and the various geometric channel 

parameters was thus possible. These measurements had a range 

in discharge from 12.3 to 505,000 cfs and a range in velocity from 

0.27 to 11.37 fps. Roughness coefficients (Manning's ri) were selected 

for each site, usually by on-site inspection, although a few were 

selected from pictures. Some complex cross sections (see fig. 3) 

were divided into subsections, and n values were selected for each 

subsection. Table 5 contains the name, location, type of cross 

section, and other pertinent data for each 0.2c£/0.8<2-depth velocity 

measurement. The formula used for the computation of alpha gave 

equal weight to velocity observations at the 0.2-depth and 0.8- 

depth positions.

ONE-POINT (0.6ef) VELOCITY MEASUREMENTS

None of the discharge measurements selected for analysis was made 

by the O.Qd method. By abstracting the Q.Qd observations included 

in the discharge measurements made by the multiple-point velocity 

method, however, 173 one-point velocity measurements were obtained 

for use in computation of alpha coefficients (a0 .6d).

ANALYSIS OF VABIATIONS OF ALPHA 

RANGE OF ALPHA

Table 2 summarizes the maximum, minunum, and median values 

of alpha determined for each type of cross section. This table
CIO RIVER HYDRAULICS

Index No. 

912

10

IU

u.

I ° 

I

LJ

Q 5

10

1 7i = 0.065 11

914

916

918

n = 0.060

a = 1.82 

ax = 1.24 

a. = 1.97

n = 0.055

a = 1.46 

ax = 1.31 

a« = 2.01

n = 0.050

5 -

10 -

40 80 120 160 

DISTANCE, IN FEET

200 240

FIGURE 3. Typical complex cross sections, Pit River near Bieber, Calif.

includes the results obtained from all multiple-point velocity and 

two-point (0.2d/0.8cO velocity measurements. The alpha coefficients 

computed for the 0.2d/O.Sd measurements were adjusted by the 

equation next described.

TABLE 2, Summary of alpha coefficients for various types of cross sections

Type of cross section

A___. ________________

B.__.._. -.-___._._.__

C________--_-_______-

D _________ _ _ .__

E _____ .... ________

Number of 

measurements

402 

97 

73 

170

8

Alpha coefficient (a)

Minimum

1.09 

1. 06 

1.03 

1. 18 

1. 10

Maximum

2.90 

4.70 

1.76 

2.99 

1.32

Median

1.40 

1.45 

1. 10 

1.46 

1. 14
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS Cll

RELATION OF ALPHA COMPUTED FROM MULTIPLE-POINT

VELOCITY MEASUREMENTS TO ALPHA COMPUTED FROM

TWO-POINT (0.2ef/0.8ef) VELOCITY MEASUREMENTS

Multiple-point velocity measurements made in types A and C cross 

sections were studied first. A highly significant correlation was found 

to exist between the values of alpha computed from multiple-point 

velocity observations (a) and those of alpha computed solely on the 

basis of the Q.2d/Q.8d observations (a0 . Zd/0 , Sd ), which were abstracted 

from the complete array of point velocities (fig. 4). The regression

2,0

1.8

1.6

1.4

1.2

1.0

ec = 0.985 « o.a<*/o.8it+ 0-057

1.0 1.2 1.4 

ALPHA 0.2.0,8 («0.

1.6 1.8

FIGURE 4. Relation of alpha computed from multiple-point velocity observations 

(a) to alpha computed from 0.2d/0.8d velocity observations

equation is

(2)

The correlation coefficient is 0.999, which is significant at the 

1-percent level. The establishment of this relation was very impor223-866 66 3
C12 EIVEE HYDEAULICS

tant because it permitted the use of an almost limitless quantity of 

data fin the form of the conventional 0.2d/0.Bd discharge measurements) for detailed study of the relation between alpha and the 

various channel and flow parameters.

RELATION OF ALPHA COMPUTED FROM MULTIPLE-POINT

VELOCITY MEASUREMENTS TO ALPHA COMPUTED FROM

ONE-POINT (0.6<f) MEASUREMENTS

Again, using only multiple-point velocity measurements made in 

types A and C cross sections, a highly significant relation, shown 

in figure 5, was found to exist between the values of, alpha computed 

from multiple-point velocity measurements and those of alpha computed only from point velocities at the 0.6<Z (a0 .6<0- The regression 

equation is

a=1.43a0 .6 d 0.39.

The correlation coefficient is 0.975, which is significant at the 1-percent 

level.

CORRELATION OF ALPHA WITH ROUGHNESS COEFFICIENT

The only channel parameter that correlated significantly with 

alpha was the roughness coefficient n. This correlation (fig. 6) is 

based upon 371 discharge measurements made in types A and C 

cross sections. The correlation coefficient is 0.504, which is significant 

at the 1-percent level. The regression equation is

a= 14.8^+0.884.

This correlation is fairly well defined between the n values of 

0.012 (a=1.06) and 0.070 (a=1.92). The scatter of plotted points 

in figure 6 indicates that factors other than n evidently influence the 

value of alpha. The combination of factors that results in values 

greater than 2.00 is not common in problems involving types A and C 

cross sections; therefore, 2.00 should be considered as the maximum 

alpha value for these cross sections.

For convenience, equation 4 is expressed in tabular form in table 3.

OTHER CORRELATIONS STUDIED

Correlations of alpha with 18 different parameters and various combinations of parameters were investigated to explain the scatter of 

points shown in figure 6. The parameters used included hydraulic 

radius, Froude number, maximum velocity, mean velocity, mean 

depth, standard deviation of depths, tangent length, channel curvature, stream width, and various combinations of these. None of the 

correlations with these parameters, either singly or in combination, 

yield statistically significant results. These correlation studies indicated, however, that the large alpha values were associated with cross
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS CIS

2.0

1.8

1.6

1.4

1.2

1.0

a = 1.43 a 0.6<r°-39

1.0 1.2 1.4 1.6 1.8

ALPHA 0.6 ( o 0.6d >

FIGURE 5. Relation of alpha computed from multiple-point velocity observations (a) to alpha computed from 0.6e? velocity observations (00.6,1).

sections in which large variations in velocity occurred horizontally 

across the section in general, those sections with wide flood plains. 

Manipulation of equations 2 and 3 will demonstrate that the horizontal 

distribution of velocity is a dominant factor in the magnitude of alpha. 

The vertical distribution of velocity is of much less significance. This 

can also be demonstrated by a comparison of the empirically defined 

alpha coefficients of this study with the theoretical values which 

Streeter (1942) derived on the basis of the logarithmic law of velocity 

distribution in the vertical.
C14 RIVER HYDRAULICS

TABLE 3. Alpha coefficients, as based on~n values

n 

0.012 _ _____ __

.013 __ _ _______

014

. 015

. 016

.017. _ ________

.018 __ _ ______

. 019

.020 _ _____ ___

.021 __ _ ___ __

.022 _ ____ _____

.025____ _______

.026 __ ___ _____

.027 _ ____ _____

.028 _ _____ _ _

.029. __ .__ _ _

. 030

.031

Alpha 

1.06

1.08

1.09

1.11

1.12

1.14

1.15

1.17

1.18

1.19

1.21

1.22 

1.24

1.25

1.27

1.28

1.30

1.31

1.33

1.34

n 

0. 032____________

.033_ __ _______

.034. _ ________

.036 _ _________

.037 ___ _ ___ _

039

040

041

.042

.043 _ _________ 

.044 ___ _______

.046. _ __ _ ___

.048___ ____ __

050

.051 _ .__ ______

Alpha 

1.36

1.37

1.39

1.40

1.42

1.43

1.45

1.46

1.48

1.49

1.51

1.52 

1.54

1.55

1.56

1.58

1.59

1.61

1.62

1.64

n 

0.052 _ _________

.053 _ _________

0^4-

.056 _ _________

058

f|CQ

.061 _ -_. _ ___

.063 ____ ______ 

.064 _ _________

066

067

.068 __ ________

.069 _ _________

.070 _ -_-_-___.

Alpha 

1.65

1.67

1.68

1.70

1.71

1.73

1.74

1.76

1.77

1.79

80

82

83

1.85

1.86

89

91

92

i__________ 2.00

FIGURE 6. Correlation between alpha and Manning's roughness coefficient (ri).

Streeter showed that for wide channels alpha, expressed as a 

function of Chezy's C, ranges from 1.02 (#=180) to 1.12 (Of «65). 

A direct comparison between Chezy's C and Manning's n can be
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS CIS

made by use of the equation C= R1/& , For example, if we assume

a hydraulic radius of 3.0, then for a C of 180 we can compute n=Q.QW, 

and for C of 65 we can compute 71=0.027. For these n values, this 

report gives alpha values of 1.03 and 1.28, respectively, as compared 

with Streeter's 1.02 and 1.12. For very smooth channels, variations 

in velocity, both horizontally and vertically, are small; thus low 

alpha coefficients result. Where roughness increases and the cross 

section becomes irregular, large velocity variations occur, particularly 

in the horizontal direction. The preceding example demonstrated 

this by the large difference between the theoretical coefficient (1.12), 

based on variation in the vertical only, and the empirical coefficient 

(1.28), which reflects both horizontal and vertical variation. Unfortunately, the horizontal velocity variation could not be related to 

any combination of the parameters measured, and use of equation 4 

(see also table 3) is the only means of estimating alpha values for 

simple geometric channels.

RECOMMENDATIONS FOB DETERMINING ALPHA

TRAPEZOIDAL CHANNELS

Equation 4, a=14.8 n-\- 0.884, is recommended for estimating alpha 

for unit-shaped trapezoidal channels (types A and C). Its value 

should be limited to 2.00 despite the fact that greater values will be 

computed when n exceeds 0.075.

CHANNELS WITH OVERFLOW SECTIONS

For a cross section that carries overflow on either or both banks, 

the overflow areas are generally treated as separate units or subsections (fig. 3). To obtain the value of alpha for the entire cross 

section, an individual value of alpha is first determined for each 

subsection by use of equation 4, and a composite value of alpha for 

the entire cross section is then computed by the following equation:

3 ZT3 ZT3 **- 2 I -"-«

-7¥ + Otn-TJ

12

in which the subscripts refer to individual subsections.

Equation 5 is derived from equation 1 as follows: Let Vi, Vz- . . 

Vn, «i, «2 . . . an, and Alt Az . . . An be the mean velocities, 

alpha coefficients, and areas respectively, of the subsections. Let 

V be the mean velocity and A} the cross-sectional area of the entire 

section. From the equations Q=AiVi+AzVz+AnVn and Q= 

the following can be written:
C16 RIVER HYDRAULICS

. . . VnA

and

V= (6)

Equation 5 is obtained by substituting V from equation 6 in equation 

1 and simplifying. 

The following example illustrates the application of this procedure.

Example: Determining alpha for a subdivided type section. 

Given:

©

n = o.o so

- 10 ft > 

(2)

v-/ % = 0.040

1 t 

1 i

in

J

£U K '

Determine alpha:

At =50 sq ft

Pi=18ft 

#!=2.78 ft

2

jR^ssl.98

« 1.486(50)1.98

1 0.030 ' 

.4=70 sq ft

1 o T: I * /\ JLU Al

^2=20 sq ft

P2=12ft

#2=1.67 ft

#2^=1.41

 1.486(20)1.41

K2 0.040 1>0

SK=4904 + 1048=5952

yU4 773

2i=2.88X106

(S.K) 3 5,9523

^2 7Q2 43.0X10<i

From table 3: alpha for n=0.030 is 5.33, and

alpha for n=0.040 is 1.48; accordingly,
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C17

K3 K3

ai ZF +a2 2g_1.33(47.2) + 1.48(2.88) 1 

a~ ~ 43.0

Because the manner in which a cross section is subdivided has a 

pronounced effect upon the magnitude of alpha, use of a consistent 

method in subdividing the cross section in a slope-area reach is 

desirable. Thus, if one cross section of the reach is subdivided, the 

next cross section should be subdivided in the same manner. Computation procedures used for evaluating alpha in complex cross sections 

are, at best, only approximations, and errors introduced by the subdivision process will be minimized if all cross sections in a slope-area 

reach axe subdivided in the same way.

COMPARISON WITH PRESENT METHOD OP COMPUTATION

The need for a method of estimating alpha for use in indirect determinations of discharge has long been recognized by the Geological 

Survey. At present, only limited data summarizing alpha coefficients applicable to open channels are to be found in the literature. 

The most readily available published data are those of King (1954), 

Kolupaila (1956, 1961), and O'Brien and Hickox (1937). The published figures, however, are too generalized to be of much assistance 

in making a reliable estimate of alpha. Lacking more suitable information, hydrologists, including those of the Geological Survey, 

have usually used an alpha value of 1.00 for unit-shaped trapezoidal 

sections and for each subsection of complex channels where equation 

5 has been applied. For most slope-area determinations this assumption has little effect on the computed discharge because the channel 

reaches selected for study are generally fairly uniform in crosssectional area, and velocity head is therefore a minor factor. In 

steep channels that are contracting in area, however, the use of the 

alpha value of 1.00 can lead to an appreciable error in the computed 

discharge.

Figure 7 shows alpha values (ak) for 41 complex sections (type D 

sections) computed from equation 5 by the conventional method, 

where the a for each subsection is assumed equal to 1.00, compared 

with values of alpha derived from multiple-point velocity measurements. Figure 8 shows alpha values (an) for the same group of sections computed from equation 5 by the method recommended in this 

study, where a for each subsection is computed from table 3, compared 

with the alpha values derived from the multiple-point velocity 

measurements. The improved accuracy resulting from the procedure 

recommended in this report is quite apparent.
CIS EIVEE HTDBAULICS

2.2

2.0

^ 1.6

1.4

1.2

1.0 ' _____ 1

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 

ALPHA K (aK )~S (K*/AZ )/

FIGURE 7. Alpha computed from multiple-point velocity discharge measurements 

in complex cross sections compared with alpha computed from equation 5, 

assuming the alpha value to be 1.00 in each subsection

SUMMARY AND CONCLUSIONS

This study demonstrates a reliable method of computing the 

energy-head coefficient, alpha, from conventional current-meter measurements of discharge, hi which velocities are observed at 0.2 and 0.8 

depths in each subsection. It also demonstrates that reasonable 

estimates of alpha for channels having no overflow can be made solely 

on the basis of the Manning roughness coefficient, n. This determination is important because the usually made assumption that the alpha 

value equals 1.00 in a channel with no overflow is greatly in error, 

particularly in the rougher channels. A rational method of estimating 

alpha for channels with overflow sections, based on Manning's n and 

on channel conveyance, K, is also presented in this report.

A major conclusion, illustrated by the study of factors influencing 

the magnitude of alpha, is that variation in the horizontal distribution 

of velocities is of even greater significance than variation in the vertical. 

Accordingly, these authors believe that a more intensive investigation
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C19

2.2

2.0

Q

£ 1.8 r

1.6 r

1.4

/

/

* .

'. £ : 

t 

' 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4- 3.2

ALPHA n (a n )

FIGURE 8. Alpha computed from multiple-point velocity discharge measurements in complex cross sections compared with alpha computed from equation 

5, in which alpha in each subsection has been computed from table 3 (« ).

of factors influencing the horizontal distribution of velocity should be 

included in future studies. Data for this study were obtained from 

standard current-meter measurements, which were usually made at 

sites where roughness was low or in channels that were fairly straight. 

Data did not include information as to the amount of contraction in 

the reach or the significance of obstructions in the reach upstream from 

the point of measurement.

If further study is to be made, the authors suggest that it be done 

under more carefully selected conditions, where various parameters 

can be isolated and studied in detail. Methods should be devised to 

measure the expansion or contraction of the channel, the profile of 

the streambed and the water surface, the slope, and other physical 

characteristics, such as distance upstream to riffles, bends, or other 

obstructions that might affect the velocity distribution in the channel. 

The study of channels that have high roughness coefficients (n values 

of 0.070 or greater) would also be of value.

Routine discharge measurements do not provide enough specialized 

information, and more detailed field surveys will be required to refine 

results beyond that of this report.

223-866 66 4
C20 RIVER HYDRAULICS

SELECTED REFERENCES

Argyropoulas, P. A., 1962, Water surface profiles in irregular natural streams:

Am. Soc. Civil Engineers Proc., v. 88, no. HY3, p. 205-207. 

Bakhmeteff, B. A., 1941, Coriolis and the energy principle in hydraulics: Pasadena, Calif., Theodore Von Karman anniversary volume, p. 59-65. 

Chow, Ven Te, 1959, Open channel hydraulics: New York, McGraw Hill Book

Co., p. 27-29. 

Dalrymple, Tate, and others, 1937, Major Texas floods of 1936: U.S. Geol.

Survey Water-Supply Paper 816, 146 p. 

Johnson, Hollister, 1936, The New York State flood of July 1935: U.S. Geol.

Survey Water-Supply Paper 773-E, p. 233-268. 

King, H. W., 1954, Handbook of hydraulics, 4th ed., revised by E. F. Brater:

New York, McGraw-Hill Book Co., p. 7, 9-13. 

Kolupaila, S., 1956, Methods of determination of the kinetic energy factor:

Calcutta, India, The Port Engineer, v. 5, no. 1, p. 12-18. 

 1961, Water surface profiles in irregular natural streams: Am. Soc.

Civil Engineers Proc., v. 87, no. HY6, p. 271-272. 

O'Brien, M. P., and Hickox, G. H., 1937, Applied fluid mechanics: 1st ed.,

New York, London, McGraw-Hill Book Co., p. 271-273. 

O'Brien, M. P., and Johnson, J. W., 1934, Velocity-head correction for hydraulic

flow: Eng. News-Rec., v. 113, no. 7, p. 214-216. 

Posey, C. J., 1942, Variations in correction factors for pipes and open channels:

Easton, Pa., Civil Eng., v. 12, no. 7, p. 398. 

Streeter, V. L., 1942, The kinetic energy and momentum correction factors for

pipe and for open channels of great width: Civil Eng., v. 12, no. 4, p. 212-213. 

Woodward, S. M., and Posey, C. J., 1941, The hydraulics of steady flow in open

channels: New York, John Wiley & Sons, p. 46-48.
BASIC DATA
TABLE 4. Multiple-point velocity discharge-mea

Index

No. Station and location

Caney Fork near Rock Island, Tenn_____ - 

Big River at Bymesville, Mo_.___--___- 

Pee Dee River at Pee Dee, S.C_. 

Snake Creek at S-29, North Miami Beach, Fla_ 

Shiawassee River near Fergus, Mich__-____

6 Peace River at Arcadia, Fla...____._-_ - . B

7 Saco River at Cornish, Maine__ __._--__- - _ A 

	Rio Grande below Elephant Butte Dam, N. Mex_.. A 

	Clark Fork near Plains, Mont___...__ __ - A

10 Ochlockonee River near Havana, Fla,- ____.. B

11 Conetoe Creek near Bethel, N.C.._____________ B

12 Pearl River at Jackson, Miss_____ __ -___ D

13 Pearl Biver at Edinburg, Miss.. --------------- A

14 Sangamon River at Monticello, 111--_____ . - B

15 Pearl River at Monticello, Miss...--_. ._ - --- B

16 Genesee River at Avon, N.Y...__.._____-. .- A

17 Wabash River at Vincennes, Ind_____ - _-_ . - B

18 Sugar Creek at Milford, HL____-_. -. -- B

19 Vermilion River below Lake Vermilion near Tower, Minn. A

20 Missouri River at Boonville, Mo..______________ B

21 Savannah River near Clyo, Ga. _ ____ __ ___ - A

22 Kanawha River at Charleston, W. Va_____ ______ B

23 Missouri River at Toston, Mont___ _________- _ A

24 Boise River (below Lucky Peak Dam) near Boise, Idaho. D

25 Susquehanna River at Danville, Pa......._ .. __ B

26 White River at DeValls Blufi, Ark...-.__- . ._- B

27 Trinity River at Romayor, Tex__ ____________ B

28 Petit Jean Creek at Danville, Ark.---__. . B

29 Connecticut River at Montague City, Mass._-__ ... A

30 Merrimack River at Franklin Junction, N.H-.._____ A

Angelina River at Horger, Tex____. 

Ohoopee River near Reidsville, Ga.--. 

Nahunta Swamp near Shine, N.C._. 

Saluda River near Greenville, S.C . 

Farmington River at Rainbow, Conn.

Red River at Grand Forks, N. Dak...

Type of

cross 

section 1

Width 

(ft)

127

129

381

111

165

170

250

102

500

320

45

362

118

127

188

572

168

50

1,322

360

918

365

261

1,305

592

195

138

460

227

138

57

127

90

188

Area 

(Sd ft)

1,565

1,080

5,810

1,192

1,212

1,140

3,190

638

6,596

2,173

369

3,418

1,677

873

3,747

2,704

6,125

1,381

346

14, 500

3,481

10,860

1,422

1,945

7,998

17, 570

3,170

1,128

5,383

3,565

4,466

1,332

339

410

649

1,247

Mean

velocity

(fps)

2.11

1.18

1.88

.40

1.20

3.48

2.34

2.74

1.55

1.75

2.08

1.03

.66

2.25

2.28

2.69

.87

.53

3.55

2.08

2.54

2.67

1.78

4.34

1.34

.69

1.88

2.79

3.06

2.08

1.6

2.6

2.6

3.9
37

38

39

4(1

41

49

43

45

46

47

48

49

fiO

51

5?,

53

54

5fi

56

57

58

f>9

<n

fii

fi?,

63

fi4

65

66

67

fi8

fi9

70

71

7?,

73

74

75

76

77

Ail-American Canal (Station 60) near Imperial Dam, 

Ariz.-Calif.

Wolf River, above West Branch Wolf River, near Keshina, Wis

Arkansas River below John Martin Reservoir, Caddoe, 

Colo. 

Cowlitz River near Kosmos. Wash. __ ....... ......

ABBAABOBC

A ABBBAAABBADABoBAADB

T>AAAABABoBDA

132

142

142

266

111

107

18.1

308

213

59

357

153

467

200

130

272

100

179

170

196

694

447

320

112

560

95

264

342

93

512

440

242

135

236

1,154

368

520

26

606

194

168

1,261

752

1,053

2,271

323

529

107

3,501

2,967

155

3,734

636

6,490

454

622

2,928

459

1,227

1,320

472

4,739

3,076

1,013

1,615

2,246

408

5,997

1,980

441

4,318

3,229

1,457

1 flfiQ 1. UUI7

1,444

15, 170

2,436

3,145

81.1

1,767

435

1,422

1.5

3.5

1.7

4.7

1.7

1.3

6.0

2.6

2.5

1.8

2.9

.5

2.4

1.5

2.2

7.0

1.8

.5

.7

2.0

2.2

4.1

2.9

.7

1.6

4.5

4.6

2.7

.7

4.4

2.9

4.0

3.3

2.6

4.3

5.5

1.1

2.0

1.3

2.3

4.1

See footnotes at end of table.
TABLE 4. Multiple-point velocity discharge-measurem

Index 

No. Station and location

Type of

cross 

section 1

Width 

(ft)

Area 

(set ft)

Mean

velocity

(fps)

101

102

103

104

105

106

107

108

109

110

111

112

113

78 Yodkln River at Wilkesboro, N.C. . .......... .. A

79 Sacramento River near Bed Bluff, Calif.. . D

80 Snake .River near Irwin, Idaho. A

81 Schroon River at Riverbank, N.Y____.___ __ A

82 Wabash River at Delphi, Ind__ _ - B

83 Kootenai River near Bonners Ferry, Idaho....__-__.. A

84 Broad River near Bell, Ga____ __....__ ... B

85 Calcasieu River near Oberlin, La . _... . B

St. Croix River near Rush City, Minn__ _ . A

87 Pecos River at damsite 3, near Carlsbad, N. Mex.. . A

North Platte River near Goose Egg, Wyo_____ __ D

Mississippi River at Chester, 111...- ... _ B

90 Missouri River at Pierre, S. Dak.. . .... __ ... A

91 Pudding River at Aurora, Oregon . A

92 Colorado River along Colorado-Utah State Line... _ A

Grond River at Ionia, Mich.._ _ B

94 Wabash River near New Corydon, Ind.. _ A

95 Crooked River near Culver, Oreg_...___ ...__ A

96 Mississippi River at Thebes, 111_ . B

97 Mississippi River at Alton, 111.... --__ ... B

Sangamon River at Mahoment, 111.- . . B

Grand River at Lansing, Mich_ B

100 Bel River at Scotia, Calif_______________-__.. B

Atwater Canal, near Atwater, Calif., site 1. __.....

._.do....._______.__.__.sitel ....___-

.....do_ __.__ ___ site 2.. __ ...

.. do_ __ __ site 2. ...........

. do. sites -. - -.

. do. .. sites .....

.do__.____________ site 4_.___...

.. do_ ............. .site 4.

Arena Canal near Livingston, Calif., site 1.. 

. do. . sitel..

.do..........

.do.........

-do...-... 

._____site 2. 

... . site 2. 

________site 3.

115

512

34.1

82

350

615

201

212

490

124

108

1,769

315

74

321

369

76

108

2,319

1,824

71

205

441

17.2

17.3

16.9

17.3

15.6

16.1

15.9

15.7

17.5

18.0

17.8

17.7

17.8 I

740

2,737

1,942

624

1,579

8,250

1,836

1,548

3,696

233

447

47,040

6,492

360

2,360

3,705

448

950

49,270

46,870

270

1,140

2,056

46.0

46.3

43.2

46.2

36.2

37.3

37.0

36.9

47.0

47.3

46.4

46.1

47.5

2.36

6.40

6.25

2.00

.1.93

3.39

1.74

2.87

1.96

3.18

4.40

5.67

1.62

3.86

2.78

1.13

2.59

4.36

4.08

1.53

2.57

3.18

2.56

2.59

5.92

2.42

3.04

3.08

3.05

3.04

2.57

2.47

2.59

2.58

2.63
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C25

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TABLE 4. Multiple-point velocity discharge-measurem

Index

No.

199

202

203

204

205

206

207

208

ono

211

212

213

1155

1158

1159

1160

1169

1179

Station and location

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

. ....do.. ............ .................. ....... .............

. _ .do... ... _ 

 -do.. . 

 .do.... . _ 

 .do.. .

 .-do.. . .

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

 do..... ........

 do. ...... . ... 

 .do..... 

- .do 

 do. 

Type of 

cross 

section >

D

D

D

D

D

D

Width 

(ft)

3.5

3.5

3.5

3.5

3.5

3.5

3.5

3.5

3.5

3.5

3.5

3.5

353

352

410

354

206

176

Area 

(sq ft)

.6

1.3

1.0

1.2

1.0

1.1

1.1

1.5

.9

.7

.7

.7

880

910

1,110

1,530

854

254

Mean 

velocity 

(fps)

8.35

2.25

1.71

2.17

2.20

3.91

5.73

1.53

3.67

5.28

1.57

3.00

2.08

2.24

2.99

2.25

3.57

1.39

' Definitions of cross-section types is given on p. C8. 2 Subdivided 
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C27

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lOrH CN *!

CM M3 C

CD CO CD CC CD OCN CO 

iOlO 10

223-866 66
TABLE 5. Two-point (0.#d/0.<Sd) velocity discharge-measu

Index 

No.

519 

524

534

635 

539 

542 

544

545

554 

556

657 

559 

560

562 

563

564 

565 

566

567 

568 

569 

570 

671

572 

573 

574 

575 

576

577 

578 

579 

580

Station and location

Big Black River at State Highway 16 near

 .do 

Pearl River at Meek's Bridge, near Canton. 

Miss 

West Fork Tombigbee River at Nettleton,

South Fork American River near Kyburz, 

Calif.- 

 do 

West Fork Tombigbee River near Nettleton,

Miss.

do

 --do. . . 

... ..do..... .

do -

South Fork American River near Camino, Calif. 

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

Klamath River at Somesbar, Calif. ............

 do ... ....... .......... ....... ......... .

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

.... .do... ........ ......... .......... ... .........

 ..do . 

Klamath River near Zlamath, Calif.. ...... 

..... do... ....... . ..................

 do...... ...... ...... .. 

 do... 

District 

No.

339

327 

331

289 

35

56

31 

43 

32 

305 

315

243 

286 

218 

279 

270

20 

31 

27 

46

Type 

of cross 

section

B... ....

B. ......

B-.. 

B... 

B -

B.___-_

B --

B ...

B-......

D ....

A 

B

B 

D

A

A 

A 

A

D 

D

A 

A 

A 

A 

A

A

A 

D 

D

Width 

(ft)

1,360

674 

630

383 

626 

358 

405

570 

640

1,240 

553 

2,000

89

110 

1,255

545 

314 

328

345 

330 

367 

113 

129

160 

170 

201 

220 

246

690 

660 

610 

454

Area 

(sq ft)

9,360

6,990 

4,880

7,690 

13,000 

3,490 

2,860

12,300 

5,750

8,600 

6,100 

59, 300

349

477 

12,600

2,780 

1,760 

2,770

3,430 

4,830 

6,540 

536 

826

877 

1,090 

2,420 

3,550 

5,560

15,100 

9,180 

4,100 

1,660

Mean 

velocity 

(fps)

2.01

2.99 

.87

3.88 

2.50 

1.62 

2.27

2.79 

1.64

3.30 

2.77 

4.03

1.12

2.77 

4.96

2.33 

2.74 

5.99

5.95 

6.60 

7.16 

2.29 

3.17

1.10 

1.75 

4.00 

7.28 

7.84

8.68 

5.76 

3.66 

1.93
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C29

3§?

t- COi-HOO»I>.O-^O»i-H*O Oftt-^CO i-* tO ^i^CC *O t»*O O-** <N COOiCO GCOi t*»<NCOt*rH tOi-iCOCDCO COO 

O i-H t-O OOOQ OO W 33OOO O O i-H«OO

10 c4i-4TfitDujclod>ocoi-H * ' cs 10 co co c4 *<0i-i ^ o> t^ id r-n koeo<M<^^H ^ <N* co co * cdi-icjcoco co co

S3 SSS§||S|§2 2§|=§ S3 S 33§!

as o oocn t*o^i*ocBOc 5 to o (-

0 

&

§11 a" S

 S I 

o i a

\>

°

ft 

!O

!M

> so eo eo eo ^ co co
TABLE 5. Two-point (0.#d/0.Sd) velocity discharge-measu

Index 

No.

636

637

638

639

640

641

643

645

ft!7

648

649

650

651

652

653

654

655

657

658

659

660

662

663

664

665

666 

667

668

669

670

671

672

673

674

676

Station and location

Tule River near Springville, Calif. ...... .......

- do... __ . _ - ___ . _ ...- ...-..-...-

_ ..do..... __ . _ - ___ . _ - __ ...........

 ..do ... ... 

.... .do.... ............ - ..-.. _....

 do-.... _ _ ... 

 do 

..... do... ..... ... ..... ... ....

..... do ... ... 

..... do... . ................ ...

 do........ _ ... ... __ ..........

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

 ..do .... ... ... .... .... ..

South Fork Kern River near Onyx, Calif ......

 do. - _ ..... .......

_ do ... ________ ___ . ___ ..

 .do ... ..... -

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

 .do ..... 

- -do- . __ ... ..... ......

 -do - _ ..... .....

Silver Creek below Camino diversion dam, 

Calif. 

 .do ... ..... ... 

 -do - __ . _ ....... ......... _ .

 do.. ... ..... ..... .... ... ...... ....

. do.. ...

 __do .... ..... ... ..... ......

. do ....

..... do ........ ...... .... ... 

_ ..do.. ... ..... ..... .... . ..... ..... ....

District 

No.

75

26

73

24

12

18

22

246

248

247

186

179

183

185

138

450

490

440

438

439

229

234

222

205

216

25

ID

20

22

23

26

QOQ

291

279

305

Type 

of cross 

section

A

A

A

A

D

D

D

A

A

A

A

A

A

D

A

A

A

A

A

A

D

D

D

D

D 

D

D

D

D

A

D

D

D

D

Width 

(ft)

45

53

53

57

60

72

223

75

81

81

84

85

84

90

282

40

46

51

62

63

58

78

78

104

113

83

7O

O9

91

91

91

140

172

183

209

Area 

(sq ft)

169

177

191

201

211

240

552

265

300

351

396

451

466

587

1,660

93.1

108

156

204

239

306

426

438

544

690

211 

246

265

290

285

322

01 1

409

492

623

Mean 

velocity 

(fps)

2.25

2.76

2.76

3.48

3.95

4.30

5.85

2.79

3.67

3.94

4.82

5.50

5.79

5.10

4.79

.58

1.05

2.44

4.75

5.02

.52

1.42

1.65

2.70

3.91

2.32

2.85

3.36

3.38

3.54

4.07

2.39

2.57

3.01

4.16
677

678

679

680

681

682

683

684

685

686

687

690

691

693

695

696

700

701

702

703

704

705

706

707

708

709

710

711

712

713

714

715

716

717

718

719

721

 -.do.- 

.... .do 

... ..do.... 

.....do .

Big Greek above Pine Flat Reservoir, Calif. 

do 

do 

do

Kings Eiver below North Fork, Calif. 

do.

. do. 

do

.do

.do. 

-do.

Kings River below Pine Flat Dam, Calif., 

. do .

 do... .

.do.

.do.

-do.

-do. 

.do.

.do. 

-do.

-do.

Kings River near Hume, Calif. 

.__do_____________.

-do.

-do.

Fresno River near Dalton. Calif. 

.. do , 

. do.. .. .

.do. 

.do.

.do.

San Joaquin River near Newman, Calif. 

. do. __ . _ 

.do. 

.do. 

.do. 

.do. 

-do.

.do.

316

317

320

318

50

45

188

166

256

267

252

247

242

265

125

286

296

301

320

331

221

330

328

327

180

184

57

58

59

62

349

424

383

426

425

348

633

676

682

686

681

685

680

626

DDDDAAAADDDDDDDAAAAAAAAAAADDDDDDDDDADDAADAAA212

213

225

220

59

71

87

95

140

156

174

213

224

259

295

284

290

300

309

307

317

324

356

359

372

380

136

161

165

197

163

175

178

181

180

186

213

220

235

226

270

282

324

403

706

820

919

1,070

110

170

304

269

346

507

618

857

1,040

1,230

1,980

984

1,180

1,510

1,700

1,840

2,000

2,110

2,450

2,500

2,900

3,130

317

571

603

933

494

586

674

757

735

1,090

1,250

995

1,160

1,170

1,420

1,740

2,830

4,430

4.48

5.10

5.74

6.39

.59

1.27

2.72

4.31

.82

1.91

2.30

3.13

3.79

4.71

5.91

.61

.83

1.28

1.52

1.63

2.04

2.27

2.78

2.81

3.20

3.61

3.31

6.15

6.67

9.60

3.81

4.73

4.72

4.77

5.47

5.66

.52

1.06

1.52

1.75

1.79

1.96

2.38

3.25
TABLE 5. Two-point (O.Sd/0.8d) velocity discharge-measu

Index 

No.

723

724

725

726

729 

730

731

732

733

734 

735

737

738

739

740

741

743

744

745

746

747

748

749

750

751

752

753

754

755

757

758

760

761

762

Station and location

Merced River at Pohono Bridge. Yosemite, 

Calif.. ._ 

 -do.... .

 .. do..... ... . ....... _ _.-.-. -.-

. .do.... _._ . _- 

South Fork Merced River at Wawona, Calif. - 

 -do..... . .

. _ do..... _ ..... __ . _ .... _ -

 ..do..... ... . 

. -do-- 

South Fork Merced River nearBl Portal, Calif. . 

 -do.... - . _ 

 ..do 

 do.... 

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

do

Merced River at Bagby, Calif _________

 . .do . . . . ._

 -do....... 

.....do... .....

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

 ..do--. 

Merced River at Happy Isles Bridge near

 ..do-.- 

Merced River at Happy Isles Bridge near 

Yosemite, Calif. _. . ...

... -do... 

..... do..... .... . ........

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

 ..do...... ........... ....... .......

.... .do...... ..... ... ... ...... 

 ..do.. 

. _ .do... ......... ....... ..... .

District 

No.

316

341

329

350

29 

17

18

19

5

84 

108

94

96

74

78

123

151

141

165

142

126

125

356

333

347

348

367

332

315

337

336

300

389

393

Type 

of cross 

section

A

A

A

D

A 

A

A

A

A

A 

A

A

A

D

D

D

A

A

A

A

A

A

B

B

B

B

B

B

D

D

D

A

A

A

Width 

(ft)

104

105

114

123

76 

79

79

80

75

78 

83

83

82

87

99

141

144

145

150

149

152

165

79

78

82

76

73

91

124

172

180

184

122

135

Area 

(set ft)

242

288

326

395

175 

196

222

239

272

393 

420

452

456

483

585

689

951

1,060

1,160

1,200

1,260

1,550

209

209

232

330

330

456

273

690

889

1,170

1,030

810

Mean 

velocity 

(fps)

3.02

3.27

3.65

4.56

2.12 

2.41

3.10

3.32

4.26

.52 

1.17

1.66

2.04

2.71

4.03

1.23

2.21

2.49

3.41

3.73

4.41

5.68

2.36

2.64

2.67

4.67

5.15

5.90

1.40

3.67

4.41

5.16

1.08

1.90
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C33

t-.-t 00 tO «JIO1O«5T|<

cococococ*3 ^ ^ 3C 3C 3C 3C 3C ^ 3C 2C 2C ^* 2C "** ^f ^^ « 3U 2C "^ 2C 5s 2C ^ 52 22 ^ 2§ S2 2§ ^ <NCS

WI>*OOI>*Q OI>*OiOOi ^SJ 00 *0 ^ SS

rH tH

(N WO 0000 ^*r-tOOOO"3 -^* t^ W 00 O t-^

SSgaa « toto^, ..

*-t tO t S O IO r-t

csoco^a mmooo^x -Hcscoato omoo i-r- i-coo r-m oc

rH rHnH r-(

SSS feSSSS §

-*«« ^r-oowiN o

o>

>-i 

^

co co coo ujtdtot^od t^od t^oe

^t0 OO OOC^IkO CC 1^* O)t>* iH C

tcat-fco Qr-iNcjc- r»cgo ran ooioco ooto oir IMWJ«IOO» ^ ioSfe'0 «So to« t~t~co «* r-i

c^ooo oco cct»rH 060 »o»-iSfH '""' 1""1 55

too^^o o*-4cc 4* <4* ^^^t* woo

QftQ <! <! «! «! «! Qfi QQQQ<J OO

cococ

CO CO 1*?*!-* CO COQCO COO iOiHI>»OC4 *»o t>«>^* i-ic-* -^t^c^t^io

!O

o o 052 £ o o 013132 - 0 O C _

 013137313

3 O to to <O CD to

r

r»r»r J^'tot-.c

:SKKI OSONgJ gi

iOi CT»O O f-t-OOCO
TABLE 5. Two-point (0.2d/0.8d) velocity discharge-measur

Index

No.

810 

811

813

814

815

816

817

819

820 

822

823

825 

827 

828

829

830

833

834

837

838

839

840

841

842

843

845

846

848

849

851

Station and location

Stanislaus River below Goodwin Dam near 

Knights Ferry, Calif.

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

. .do. 

do - - __ .. _____ _____ ___ .

do . _ ____ _________ __

 .do.. ___ . _ __ - __ . __ -

 do-. 

do

South Fork Calaveras River near San Andreas, 

Calif.

 do... 

Calaveritas Creek near San Andreas, Calif __ 

Mokelumne River near Mokelumne Hill, Calif, 

 do.....- 

... ..do -

do

 do 

 do. 

North Fork Cosumnes River near Eldorado, 

Calif. __ . _ _________

 do 

do

 do. 

do _ .. . __ _ __ __ 

 do 

do .

 do . 

South Fork Cosumnes River near River Pines, 

Calif. 

 do...... .......... .......... ........

District 

No.

42

47

16

15

442

399

449

443

389

49 

100

48

44 

1,041 

1,039

1,033

1,037

9 fi^R

63

2,653

2,656

101

123

122

100

99

75

386

366

365

6

24

Type 

of cross 

section

A 

A

A

A

D

A

D

D

D

D

A

A

A 

A 

A

A

A

A

A

A

A

A

A

A

A

A

A

B

B

D

A

A

Width 

(ft)

125 

125

153

151

83

93

122

136

197

101 

110

113

93 

103 

101

112

128

50

58

61

81

80

81

84

87

88

96

134

125

155

36

40

Area 

(sq ft)

622 

639

1,120

1,240

208

302

650

1,110

2,850

439 

575

725

441 

329 

333

346

555

137

263

331

805

208

244

371

391

415

565

697

890

1,430

111

202

Mean 

velocity 

(fps)

2.86 

3.21

4.35

4.77

1.73

1.80

1.68

1.94

2.97

.80 

1.93

4.50

6.46 

3.03 

3.12

3.21

4.38

1.68

2.09

2.23

2.89

1.42

1.40

2.09

2.29

2.60

4.37

3.36

3.68

5.16

1.96

4.89
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C35

N Ci N CO !> O CO CO t^ OW^^»0 QQ*OCOU3d THC^r-lcOO SO CO SO W 00 *«f SO O »O O

iO^CDOO ^ C1* O O O ^ O ^ »"" O O3 »"" »"" »"" »" W N r-1 ? t W NCOOr-IO r-1 »H i ^ T I W

^HrHr-lr-l r-lC^C^NN r-lC^r-lNN C^»"tfHr-lr-l r-i r-i rt i-H »-H i 4 r-i r-t r-t rH r-J r-i ^H r-t r-J rHr-JrHr-lrH rHrHr-l»-H

r-t WWWNCO CO r-tr-t N (N rH OJ W CO CO N N M ^ i-H r-t §5 r-t

o>J>«cooo osorHOsoo $^*t*-oo> o i ^ co oo co cooc&coco ooocOi ^w^ i>«oo^*5OOi os^t^-r-ic1^ SSo>ooo

OiO^*Tt* COCOCO^*N OOOOO OOOOO OOOOO OOOOO OOOOiO OOOOOO l^COC^wa

tNCO«-lC^ C^^*^3(OOi COOr-t£-»CO t*OOiM^CX3 lOE-^OSCOC^ NJ>-600O?O CO^fOOtO OOW^OE^-O »-tr-trHrH

i3^O01OC9 CX)t»COCOC^ OOSCOOCO t>-r-10QCO(

-O^)"fC§ ««t»t-t- S«tOtOr-l r-lr-lr-1

 a-c-oia 

S

'O'O'O'O «T3T3i3T3 -O gi3T: 'O

1 83

|§

T:I:PH -c -c -c -c «

3 OOOOOO 00 00 OOOOOO OOaOQOOOC

r-oooso IH . ___.. OS o>a>ososa> asa>a>as
TABLE 5. Two-point (0.2d/0.8d) velocity discharge-measur

Index

No.

911

912

913

914

915

916

917

918

919

920

922

923

094.

925

927

928

929

930

931

932

933

934

935

936

937

938

939

940

Qdl

942

943

944

945

946

947

948

Station and location

Pit River near Bieber, Calif. _________

 do.... 

.-...do. 

..... do.... 

.... .do .

 do 

do. .. . _ ... ..... ... __ . . .....

... ..do.... . .

..... do .... ... ... ... ... ..... .... .....

..... do.... .... _ ........

do . _____ _ . .

.... .do.. ...

do

 ..do .

... ..do ... ... ........... ... .....

. .do....... - _____

do

_ do.... 

 .do.... .... .... . ......... ......

.... . do ... ..... 

.....do .

 do.. ... ... ...

Mill Creek near Los Molinas, Calif ............

.....do... 

 ..do...... ... .......... ............... .

... ..do... .................

do

Thomas Creek at Paskenta, Calif. . .. 

 ..do 

. do......... 

do . _____ . - ...

 do.... 

Cow Creek near Millville. Calif . , ....

District

No.

52

78

70

46

39

61

31

30

238

262

233

223

231

127

106

105

87

86

97

118

106

126

96

136

135

427

443

399

435

404

288

262

271

261

278

107

Type 

of cross 

section

D

D

D

D

D

D

D

D

A

A

A

D

A

A

D

A

A

D

A

A

j^

A

A

A

A

A

A

A

A

A

A

D

D

A

Width 

(ft)

130

1 ^7

9ftfl

210

91 7

224

OOO

240

100

98

104

107

130

96

105

111

125

f QQ

79

73

73

72

76

80

80

60

67

66

63

66

88

100

107

157

158

163

Area 

(sq ft)

290

357

5AO

646

OQO

1,040

i 97O

1,410

255

332

364

705

OQ9

480

623

749

QHA

251

300

338

306

49Q

554

561

211

228

257

97 fi

323

256

9Q7

381

478

728

468

Mean 

velocity 

(fps)

OK

1.17

1.57

1.87

2 

Oft

3.51

4 00

4.45

3

9C

3.57

4.34

4.40

6.26

3.77

5.63

6.57

7 00

QO

1.21

1.76

2.35

9 Q1

3.21

3.37

1.46

1 7R

2.58

3.22

3 Oft

4.34

4.81

5.59

6 QQ

7.01

1.31
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C37

tO IO to tOto*OtoO O O O *O to IO O O O O OOOOO O O O to »O to O O O to 10 lO to *

co «< i« ;£ « 3* "it s« «3>5ai3! S'SIS'SS ^rtt^i^t^i "*S3!?S2J

OOO OOOOO OOOO

osootMt- i~- foo-^tto o^£.ioog toooor»io iocnSoo -oicoN.-<t, «^"O>t-S ooioooos

co'>jit^t>i 10 10 06 ci >o cd<o'cdi^c4 w^«'>ji'>jit^

»rs.>o os to a> 

0061-! IN' 10

Tjt^OO I»OOeiaO<£> t-r-lMtOrt COt-Wr-100

>o ci o o * oo t^ co IM' cieceoweo coco^^id cootosec od>o>oo6od

r-I^COt^CO t~ O> r-l rl * to tO t- 00 « r-l * 1-1 O OS r-1 tO CO 00 tO CO N 00 r-t O « tO r-l OS

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ttt->O «>OO_I>O ^"NMOOr-l 'SS'"1 ®

CC ^ t^OO»Ht» tO-^^00 1^* OOOCOr-t

COr-tCOOOiO COr-tCO CQOt»t>00 t-ooN CC l^ r-t O Or-t

tooo^t*Oco t-i c coocor^o i-i

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§

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d^ =

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TABLE 5. Two-point (O.SdjO.Sd) velocity discharge-measu

Index 

No.

994 

995

996

997

998

999

1000

1001

1002

1006 

1007

1009

1010

1011

1012

1013

1015

1016

1017

1018

1019

1021

1022

1023

1024

1025

1027

1028

1029

1030

1031

1032

Station and location

Middle Fork Feather River below Sloat, Calif.. 

 . .do............................. ....... ....

 . -do..... --_.-. ...................

 do.. ... 

do

South Fork Feather Eiver near Forbestown, 

Calif..... __ ................... ___ .......

 ..do............. ._. ...-_ __. 

. -do 

-...do . _ . 

South Fork Feather River at Enterprise, Calif..

. .do.... __-__ 

 do 

 ..do...-....... _ __ -

... ..do.... ................ 

West Branch Feather River near Yankee Hill, 

Calif.... 

 ..do.........................................

..... do... 

 .do.__ _ 

 do 

 .do ...

West Branch Feather River near Paradise, 

Calif... ....... 

 do 

 do 

do

 ..do.... ... ... - _.. 

 .do.... ...... 

Spanish Creek above Blackhawk Creek at 

Keddie, Calif.... ...

 do........ ... ... 

 do.... . 

---do.. 

District

No.

142 

194

136

151

137

30

31

14

20

304 

346

205

221

222

213

214

309

286

308

307

274

271

45

15

14

55

10

9

189

226

223

191

Type 

of cross 

section

A 

A

A

A

A

A

D

A

A

A 

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

D

D

D

D

Width 

(ft)

110 

110

112

121

130

78

83

87

91

95 

102

170

173

173

175

176

93

93

96

96

97

105

66

66

75

79

83

87

90

94

94

95

Area 

(sq ft)

312 

376

506

665

924

189

264

357

447

575 

571

739

665

866

1,120

1,340

499

521

560

594

630

855

191

275

345

465

629

704

236

276

339

399

Mean 

velocity 

(fps)

5.22 

6.33

6.84

9.56

8.84

1.75

2.68

3.89

5.59

2.49 

5.34

1.08

1.91

2.41

2.79

2.96

.54

.68

.89

1.26

1.98

5.27

1.27

2.36

3.19

4.28

6.38

6.41

.27

.84

1.32

2.38
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C39

OOOCOO CTNiON'* t~.-tO»tO>O 

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TABLE 5. Two-point (0.8d/0,8d) velocity discharge-measu

Index

No.

1082 

1085

1088

1089 

1090

1091

1092

1094

1095

1096

1098

1099

1100

1103

1104

1105

1106

1107

1108 

1109

1110

1111

1112

1113

1116

1117

1118 

1119

1120

1121

1122

1123

1124

1125

Station and location

Middle Yuba Elver above Oregon Creek, Calif.

 do_.._ 

Middle Yuba River near Allegheny, Calif _ -- 

__ do _ __ ___ . __ 

 do.... 

 ..do.... 

Bear River near Auburn, Calif __ . ____ 

.... .do.... . ...

 .do.... 

..... do........... .. ..... ..........

 ..do.... 

..... do. _... ......

Middle Fork American River near Auburn, 

Calif. 

.... .do... . ... .......... ..........

.....do _ ............... .. . ........

.....do...... - , ....... .......

... ..do. _. ....... .........

Middle Fork American River near Foresthill, 

Calif. 

 . .do.... ... ... ... ..... ..... 

 ..do... . .-

do . ________ 

.... .do........ ...... ........ . .. 

Rubicon River near Georgetown, Calif . 

 .do . , .................................

.....do...................... ....................

Rubicon River near Rubicon Springs, Calif. ...

do ____ -

 ..do................... .... .......

.....do.... ..... 

do . .

 do......................... .................

District 

No.

165 

149

147

33 

6

10

9

178

191

166

165

155

157

378 

364

382

377

266

26 

33

13

31

39

107

88

100

24 

8

40

9

7

17

11

21

Type 

of cross 

section

A 

j^

A

D 

D

A

A

A

D

A

A

j^

A

A 

A

A

A

j^

D 

D

A

A

D

A

A

A

A 

A

D

D

D

D

D

D

Width 

(ft)

77 

81

93

60 

66

65

70

58

74

73

89

116

118

104 

109

112

114

141

109 

121

140

144

150

95

105

114

44 

56

73

86

96

97

70

80

Area 

(sq ft)

228 

349

491

224 

289

341

399

132

199

209

309

641

762

511 

650

746

962

1,550

362 

428

636

735

744

338

572

728

109 

240

285

364

517

585

190

266

Mean 

velocity 

(fps)

2.93 

4.73

6.64

1.40 

2.39

2.99

3.96

2.04

2.68

3.06

3.95

5.83

5.88

1.69 

2.22

3.86

4 33

7.94

2-52 

3.55

4.56

4.94

6.91

1.83

3.37

5.12

1.65 

1.82

2.03

2.06

2.03

1.98

1.80

2.72
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C41

OSOO t^t~ >O r t~C6 <N r-tr-t CNC '-'S £2 r-io o

ooo o ooo o>o o 10 io us i

SoS S SSs So1 SSSS« SSSSS

COtOtOCO tOW*-*'* *

8E>3S SSSSS 3

citato r-oo oo»o»^t|to t-w>ji oeo .-iNeotoo ts.oo ooogcft >-< «>-ir-io i»ooi~i ooi-i ocoi-i««o ooi oo oo .-<otoiat~ i-ios esooo m tococs 1*

CSCMIOOOIN * to r» o» to

"5 s' « to toos

coo cococo oo ?ocob-o oio-^oor-i co 

o»co <o>rfo6 c> ^!io«di»C i> * r-< r-i ri <rf

«<0t>. CO OsOOO OOS OOl*lOt~t~ NOW t-CO i-l-<J1«OO». t-(I>. ts.t~.-( O> COOr-C* i-l» r-t *> « IM 

CO -* «O CJ C4^CO ^ >O l^ QO CO "O O COtCoO CJOO O "O 1^ t-I O CD t-^ COOJCD t^ >* * tO O 1^ CO r-i r-< r-i CO

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C^«3JNtOO» «r-tO W>O t»^«T-(®t-

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t~-i to oo"

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T«J>. CO 1O 00 CD CO OWi « * t»OOi-l«O 

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COt»00 1 I N CO^WJCOOO CON & CN CO *^* rHfl»H»-l »^

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to«or-"*io m* oicoto-^tto csiO.-i «oooo5>Oi-i r-i^i T-I c5 * ui >o "

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TABLE 5. Two-point (0.M/0.#d) velocity discharge-measure

Index

No.

1182

1183

1184

1185

1187

1189

1192

1193

1195

1196

1197

1198

1199

1200

1201

1202

1203

1204

1205

1207

1209

1210

1212

1213

1214

1216

1217

1218

1219

1220

1222

1223

Station and location

do

Huntiugton-Shaver conduit at outlet, Call-

____. do... 

.... .do.. 

Marble Fork Kaweah conduit 3 near Potwisha

.....do.. _ . . 

 ..do.... _ __ -

 ..do..... ..........

do __

 ..do.--- 

- _ .do.. ...... 

Kern River conduit 1 near Democrat Springs. 

Calif-. . ...

do

 do.- 

do. _ ___ . . - __

-....do..-.- 

do

do

Pacific Gas & Electric Co. conduit 3 below 

Bass Lake, Calif _ _______ - _____

 do. 

Southern California Electric Co. conduit on

__ do.. _ . _ ________ ______

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

do

do

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

District 

No.

307

305

298

279

91i

224

236

243

243a

640

660

652

651

661

189

190

206

193

207

320

321

316

215

151

318

317

307

316

509

510

511

Type of 

cross 

section

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

Width 

(ft)

16.3

16.7

10.9

10.9

10.7

6.0

6.0

9.3

9.5

8.5

8.5

8.5

8.5

8.5

8.1

8.1

8.1

8.1

8.1

19.8

21.4

22.4

10.5

11.5

5.8

7.8

8.5

8.5

9.1

31.0

32.6

32.7

Area 

(sq ft)

63.5

69.3

38.6

43.0

46.5

13.0

12.9

22.7

22.2

23.5

 17 i

51.2

70.2

21.1

26.7

32.6

41.6

58.3

78.0

143

173

21.7

27.2

15.1

9.6

12.2

15.1

89.8

150

200

Mean 

velocity 

(fps)

2.16

2.19

.80

1.25

2.49

4.27

5.23

3.10

4.28

6.26

6.13

7.25

8.30

8.87

4.49

5.17

5.58

6.15

6.54

3.90

6.71

7.69

4.61

5.84

3.70

2.00

2.23

2.44

2.41

3.83

5.49

6.30
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C43

£2 rf pHOOCO^N OiCO*-)OiO NNOiOM WiQOiOOCO O i> N DC CO OO CO ^ rH CO l^Oi-H^t^ Tjf g T£ CO **< O*

00

MO NN^*OSO O3 t>-t>-^ CO O O3 O t>-00 »Q OO *~< ^! ^ Oi ^ LO CO i-H CO CO O t*- O O3 CO »O a Op CO O3 O3 O i-H i-H

-COOO -^COCOCOCO Ot^^l>00 OOiCOCOOi Tjf 2> »O N O OCHQd^CO XCCCCCCi> OIOIOOOOT i-HCDi>-CCN N

«> t-^ oi o> t^ Tji c<i Tj< -^ Tji Tji * N* oi os od CD eo* -^ co oi oi t-* o* i> oJ 10" o" »4 o Tji ci oi CD eo co Oi co " IH i-i co od

i-H iH T-< i-H iH

tOCO O5CO*Ot*-O COOJf-OOO OSOI^OO 1^ OO CO OO-^ i-H kOkOOUS^ O O «3 O i-H C5 N O CO *Q i-( O CD N «3 O

odo> Tgot^cios i-ico*o$c<ieo" t^co^co'c<i i-iooiodoo* CC»OCO^G> oswa^cjod t^i-nc<ii-H^ oi^'co^co" co

4OCO i-HCO^OOi Oil lt*-t*-*Q kO,-(t>-W3O OONoOOOt* ^Oi-Ht^t^ COOSNNW3 1-HCOCOCOW3 OCOOOO 1^ CO

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^f» t- O i I O 00 CO CO 00 00 Ol CO OOO^t^CO CO -^ Ol M i I CO O i I -^ 00 O I-H O *O i I 00 i I »O Ol t^- b- «3 00 00 »O »5

xdco oo*co*«3<NtH cici<Nci * iHwiwi^'co co'oii-Hi-HT-J ^co'^waN oo't^cdci^I 'cocooio i-J " * "o «5

ot-eoeo eoeocoe

3N^*I^N COCOT*(«3U3 «3COCOt-O C5NOC5Q QOOOOoO*' .cotOTj<Tj< OiC^ooptfa cocpOTjfkO Tjfoooooow 25oa3!i>-c

oo

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r-r- C» CO « CO (-- O .-1 C» CO * OS

cococococo cococococo cot

o o o o
TABLE 5. Two-point (0.2d/0.8d) velocity discharge-measur

Index 

No. Station and location

....do.-.. . . 

....do..........................................

__ do..... _ .... __ . ___ . __ .... _ . .....

....do. ___ .. __ ...... ______ .... . 

... .do....... ... ... ... ... ... ... ... ... ... 

 .do............... ... ...

. do ._ _ 

... .do... ................. . _ 

do _ . ...

 ..do . __ - _ ... ... ..... .....

... .do. ... ... ... ... ... ....... ..... ... ... ...

do _ . ___ . _

. __ do ____ ... .. _ .- ....

... ..do. ...... .............................

... ..do........ . 

.....do _____ .... __ ..... __ ............

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

 ..do......... _ ... _ . _ ... _ ......... _ ..

.....do _-. . _ .. _ ..... _ .....

..... do... _ .._._ . _ 

.. do... ......... .. .....

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

 ..do............... ............ ............

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

... ..do................. ......

 do... ...... ... ..

. __ do _ ___ __ .....

 .do... ____ .___ ...... .......... ......

 .do ............... ........ .............

 ..do.........................................

 .do... . .. 

District 

No.

221

222

994

225

226

227

9«»7

258

259

260

262

263

264

9fi«»

9fifi

202

241

252

253

257

262

9fi«»

266

267

275

276

277

278

281

288

293

295

296

299

303

306

Type 

of cross 

section

Width 

(ft)

475

475

300

300

234

140

161

120

140

190

284

OKK

184

130

1 t\*\

574

580

550

542

519

511

«»97

578

519

526

527

KOA

517

511

504

509

513

510

510

511

517

Area 

(sqft)

4 450

4,520

1,700

1,770

1,190

461

1O4

516

695

1,300

2,180

1,870

1,170

605

352

11,600

11,800

8,460

7,170

4,370

2,700

5,820

11,300

4,440

5,050

5,690

4,830

4,540

2,460

1,940

2,260

3,720

3,110

2,810

3,020

5.370

Mean 

velocity 

(fps)

8.09

7.88

5.16

5.41

5.24

3.43

1.30

2.17

3.55

4.42

6.33

5.99

3.25

1.37

1.26

6.91

6.62

4.99

4.49

3.02

1.62

4.00

6.90

3.15

3.68

4.06

3.35

3.26

1.51

1.09

1.37

2.59

2.08

1.88

2.01

3.78
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