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TRANSCRIPT
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
er a
t R
iver
bank
, N
.Y____._
__ _
_
A82
W
abas
h R
iver
at
Del
phi, In
d_
_
_
-
B
83
Koo
tena
i R
iver
nea
r B
onne
rs F
erry
, Id
ah
o..
.._
_-_
_..
A
84
Bro
ad R
iver
nea
r B
ell,
Ga____ __....__ ...
B85
C
alca
sieu
Riv
er n
ear
Obe
rlin
, L
a . _
... .
B
St.
Cro
ix R
iver
nea
r R
ush
Cit
y, M
inn
__
_
.
A
87
Peco
s R
iver
at
dam
site
3, n
ear
Car
lsba
d, N
. M
ex.. .
AN
orth
Pla
tte
Riv
er n
ear
Goo
se E
gg, W
yo
__
__
_ _
_
DM
issi
ssip
pi R
iver
at
Che
ster
, 11
1...-
. .. _
B90
M
isso
uri
Riv
er a
t Pi
erre
, S.
Dak
.. .
...
. _
_
...
A
91
Pud
ding
Riv
er a
t A
uror
a, O
regon .
A92
C
olor
ado
Riv
er a
long
Col
orad
o-U
tah
Sta
te L
ine... _
A
Gro
nd R
iver
at
Ioni
a, M
ich
.._
_
B94
W
abas
h R
iver
nea
r N
ew C
oryd
on, I
nd
..
_
A
95
Cro
oked
Riv
er n
ear
Cul
ver,
Ore
g_..._
__ ...__
A
96
Mis
siss
ippi
Riv
er a
t T
hebe
s, 1
11_ .
B97
M
issi
ssip
pi R
iver
at
Alto
n, 1
11.... -
-__ ...
BSa
ngam
on R
iver
at
Mah
omen
t, 111.-
. .
BG
rand
Riv
er a
t L
ansi
ng, M
ich_
B10
0 B
el R
iver
at
Scot
ia, C
ali
f_______________-_
_..
B
Atw
ater
Can
al, n
ear
Atw
ater
, C
alif
., si
te 1
. _
_..
...
._.d
o....._
______._
_._
_.s
itel
....___-
....
.do
_ _
_._
_
__
_ s
ite 2
.. _
_
...
.. d
o_ _
_
__ s
ite 2
. ..
....
....
.. d
o. sites -. - -.
. d
o.
.. s
ites
..
...
.do__._
___________ s
ite 4
_._
__...
.. d
o_
.
....
....
....
.
sit
e 4
.A
rena
Can
al n
ear
Liv
ings
ton,
Cal
if.,
site
1..
. d
o.
. s
itel..
.do..........
.do.........
-d
o..
.-...
.__
__
_si
te 2
. ..
. .
sit
e 2
. ________si
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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;
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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
u:° «o co id 06 os IH oi t CN Tj< T| *
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K S'O; _S ca 3 t-
t»T|l«OCO O tOOcN«O t^ «OOOi-lt>00 t^ 00 O COCN O OO O i-l «>
OOOOOO-^H CM CO*i-Hi-*Os' -^J t^OOCNCM* CO OO 00 Old l> CO 1^' CO* i-iCOCO"^*^ CO CO"^*^*1N CO CO-^^COCO CO t-H i-l ** i-l TH
o gi-H 00
t*- l> TH O ^tl OO ^* OO OS O OS CNCN CN-*«>rH £>]
i-H 00 CO O OS CO I'-t JrHOOCO CN OOCNCO-flt * t>TPCNOSCO CM O OS OS-* i-H ^f OS
4i-Hos'i-H co* CD'CAOSIO CD* t* oi os o o o CN c4 CM'CO co CN'I-H
St^rHCO CO Ot~CNOS CNg 1 § o o oo o
O OO lOO 00
oT oTco'-*'>o' id"CO -*1010CO CO
S8S8 Si-H i-l t- t> Ol
«o poopooooi-< CD t~ Tl<
lOrH CN *!CM M3 C
CD CO CD CC CDOCN CO
iOlO 10
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. ..
. ..
. ...
... .
.. ..
...
.... .d
o..
. .....
... .
....
....
....
....
.. ..
. .........
..d
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§?
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O i-H t-O OOOQ OO W 33OOO O O i-H«OO
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S3 SSS§||S|§2 2§|=§ S3 S 33§!
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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-(
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
cococCO 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 torr»r»r J^'tot-.c
:SKKIOSONgJ gi
iOi CT»O O f-t-OOCO
TABL
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
. _
__
__
_________ _
_
.do.. _
__
. _ _
_ - _
_ . _
_ -
do-.
doSo
uth
Fork
Cal
aver
as R
iver
nea
r Sa
n A
ndre
as,
Cal
if.
d
o...
Cal
aver
itas
Cre
ek n
ear
San
And
reas
, C
alif
__
M
okel
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.
__ . _
_
__
__
__
__
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
co
effi
ci
ent
(«)
0.05
5
.055
.050
.050
.035
.035
.035
.035
.035
.045
.045
.045
.035
.0
45
.045
.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
1.25
1.35
1.40
I i i o CD
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 OiO^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
i-
3^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
TAB
LE 5
. T
wo-
poin
t (0
.2d/
0.8d
) ve
loci
ty d
isch
arge
-mea
sure
men
t data
Con
tinu
edo
Inde
xN
o. 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
Sta
tion
and
loca
tion
Pit
Riv
er n
ear
Bie
ber,
Cal
if. _
__
__
__
__
d
o....
.-...do.
..... d
o..
..
....
.do .
d
o
do.
.. .
_
... .
.... .
.. _
_ .
. ..
...
... .
.do.... . .
..... d
o .
... .
.. ..
. ... ..
. ..
... .
... .
....
..... d
o.... .... _
..
....
..
do
. _____ _
.
...
.. .d
o.. ..
.
do ..
do
.
... .
.do
..
. ... ..
......... .
.. ..
...
. .d
o..
....
. - _
____
do_
do
....
.d
o.... ..
.. ..
.. . ..
....
... .
....
...
.. . d
o ..
. ..
...
....
.do
.
d
o.. ..
. ... ..
.M
ill
Cre
ek n
ear
Los
Mol
inas
, C
alif
............
.....d
o...
..
do
....
.. ...
..
....
....
..
....
....
....
. .... .
.do
...
..
...............
doT
hom
as C
reek
at
Pas
kent
a, C
alif
. . ..
..d
o
. d
o.........
do
. _
__
__
.
- ...
d
o....
Cow
Cre
ek n
ear
Mil
lvil
le.
Cal
if . , .
...
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
e of
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
O
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
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.
37
Rou
gh
ness
co
effi
ci
ent
(re)
0.06
5
nflf;
.060
.060
AC
K
.055
.050
.050 fU
<5
.045
.045
.045 fU
K
.050
.050
.050
.050
.050
.040
.040
.040
.040
.035
.035
.035
.040
.040
.040
.040
.040
.035
.035
.035
.035
.035
.035
Alp
ha
coef
fi
cien
t («
) i on
2 04
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
1.21
1.48
5 CQ
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!?S2JOOO OOOOO OOOO
osootMt- i~- foo-^tto o^£.ioog toooor»ioiocnSoo -oicoN.-<t, «^"O>t-S ooioooosco'>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
NoJcoco-* ^j«c>ic<ici« « « ui to rH oiNcom'* loeocotdtd t^i^odoi
ooooo OOOON t-ioooco *-» N w o oIM^«TlHO tOCq^OCO CCONOdr-l CQCOOCOt- ^*t^OJr-t tOeoOr-IO 00 O »M ^ -^* lOr*»O3OC<l
0^4 LCOOOO o^i*cx)aso oooottt->O «>OO_I>O ^"NMOOr-l 'SS'"1 ®
CC ^ t^OO»Ht» tO-^^00 1^* OOOCOr-t
COr-tCOOOiO CQOt»t>00COr-tCOt-ooN CC l^ r-t O Or-t
tooo^t*Oco t-i c coocor^o i-iOOlOOir-t t^t-NNWJl ^t
ootooo go>oior~to rttt r»oooo Of-Hr-(eoo oa
i-iwoasr- oooooooboa
QQQQQ
§ ooo«p f-<N«5ooo«pr» O»<M«-*OO .t~00 INWOOc
528 §83§OOOt- !M I CO CO * C<ltocOeocM i-lr i-IOOOO r-lr-lt^lOO « M i-l OJ 5O tO 5
c c Oid c c c c
j3O 8
I3 C
6s03
§ s§ o a0i-2"c 8o
c<e c c
J
O"8p
1oi!1a? c
53 "C"c8
n
c c ^ c T:
^_
Ca
1>
e %$ t-<a h-ifi
C c c c c c T
c c
«*.
i ogSs1 P aa£ «3
§
C
1
C c ^ TCT
c d c «
i
]L|u' S
j|! £
i*'^ ; <»!£
d^ =H3 fcj -C
JA|0
C c T
c ^
c
y1 CO:°
ilili§III s!.Sifn ilipH 1 (U
Ond c ^S 7-'S!^
C-c c c C c c c c c T T
*»QCDOO0> OrHNCO^^10*0100 cojpjpcoc
r-l(N«^< to O t- OO O» S S OO C
TAB
LE 5
. T
wo-
poin
t (O
.Sdj
O.S
d) v
eloc
ity d
isch
arge
-mea
sure
men
t data
Con
tinu
edo
Inde
x N
o. 994
995
996
997
998
999
1000
1001
1002
1006
10
07
1009
1010
1011
1012
1013
1015
1016
1017
1018
1019
1021
1022
1023
1024
1025
1027
1028
1029
1030
1031
1032
Stat
ion
and
loca
tion
Mid
dle
Fork
Fea
ther
Riv
er b
elow
Slo
at,
Cal
if..
. .
do
......
....
....
....
....
....
... .
....
.. ..
.. . -
do...
.. --_
.-. ...................
do.. ..
.
doSo
uth
Fork
Fea
ther
Eiv
er n
ear
Forb
esto
wn,
C
alif
..... _
_ ..
................. _
__ ..
....
.
..
do..
....
....... ._
. ...-
_ _
_.
. -do
-...
do
. _
.
Sout
h Fo
rk F
eath
er R
iver
at
Ent
erpr
ise,
Cal
if..
. .d
o.... _
_-__
d
o
..
do
...-
....
...
_ __ -
... .
.do..
.. .
...............
Wes
t B
ranc
h Fe
athe
r R
iver
nea
r Y
anke
e H
ill,
Cal
if...
.
..d
o........
....
....
....
....
....
....
....
....
...... d
o...
.d
o._
_
_
do
.do ..
.W
est
Bra
nch
Feat
her
Riv
er n
ear
Para
dise
, C
ali
f...
...
....
d
o
d
o
do
..
do....
... ..
. - _
..
.do....
..
....
Span
ish
Cre
ek
abov
e B
lack
haw
k C
reek
at
K
eddi
e, C
ali
f.... ..
. d
o........
..
. ...
d
o..
..
.
---d
o..
Dis
tric
tN
o. 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 c
ross
se
ctio
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
th
(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
01,
340
499
521
560
594
630
855
191
275
345
465
629
704
236
276
339
399
Mea
n ve
loci
ty
(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
Dis
char
ge
(cfs
)
1,63
0
2,38
03,
460
6,36
08,
170
331
708
1,39
02,
050
1,43
0 3,
050
797
1,27
02,
090
3,13
03,
970
271
353
501
752
1,25
0
4,51
0
242
650
1,10
01,
990
4,01
04,
510 64
.723
244
8
950
Hy
dra
uli
c ra
diu
s (f
t) 2.8
3.4
4.4
5.4
6.9 2.4
3.1
4.0
4.6
5.7
5.4
4.3
3.8 4.9
6.2
7.3
5.1
5.3
5.5
5.7
6.1
7.6
2.8
3.9
4.4
5.5
6.8
7.3
2.6
2.8
3.5
4.1
Max
i
mum
de
pth
(ft) 3.
6
4.0 5.5
7.0
9.9
3.4
4.4
5.6
6.6
8.3
7.2
7.4
5.1
6.2
8.0
9.8
9.4
9.7
9.9
10.2
10.2
13.2
4.7
6.5
7.4
8.7
11.5
12.3
5.1
5.6
6.1
6.8
Max
i
mum
p
oin
t vel
oci
ty
(fps
)
7.55
9.31
9.94
12.9
915
.09
3.04
5.19
7.82
8.90
3.76
8.
46
1.59
2.62
3.23
3.85
3.92 .89
1.11
1.47
1.91
2.94
7.98
2.08
4.08
5.34
7.99
11.8
711
.59
.34
1.16
1.95
3.45
Rou
gh
ness
co
effi
ci
ent
(»)
0.05
0
.050
.050
.050
.050
.070
.060
.055
.050
.035
.0
35
.040
.040
.040
.040
.040
.045
.045
.045
.045
.045
.045
.045
.045
.045
.045
.045
.045
.030
.030
.030
.030
Alp
ha
coef
fi
cien
t (a
) 1.23
1.24
1.24
1.22
1.43
1.64
1.61
1.70
1.73
1.37
1.
40
1.28
1.13
1.14
1.16
1.16
1.25
1.32
1.42
1.30
1.30
1.25
1.46
1.57
1.57
1.76
1.72
1.76
1.18
1.16
1.26
1.22
ft) g
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C39
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TABL
E 5.
Two-
poin
t (0
.8d/
0,8d
) ve
loci
ty d
isch
arge
-mea
sure
men
t data
Con
tinu
ed
Inde
xN
o. 1082
10
8510
88
1089
10
9010
9110
9210
94
1095
1096
1098
1099
1100
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1116
1117
1118
11
19
1120
1121
1122
1123
1124
1125
Stat
ion
and
loca
tion
Mid
dle
Yub
a E
lver
abo
ve O
rego
n C
reek
, Cal
if.
d
o_
.._
Mid
dle
Yub
a R
iver
nea
r Alle
ghen
y, C
alif
_ --
__ do
_ _
_ _
__
. _
_
do....
..
do..
..
Bea
r R
iver
nea
r Aub
urn,
Cal
if __
. __
__
.... .d
o....
. ..
. .d
o....
....
. do......
....
. ..
..
...
..........
..do....
....
. do.
_
... ..
....
Mid
dle
Fork
Am
eric
an R
iver
nea
r A
ubur
n,
Cal
if.
....
.do
...
. ... ..
........ ..
....
....
....
.do _
....
....
....
...
.. . ..
....
....
...d
o..
.... - , ..
....
. ...
....
... .
.do. _
. ..
....
. .........
Mid
dle
Fork
Am
eric
an R
iver
nea
r Fo
rest
hill,
C
alif
. . .
do
....
... .
.. ..
. ..... ..
...
..
do... . .-
do
.
__
__
__
__
.... .d
o........ ..
....
........ . ..
Rub
icon
Riv
er n
ear
Geo
rget
own,
Cal
if .
.d
o . , .
....
....
....
....
....
....
....
....
.....d
o........
.............. ..
..................
Rub
icon
Riv
er n
ear
Rub
icon
Spr
ings
, Cal
if. ...
do
____ -
..
do
................... .
...
..
....
......d
o....
..
...
do
. .
do
....
....
................. .
....
....
....
....
Dis
tric
t N
o. 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
Typ
e of
cro
ss
sect
ion
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
Wid
th
(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
Are
a (s
q ft
)
228
349
491
224
289
341
399
132
199
209
309
641
762
511
650
746
962
1,55
0
362
428
636
735
744
338
572
728
109
240
285
364
517
585
190
266
Mea
n ve
loci
ty
(fps
)
2.93
4.
736.
64
1.40
2.
392.
993.
962.
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
Dis
char
ge
(cfe
) 669
1,65
03,
260
313
690
1,02
01,
580
269
533
640
1,22
03,
740
4,48
0
865
1,44
02,
880
4,17
012
,300 91
2
1,52
02,
900
3,63
05,
140
618
1,93
03,
730
180
438
579
749
1,05
01,
160
343
725
Hy
dr
aulic
ra
dius
(f
t) 2.9
4.2
6.1
3.5
4.1
40
5.2
2.2
2.6
2.8
3.4
5.4
6.3
4.8
6.8
6.3
7
0
10.4
3.2
3.5
4K
5.0
4.8 3.4
5.2
6.1
2.4
4.1
3.7
4.1
5.1
5.7
2.6
3.1
Max
i
mum
de
pth
(ft) 3.
75.
07.
5
7.2
7.2
7 9
8.5
3.7
4.5
4.7
5.7
91
10.0
6.6
7.6
8.5
10.7
15.7
6.1
6.7
8.0
8.8
7.7
5.8
7
Q
9.6
3.3
5.3
6.0
79
8.8
9 6
4.6
5.3
Max
i
mum
po
int
velo
city
(f
ps)
5.53
7
ftO
11.1
5
2.37
4Q
7
600
2O
7
4.20
4.60
6.12
11.0
710
.93
2.86
3.93
6.78
7A
Q
11.6
8
3.33
4.60
5.84
6C
Q
10.2
0
3.11
6.32
8.31
2.72
3.
03
3.07
3.45
3.39
3O
Q
3.11
4.59
Rou
gh
ness
co
effi
ci
ent
(«)
0.06
0 .0
80.0
60
.050
.0
50.0
50.0
45.0
45
.045
.045
.045
.045
.045
.040
040
.040 run
.045
.040
.040
.040
.040
.040
.060
.055
.055
.035
.0
35
.035
.040 04
0j\
AK
.
.045
Alp
ha
coef
fi
cien
t («
) 1.43
1.
591.
66
1.58
1.
521
01
1.33
1.37
1.51
1.34
1.41
1.74
1.94
1.63
1.63
1.58
IR
Q
1.40
1.14
1.15
1.21
1.20
1.29
1.50
1.64
1.47
1.43
1.
70
1.34
1.52
1.50
1.54
1.71
1.56
O CQ
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C41
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TAB
LE 5
. T
wo-
poin
t (0
.M/0
.#d)
vel
ocity
dis
char
ge-m
easu
rem
ent data
Con
tinu
ed
Inde
xN
o. 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
Stat
ion
and
loca
tion
doH
untiu
gton
-Sha
ver
cond
uit
at
outle
t, C
all-
____
. do...
.... .d
o..
Mar
ble
Fork
Kaw
eah
cond
uit 3
nea
r Pot
wis
ha
.....d
o.. _
. .
..d
o....
_
_
_ -
..d
o..
...
..
....
....
do
__
..
do
.---
- _ .d
o..
..
....
Ker
n R
iver
con
duit
1 ne
ar D
emoc
rat
Sprin
gs.
Calif-. . ..
.do
do.-
do.
_
___
. .
- _
_-.
...d
o..-.
-
do doPa
cific
Gas
& E
lect
ric
Co.
con
duit
3 be
low
B
ass
Lak
e, C
alif _
_______ -
__
__
_ do
.
Sout
hern
C
alifo
rnia
Ele
ctri
c C
o. c
ondu
it on
__ d
o.. _
. _
__
__
__
__
__
__
__
--.d
o... .
....
. ..
do do..
do
.--.
................... ... .
Dis
tric
t N
o. 307
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
Typ
e of
cr
oss
sect
ion
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
Wid
th
(ft) 16
.316
.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
Are
a (s
q 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
.727
.215
.1
9.6
12.2
15.1
89.8
150
200
Mea
n ve
loci
ty
(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
Dis
char
ge
(cfs
) 137
152 30
.853
.8
116 44 4
68.0
40.0
97.1
139
144
269
425
623 94
.813
818
225
638
1
304
959
1,33
0
100
159 55
.8
19.2
27.2
31.7
36.4
344
824
1,26
0
Hy
dr
auli
c ra
dius
(f
t) 3.9
4.1
3.4
3.8
4.0
1.6
2.0
1.4
2.3
2.5
2.6
4.0
5.3
6.9
2.4
3.1
3.7
4.6
6.1
3.9
6.6
7.6
2.1
2.4
2.4
3.6
1.4
1.5
1.7
2.9
4.6
6.1
Max
i
mum
de
pth
(ft) 5.
15.
4
4.0
4.4
4.7
1.8
2.2
1.6
2.6
2.7
2.8
4.4
6.0
8.4
2.6
3.3
4.0
5.2
7.2
4.3
7.5
8.7
3.0
3.5
2.6
1.6
1.9
2.0
2.3
3.5
5.3
6.9
Max
i
mum
po
int
velc
oity
(f
ps) 2.75
2.65
1.15
1.81
3.29
5.23
6.33
3.82
4.99
7.80
7.47
8.42
9.95
10.1
4
5.34
6.19
6.58
7.28
7.62
4.37
7.47
8.59
5.76
7.25
4.14
2.62
2.88
3.14
3.08
4.68
6.44
7.46
Rou
gh
ness
co
ef
ficie
nt
(ri) 0.02
0.0
20
.020
.020
.020
.014
.014
.014
.014
.020
.020
.020
.020
.020
.020
.020
.020
.020
.020
.015
.015
.015
.015
.015
.015
.025
.025
.025
.025
.015
.015
.015
Alp
ha
coef
fi
cien
t («
) 1.15
1.11
1.22
1.22
1.17
1.04
1.05
1.06
1.04
1.07
1.07
1.04
1.04
1.03
1.03
1.04
1.04
1.04
1.04
1.02
1.03
1.03
1.08
1.08
1.03
1.10
1.09
1.09
1.10
1.07
1.04
1.03
VELOCITY-HEAD COEFFICIENTS IN OPEN CHANNELS C43
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TAB
LE 5
. Tw
o-po
int
(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
....do.-.. . .
....d
o..........................................
__ d
o..
... _
....
__
. ___ . _
_ ..
.. _
. .....
....d
o. _
__
.. _
_ ..
....
__
__
__
....
.
... .
do
....
... .
.. ..
. ... ..
. ... ..
. ... ..
. ...
.d
o..
......
....
...
..
. ...
. d
o ._
_
... .
do..
. ................. . _
do _
. ...
..d
o . _
_ - _
... .
.. ..
... .
....
... .
do
. .
.. ..
. ... ..
. ... ..
....
. ..... ..
. ... ..
.
do _
. _
__ .
_
. __ d
o _
__
_ ..
. ..
_ .- .
...
... .
.do
. ..
.... ..
....
....
....
....
....
....
...
... .
.do..
....
.. .
....
.do
____
_ ..
.. _
_ ..
... _
_ ..
..........
.... .d
o..
.. .. . -
..d
o..
....
... _
... _
. _ ..
. _ ..
....
... _
....
...d
o _
-. . _
.. _
..... _
....
.
..... d
o... _
.._
._
. _
.. d
o... ..
....... .
. ..
...
-.. .
do
.....
....
....
....
....
....
....
....
....
.. ..d
o............... ..
....
....
.. ..
....
....
...... .d
o..
.. ..
. .. .-.. . ..
....
... .
.do..
....
....
....
...
..
....
do..
. ...... ... ..
. __
do _
___
__
.....
.d
o..
. ___
_ ._
__ ..
....
....
....
.. ......
.do
....
....
....
... .
....
... .
............
..d
o..
....
....
....
....
....
....
....
....
....
...
.d
o... . ..
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
,000
14, 0
00
18,6
0023
,100
16,2
0014
,800
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
.08.
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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