Lecture 12
Calibration of Canal Gates
I. Free-Flow Rectangular Gate Structures
•
For a rectangular gate having a gate opening, Go, and a gate width, W, the freeflow discharge equation can be obtained from Eq. 26 of the previous lecture,
assuming that the dimensionless velocity head coefficient is equal to unity:
(
Qf = CdGoGw 2g hu − CgGo
)
(1)
where Go is the vertical gate opening; Gw is the gate width; GoGw is the area, A,
of the gate opening; and, Cg is between 0.5 and 0.61
•
•
•
•
•
•
•
•
•
•
The upstream flow depth, hu, can be measured anywhere upstream of the gate,
including the upstream face of the gate
The value of hu will vary only a small amount depending on the upstream location
chosen for measuring hu
Consequently, the value of the coefficient of discharge, Cd, will also vary
according to the location selected for measuring hu
One of the most difficult tasks in calibrating a gate structure is obtaining a highly
accurate measurement of the gate opening, Go
For gates having a threaded rod that rises as the gate opening is increased, the
gate opening is read from the top of the hand-wheel to the top of the rod with the
gate closed, and when set to some opening, Go
This very likely represents a measurement of gate opening from where the gate
is totally seated, rather than a measurement from the gate lip; therefore, the
measured value of Go from the thread rod will usually be greater than the true
gate opening, unless special precautions are taken to calibrate the thread rod
Also, when the gate lip is set at the same elevation as the gate sill, there will
undoubtedly be some flow or leakage through the gate
This implies that the datum for measuring the gate opening is below the gate sill
In fact, there is often leakage from a gate even when it is totally seated because
of inadequate maintenance
An example problem will be used to illustrate the procedure for determining an
appropriate zero datum for the gate opening
Sample Calibration
•
•
Calibration data (listed in the table below) were collected for a rectangular gate
structure
The data reduction is listed in the next table, where the coefficient of discharge,
Cd, was calculated from Eq. 27
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Gary P. Merkley
Discharge, Qf
(m3/s)
0.0646
0.0708
0.0742
0.0755
0.0763
0.0767
Qf
(m3/s)
0.0646
0.0708
0.0742
0.0755
0.0763
0.0767
Gate Opening, Go
(m)
0.010
0.020
0.030
0.040
0.050
0.060
hu
(m)
1.838
0.698
0.375
0.242
0.175
0.137
Go
(m)
0.010
0.020
0.030
0.040
0.050
0.060
Upstream Benchmark
Tape Measurement (m)
0.124
1.264
1.587
1.720
1.787
1.825
Cd
0.756
0.677
0.654
0.635
0.625
0.620
Note: The discharge coefficient, Cd, was calculated
using the following equation:
G ⎞
⎛
Qf = CdGoGw 2g ⎜ hu − o ⎟
2 ⎠
⎝
•
A rectangular coordinate plot of Cd versus the gate opening, Go, is shown in the
figure below
Coefficient of discharge, Cd
0.76
0.74
0.72
0.70
0.68
0.66
0.64
0.62
0.01
0.02
0.03
0.04
0.05
0.06
Gate opening, Go (m)
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•
•
Notice that the value of Cd continues to decrease with larger gate openings
One way to determine if a constant value of Cd can be derived is to rewrite Eq. 5
in the following format (Skogerboe and Merkley 1996):
G + ∆Go ⎞
⎛
Qf = Cd ( Go + ∆Go ) Gw 2g ⎜ (hu )∆G − o
⎟
o
2
⎝
⎠
(2)
where ∆Go is a measure of the zero datum level below the gate sill, and
(hu )∆Go
•
•
•
•
•
= hu + ∆Go
(3)
Assuming values of ∆Go equal to 1 mm, 2 mm, 3 mm, etc., the computations for
determining Cd can be made from Eq. 3
The results for ∆Go equal to 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, 7 mm, 8
mm and 12 mm (gate seated) are listed in the table below
The best results are obtained for ∆Go of 3 mm − the results are plotted in the
figure below, which shows that Cd varies from 0.582 to 0.593 with the average
value of Cd being 0.587
For this particular gate structure, the discharge normally varies between 200 and
300 lps, and the gate opening is normally operated between 40-60 mm, so that a
constant value of Cd = 0.587 can be used when the zero datum for Go and hu is
taken as 3 mm below the gate sill
Another alternative would be to use a constant value of Cd = 0.575 for ∆Go = 4
mm and Go greater than 30 mm
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II. Submerged-Flow Rectangular Gate Structures
•
Assuming that the dimensionless velocity head coefficient in Eq. 27 is unity, the
submerged-flow discharge equation for a rectangular gate having an opening,
Go, and a width, W, becomes:
Qs = CdGoGw 2g (hu − hd )
(4)
where GoGw is the area, A, of the orifice
•
•
•
Field calibration data for a rectangular gate structure operating under
submerged-flow conditions are listed in the table below
Note that for this type of slide gate, the gate opening can be measured both on
the left side, (Go)L, and the right side, (Go)R, because the gate lip is not always
horizontal
The calculations are shown in the second table below
Gate Opening
Discharge, Qs
(m3/s)
(Go)left
(m)
(Go)right
(m)
Upstream
(m)
Downstream
(m)
0.079
0.095
0.111
0.126
0.141
0.155
0.101
0.123
0.139
0.161
0.180
0.199
0.103
0.119
0.139
0.163
0.178
0.197
0.095
0.099
0.102
0.105
0.108
0.110
0.273
0.283
0.296
0.290
0.301
0.301
Qs
(m3/s)
0.079
0.095
0.111
0.126
0.141
0.155
•
•
Benchmark Tape Measurements
Go
(m)
0.102
0.121
0.139
0.162
0.179
0.198
hu
(m)
0.823
0.819
0.816
0.813
0.810
0.808
hd
(m)
0.643
0.633
0.620
0.626
0.615
0.615
h u - hd
(m)
0.180
0.187
0.196
0.187
0.195
0.193
Cd
0.676
0.674
0.668
0.666
0.660
0.659
As in the case of the free-flow orifice calibration in the previous section, a trialand-error approach can be used to determine a more precise zero datum for the
gate opening
In this case, the submerged flow equation would be rewritten as:
Qs = Cd ( Go + ∆Go ) Gw 2g (hu − hd )
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where ∆Go is the vertical distance from the gate sill down to the zero datum level,
as previously defined in Eq. 2
Qs
Go
h u - hd
(m3/s)
(m)
(m)
∆Go = 4 mm
∆Go = 6 mm
∆Go = 8 mm
0.079
0.102
0.1801
0.650
0.638
0.626
0.095
0.121
0.1865
0.651
0.641
0.631
0.111
0.139
0.1960
0.649
0.640
0.631
0.126
0.162
0.1869
0.650
0.642
0.635
0.141
0.179
0.1949
0.646
0.639
0.632
0.155
0.198
0.1931
0.646
0.640
0.634
Cd
Note: The discharge coefficient, Cd, was calculated from Eq. 32:
•
•
As before, the criteria for determining ∆Go is to obtain a nearly constant value of
the discharge coefficient, Cd
The above table has the example computational results for determining the
discharge coefficient, Cd, according to adjusted gate openings, Go, under
submerged flow conditions
III. Calibrating Medium- and Large-Size Gate Structures
•
•
•
A different form of the submerged-flow rating equation has been used with
excellent results on many different orifice-type structures in medium and large
canals
The differences in the equation involve consideration of the gate opening and the
downstream depth as influential factors in the determination of the discharge
coefficient
The equation is as follows:
Qs = Cs hs Gw 2g (hu − hd )
(6)
and,
β
⎛G ⎞
Cs = α ⎜ o ⎟
⎝ hs ⎠
(7)
where hs is the downstream depth referenced to the bottom of the gate opening,
α and β are empirically-fitted parameters, and all other terms are as described
previously
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Gary P. Merkley
hu G
o
hs
hd
•
•
•
Note that Cs is a dimensionless number
The value of the exponent, β, is usually very close to unity
In fact, for β equal to unity the equation reverts to that of a constant value of Cs
equal to α (the hs term cancels)
•
The next table shows some example field calibration data for a large canal gate
operating under submerged-flow conditions
The solution to the example calibration is: α = 0.796, and β = 1.031
This particular data set indicates an excellent fit to Eqs. 6 and 7, and it is typical
of other large gate structures operating under submerged-flow conditions
•
•
Data
Set
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Discharge
(m3/s)
8.38
9.08
5.20
4.27
5.45
12.15
5.49
13.52
14.39
16.14
6.98
11.36
7.90
7.15
7.49
10.48
12.41
8.26
Go
(m)
0.60
0.70
0.38
0.30
0.40
0.95
0.38
1.10
1.00
1.13
0.50
0.58
0.42
0.38
0.51
0.70
0.85
0.55
∆h
(m)
3.57
3.00
3.31
3.41
3.43
2.63
3.72
2.44
3.84
3.79
3.70
7.64
6.76
6.86
3.98
3.92
3.76
3.91
hs
(m)
2.205
2.010
1.750
1.895
2.025
2.300
1.905
2.405
2.370
2.570
1.980
2.310
2.195
2.110
2.090
2.045
2.205
2.065
Go/hs
Cs
0.272
0.348
0.217
0.158
0.198
0.413
0.199
0.457
0.422
0.440
0.253
0.251
0.191
0.180
0.244
0.342
0.385
0.266
0.206
0.268
0.168
0.125
0.149
0.334
0.153
0.369
0.318
0.331
0.188
0.183
0.142
0.133
0.184
0.266
0.298
0.208
Note: the data are for two identical gates in parallel, both having the
same opening for each data set, with a combined opening width of 2.20
m.
Gary P. Merkley
130
BIE 5300/6300 Lectures
•
•
•
A similar equation can be used for free-flow through a large gate structure, with
the upstream depth, hu, replacing the term hs, and with (hu - Go/2) replacing (hu hd)
As previously mentioned, the free-flow equation can be calibrated using (hu 0.61Go) instead of (hu - Go/2)
The following figure shows a graph of the 18 data points; the straight line is the
regression results which gives α and β
-0.6
-0.8
alpha = 0.796
beta = 1.031
-1.0
ln(Cs)
-1.2
-1.4
-1.6
-1.8
-2.0
-2.2
-2.4
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
ln(Go/hs)
IV. Radial Gate Orifice-Flow Calibrations
•
•
•
•
This structure type includes radial (or “Tainter”) gates as calibrated by the USBR
(Buyalski 1983) for free and submerged orifice-flow conditions
The calibration of the gates follows the specifications in the USBR “REC-ERC83-9” technical publication, which gives calibration equations for free and
submerged orifice flow, and corrections for the type of gate lip seal
The calibration requires no field measurements other than gate dimensions, but
you can add another coefficient to the equations for free flow and orifice flow in
an attempt to accommodate calibration data, if available
Three gate lip seal designs (see figure below) are included in the calibrations:
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Gary P. Merkley
1. Hard-rubber bar;
2. Music note; and,
3. Sharp edge
•
•
•
The gate lip seal is the bottom of the gate leaf, which rests on the bottom of the
channel when the gate is closed
The discharge coefficients need no adjustment for the hard-rubber bar gate lip,
which is the most common among USBR radial gate designs, but do have
correction factors for the other two lip seal types
These are given below for free and submerged orifice flow
Gr
hu
Go
•
•
•
P
hd
The gate radius divided by the pinion height should be within the range 1.2 ≤ Gr/P
≤ 1.7
The upstream water depth divided by the pinion height should be less than or
equal to 1.6 (hu/P ≤ 1.6)
If these and other limits are observed, the accuracy of the calculated flow rate
from Buyalski’s equations should be within 1% of the true flow rate
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Free Orifice Flow Free, or modular orifice flow is assumed to prevail when the
downstream momentum function corresponding to CcGo, where Go is the vertical
gate opening, is less than or equal to the momentum function value using the
downstream depth. Under these conditions the rating equation is:
Ff = Qf - CfcdaGoGw 2ghu = 0
(8)
where Cfcda is the free-flow discharge coefficient; Go is the vertical gate
opening (m or ft); Gw is the width of the gate opening (m or ft); and hu is the
upstream water depth (m or ft); Cfcda is dimensionless
•
•
Cfcda is determined according to a series of conic equations as defined by
Buyalski (1983) from an analysis of over 2,000 data points
The equations are lengthy, but are easily applied in a computer program
Eccentricity
2
⎛
⎛ Gr
⎞ ⎞
AFE = 0.00212 ⎜ 1.0+31.2 ⎜
− 1.6 ⎟ ⎟ + 0.901
⎜
P
⎝
⎠ ⎟⎠
⎝
(9)
2
⎛
⎛ Gr
⎞ ⎞
BFE = 0.00212 ⎜ 1.0+187.7 ⎜
− 1.635 ⎟ ⎟ − 0.079
⎜
P
⎝
⎠ ⎟⎠
⎝
(10)
⎛G ⎞
FE = AFE − BFE ⎜ o ⎟
⎝ P ⎠
(11)
where Gr is the gate radius (m or ft); and P is the pinion height (m or ft)
Directrix
2
⎛
⎛ Gr
⎞ ⎞
AFD = 0.788 − 0.04 ⎜ 1.0+89.2 ⎜
− 1.619 ⎟ ⎟
⎜
P
⎝
⎠ ⎟⎠
⎝
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Gary P. Merkley
⎛G
BFD = 0.0534 ⎜ r
⎝ P
⎞
⎟ + 0.0457
⎠
(13)
2
⎛
⎛ Go
⎞ ⎞
FD = 0.472 − BFD ⎜ 1.0- ⎜
− AFD ⎟ ⎟
⎜
P
⎝
⎠ ⎟⎠
⎝
(14)
Focal Distances
⎛G ⎞
FX1 = 1.94 ⎜ o ⎟ − 0.377
⎝ P ⎠
⎛G ⎞
FX1 = 0.18 ⎜ o ⎟ + 0.111
⎝ P ⎠
Go
≤ 0.277
P
Go
> 0.277
P
⎛G ⎞
FY1 =0.309 − 0.192 ⎜ o ⎟
⎝ P ⎠
(15)
(16)
and,
FXV =
hu
− FX1
P
(17)
The correction on Cfcda for the “music note” gate lip seal design is:
⎛G ⎞
Ccorrect = 0.125 ⎜ o ⎟ + 0.91
⎝ P ⎠
(music note)
(18)
The correction on Cfcda for the “sharp edge” gate lip seal design is:
⎛G ⎞
Ccorrect = 0.11⎜ o ⎟ + 0.935
⎝ P ⎠
(sharp edge)
(19)
For the hard-rubber bar gate lip seal design, Ccorrect = 1.0. The preceding corrections
on Cfcda for the “music note” and “sharp edge” gate lip seal designs were chosen
from the linear options proposed by Buyalski (ibid).
Gary P. Merkley
134
BIE 5300/6300 Lectures
Finally,
2
⎛
⎞
Cfcda = Ccorrect ⎜ FE2 (FD + FXV ) − FXV 2 + FY1 ⎟
⎝
⎠
(20)
Radial gates in parallel at a check structure
Submerged Orifice Flow The submerged orifice rating equation is:
Fs = Qs - CscdaGoGw 2ghu = 0
(21)
where Cscda is the submerged-flow discharge coefficient; and all other terms
are as previously defined; both Cscda and Cds are dimensionless
•
•
Note that the square-root term does not include the downstream depth, hd,
but it is included in the lengthy definition of Cscda
As in the free-flow case, Cscda is determined according to a series of conic
equations:
Directrix
⎛
⎛G
ADA = ⎜ 11.98 ⎜ r
⎝ P
⎝
BIE 5300/6300 Lectures
⎞
⎞
⎟ − 26.7 ⎟
⎠
⎠
135
−1
(22)
Gary P. Merkley
⎛ P⎞
ADB = 0.62 − 0.276 ⎜ ⎟
⎝ Gr ⎠
⎛
⎞
⎛G ⎞
AD = ⎜ ADA ⎜ o ⎟ + ADB ⎟
⎝ P ⎠
⎝
⎠
⎛G
BDA = 0.025 ⎜ r
⎝ P
(23)
−1
(24)
⎞
⎟ − 2.711
⎠
(25)
⎛G ⎞
BDB = 0.071 − 0.033 ⎜ r ⎟
⎝ P ⎠
(26)
⎛G ⎞
BD = BDA ⎜ o ⎟ + BDB
⎝ P ⎠
(27)
⎛h ⎞
DR = AD ⎜ d ⎟ + BD
⎝P⎠
(28)
D = DR −1.429
(29)
⎛G ⎞
AEA = 0.06 − 0.019 ⎜ r ⎟
⎝P ⎠
(30)
⎛G ⎞
AEB = 0.996 + 0.0052 ⎜ r ⎟
⎝P ⎠
(31)
Eccentricity
⎛
⎞
⎛G ⎞
AE = ⎜ AEA ⎜ o ⎟ + AEB ⎟
⎝ P ⎠
⎝
⎠
Gary P. Merkley
136
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(32)
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⎛G ⎞
BEK = 0.32 − 0.293 ⎜ r ⎟
⎝P ⎠
2
⎛
⎛ Go
⎞ ⎞
BE = BEK + 0.255 ⎜ 1.0 + 1.429 ⎜
− 0.44 ⎟ ⎟
⎜
P
⎝
⎠ ⎟⎠
⎝
(33)
(34)
ER = AE (D ) + BE
(35)
⎛ ER ⎞
E = ln ⎜
⎟
⎝ D ⎠
(36)
Vector V1
V1 =
E (D )
1.0 + E
(37)
Focal Distance
⎛P⎞
AFA = 0.038 − 0.158 ⎜ ⎟
⎝ Gr ⎠
(38)
⎛G ⎞
AFB = 0.29 − 0.115 ⎜ r ⎟
⎝ P ⎠
(39)
⎛G ⎞
AF = AFA ⎜ o ⎟ + AFB
⎝ P ⎠
(40)
⎛P
BFA = 0.0445 ⎜
⎝ Gr
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⎞
⎟ − 0.321
⎠
(41)
Gary P. Merkley
⎛P⎞
BFB = 0.155 − 0.092 ⎜ ⎟
⎝ Gr ⎠
(42)
⎛ P ⎞
BF = BFA ⎜
⎟ + BFB
⎝ Go ⎠
(43)
FY = BF −
•
AF (hd )
(44)
P
If FY ≤ 0, then let FY = 0 and FX = 0. Otherwise, retain the calculated value
of FY and,
FX = V12 + FY 2 − V1
VX =
(for FY > 0)
(45)
hu
h
− V1 − d − FX
P
P
(46)
The correction on Cscda for the “music note” gate lip seal design is:
⎛G ⎞
Ccorrect = 0.39 ⎜ o ⎟ + 0.85
⎝ P ⎠
(music note)
(47)
The correction on Cscda for the “sharp edge” gate lip seal design is:
⎛G ⎞
Ccorrect = 0.11⎜ o ⎟ + 0.9
⎝ P ⎠
•
•
(sharp edge)
(48)
For the hard-rubber bar gate lip seal design, Ccorrect = 1.0
The preceding corrections on Cscda for the “music note” and “sharp edge” gate
lip seal designs were chosen from the linear options proposed by Buyalski
(ibid)
Finally,
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2
⎛
⎞
Cscda = Ccorrect ⎜ E2 (D + VX ) − VX 2 + FY ⎟
⎝
⎠
(49)
References & Bibliography
Buyalski, C.P. 1983. Discharge algorithms for canal radial gates. Technical Report REC-ERC-83-9.
U.S. Bureau of Reclamation, Denver, CO. 232 pp.
Brater, E.F., and H.W. King. 1976. Handbook of hydraulics. 6th edition. McGraw-Hill Book Company,
New York, N.Y. 583 pp.
Buyalski, C.P. 1983. Discharge algorithms for canal radial gates. Technical Report REC-ERC-83-9.
U.S. Bureau of Reclamation, Denver, CO. 232 pp.
Chow, V.T. 1959. Open-channel hydraulics. McGraw-Hill Book Company, New York, N.Y. 680 pp.
Daugherty, R.L., and J. B. Franzini. 1977. Fluid mechanics with engineering applications. 7th edition.
McGraw-Hill Book Company, New York, N.Y. 564 pp.
Davis, C.V. and K.E. Sorensen (eds.). 1969. Handbook of applied hydraulics. McGraw-Hill Book
Company, New York, N.Y.
French, R.H. 1985. Open-channel hydraulics. McGraw-Hill Book Company, New York, N.Y. 705 pp.
Hu, W.W. 1973. Hydraulic elements for USBR standard horseshoe tunnel. J. of the Transportation
Engrg. Div., ASCE, 99(4): 973-980.
Hu, W.W. 1980. Water surface profile for horseshoe tunnel. Transportation Engrg. Journal, ASCE,
106(2): 133-139.
Press, W.H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. 1992. Numerical recipes in C: the
art of scientific computing. 2nd Ed. Cambridge Univ. Press, Cambridge, U.K. 994 pp.
Shen, J. 1981. Discharge characteristics of triangular-notch thin-plate weirs. Water Supply Paper
1617-B. U.S. Geological Survey.
Skogerboe, G.V., M.L. Hyatt, R.K. Anderson, and K.O. Eggleston. 1967. Cutthroat flumes. Utah Water
Research Laboratory Report WG31-4. 37 pp.
Skogerboe, G.V., L. Ren, and D. Yang. 1993. Cutthroat flume discharge ratings, size selection and
installation. Int’l Irrig. Center Report, Utah State Univ., Logan, UT. 110 pp.
Uni-Bell Plastic Pipe Association. 1977. Handbook of PVC pipe: design and construction. Uni-Bell
Plastic Pipe Association, Dallas, TX.
Villamonte, J.R. 1947. Submerged-weir discharge studies. Engrg. News Record, p. 866.
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