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

W-

Velocity- Head Coefficients in Open ChannelsBy 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_____________________________________________________ ivAbstract_____________________________________________________ ClIntroduction._______________________________________________ 1

Purpose and scope ________________________ 1Acknowledgments. ________________________________________ 2

Definition of kinetic-energy coefficient_____________________________ 2Sources of velocity data._____________________________ 3

Two-point (0.2d/0.8<f) velocity method. _ ________________ 3One-point (0.6<£) velocity method____ _ __ _ ___ _____ _ __ 3Multiple-point velocity method______________________________ 3

Computation procedures_________________________________________ 4Arithmetic method__________________________________________ 4Graphic method_______________________________________________ 4

Computer program.___________________________________________ 4Comparison of alpha determined graphically and arithmetically _____ 7Types of cross sections.________________________________ 8

Discharge measurements used_______________________________________ 8Multiple-point velocity measurements_________________________ 8Two-point (0.2d/0.8cO velocity measurements _______ ___ ________ 9One-point (0.6d) velocity measurements__________________ 9

Analysis of variations of alpha...______________________ 9Range of alpha________________________________ 9Relation of alpha computed from multiple-point velocity measure­

ments to alpha computed from two-point (0.2d/0.8d) velocitymeasurements_________________________________ 11

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

Correlation of alpha with roughness coefficient..______________ 12Other correlations studied...______________________ 12

Recommendations for determining alpha...._______________ 15Trapezoidal channels___________________________ 15Channels with overflow sections.____________________ 15Comparison with present method of computation__ _______ _ 17

Summary and conclusions..__________________________. 18Selected references______________________._______ 20Basic data__________________..._______________________ 21

ILLUSTRATIONS

PseeFIGURE 1. Sketch illustrating computation of alpha by arithmetic inte­

gration_ __ . ._ C5 2. Graph showing alpha values computed graphically compared

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

IV CONTENTS

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

4. Graph showing relation of alpha computed from multiple- point 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 multiple- point velocity observations (a) to alpha computed from 0.6d velocity observations (ao.ed)___________________________ 13

6. Graph showing correlation between alpha and Manning'sroughness coefficient (n)_______________________________ 14

7. Graph showing comparison of 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.... 18

8. Graph showing comparison of alpha computed from multiple- point 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 sec­ tions.... ____________________________________________ 10

3. Alpha coefficients, as based on n values___________.____ 144. Multiple-point velocity discharge-measurement data.________ 225. 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 486n

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 multiple-

point 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 coeffi­ cient, 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 corre­ lations 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 fre­ quently 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 measure­ ments 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 tech­ nical 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 measure­ ments of discharge and other pertinent data is also gratefully acknowledged.

DEFINITION OF KINETIC-ENERGY COEFFICIENT

Streambed roughness, irregularity of channel-bank and bed con­ figuration, 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

^9is 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 proposedit 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

AAwvAA. The kinetic energy of water passing AA per unit time is wiP -* This^9v2

is equivalent to the product of the weight wvAA and the velocity head jj The*g AAtotal 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 measure­ ment, 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 measure­ ments 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. Distribu­ tion 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 observa­ tions 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 sus­ pended 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 incre­ ment 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 correspond­ ingly with the number of point-velocity observations in the measure­ ment.

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 computa­ tion 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 V1

,-L,-.

i' d

\

<r-L 2 ->

} 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 im­ portant 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 at0.6 depth in each subsection.

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

observation depth to total depth, measured from thewater 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 multiple- point 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 coef­ ficients 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 vertical1.1601.1601.1491.1301.1081.0671.020.953.871.746.648

If more than three observations were made, each item was ex­ amined 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 measure­ ments 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 ob­ tained 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 treat­ ment given to the bottom velocities in each vertical and to the sub­ jectivity 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 1.6I

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 man-

made 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 avail­ able 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 multiple- point 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 (Man­ ning'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

IUu.

I ° ILJQ 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

1708

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-POINTVELOCITY 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 impor-

223-866 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 measure­ ments) for detailed study of the relation between alpha and the various channel and flow parameters.

RELATION OF ALPHA COMPUTED FROM MULTIPLE-POINTVELOCITY 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 com­ puted 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 com­ binations 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 curva­ ture, 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 in­ dicated, 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 1.6 1.81.4 ALPHA 0.6 ( o 0.6d >

FIGURE 5. Relation of alpha computed from multiple-point velocity observa­ tions (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 valuesn

0.012 _ _____ __.013 __ _ _______

014. 015. 016

.017. _ ________

.018 __ _ ______

. 019

.020 _ _____ ___

.021 __ _ ___ __

.022 _ ____ _____

.025____ _______

.026 __ ___ _____

.027 _ ____ _____

.028 _ _____ _ _

.029. __ .__ _ _

. 030

.031

Alpha 1.061.081.091.111.12

1.141.151.171.181.19

1.211.22 1.241.251.27

1.281.301.311.331.34

n 0. 032____________

.033_ __ _______

.034. _ ________

.036 _ _________

.037 ___ _ ___ _

039040041

.042

.043 _ _________

.044 ___ _______

.046. _ __ _ ___

.048___ ____ __

050.051 _ .__ ______

Alpha 1.361.371.391.401.42

1.431.451.461.481.49

1.511.52 1.541.551.56

1.581.591.611.621.64

n 0.052 _ _________.053 _ _________

0^4-

.056 _ _________

058f|CQ

.061 _ -_. _ ___

.063 ____ ______

.064 _ _________

066

067.068 __ ________.069 _ _________.070 _ -_-_-___.

Alpha 1.651.671.681.701.71

1.731.741.761.771.79

808283

1.851.86

899192

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. Un­ fortunately, 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 subsec­ tions (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 ZT 3 **- 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 . . . a n, 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 ftPi=18ft #!=2.78 ft

2

jR^ssl.98« 1.486(50)1.98

1 0.030 ' .4=70 sq ft

1 o T: I * /\ JLUAl^2=20 sq ftP2 =12ft

#2=1.67 ft

#2^=1.41

1.486(20)1.41K2 0.040 1>0

SK=4904 + 1048=5952yU4 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, andalpha for n= 0.040 is 1.48; accordingly,

VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C17

K3 K3ai 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. Compu­ tation procedures used for evaluating alpha in complex cross sections are, at best, only approximations, and errors introduced by the sub­ division 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 deter­ minations of discharge has long been recognized by the Geological Survey. At present, only limited data summarizing alpha coeffi­ cients 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 pub­ lished figures, however, are too generalized to be of much assistance in making a reliable estimate of alpha. Lacking more suitable in­ formation, 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 assump­ tion has little effect on the computed discharge because the channel reaches selected for study are generally fairly uniform in cross- sectional 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 measure­ ments. Figure 8 shows alpha values (a n) for the same group of sec­ tions 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 ' _____ 11.0 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 meas­ urements 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 determina­ tion 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 measure­ ments 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: Pasa­ dena, Calif., Theodore Von Karman anniversary volume, p. 59-65.

Chow, Ven Te, 1959, Open channel hydraulics: New York, McGraw Hill BookCo., 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 hydraulicflow: 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 forpipe 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 openchannels: New York, John Wiley & Sons, p. 46-48.

BASIC DATA

TAB

LE 4

. M

ulti

ple-

poin

t ve

loci

ty d

isch

arge

-mea

sure

men

t da

ta8

Inde

xN

o.S

tati

on a

nd lo

catio

n

Can

ey F

ork

near

Roc

k Is

land

, T

en

n_

__

__

- B

ig R

iver

at

Bym

esvi

lle, M

o_

.__

_--

__

_-

Pee

Dee

Riv

er a

t Pe

e D

ee, S

.C_.

Snak

e C

reek

at

S-29

, N

orth

Mia

mi

Bea

ch,

Fla_

Sh

iaw

asse

e R

iver

nea

r Fe

rgus

, M

ich__-_

___

6 Pe

ace

Riv

er a

t A

rcad

ia, F

la..._

___._

-_ -

.

B7

Saco

Riv

er a

t C

orni

sh, M

ain

e_

_ _

_._

--_

_-

- _

A

Rio

Gra

nde

belo

w E

leph

ant

But

te D

am,

N. M

ex

_..

A

Cla

rk F

ork

near

Pla

ins,

Mo

nt_

__

..._

_

__

-

A10

O

chlo

ckon

ee R

iver

nea

r H

avan

a, F

la,-

____..

B

11

Con

etoe

Cre

ek n

ear

Bet

hel,

N.C

.._____________

B12

P

earl

Riv

er a

t Ja

ckso

n, M

iss_

__

__

__ -___

D13

P

earl

Biv

er a

t E

dinb

urg,

Mis

s.. ---------------

A14

Sa

ngam

on R

iver

at

Mon

ticel

lo, 111--_____ . -

B15

P

earl

Riv

er a

t M

ontic

ello

, Mis

s...-

-_. ._

-

---

B

16

Gen

esee

Riv

er a

t A

von,

N.Y

..._

_..

__

__

_-.

.-

A17

W

abas

h R

iver

at

Vin

cenn

es, In

d_____ - _-_ . -

B18

Su

gar

Cre

ek a

t M

ilfor

d, H

L_

__

_-_

. -. --

B19

V

erm

ilion

Riv

er b

elow

Lak

e V

erm

ilion

nea

r T

ower

, Min

n.

A20

M

isso

uri

Riv

er a

t B

oonv

ille,

Mo..______________

B

21

Sava

nnah

Riv

er n

ear

Cly

o, G

a. _

____ _

_ _

__

- A

22

Kan

awha

Riv

er a

t C

harl

esto

n, W

. Va_____ _

_____

B23

M

isso

uri

Riv

er a

t T

osto

n, M

on

t__

_ _

__

__

__

__

- _

A24

B

oise

Riv

er (

belo

w L

ucky

Pea

k D

am)

near

Boi

se, I

daho

. D

25

Sus

queh

anna

Riv

er a

t D

anvi

lle, P

a..

....

._ .. __

B

26

Whi

te R

iver

at

DeV

alls

Blu

fi, A

rk...-

.__- . ._-

B27

T

rini

ty R

iver

at

Rom

ayor

, T

ex__ _

__

__

__

__

___

B28

P

etit

Jea

n C

reek

at

Dan

ville

, A

rk.-

--__. .

B29

C

onne

ctic

ut R

iver

at

Mon

tagu

e C

ity,

Mass

._-_

_ ...

A30

M

erri

mac

k R

iver

at

Fra

nkli

n Ju

ncti

on, N

.H-.

._____

A

Ang

elin

a R

iver

at

Hor

ger,

Tex

____.

Oho

opee

Riv

er n

ear

Rei

dsvi

lle,

Ga.

--.

Nah

unta

Sw

amp

near

Shi

ne, N

.C._

. Sa

luda

Riv

er n

ear

Gre

envi

lle, S

.C .

Far

min

gton

Riv

er a

t R

ainb

ow,

Con

n.

Red

Riv

er a

t G

rand

For

ks,

N.

Dak

...

Typ

e of

cros

s se

ctio

n 1

Wid

th

(ft) 12

712

938

111

116

5

170

250

102

500

320 45 362

118

127

188

572

168 50

1,32

2

360

918

365

261

1,30

5

592

195

138

460

227

138 57 127 90 188

Are

a (S

d ft

)

1,56

51,

080

5,81

01,

192

1,21

2

1,14

03,

190

638

6,59

62,

173

369

3,41

81,

677

873

3,74

7

2,70

46,

125

1,38

134

614

, 500

3,48

110

,860

1,42

21,

945

7,99

8

17, 5

703,

170

1,12

85,

383

3,56

5

4,46

61,

332

339

410

649

1,24

7

Mea

nve

loci

ty(f

ps) 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

1.62

2.63

2.68

3.93

Dis

char

ge

(cfs

)H

ydra

ulic

radi

us(f

t)

3,30

01,

270

10,9

00 482

I,45

0

950

II,1

00

1,50

018

,100

3,

370

646

7,11

01,

850

576

8,43

0

6,18

016

, 500

1,20

018

351

, 500

7,23

027

, 600

3,80

03,

470

34,7

00

23,6

002,

190

2,12

015

, 000

10, 9

00

9,30

02,

160

892

1,10

02,

550

1,23

0

10.7 8.2

14.9 6.2

7.2

6.6

12.4 3.0

13.1 6.7

6.8

9.3

14.2 6.6

10.4

13.2

10.0 7.9

5.6

10.5 9.5

11.3

3.

9 7.

3 6.

3

22.8

14.8 7.2

11.6

13.2

18.3

9.

2 4.

8 3.

1 6.

9

6.5

Max

i­

mum

de

pth

(ft) 21

.112

.521

.215

.511

.1

11.7

17.0

9.2

19.2

14.7

10.5

18.7

19.5

10.3

20.0

17.1

13.8

12.6

10.1

23.5

13.2

16.5

6.0

13.0

11.6

45.9

31.0

14.2

17.6

20.7

27.0

13.0

8.7

5.0

10.8

8.7

Max

i­ m

um

poin

t ve

loci

ty

(fps

)

3.55

2.69

3.67 .73

2.60

2.28

5.42

3.75

4.21

3.29

3.32

3.50

2.26

1.12

3.31

3.39

3.85

2.27 .92

5.82

2.94

3.76

4.46

3.19

6.35

2.05

1.04

3.42

4.73

5.97

3.32

2.44

4.18

5.50

5.38

1.59

Rou

gh­

ness

co­

ef

fici

ent

0.06

0.0

35.0

36

.035

.038

.036

.030

.025 ) .035

.035

.030

.035

2) .035

.045

.030

.035

.030

.035

.030

.032

.030

.030

.032

.035

(2)

(2) .0

40

.030

Alp

ha

coef

fi­

cien

t

1.38

21.

545

1.48

41.

443

1.67

3

2.70

71.

256

1.46

41.

265

2.06

5

1.77

61.

507

1.85

01.

677

1.25

5

1.28

81.

222

2.20

51.

493

1.24

6

1.16

21.

276

1.42

11.

518

1.19

2

1.30

11.

292

1.49

51.

503

1.58

8

1.33

41.

368

1.36

61.

923

1.23

2

1.44

8

W K| o W 5 f i i 0 02

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-

Am

eric

an

Can

al (

Sta

tion

60)

ne

ar I

mpe

rial

Dam

, A

riz.

-Cal

if.

Wol

f R

iver

, ab

ove

Wes

t B

ranc

h W

olf

Riv

er,

near

Ke-

sh

ina,

Wis

Ark

ansa

s R

iver

bel

ow J

ohn

Mar

tin

Res

ervo

ir,

Cad

doe,

C

olo.

C

owlit

z R

iver

nea

r K

osm

os. W

ash.

_

_ ..

..... .

....

.

A B B A A B O B C A A B B B A A A B B A D A B o B A A D B T> A A A A B A B o B D A

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

1,15

4368

520 26 606

194

168

1,26

1752

1,05

32,271

323

529

107

3,501

2,96

7

155

3,734

636

6,490

454

622

2,928

459

1,22

71,

320

472

4,739

3,076

1,013

1,61

5

2,24

6408

5,99

71,980

441

4,318

3,229

1,45

71

flfiQ

1. UUI7

1,444

15, 17

02,

436

3,145

81.1

1,767

435

1,422

1.55

3.54

1.74

4.71

1.74

1.38

6.00

2.60

2.57

1.88

2.92 .58

2.46

1.56

2.25

7.00

1.83 .52

.76

2.06

2.26

4.16

2.92 .79

1.65

4.58

4.68

2.70 .71

4.47

2.97

4.06

3.31

2.60

4.38

5.54

1.19

2.08

1.37

2.39

4.14

1,95

02,660

1,83

010

,700 561

728

643

9,110

7,620

292

10,9

00 371

16,0

00 707

1,40

020,500 841

645

997

975

10, 700

12, 800

2,96

01,280

3,710

1,87

028

, 10

05,350

313

19, 300

9,600

5,920

3KA

f\

. utu

3,760

66, 400

13,5

003,740

169

2,420

1,04

0

5,880

9.2

5.1

7.0

8.4

2.9

4.2

3.6

11.2

13.4 2.5

10.3 4.1

13.4 2.3

4.7

10.6 4.4

6.8

7.6

2.4

6.8

6.8

3.8

13.1 3.9

4.2

21.4 5.7

4.7

8.4

7.3

6.0

7.6

6.0

12.5 6.6

7.0

2.8

3.1

2.2

8.3

15.0 9.9

10.8

12.2 3.5

9.6

5.9

14.9

17.2 5.6

14.1 7.2

22.5 3.3

6.4

17.4 6.4

11.1

12.1 3.0

10.8 8.5

5.5

19.8 6.9

7.0

34.9 9.2

6.2

12.6

10.5 8.7

8.7

27.2 9.0

13.9 4.3

4.6

3.4

11.6

4.80

2.70

6.58

2K

K

, U

U

2 C

O

. \J

&

7.03

4.01

3.31

2.65

4.19

1 19

3! 9

32.

32

3.44

10.0

72.

781.

231.

14

3.07

4.94

5.52

4.38

1.63

3.07

6.80

8.28

3.94

1.08

6.33

4.36

5 Q

ft

. yo

5.57

3.56

8.35

9.57

1.86

3.06

2.59

3.71

6.84

.035

.025

.010

(2)

(2)

09 .030

.030

.038

.035

.040

(s) .0

35

.030

.028

.035

(2)

(2) .0

45.0

35.0

25.0

35

.030

.025

(2) .0

32

.030

.030

(s) .0

20.0

35

(2)

1.40

61.

203

1.50

41.

239

1.30

91.

693

1.07

41.

241

1.13

7

1.24

3

See

foot

note

s at

end

of t

able

.

1.28

32.

152

1.26

51.

210

1.45

21.

248

1 35

8L

8B5

1.25

6

1.17

91.

662

1.13

01.

241

1.76

1

1.40

11.

306

1.57

61.

201

1.27

3

1.20

81.

214

1.26

71.

550

1.16

4

1.13

61.

312

1.36

9 1.

361

1.54

7

1.25

0

1.51

6

i M 5 5 O O H SI i i

O H 2 CO j^l

^ s H O S g H f

CO s CO

TAB

LE 4

. M

ulti

ple-

poin

t ve

loci

ty d

isch

arge

-mea

sure

men

t d

ata

Con

tinu

edO

to

Inde

x N

o.S

tati

on a

nd lo

catio

nT

ype

ofcr

oss

sect

ion

1

Wid

th

(ft)

Are

a (s

et f

t)M

ean

velo

city

(fps

)

Dis

char

ge

(cfs

)H

ydra

ulic

radi

us(f

t)

Max

i­

mum

de

pth

(ft)

Max

i­

mum

po

int

velo

city

Rou

gh­

ness

co­

ef

fici

ent

Alp

ha

coef

fi­

cien

t

101

102

103

104

105

106

107

108

109

110

111

112

11378

Yod

kln

Riv

er a

t W

ilkes

boro

, N.C

. . .......... ..

A79

S

acra

men

to R

iver

nea

r B

ed B

luff

, C

alif..

.

D

80

Snak

e .R

iver

nea

r Irw

in, I

daho.

A

81

Schr

oon

Riv

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t R

iver

bank

, N

.Y____._

__ _

_

A82

W

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h R

iver

at

Del

phi, In

d_

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B

83

Koo

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i R

iver

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r B

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rs F

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ah

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A

84

Bro

ad R

iver

nea

r B

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Ga____ __....__ ...

B85

C

alca

sieu

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ear

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a . _

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B

St.

Cro

ix R

iver

nea

r R

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Cit

y, M

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__

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A

87

Peco

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dam

site

3, n

ear

Car

lsba

d, N

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ex.. .

AN

orth

Pla

tte

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ear

Goo

se E

gg, W

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ster

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1...-

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M

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A92

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A

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nd R

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a, M

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_

B94

W

abas

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..

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A

95

Cro

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Riv

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g_..._

__ ...__

A

96

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B97

M

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pi R

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at

Alto

n, 1

11.... -

-__ ...

BSa

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at

Mah

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t, 111.-

. .

BG

rand

Riv

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t L

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ng, M

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0 B

el R

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f_______________-_

_..

B

Atw

ater

Can

al, n

ear

Atw

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, C

alif

., si

te 1

. _

_..

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._.d

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______._

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itel

....___-

....

.do

_ _

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_

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.. _

_

...

.. d

o_ _

_

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ite 2

. ..

....

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o. sites -. - -.

. d

o.

.. s

ites

..

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___________ s

ite 4

_._

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o_

.

....

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sit

e 4

.A

rena

Can

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ton,

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if.,

site

1..

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te 2

. ..

. .

sit

e 2

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te 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

3,69

6233

447

47,040

6,49

2

360

2,36

03,

705

448

950

49,2

7046

,870 270

1,14

02,056 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

2,73

06,460

12,500

3,900

3,160

15,9

006,230

2,690

10,600 458

1,42

0207,000

36,8

00 582

9,110

10,3

00 508

2,460

215,000

191,000

414

2,930

6,530

118

120

256

112

110

115

113

112

121

117

120

119

125

6.2

5.3

5.7

7.0

4.5

13.3

7.

9 6.

7

7.5

15.6 4.0

24.6

19.5 4.7

7.3

9.9

5.6

7.9

20.5

23.3 3.7

5.5

4.6

2.3

2.3

2.5

2.3

2.1

2.1

2.1

2.1

2.4

2.3

2.3

2.3

2.4

8.3

9.3

6.8

11.2 6.1

17.0

12.1

10.4 2.8

8.2

37.2

32.5 7.5

13.0

18.8 7.5

14.6

35.7

57.1 4.7

7.6

9.0

4.3

4.2

4.0

4.1

3.6

3.6

3.6

3.6

4.0

4.0

3.8

3.9

4.0

4.84

3.74

9.20

7.58

3.59

2.86

5.22

3.04

4.55

3.05

5.24

6.11

8.24

2.05

5.58

4.83

1.77

4.42

6.48

7.52

2.32

4.34

4.93

3.28

3.27

3.20

2.98

3.79

3.87

3.79

3.88

3.08

3.13

3.06

3.19

3.13

0.032

.030

.030 .035

(3

) .030

(3

) .035

.040

.040

.027

.030

.035

.040

.030

.026

.028

.035

.045

.035

1.17

61.

333

1.23

1

1.08

61.308

1.199

1.25

71.

574

1.27

61.

271

1.398

1.172

1.193

1.103

1.21

81.736

1.32

91.

517

1.136

1.272

1.258

1.55

51.292

1.121

1.162

1.10

41.103

1.10

2

1.111

1.14

31.

111

1.093

1.132

1.09

61.118

1.109

VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C25

1 ill fil I

OJOS »gp^tOSCO AOrHrH^* CO OS l^- 1^- fH CO ^1 i-l i-l »O ^* O ^H CO C^^«'^*COI>' Cd^HGOOOO CO CO 00 !> »O Is- CD GO OS Oi GO!**

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Calif e, C

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1^ M .S t

«

er below Bullards rat Keswick, Cali abella Dam, Calif at the Dalles, Ore

on Ferry, port, Wa

;

D O

^15 1^9-§9 ^§-§15 15C C

Dg

Trinidad, Wash. at Kerkhoff pow tal Canals at Me

111

al

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ki 03==53 £ >

&

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^<NCO-*»O tpt>OOOlO r-ttfimrMio CO * r-l<N CO * >O 03 b. OO OS O i-H CO «eococoeow Ss co co « * » * * * * * <o oo oo So ooooooSooo cooJOicSeb

TABL

E 4.

Mul

tipl

e-po

int

velo

city

dis

char

ge-m

easu

rem

ent data

Con

tinu

ed

Inde

xN

o. 199

202

203

204

205

206

207

208

ono

211

212

213

1155

1158

1159

1160

1169

1179

Sta

tion

and

loc

atio

n

....

-do..... . .

. ....d

o.. ..

....

....

.. ..

....

....

....

....

....... .

....

....

....

. _ .d

o..

. ..

. _

-do.. .

.d

o.... . _

.d

o.. .

.-do.. . .

- d

o..

. ... .

.. ..

. ..

......

d

o..

... ..

......

d

o.

..

....

. ...

.d

o.....

- .d

o

d

o.

Typ

e of

cr

oss

sect

ion

>

D D D D D D

Wid

th

(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

Are

a (s

q ft

) .6 1.3

1.0

1.2

1.0

1.1

1.1

1.5 .9 .7 .7 .7

880

910

1,11

01,

530

854

254

Mea

n ve

loci

ty

(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

Dis

char

ge

(cfs

) 5.0

3.0

1.7

2.6

2.2

4.3

6.3

2.3

3.3

3.7

1.1

2.1

1,83

02,

040

3,31

03,

450

2,96

035

4

Hyd

raul

ic

radi

us

(ft) 2.

51.

3

2.9

4.3

4.1

1.4

Max

i­

mum

de

pth

(ft) .1

9

.56

.46

.51

.39

.40

.40

.53

.35

.29

.29

.30

5.6

5.6

7.7

7.4

7.7

4.7

Max

i­

mum

po

int

velo

city

(f

ps)

8.89

2.90

2.18

2.85

2.64

4.94

7.24

1.88

4.77

6.96

2.02

3.92

3.51

4.08

5.66

4.28

5.66

2.70

Rou

gh­

ness

co­

ef

fici

ent

(n)

Alp

ha

coef

fi­

cien

t («

) 1.06

6

1.14

01.

140

1.20

0

1.09

0

1.00

01.

080

1.13

01.

180

1.19

61.

180

1.60

01.

750

1 88

01.

920

1.56

01.

510

o to w

' Def

initi

ons

of c

ross

-sec

tion

type

s is

giv

en o

n p.

C8.

2 Su

bdiv

ided

sec

tion,

no

com

posi

te n

val

ue a

vaila

ble.

VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C27

co-*-*co o *« * 00 »O t^ CO CM M3 i-H i-l 1s- Q r* O 00 SS * >0t> * 85

» «el O

CO CO CM i-l CM OO1--COC

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o gi-H 00

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223-866 66

TAB

LE 5

. Tw

o-po

int

(0.#

d/0.

<Sd)

vel

ocity

dis

char

ge-m

easu

rem

ent d

ata

Con

tinu

edO

Inde

x N

o. 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

Sta

tion

and

loca

tion

Big

Bla

ck R

iver

at

Sta

te H

ighw

ay 1

6 ne

ar

.d

o

Pea

rl R

iver

at

Mee

k's

Bri

dge,

nea

r C

anto

n.

Mis

s

Wes

t F

ork

Tom

bigb

ee

Riv

er

at

Net

tlet

on,

Sou

th

For

k A

mer

ican

R

iver

ne

ar

Kyb

urz,

C

ali

f.-

do

Wes

t F

ork

Tom

bigb

ee R

iver

nea

r N

ettl

eton

,M

iss.

do

--do. . .

... .

.do..

... .

do -

Sou

th F

ork

Am

eric

an R

iver

nea

r C

amin

o, C

alif

. ..

.. -do.... .

....

. ..

.. ..

....... .

..... ..

. .

Kla

mat

h R

iver

at

Som

esba

r, C

alif

. ...

....

....

. d

o

... .

...... ..

....

....

....

... .

........ .

-.-

do. ..

. ..

. ...

... .

.. ..

...

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o..

. .....

... .

....

....

....

....

.. ..

. .........

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o .

Kla

mat

h R

iver

nea

r Z

lam

ath,

Cal

if.. ..

....

..... d

o...

....... . ..

....

....

....

....

d

o......

..

....

...... ..

do...

Dis

tric

t N

o. 339

327

331

289 35 56 31

43

32

305

315

243

286

218

279

270 20

31

27

46

Type

of c

ross

se

ctio

n

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

Wid

th

(ft)

1,36

0

674

630

383

626

358

405

570

640

1,24

0 55

3 2,

000 89 110

1,25

5

545

314

328

345

330

367

113

129

160

170

201

220

246

690

660

610

454

Are

a (s

q ft

)

9,36

0

6,99

0 4,

880

7,69

0 13

,000

3,

490

2,86

0

12,3

00

5,75

0

8,60

0 6,

100

59, 3

00 349

477

12,6

00

2,78

0 1,

760

2,77

0

3,43

0 4,

830

6,54

0 53

6 82

6

877

1,09

0 2,

420

3,55

0 5,

560

15,1

00

9,18

0 4,

100

1,66

0

Mea

n ve

loci

ty

(fps

) 2.01

2.99

.8

7

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

Dis

char

ge

(cfs

)

18,8

00

20,9

00

4,26

0

29,8

00

32,5

00

5,66

0 6,

490

34,3

00

9,41

0

28,4

00

16,9

00

239,

000 390

1,32

0 62

,500

6,49

0 10

,100

16

,600

20,4

00

31,9

00

46,8

00

1,23

0 2,

620

965

1,91

0 9,

680

25,9

00

43,6

00

131,

000

52,9

00

15,0

00

3,21

0

Hy-

dr

auli

c ra

dius

(ft) 6.

8

10.4

9.

1

19.4

20

.2

9.5

6.9

16.5

8.8

6.9

10.5

27

.8 3.8

4.3

9.9

5.0

5.6

8.3

9.8

14.1

17

.3

4.5

6.1

5.4

6.3

12.1

15

.2

21.4

21.5

13

.8

6.7

3.6

Max

i­

mu

m

dep

th

(ft)

6.9

8.4

31.3

11.7

9.

0 11

.2

12.5

18

.0

25.0

10

.2

12.7

7.9

9.6

16.8

15

.0

33.6

31.5

21

.5

12.7

7.7

Max

i­

mum

po

int

velo

city

(f

ps) 1.71

4.98

9.

94

4.98

9.

76

9.33

10.5

6 10

.06

12.4

7 3.

91

5.22

2.26

3.

56

9.08

13

.20

15.0

3

12.1

0 8.

24

4.69

2.

51

Rou

gh­

ness

co

effi

­ ci

ent

(») 0.04

0 .0

38

.038

.0

35

.035

.0

45

.042

.045

.0

40

.038

.0

38

.038

.035

.0

35

.038

.0

42

Alp

ha

coef

fi­

cien

t («

) 2.91

1.42

2.

06

1.54

2.

03

2.04

1.

86

2.27

1.93

2.62

1.

71

1.20

1.30

1.40

1.

61

1.46

1.

40

1.39

1.60

1.

48

1.73

1.

64

1.58

1.82

1.

68

2.32

1.

90

2.17

1.20

1.

25

1.14

1.

19

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 &

§11a" S S I

o i a

\>°

ft !O

!M

> so eo eo eo ^ co co

TAB

LE 5

. Tw

o-po

int

(0.#

d/0.

Sd)

velo

city

dis

char

ge-m

easu

rem

ent data

Con

tinu

ed

Inde

x N

o. 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

Sta

tion

and

loca

tion

Tul

e R

iver

nea

r S

prin

gvil

le,

Cal

if. ...... .

......

- d

o..

. __ . _

- __

_ . _

...-

...-..-...-

_ ..

do

..... _

_ . _

- _

__

. _

- __ ..

.........

..

do .

.. ..

.

.... .d

o..

.. .

........... - ..-.. _

....

do-.... _

_

..

.

d

o

..... d

o... .

....

..

. ..

... .

.. ..

....... d

o ..

. ...

....

. do..

. . ................ ...

d

o..

....

..

_ ..

. ... _

_ ..

........

..

do... .

........... .

.-.... ..

.. ..

. ..d

o .

... ..

. ... ..

.. ..

.. ..

Sou

th F

ork

Ker

n R

iver

nea

r O

nyx,

Cal

if ..

....

do. - _

..

... .

......

_

do .

..

________ _

__ . ___

..

.do ..

. ..

... -

... -

do

..

. ..... ..

.. ..

....

. .

.d

o .

....

- -do- . _

_ ..

. ...

.. ..

....

-do - _

..... ..

...

Sil

ver

Cre

ek

belo

w

Cam

ino

dive

rsio

n da

m,

Cal

if.

.do .

.. ..

... ..

.

-do - _

_ . _

....... ..

....... _ .

d

o..

... ..... ..

... .

... .

.. ..

.... ..

... do.. ..

. _

_d

o .... ..

... .

.. ..

... ......

. do

..

..

....

. do .

....... .

..... ..

.. ..

.

_ ..d

o..

... .

.... ..

... .

... .

..... .

....

....

Dis

tric

t N

o.

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

QO

Q

291

279

305

Type

of c

ross

se

ctio

n

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

Wid

th

(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

Are

a (s

q ft

)

169

177

191

201

211

240

552

265

300

351

396

451

466

587

1,66

0 93.1

108

156

204

239

306

426

438

544

690

211

246

265

290

285

322

01 1

409

492

623

Mea

n ve

loci

ty

(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

Dis

char

ge

(cfs

) 380

489

528

699

833

1,03

03,

230

740

1,10

01,

380

1,91

02,

480

2,70

0

3,58

07,

950 53

.711

338

1

970

1,20

015

960

572

3

1,47

02,

700

489

702

890

979

1,01

01,

310

7A<?

1,05

0

1,48

02,

590

Hy­

dr

aulic

ra

dius

(f

t) 3.6

3.1

3.5

3.4

3.4

3.2

2.4

3.5

3.6

4.2

4.6

5.1

5.3

6.2

5.8

2.2

2.3

3.0

3.2

3.6

5.0

5.2

5.4

5.0

5.9

2.4

3.0

2.8

3.1

3.0

3.4

2.2

2.4

2.7

3.0

Max

i­

mum

dep

th

(ft) 4.

95.

05.

1

5.3

5.8

6.5

7.5

5.1

5.2

6.2

6.8

7.4

7.6

9.1

10.6

2.9

3.1

4.3

5.1

6.0

7.9

9.6

9.7

10.9

12.0 4.6

5.7

5.7

5.9

3.6

3.9

4.8

Max

i­

mum

po

int

velo

city

(f

ps)

4.19

4.99

5.68

6.29

7.27

7.97

13.6

03.

91

5.00

5.50

6,57

7.64

8.21

9.12

7.47 .88

2.11

3.33

6.71

6.99

1.34

3.69

3.80

5.36

7.07

5.74

9.13

8.95

10.1

9

4.03

4.77

6.22

Rou

gh­

ness

co

effi­

ci

ent

(n)

0.04

0.0

40.0

40

.040

.040

.040

.040

.050

.050

.050

.050

.050

.050

.050

.050

.032

.032

.032

.032

.032

.040

.040

.040

.045

.045

.055

.055

.055

.055

.055

.055

.035

.035

.035

.035

Alp

ha

coef

fi­

cien

t («

) 1.66

1.56

1.82

1.57

1.67

1.65

2.21

1.32

1.30

1.30

1.19

1.21

1.21

1.34

1.28

1.35

1.41

1.21

1.25

1.25

2.89

2.96

2.19

1.83

1.71

2.74

2.78

2.80

2.98

2.63

2.84

1.33

1.34

1.34

1.32

w Ed

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

-.d

o.-

.... .d

o

... .

.do

....

.....d

o .

Big

Gre

ek a

bove

Pin

e Fl

at R

eser

voir

, C

alif

. do

do

do

Kin

gs E

iver

bel

ow N

orth

For

k, C

alif

. do

.. d

o.

do .do

.do.

-d

o.K

ings

Riv

er b

elow

Pin

e Fl

at D

am,

Cal

if.,

. do .

d

o... .

.do.

.do.

-do.

-do.

.d

o.

.do.

-d

o.-d

o.K

ings

Riv

er n

ear H

ume,

Cal

if.

.__

do

__

__

__

__

__

__

_.

-do.

-do.

Fres

no R

iver

nea

r D

alto

n. C

alif

. .. do ,

. d

o.. .. .

.do.

.d

o..d

o.Sa

n Jo

aqui

n R

iver

nea

r N

ewm

an, C

alif

. . d

o. __ . _

.do.

.d

o.

.do.

.d

o.

-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

D D D D A A A A D D D D D D D A A A A A A A A A A A D D D D D D D D D A D D A A D A A A

212

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

1,04

0

1,230

1,98

0984

1,18

01,

510

1,700

1,84

02,000

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

1,74

02,830

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

3,16

04,180

5,280

6,84

0 65.2

216

826

1,160

284

968

1,42

02,680

3,940

6,790

11,700 598

984

1,93

0

2,590

3,000

4,070

4,800

6,810

7,020

9,290

11,3

001,050

3,510

4,02

08,960

1,880

2,770

3,180

3,610

4,020

6,170

648

1,050

1,770

2,050

2,540

3,420

6,750

14,400

3.3

3.8

4.1

4.8

1.8

2.3

3.4

2.8

2.5

3.2

3.5

4.0

4.6

4.7

6.7

3.5

4.1

5.0

5.5

5.9

6.3

6.5

6.9

6.9

7.8

8.2

2.3

3.5

3.6

4.7

3.0

3.3

3.8

4.1

4.0

5.8

5.8

4.5

4.9

5.1

5.2

6.1

8.6

10.9

5.0

5.6

5.6

6.8

3.0

3.2

5.5

4.1

4.1

5.4

6.1

7.4

8.2

9.5

11.5

4.5

5.2

6.3

7.0

7.2

7.8

8.2

9.1

9.3

10.5

11.0

3.8

5.4

5.3

7.1

6.3

6.7

6.6

7.2

6.7

11.0

8.9

7.5

8.4

7.6

10.0

10.1

15.0

20.7

7.16

8.03

9.03

9.75 .96

2.02

4.40

6.86

1.42

2.62

3.42

4.58

5.68

6.59

8.75 .86

1.26

1.97

2.30

2.44

2.88

3.20

3.96

4.05

5.46

5.87

5.33

9.18

10.1

315

.91

6.08

6.61

7.14

6.87

7.23

8.22 .79

1.87

1.15

2.55

2.38

2.90

3.41

4.42

.040

.040

.040

.040

.045

.045

.040

.040

.065

.060

.060

.050

.050

.050

.045

.040

.040

.035

.035

.035

.035

.035

.035

.035

.035

.035

.060

.055

.055

.050

.035

.035

.035

.035

.035

.035

.030

.030

.030

.030

.03

0.0

30

.030

.030

1.41

1.41

1.41

1.38

1.36

1.34

1.45

1.37

1.32

1.21

1.24

1.34

1.33

1.23

1.29

1.20

1.22

1.23

1.24

1.29

1.26

1.20

1.23

1.24

1.42

1.36

1.33

1.27

1.28

1.36

1.34

1.22

1.26

1.24

1.14

1.22

1.28

1.49

1.25

1.25

1.24

1.34

1.28

1.29

TABL

E 5.

Two-

poin

t (O

.Sd/

0.8d

) ve

loci

ty d

isch

arge

-mea

sure

men

t data

Con

tinu

ed

Inde

x N

o. 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

Stat

ion

and

loca

tion

Mer

ced

Riv

er a

t Po

hono

Bri

dge.

Yos

emite

, C

ali

f.. ._

-do.... .

..

do.....

...

. ..

....

. _ _

.-.-

. -.-

. .d

o..

.. _

._ . _

-

Sout

h Fo

rk M

erce

d R

iver

at

Waw

ona,

Cal

if. -

-d

o..... . .

. _ d

o..

... _

....

. __

. _ .... _

-

..

do..

... ..

. .

. -do--

Sout

h Fo

rk M

erce

d R

iver

nea

rBl P

orta

l, C

alif

. .

-d

o..

.. -

. _

..d

o

d

o..

..

... -

do . .. . .-.

doM

erce

d R

iver

at

Bag

by, C

alif _

__

__

__

__

. .

do

. . . . ._

-d

o.......

....

.do

...

..

...

....

.d

o..

..

....

. ..... ..

....

- ..

do--

.

Mer

ced

Riv

er

at

Hap

py

Isle

s B

ridg

e ne

ar

..d

o-.-

Mer

ced

Riv

er

at

Hap

py

Isle

s B

ridg

e ne

ar

Yos

emite

, C

alif

. _. . ...

... -

do

...

....

. do....

.

.... . ..

....

.. . -

do

.. .. . .

....... -

.... . ..

....

.

..d

o...... ..

......... ...

....

..

....

..... .d

o..

....

..

... ..

. ... ......

..

do..

. _ .do..

. .

........ ..

....

. ..... .

Dis

tric

t N

o. 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 c

ross

se

ctio

n

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

Wid

th

(ft) 10

410

511

412

3 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

Are

a (se

t ft)

242

288

326

395

175

196

222

239

272

393

420

452

456

483

585

689

951

1,06

01,

160

1,20

01,

260

1,55

0

209

209

232

330

330

456

273

690

889

1,17

01,

030

810

Mea

n ve

loci

ty

(fps

)

3.02

3.27

3.65

4.56

2.12

2.

413.

103.

324.

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

Dis

char

ge

(cfe

)

730

941

1,19

01,

800

372

472

688

793

1,16

0

205

490

751

929

1,31

0

2,36

084

52,

100

2,64

03,

950

4,48

05,

560

8,80

0

494

551

619

1,54

01,

700

2,69

038

3

2,53

03,

920

6,04

01,

110

1.54

0

Hy­

dr

aulic

ra

dius

(f

t) 2.3

2.7

2.8

3.2

2.3

2.4

2.7

2.9

3.5

4.9

4.9

5.3

5.3

5.3

5.7

4.8

6.5

7.2

7.6

7.9

8.1

9.1

2.6

2.6

2.8

4.1

4.2

4.8

2.2

4.0

4.9

6.2

8.1

5.8

Max

i­

mum

dep

th

(Ft) 3.

53.

94.

24.

8

2.9

3.3

3.7

3.8

4.6

7.1

7.2

7.7

7.9

8.2

9.3

7.0

10.5

12.2

13.0

12.9

13.0

15.9

3.7

3.7

4.1

5.4

5.2

6.9

3.2

6.1

7.2

8.9

11.8

9.4

Max

i­

mum

po

int

velo

city

(f

ps)

4.40

4.69

5.60

6.87

3.24

3.

654.

705.

276.

39

1.01

2.

533.

514.

446.

11

7.71

2.07

3.37

4.38

5.18

5.53

7.36

10.7

8

3.93

5.00

4.17

6.89

8.00

9.34

2.05

5.01

6.26

7.66

1.76

2.68

Rou

gh­

ness

co

effi

­ ci

ent

(»)

0.04

5.0

45.0

40.0

40

.040

.0

40.0

40.0

40.0

40

.045

.0

45.0

45.0

45.0

40

.040

.045

.045

.045

.045

.040

.040

.040

.055

.055

.055

.050

.050

.050

.040

.040

.040

.040

.030

.030

Alp

ha

coef

fi­

cien

t («

) 1.25

1.30

1.33

1.25

1.30

1.

331.

331.

401.

31

1.69

2.

162.

082.

462.

54

2.19

1.38

1.41

1.55

1.33

1.23

1.39

1.67

1.29

1.87

1.35

1.23

1.25

1.39

1.30

1.22

1.19

1.21

1.48

1.25

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-(

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E 5

. Tw

o-po

int

(0.2

d/0.

8d)

velo

city

dis

char

ge-m

easu

rem

ent

data

Conti

nued

Inde

xN

o. 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

Stat

ion

and

loca

tion

Stan

isla

us

Riv

er b

elow

G

oodw

in D

am n

ear

Kni

ghts

Fer

ry, C

alif.

-d

o...... .. .. ..

.. ..

... .d

o.

do

- - _

_ ..

_____ _

__

__

___ .

do

. _

__

__

_________ _

_

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__

. _ _

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_ . _

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doSo

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Fork

Cal

aver

as R

iver

nea

r Sa

n A

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Cal

if.

d

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Cal

aver

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Cre

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ear

San

And

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, C

alif

__

M

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umne

Riv

er n

ear

Mok

elum

ne H

ill,

Cal

if,

d

o.....-

... .

.do

-

do

d

o

do.

Nor

th F

ork

Cos

umne

s R

iver

nea

r E

ldor

ado,

C

ali

f.

__ . _

_

__

__

__

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do

do d

o.

do _ .

. .

__ _

_

_

__

d

o

do

. d

o .

Sout

h Fo

rk C

osum

nes

Riv

er n

ear

Riv

er P

ines

, C

alif.

do...... ..

....

.... ..

....

....

........

Dis

tric

t N

o.

42 47 16 15 442

399

449

443

389 49

100 48 44

1,04

1 1,

039

1,03

3

1,03

79

fi

^R 632,

653

2,65

6

101

123

122

100 99 75 386

366

365 6 24

Typ

e of

cros

s se

ctio

n

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

Wid

th

(ft) 12

5

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

Are

a (s

q ft)

622

639

1,12

01,

240

208

302

650

1,11

02,

850

439

575

725

441

329

333

346

555

137

263

331

805

208

244

371

391

415

565

697

890

1,43

0

111

202

Mea

n ve

loci

ty

(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

Dis

char

ge

(cfs

)

1,78

0

2,05

04,

870

5,92

036

054

4

1,09

02.

150

8,46

035

0

1,11

0

3,26

02,

850

996

1,04

01,

110

2,43

023

055

073

82,

330

296

343

777

897

1,08

0

2,47

02,

340

3,28

07,

380

218

988

Hy­

dr

aulic

ra

dius

(f

t) 4.9

5.0

7.1

8.0

2.4

3.2

5.2

7.8

13.8

4.3

5.1

6.2

4.6

3.2

3.3

3.1

4.3

2.6

4.2

5.0

9.0

2.5

2.9

4.2

4.3

4.5

5.7

5.1

6.8

8.9

2.9

4.5

Max

i­ m

um

dept

h (f

t) 7.6

7.6

11.4

12.5 6.0

4.3

8.1

13.1

23.6

6.8

8.2

9.3

8.8

4.4

4.4

4.5

6.0

4.5

7.2

8.2

14.8

3.3

4.6

6.2

5.8

6.7

7.6

6.9

9.6

14.4

4.6

7.0

Max

i­ m

um

poin

t ve

loci

ty

(fps) 6.

22

6.59

8.22

9.59

2.50

2.34

2.73

3.73

4.98

1.28

3.12

7.56

11.0

8 4.

34

4.54

4.59

7.08

2.62

3.12

3.29

4.16

2.28

2.53

3.55

3.86

4.38

7.47

5.22

5.18

7.25

3.04

8.26

Rou

gh­

ness

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(«)

0.05

5

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45

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.045

.045

.035

.035

.040

.040

.035

.035

,035

.035

.035

.035

.030

.030

.030

.040

.040

Alp

ha

coef

fi­

cien

t (a

) 2.10

1.87

1.82

1.74

1.27

1.12

1.43

2.02

1.71

1.37

1.48

1.40

1.61

1.

26

1.27

1.25

1.38

1.48

1.41

1.44

1.36

1.40

1.75

1.69

1.62

1.44

1.56

1.13

1.20

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I i i o CD

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TAB

LE 5

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loci

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-mea

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men

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Con

tinu

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Inde

xN

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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

Sta

tion

and

loca

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Pit

Riv

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Cal

if. _

__

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d

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Mil

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Cal

if . , .

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Dis

tric

tN

o.

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

Typ

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cro

ss

sect

ion

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

Wid

th

(ft) 13

0

1 ^7

9ftf

l

210

91 7

224

OO

O

240

100 98 104

107

130 96 105

111

125

f Q

Q

79 73 73 72 76 80 80 60 67 66 63 66 88 100

107

157

158

163

Are

a (s

q ft

)

290

357

5AO

646

OQ

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1,04

0

i 97

O1,

410

255

332

364

705

OQ

9

480

623

749

QH

A

251

300

338

306

49Q

554

561

211

228

257

97

fi

323

256

9Q7

381

478

728

468

Mea

n ve

loci

ty

(fps

) OK

1.17

1.57

1.87

2 O

ft

3.51

4 00

4.45

39C

3.57

4.34

4.40

6.26

3.77

5.63

6.57

7 00 Q

O

1.21

1.76

2.35

9

Q1

3.21

3.37

1.46

1 7R

2.58

3.22

3 O

ft

4.34

4.81

5.59

6Q

Q7.

011.

31

Dis

char

ge

(cfs

) 246

lift

1,21

02,

580

5,08

06,

280

oo-i

079

1 dir

t

1,60

04,

410

QQ

A

1,81

03,

510

4,92

06,

340

233

364

594

718

1,25

01,

780

1,89

030

8

an«

663

869

1,28

01,

110

1,43

02,

130

3,34

05,

100

615

Hy­

dr

auli

c ra

dius

(f

t) 9

9

20

9

^

3.1

4.1

4.6

5 4

5.8

2.5

27

3.1

3.3

50

4.0

4.4

5.5

6.0

6.4

3.4

3.9

4.5

4.1

5 A

6.5

6.6

3.4

3.3

3.7

4.1

4.7

2.8

2.9

3.5

3.0

4.5

2.8

Max

i­

mum

de

pth

(ft) 4.

1

4.6

5.4

5.9

7.0

7.7

8.6

9.2

4.1

49

4.9

5.3

81

6.1

6.6

8.1

9.5

10.0 5.2

7.5

6.8

6.8

7.7

11.5

11.4 4.2

4.0

4.5

15 9

6.1

4.0

4.1

5 7

5.6

8.9

4.3

Max

i­

mum

po

int

velo

city

(f

ps)

1.81

2.73

3.54

3.82

5.34

5.76

6.61

7.28

6.47

6.08

7.44

7.28

10.8

93.

384.

987.

28

8.58

9.28

1.39

1.89

2.57

3.40

4.29

4.87

9.26

1.94

2.56

3.59

4.67

5.80

6.31

6.96

7.83

10.3

39.

852.

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Rou

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0.06

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1.76

1.82

1.58

1.46

1 48

1.41

1.41

1.42

1.44

1.37

1.60

1.17

1.17

1.12

1.14

1.19

1.29

1.43

1.36

1.28

1.37

1.40

1.36

1.13

1.20

1.17

1.19

1.18

1.24

1.25

1.18

1.24

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-mea

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men

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Con

tinu

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Inde

x N

o. 994

995

996

997

998

999

1000

1001

1002

1006

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1010

1011

1012

1013

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1017

1018

1019

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1022

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Stat

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Mid

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Dis

tric

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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 c

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se

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n

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

Wid

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(ft) 11

0

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

Are

a (s

q ft)

312

376

506

665

924

189

264

357

447

575

571

739

665

866

1,12

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340

499

521

560

594

630

855

191

275

345

465

629

704

236

276

339

399

Mea

n ve

loci

ty

(fps

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5.22

6.33

6.84

9.56

8.84

1.75

2.68

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Max

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1.57

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Inde

xN

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1089

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9110

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1096

1098

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1100

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1104

1105

1106

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1108

1109

1110

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1112

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178

191

166

165

155

157

378

364

382

377

266 26

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D A A A D A A j^ A A

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118

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109

112

114

141

109

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Are

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228

349

491

224

289

341

399

132

199

209

309

641

762

511

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746

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428

636

735

744

338

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109

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3.55

4.56

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6.91

1.83

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3.5

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2.6

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6.3

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Max

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7.2

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8.5

3.7

4.5

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1185

1187

1189

1192

1193

1195

1196

1197

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1199

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1201

1202

1203

1204

1205

1207

1209

1210

1212

1213

1214

1216

1217

1218

1219

1220

1222

1223

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305

298

279

91

i

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

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(ft) 16

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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

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31.0

32.6

32.7

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69.3

38.6

43.0

46.5

13.0

12.9

22.7

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23.5

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51.2

70.2

21.1

26.7

32.6

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78.0

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4.27

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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

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2.23

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6.30

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Max

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1.03

VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C43

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o-po

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(0.2

d/0.

8d)

velo

city

dis

char

ge-m

easu

rem

ent data

Con

tinu

edo

Inde

x N

o.St

atio

n an

d lo

catio

n

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Dis

tric

t N

o. 221

222

994

225

226

227

9«»7

258

259

260

262

263

264

9fi«

»

9fif

i

202

241

252

253

257

262

9fi«

»

266

267

275

276

277

278

281

288

293

295

296

299

303

306

Typ

e of

cro

ss

sect

ion

Wid

th

(ft) 475

475

300

300

234

140

161

120

140

190

284

OK

K

184

130

1 t\

*\

574

580

550

542

519

511

«»97

578

519

526

527

KO

A

517

511

504

509

513

510

510

511

517

Are

a (s

qft)

4 45

04,

520

1,70

01,

770

1,19

046

11O

4

516

695

1,30

02,

180

1,87

01,

170

605

352

11,6

0011

,800

8,46

07,

170

4,37

02,

700

5,82

011

,300

4,44

0

5,05

05,

690

4,83

04,

540

2,46

0

1,94

02,

260

3,72

03,

110

2,81

0

3,02

05.

370

Mea

n ve

loci

ty

(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

Dis

char

ge

(cfs

)

36,0

0035

,600

8,78

09,

570

6,23

01,

580

511

1,12

02,

470

5,74

013

,800

11, 2

003,

800

829

445

80, 2

0078

, 100

42,2

0032

, 200

13,2

004,

390

23, 3

0078

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14, 0

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18,6

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16,2

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3,71

0

2,11

03,

090

9,65

06,

480

5,27

0

6,07

020

, 300

Hy­

dr

aulic

ra

dius

(f

t) 9.2

9.4

5.6

5.8

5.0

3.2

2.4

4.2

4.9

6.7

7.6

7.2

6.2

4.6

2.3

19.9

20.1

15.2

13.1 8.3

5.2

10.9

19.2

8.5

9.5

10.7

9.2

8.7

4.8

3.8

4.4

7.2

6.1

5.5

5.9

10.2

Max

i­

mum

de

pth

(ft) 16

.918

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79.

2

9.6

5.8

3.7

7.5

8.0

12.8

16.3

15.8

11.5

8.0

3.7

24.7

25.2

18.3

16.3

12.0

8.8

14 4

23.7

12.0

13.4

14.4

12.4

12.3

8.2

7.3

7.7

10.6

9.4

8.9

9.5

13.8

Max

i­

mum

po

int

veoc

ity

(fps

)

10.4

210

.42

8.41

9.20

9.60

6.77

1.98

4.32

6.64

9.34

11.8

211

.76

7.55

3.49

2.34

10.2

89.

427.

366.

63

4.26

2.39

5.62

10.0

34.

43

5.19

5.82

4.65

4.48

2.18

1.77

2.05

3.67

2.94

2.71

2.94

5.20

Rou

gh­

ness

co

effi

­ ci

ent

(»)

Alp

ha

coef

fi­

cien

t («

) 1.12

1.13

1.38

1.38

1.80

1.96

1.33

2.06

1.72

2.38

1.75

1.87

2.62

2.92

1.71

1.31

1.26

1.30

1.31

1.31

1.32

1.31

1.32

1.28

1.26

1.29

1.25

1.24

1.33

1.39

1.34

1.26

1.27

1.25

1.28

1.25

VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C45

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