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HYDRAULICS BRANCH OFFICIAL FILE COPY
UNITED STATES DEPARTMENT OF THE INTERIOR
BUREAU OF RECLAMATION
COMPOUND WEIR STUDY
Hydraulic Laboratory Report No. Hyd. 505
DIVISION OF RESEARCH
OFFICE OF CHIEF ENGINEER DENVER, COLORADO
April 5, 196 3
The information contained in this re -port may not be used in any publication, advertising, or other promotion in such a manner as to constitute an endorsement by the Government or the Bureau of Reclamation, either explicil or implicit, of any material, product, device, or process that may be referred to in the report.
(,
CONTENTS
Summary and Conclusions ............................. . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratory Installation ................................ . Weir Calibration ..................................... . Data Analysis ........................................ .
Page
1 2 2 3 3
Horizontal Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Sloping Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
References ........................................... 8
Figure
Field and Laboratory Installation of Compound Weirs • . . • . . 1 Laboratory Test Facility . . . . • • • . • . . . . . . . . . . . . . . . • . . . . . . 2 Weir Crests........................................... 3 V-notch with Horizontal Extensions . . • . • • . . • . • . . . • • . . . • . . 4 V-notch with 2-foot Horizontal Extensions . . . . • • . . . . • . . . . . 5 V -notch· with 1-foot Horizontal Extensions . . . • . • • • . . • • • . . . 6 V-notch with Vertical Extensions , • • . . • • . • . . . . . • . • . • . . . • . 7 V -notch with 15° slope. 1-foot Extensions . . • . . • . . . . . . • • • . 8 V -notch Data Comparison with Cohe Equation . • • . . . . . . . • . . 9 Calibration Data for 90° V-notch with Vertical and
Horizontal Extensions . • . . • • . . . . . . • .. . . . . • . . . . . • • • . . . . • 10 Head-Discharge Curves for 90° V-notch Weirs with
Vertical and Horizontal Extensions . . • . • . . . . . • . . . • . • . . • • 11 Constant Determination Curves •....•..••....•••••••..... Calibration Curve for Vertical Extensions •..•.•.......... Calibration Curve for Horizontal Extensions ...••.•....••. Calibration Data for 90° V-notch Weirs with Sloping
12 13 14
Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Head-Discharge Curves for Weirs with Sloping
Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Table
Calibration Data for V -notch with 2-foot Horizontal Extensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Calibration Data for V -notch with 1-foot Horizontal Extensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Calibration Data for V-notch with Vertical Extensions . • • . . 3 Calibration Data for V -notch with 15° slope 1-foot
Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Calibration Data for V-notch with 15° slope 2-foot
Extensions . .............. ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
FOREWORD
The studies discussed in this report were performed during
November 1959 to February 1960 by the Special Investigations
Unit of the Hydraulics Branch. Laboratory experiments were
made by W. B. McBirney, S. G. Parker and J. L. Harper under
the supervision of J. C. Schuster. The data and analysis con
tained were compiled for the report by J. M. Bergmann. The
Special Investigations Unit is in the Special Investigations Section
headed by A. J. Peterka. H. M. Martin is Chief of the Hydraulics
Branch •
UNITED STATES DEPARTMENT OF. THE INTERIOR
BUREAU OE RECLAMATION
Office of Chief Engineer Division of Research Hydraulics Branch Denver. Colorado
Laboratory Report No. Hyd. 505. Compiled by: J. M. Bergmann Checked by: J. C. Schuster Reviewed by: A. J. Peterka Submitted by: H. M. Martin April 5, 1963
COMPOUND WEIR STUDY
SUMMARY AND CONCLUSIONS
Experiments on five weirs, each composed of a 1-foot-deep V-notch weir with vertical, 1- and 2-foot horizontal or 15° upward sloping extensions (Figure 3) were performed to determine the flow characteristics in terms of head-discharge (H-Q) relationships. An analysis of the data was made to obtain correlations between the (H-Q) relationships that could be used to determine the discharge of 1-footdeep V-notch weirs having other lengths of extensions.
The V -notch weirs with horizontal extensions produced a smooth head-discharge curve except in the transition zone where the head just exceeded the depth of the V-notch portion of the weir, i.e •• heads from 1. 0 to 1. 1 feet. The thin sheet of water tended to dribble over the extension because the vertical component of velocity at the weir crest was not sufficient to establish a true contraction.
Weirs with sloping extensions from the V-notch produced better contractions of the lower surface of the nappe for very low heads resulting in a more uniform head discharge curve.
At points of change in the slope of the crest, the rates of discharge change in the H-Q relationships were not completely definable. Therefore, compound weirs should be set so that discharge determination in the transition regions will be of minimum importance. In other ranges of flow the compound weirs; were as accurate as any weir can be. The head-discharge relationships in the form of equations are cumbersome, but simple graphs and tables can be prepared for determining discharge.
Generalized head-discharge equations derived in this report from the test data need to be confirmed by further testing before they are extended to applications outside the range of the data.
INTRODUCTION
Frequently, a single water-measuring device is desired that will accurately measure a wide range of discharges, e. g. , both the normal and flood flows of streams, Figure lA. Proportional weirs and specially shaped flumes, can be designed to be generally acceptable but these devices are often complicated and may cost more to construct than is warranted by the value of the data obtained. The compound weir resolves the cost problem but introduces the problem of complicated head-discharge relationships.
Five compound weirs were tested in the Bureau's Laboratory to define the flow characteristics in terms of the H-Q relationships and to possibly correlate the discharge equations. The weirs, sharp crested and tested under free flow, contracted conditions, consisted of a 90° V-notch 1 foot deep with one of the following extensions:
1. Vertical
2. Horizontal
a. 1 foot in length on each side and vertical sides
b. 2 feet in length on each side and vertical sides
3. Sloping (15° above horizontal)
a. 1-foot horizontal length each side and vertical sides
b. 2-foot horizontal length each side and vertical sides
Accurate head and discharge measurements were used to calibrate the weirs. Equations determined by mathematical and graphical methods, were used to generalize the H-Q relationships. The sloping extensions were tested in an attempt to obtain a uniform transition of the flow from the V..;notch weir to the compound shape.
LABORATORY INSTALLATION
The weir crests were installed in the side of a 20-foot by 18-foot 9-inch head box, with the root of the V-notch portion of the Weir set 3 feet O inch above the floor of the box, Figures lB and 2. This arrangement provided a minimum of 60 square feet iri the· approach cross-section and allowed the velocity of approach for the discharges used in the study to be neglected in determining the total head on the crest. A 6-inch-thick rock baffle, 13 feet
2
..,
9 inches upstream from the crest, was placed across the head box to stabilize the flow in the weir pool. Calibrated Venturi meters were used to measure the flows from three pumps discharging up to a total of 32 cubic feet per second into the head box. The pumps and Venturi meters are permanent installations of the laboratory. Static head measurements were made with a hook gage in a stilling well located outside the head box. The stilling well connection was tapped into the side of the head box about 8 feet upstream of the weir bulkhead.
The crests, shown in Figure 3, were formed from 2-1/4- by 1/4-inch brass strips and were bolted to a 3/4-inch plywood bulkhead. The top edge of the strips was beveled to 1/8-inch thickness to form the sharp crest.
WEIR CALIBRATION
The weir·s were calibrated by measuring and recording the heads over the weir crest when steady conditions existed in the weir pool for known discharges_. The data were plotted as they were obtained ·to determine the coherency of the tests and to verify the recorded head-discharge relationship. The data, thus obtained, are presented in Tables 1 through 5. Discharges and heads for the V -notch portion of the weirs were measured in conjunction with the first weir tested, Table 1, and periodically checked at random thereafter.
A pictorial record, partially presented as Figures 4 through 8, was kept during the tests. Of particular interest are the photographs shown as Figure 4, where the head on the V -notch portion of the weir is slightly in excess of 1. 0 foot and flow is just beginning to pass over the horizontal portion of the weir. It was noted that for heads from approximately 1. 0 to 1. 1 feet, the discharge over the horizontal crests was neither uniform nor stable due to the drawdown over the V -notch. Figures 5 through 8 show four of the five weirs before and during testing.
DATA ANALYSIS
For analytical purposes, the V-notch weir with vertical extensions was considered a V-notch weir with zero-length horizontal extensions. Thus, two types of compound weirs were analyzed:
1. V-notch with extensions horizontal
2. V-notch with extensions 15° above horizontal
3
Further. the data for the 90° V-notch portion of the weirs shows good agreement. Figure 9 with the Cone Equation
Q = 2. 49H2. 48 (1)
therefore. Equation (1) was considered to be representattve of the V-notch data in the following analyses.
Horizontal Extensions
The data for the V-notches with horizontal extensions were plotted. head versus discharge. on rectangular and log-log graph paper. From the log-log plot. Figure 10. and observations during the tests. it was noted that a transition zone existed at heads between 1. 0 and 1. 1 feet for the 1- and 2-foot extensions. caused by the change from a simple weir to a compound weir. Therefore. these data were not included in determining H-Q relationships for the upper portion of the weirs. Next. it was assumed that the H-Q relationship for the remaining data was a polynomial of the form.
(2)
Successive differences of discharges at equally spaced. increasing heads indicated that the polynomial was of the second degree. Thus. Equation (2) becomes
2 Q = a1 + a2H + a3H ( 3)
The constants were determined from the data in Tables 1 through 3 for heads greater than 1.1 feet by the method of least squares. which resulted in the following equations:
1. Q0 (zero extensions) = -2. 420 + 2. 661H + 2. 126H2 (4)
2. Q1 (1-foot extensions) = -4. 579 + 1. 792H + 4. 732H2 (5)
3. Q2 (2-foot extensions) = -5. 589 -0. 859H + 8. 005H2 (6)
These equations are shown graphically on Figure 11.
Correlation of the horizontal crest lengths with the constants in Equations ( 4). (5). and ( 6). corresponding to al. a2, and a3 of Equation (3). was performed by plotting the constants against the corresponding length of horizontal crests. Figure 12. Th~ indicated trends of the constants are speculative. since there are only three points. and should not be relied on for accurate formulation. However. if horizontal weir extensions are used. in conjunction with a 1-foot V-notch. a:p. estimate of the constants in Equation (3) may be obtained from Figure 12.
4
As an alternative to the use of Equation. (3) which requires a determination of the constants, a general equation was derived for the head-discharge relationship of V-notch weirs with horizontal extensions when flows exceed the capacity of the V-notch. To derive the _g-eneral equation1 head-discharge relationships were determined for the V-notch with vertical extensions and for the discharge per foot of horizontal extension regardless of total length •.
The head-discharge relationship for the V-notch weir with vertical extensio'ns was assumed to be of the form.
Q + b = aHm (7)
By trial-and error. 1. 5 cubic feet per second was chosen for b in order to produce a linear relationship between the logarithms of the heads and the corresponding "adjusted" (Q plus b). discharges. Figure 13. The constants a and m of Equation (7) were determined from this graph. The resulting equation is:
Q = 3. 9H1. 72 -1. 5 (8)
Eleven discharges for the V-notch with vertical extensions were subtracted from the total discharges over the weirs with 1- and 2-foot extensions when under the same head. The remaining fraction of the discharge was then divided by the total length of horizontal crest. This gave a discharge per foot of horizontal crest, q. for various heads above the horizontal crest. h. Equation (9) is the resulting relationship determined from the head-discharge., log-log plot. Figure 14.
q = 3. 3 hl. 5 (9)
A general equation for computing discharges over weirs with horizontal extensions results from the combining of Equations (8). and (9). into Equation (10)
Q = 3. 9Hl. 72 -1. 5 + 3. 3Lhl. 5 (10)
where L is the total length of the horizontal extensions.
Equation (9) is in good agreement with equations determined by various investigators as reported by King (Reference 1) •
(11)
where K depends on the velocity of approach and weir pool shape.
5
Discharges· in the transition zone, heads between 1. 0 and 1. 1 feet, are affected by the approach flow characteristics and weir crest sharpness and roughness. The laboratory tests indicated the simple V-notch Equation (1) to be applicable for heads up to 1. 05 feet when the V was 1. 00 foot deep. However, in a field installa1;ion, where weir crest imperfections and small waves are more likely to occur, the decision as to when Equation (1) no longer applies may not be well defined. Therefore, the size and vertical placement of the compound weir, based on anticipated flows, should be such that heads of 1. 0 foot to 1.1 feet will be in minimum usage.
The discharge over a compound weir composed of a 1. 0-foot V -notch with horizontal extensions may be computed by either Equation (3) or Equation (10). Equation (3) requires the use of Figure 12 for determining constants in addition to knowing the head over the weir and the length of the horizontal extensions, which is required when Equation (10) is used.
Two example problems follow. The first illustrates the use of Figure 11 and the second illustrates the use of Equations (3) and (10).
Example 1. Determine from Figure 11, the discharge over a 1-foot V -notch weir with 1-foot horizontal extensions on each side, when the head is 1. 8 feet.
The discharge is obtained by going horizontally from H = 1. 8 until the 1-foot horizontal extension line is intersected. At the intersection, go vertically down to read Q = 14 cubic feet per second.
Example 2. Determine the discharge over a 1-foot V -notch weir with 18-inch horizontal extensions on both sides of the V-notch when operating under a 2. 0-foot head.
From Figure 12, for L = 3. 0 feet a1 = -5.13 a2 = 0. 69 a3 = 6. 30
therefore, by Equation (3) for H = 2.0 feet Q = -5. 13 + o. 69(2) + 6. 30(4) = 21. 45
cubic feet per second
By Equation (10), for H = 2. 0 feet, h = 1. 0 foot and L = 3. 0 feet,
Q = 3.9(2)1. 72 -1.5 + 3.3(3)(1)1. 5 = 21.28 cubic feet per second
6
Sloping Extensions
Compound weirs with sloping extensions necessitate the use of three equations to adequately express the head-discharge relationship of the weir. The three relationships correspond to the following portions of the weir:
1. The V -notch, previously discussed
2. The sloping extensions, a straight-line plot on log-log paper
3. The portion above the sloping extensions, which was assumed to be of the same form as Equation (3).
The H-Q relationship for the sloping extension portion of these compound weirs was found to be
Q = 2. 22H3· 21 (12)
from a log-log plot of the test data, Figure 15.
The relationship for the portion of the weirs above the sloping extensions was computed by the method of least squares after the form of the equation was assumed. The equations for the two weirs are
1. Q1 (1-foot extensions)= -11.345 + 7.484H + 3.360H2 (13)
2. Q2 (2-foot extensions) = -14.106 + 6. 943H + 5, llOH2 (14)
Equations (12), (13), and (14) are shown graphically on Figure 16.
There was no apparent advantage in sloping the, extensions in comparison with having them horizontal, therefore~ no further analysis of the data was undertaken. The sloping extensions do produce a more uniform transition zone at the top of ,the V-notch; however, another transition zone, at the top of the sloping extension, is encountered. Both transition zones cover a larger range of heads than the one transition zone for the horizontal extensions.
Example 3 illustrates the use of Figure 16.
Example 3. Determine, from Figure 16, the discharge over a 1-foot V-notch weir with 1-foot, 15° upward sloping extensions on each side, when the head is 1, 8 feet.
The discharge is obtained by going horizontally from H = 1. 8 until the 1-foot sloping extension line is intersected. At the intersection, go vertically down to read Q = 13. 2 cubic feet per second.
7
REFERENCES
1. King. H. W.. Handbook of Hydraulics. Third Edition, McGrawHill Book Company, Inc .• 1939.
2. USBR. Water Measurement Manual. First Edition. U.S. Government Printing Office, Washington. 1953.
8
Table 1 ·
CALIBRATION .OF COMPOUND WEIR 1-FOOT DEPTH 90° V-NOTCH
WITH 2-FOOT HORJZONTAL BLADE Head Flow·
Date run (H ft) (Q cfs) Remarks
October 29. 1959 0.670 0.903 0.040 0.0148 0.339 · 0.166 0.555 0.560 0.379 0.216 0.495 0.424 0.272 0.096 0.201 0.037
October 30, 1959 0.670 0.903 0.879 l. 779 0.384 0~216 0.772 1.287 0.956 2.209
November 2, 1959 1.014 2.552 SurfaGe tension holding bead above crest
1.021 2.599 Bead above crest 1.027 2.625 Flow over part of crest 1. 031 2.688 Flow over all of crest except
near V -notch draw down 1. 038 2.764 1.049 2.888 1~058 2.986 Flow over entire crest
November 3. 1959 1.075 ·3. 193 1.095 3.442 1.107 3.589· 1.142 4.096 1.182 4.769 1.207 5.041 1. 236 5.656 1. 267 6.207 1. 311 7.031 1. 372 8.292 1.479 10. 607 1. 479 10.621
November 4. 1959 1.537 11. 712 1. 577 12.928 Hook gage difficult to set be-
cause of head box vibration 1.633 14.261 1.671 15.177 1. 713 16.319
Table 1--Continued
Head Flow Date run (H ft) (C> cfs) Remarks
November 4, 1959 1.752 17.420 1. 819 19.301 l.877 20.978 1. 919 22.189 1.982 24.209 Head box not vibrating 2.028 25.648 2.079 27.158 2.127 28.788 2.183 31.152 2.214 31. 619 Columns of air noted to form
in the nappe from floor at discharge back into the t ank through the V -notch. The columns would collapse and then dissipate into the dis-charge with an audible noise.
Table 2
CALIBRATION OF COMPOUND WEIR 1-FOOT OEPTH 90° V-NOTCH
WITH 1-FOOT HORIZONTAL BLADES Head Flow
Date run (H ft) (Q cfs) Remarks
December 1, 1959 1.027 2.60 Impending fl.ow over horizon tal crest
1.047 2.758 · Flow over horizontal crest 1.064 2.914 1.084 3.095 1.101 3.261 1.102 3.263 1.143 3.703 1.193 4.294 1.247 4.967 1. 293 5.577 1.344 6.283 1.398 7.098 1.449 7. 894. 1. 497 8.649 1.542 9.363 1.594 10.258 1. 647 11. 159 1. 697 12.041 1.748 13.003 1.798 13.918 1.842 14.743 1. 897 16.066 1. 963 17.174
December 2, 1959 1. 991 17.814 2.040 18.851 2.088 19.835 2.148 21. 197 2.218 22.728 2.274 24.003 2.314 25.044 2.378 26.437 2.444 28.007 2.507 29.529 2.550 30.660
Note: V-notch portion not run.
Table 3
CALIBRATION OF COMPOUND WEIR 1-FOOT DEPTH 90° V-NOTCH WITH VERTICAL EXTENSION
·Head Flow .
Date run (H ft) (Q cfs) Remarks ..
December 21, 1959 1.026 2.596 1.048 2.736 1.093 3.023 1. 113 3.167 1.143 3.382 1.179 3.631 1.241 4. 114 · 1.294 4.537 1.291 4.517 1. 360 5.091 1.414 5.549 1.485 6.182 1.546 6.737 1. 615 7.396 1.661 7.845
-1. 730 8.548 1. 805 9.308 1.843 9.823 1.917 10.515
December 22, 1959 1.739 8.533 1. 954 10.868 2.095 12.521 2.239 14.231 2.383 16.043 2.534 17.992 2.655 19.627 2.804 21. 682
Table4.
CALIBRATION OF COMPOUND WEIR 1-FOOT DEPTH. 90° V-NOTCH 2-FOOT 15° BLADE
Head· Flow Date run (H ft) (Q cfs) . Remarks
January 21, 1960 0.990 2.390 Check point .on V -notch weir 0.715 1.032 Check point on V-notch weir 1.008 2.464 1.031 2.628 1. 051 2.753 Flow drawn down through V 1.074 2.918 Flow drawn over 15° weir.
Nappe is drawn back agains · V-notch
1.104 3.149 1.206 4.051 1.276 4.834 1.368 6.017 N appe getting sufficient air.
but is clinging 1.451 7.307 1.533 8.755 _Top of trapezoidal weir 1. 607 10.263 Rectangular portion of weir 1.654 11. 280 1.683 ll.972 N appe has sufficient air not
clinging 1. 810 15.012 1.924 17.949 High ridge in center of draw
down 2.036 20.944 Beautiful nappe, no clinging 2.111 23.171 2.211 26.469 2.329 30.149 2.427 33.205
t
Table 5
CALIBRATION OF COMPOUND WEIR. 1-FOOT DEPTH 90° V-NOTCH
WITH 1-FOOT 15° BLADES Head Flow
.Da,te run (H·ft) (Q cfs) ,Remarks
February 25 1 1960 1.041 2.716 Well aerated nappe 1.088 2.933 Nappe began clinging on edge
-of 15° blade 1.134 3.418 Nappe clinging 1.184 3.874 N appe clinging slightly 1.233 4.366 1.286 4.951 Nappe springing free 1.334 5.563 1.385 6.220 t.434 6.935 l.485 7.674 1.534 8.435 1.585 9.263 1.634 10.040 1.684 10.901 1. 734 11. 789
February 26 1 1960 1.809 13.138 1. 869 14.262 1.944 15.747 2.013 17.104 2.108 19. 292 · Head box surging noted 2_. 183 20.991 Head box surging noted 2.220 21. 719 Head box surging noted 2.247 22.324 2.319 24.808 Surging in head box1 difficult
to read head accurately 2.532 28.992 Surging in head box1 difficult
to read head accurately
A. Compound weir, 90° V-notch with horizontal extensions, used to measure stream flows by the United States Department of Agriculture Forest Service •
B. A general view of test facility used to study the compound weir.
COMPOUND WEIR STUDY
Field and Laboratory Weir Installations
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- 4-85"----- I/ -t-, /
,,/'\,_ •/ ' -~75a---,
/6
--26.to·:.___ /I /I
~/ -----'>-Jz
. .9 >,,
' 6' ·<Jl V,,
' ' ' ' ' ' ' I
',
_y__ _____ --- - -- -------- -- --- - - --,--::-4s~Y-' ' ' ' /
~/
/
I I I I I
I / ! I 1 ,, I I 1 / I = I
1 ,,/1
-IN N I I I
/ /
TYPICAL SECTION A-A
COMPOUND WEIR
WEIR STUD.Y CRESTS
A. 2-foot horizontal extensions.
Head = 1. 02 feet Discharge = 2. 60 cfs
Note that surface tension reduces flow over extensions.
B. 1-foot horizontal extensions.
Head = 1. 12 feet Discharge = 3. 50 cfs
COMPOUND WEIR STUDY
90° V-notch 1-foot deep with horizontal extensions. Note that head exceeds capacity of V-notch but flow over horizontal extensions is not fully developed.
Figure 4 Report Hyd. 505
A. No fl.ow.
B. Head = 1. 6 feet Discharge = 13 cfs COMPOUND WEIR STUDY
90° V-notch 1-foot deep with 2-foot horizontal extensions.
C. Head = 1. 6 feet
Discharge = 13 cfs
~1%J CD ~·· "O~ ~ '1 .+ ID
l:Il CJ1
p. CJ1 0 CJ1
-A. No flow.
B. Head = 1. 7 feet Discharge .. 12 cfs
COMPOUND WEIR STUDY
90° V-notch 1-foot deep with 1-foot horizontal extensions.
C. Head = 1. 7 feet Discharge = 12 cfs
~ ltj Cl) ....
'ti Otl 0 i::: ""l ""l .+ Cl)
tI: 0)
'< p. C11 0 C11
A. No flow.
B. Head= 1. 9 feet Discharge = 9. 8 cfs COMPOUND WEIR STUDY
C. Head = 1. 9 feet Discharge = 9. 8 cfs
90° V-notch 1-foot deep with vertic·al extensions.
!:d l'%j (1) ....
'8~ '1 '1 .... (1)
t:r::--1 « p. c.n 0 c.n
A. No flow.
B. Head= 1.2 Discharge = 3. 7
COMPOUND WEIR STUDY
90° V-notch 1-foot deep with extensions on 15° slope.
C. Head= 1,2 Discharge = 3. 7
:;c ltj (1) ....
"d~ 0 '1 ::t.(1)
::i::oo ~ p. CJ1 C CJ1
0, UI GI 1.5
.... l&J l&J IL I --:c --
0 ~ l&J :c
1.0
.90
.80
.70
. 60
.50
.40
.30 ~
.25
.20
.15 .10
_,,. ~ ~
__,,. ~
v---~
~ .. ~
~
__. K ,.,,,,.- ~ ...... 'Q= 2.49H 2•48
o-OATA FOR 90° V-NOTCH
.15 .20 .25 .30 '4-0 .50 .60 .70 .80 .90 1.0 us 2.0 2.5 3.0
DISCHARGE (Q)-CFS
COMPOUND WEIR STUDY
V-NOTCH DATA COMPARISON WITH CONE EQUATION
4.0
::v 111 "II o."TI :u--1 G)
C: :r :::u -< 1:1'1 p
<JI CD 0 OI
• GI GI 3.0
2.5 I
2D
1.5
I-II.I II.I .... I -:I: 0 <t 1.0 II.I :I:
.9
.8
.7
.6
.5
.4
,/ l..-"°
In
/ /
~x-~ ~ ~.,;.-
V ~ -_,r:;A
~ .... x--x
l/ ~_.......x
/ .LI" LP--
~~ ...., ~ --- ~ ~-~~--- x..-... ~x
~~x:..-X-TOP OF V-NOTCH-----,
::--- !
I I __ / ~- -x
..,____ ___ ·-VT '
--.!!!' I
1E XPLANATI ON -;- v- NOTCH
o VERTICAL
D 1'-HORIZONTAL
X 2°-HC>RIZONTAL
2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 30.0 DISCHARGE (Q)-CFS
COMPOUND WEIR STUDY
CALIBRATION DATA 90° V-NOTCH WITH VERTICAL AND HORIZONTAL EXTENSIONS
40.0
:,a Ill
~"II :u--tG>
C: :z::u ~I'll
~a 0 GI
a,
"' 2.8 "'
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
1,8
. I-Ill 1.7 Ill ...
• 1.6 ~ - 1.5 C
"' 111 1.4 :c
1.3
1.2
I.I
1.0 .
.9
.8
- 7 .7 I
. ,.. __
IS J
.5
.4
.3 0
/',I" v~ CD 0 = -2.420 + 2.661 H + 2.126 He / _,,. .. @ Q = -4.579 + 1.792H + 4.732 Hee / __,,.,,.. V @ Q = -5.589 - 0.859 H + 8.005 H /
/" V ~
I/ v_ ...... ©vertical- --- @1 Foot Horizonol- --.. V / 1--""'" -__,,.. --_...V / V
i..--,.......,......
V V L,..,-- ... / _/ i..--
.,..v _,/ V ..,.... < ...
/' V .,...... ~ ---@2 Foot Horizonal / ---/'I" V V ~ ./
/" v"" __,,.. v'"" /' /
,,,,. ........ ~
'I' V / V V
~, V ...-v/ ~ V 1.2
t:--<-@ I- ~ ~ ; .....-, Ill I ~ I.I p ,,,..
b# I
I :c --...--:::: ..... / I I -- i,.,
~ 1.0 .... ,_ .... / --- --- ___ J
/v-notch Ill :c
.9 ., I
3 4 5 I 2 -v- notch Portion OISCHARGE(Q), G.F.S.
5.0 10.0 15.0 20.0 25.0 30.0 35.0 ::a Ill .. "II o-
D ISCH AR GE (Q), 0. F. S. ~~ COMPOUND WEIR STUDY ~:
HEAD -.DISCHARGE CURVES ~ _ 90° V-NOTCH WITH VERTICAL ANO HORIZONTAL EXTENSIONS :-
- - . 0
I-z <r: I-(/)
z 0 0
II.. 0
l&.I :::, ..J <r: >
655
9
8
1
6
5
4
3
T 2 ii
0
-I
-2
-3 '"' -4
-5
-6
-1 0
...... FIGURE 12
REPORT HYD. 505
I
/ •.
/ /
/~",03 . /
/~
/ /
/ ------- .......,~ .,.J.12 lit!'
' ~ ~I
.EQUATIONS 0o=-2.420+2.661H + 2.126H2
01 •-4.579+1.792H+4.732H2
~ '"
02 = -5.589-0.859H+8.005H2
~ .:...91 F-. --~
1.0 2.0 3.0 4.0 5.0
TOTAL LENGTH OF HORIZONTAL CREST(L),FEET
GENERAL FORM OF EQUATION: Q = a1 + a2 H+ a3 H2
COMPOUND WEIR STUDY
VARIATION OF THE CONSTANTS IN THE DISCHARGE EQUATIONS FOR V-NOTCH WEIRS
WITH HORIZONTAL EXTENSIONS
6.0
en CII (II 5.0
4.0
3.0
2.5
I-L&J 2.0 L&J u. I -::c --
0 <( L&J :c
1.5
. 1.0
.9
.8
.7
.6
.5 1.5
I
' 2.0
V -
V ~
IV'--- ·Q=3.9H'-72
V V
V I/ .,,
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0
DISCHARGE (AJUSTED)-(Q)-CFS
COMPOUND WEIR STUDY
CALIBRATION CURVE OF VERTICAL EXTENSIONS A.BOVE 90° V-NOTCH
30.0 40.0 50,0 60.0
:::u ITI "lJ O"TI :::o-t Ci)
C: :c ::0 < 1'11 C
(JI (>I
0 (JI
0) (II
CJI
... LaJ LaJ IL I --.s= -
0 ~ LaJ
' :I:
1.0
.9
.8
.7
• 6
.5
.4
• 3
.25
.2
1 Q.H ~ i--f-,.--- Al I I I I .-+-__j_ I 2 flv Q I , , I ...!!. I h I
L--- 2 I I H ---t-+-A~ I --, I ' ' ,--- -/2--'>4 I ___ _j __ y_ I --+--•-1 ~ L , - I • I
I I 1 - I
___ ·: : 1 /)0,.-T·+-L I r<--L/2--~ I
~QT-QV - - - - ----~t- -~- ! ---r---1----
t-----t--+-----+---+- •
EXPLANATION o L: 2 FEET X L :4 FEE'T
----•r---,-,---1---t-t--t-+----t---+--'-:--.---.------,,----l----t--J-J
•, .15 ,___.....___...._ _ __., __ .._____.. _ _,__.....___.____.. ___ __._ __ _....._ _ __._ _____ ...._ ____ ....___._,_,,
.2 .25 .3 .4 .5 .6 .7 .8 .9 1.0 1.5 2 2.5 3 4 5 6 7 8
DISCHARGE (Q) - CFS PER FT.
COMPOUND WEIR STUDY
CALIBRATION CURVE OF HORIZONTAL EXTENSIONS ABOVE 90° V-NOTCH WEIR
:u f'l'I "U O"TI ::a --f Ci)
C: :::c ::u -< ITI 0
U'I~ 0 (JI
0, ca ca 3.0
2.5
2.0
1.5
I-.... .... ... I -J::
0 ct 1.0 i.iJ J:
,9
.8
.7
.6
.5
.4
[]
~/ .... {"x--
__,,,,u ~x_.......x ~x.-
TOP OF 15°-2' EXTEN.----- - ~x .... ' ~ ' ~ -- _ .i, -- n.x•
~~ ~
TOP OF 15°-1' EXTEN.----- - _
---~ ,.,.,.-,o,c•---) /~
___ .l::,·
_,~
~
EXPLANATION 0 V- NOTCH 4 15° EXTENSIONS D ABOVE 1' EXTEN, X ABOVE 2' EXTEN.
2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 15,0 20.0 30.0 DIS CHARGE (QI-CFS
COMPOUND WEIR STUDY
CALIBRATION DATA OF 90° V-NOTCH WITH· 15° UPWARD SLOPING EXTENSIONS
40.0 ;u
"' .,, 0"11 ;u--1G>
C: ::c::u -<1"11 ?_ (JI (11
0 (JI
~ m c.>
"' "' "' 0
"' en en
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
1.8
1.7
I-. l&.I 1.6 l&.I ... ,..: 1.5
J: - 1.4 Q C( l&.I 1.3 J:
1.2
I.I
1.0
.9
.8
.7
~~ 0
I
I I ""-V-notch
l5
® © ®
~ Q 2.22H3.21 Q -11.345 +7.484H + 3.360H 2
Q -14.106 +6.943H + 5.IIOH2
~ © I-Foot Sloping~ ~
~II~ ~ ~ 2 - Foot Sloping
.A"11~
I- 1.2 (----+----.-,.£----+----1-----1---...V l&.I l&.I ... ~ui-----t,,~--+----+----1------V
0 C( l&.I
J...----r-
.,___J.-f
·:i: 1.o 2 I I I I I I I I I I I I I
3 4 5 6
I I I
10
DISCHARGE (Q), C.F.S.
I I I I I I I I 15 20
DI SCH A R G E (Q), C. F. S.
COMPOUND WEIR STUDY
HEAD - DISCHARGE CURVES
25
90° V NOTCH ·WITH 15° UPWARD SLOPING EXTEN,SIONS
30 35
::u ITI "U 'Tl . o::UG) -t c:: :z:::U -c 1"11 ~ CIICJ> 0 CII
