Hydraulic Structures Structures – Head and Cross Regulators
December 12, 2010
Head and Cross Regulators The supplies passing down the parent canal and off take channel are controlled by cross regulator and head regulator respectively. A utment Pier Gate
Cross Regulator
Head Regulator
OFF TAKE CHANNEL Distributary channel
Functions of Cross Regulators 1. 2. 3. 4.
Regulation of the canal system. Raising the water level in the main canal in order to feed the off take channels. To facilitate communication by building a road over the cross regulator with little extra cost. To absorb the fluctuations in the canal system.
Functions of Head Regulators 1. To regulate and control supplies entering the off take channel (distributary) from the main (parent) canal. 2. To control silt entering into the distributary. 3. To serve for measurement of discharge.
Alignment The best alignment of the off take channel is when it makes angle zero with the parent canal initially and then separates out in a transition. See Fig. 13.1. In this case there is a transition curve for both off take and parent channel to avoid silt accumulation. Another alternative by making both channels an angle with respect to parent channel upstream. Fig. 13.2
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Hydraulic Structures – Head and Cross Regulators
December 12, 2010
In case of obligatory straight alignment of the parent channel, the usual angle of the off take channel is 60º to 80º (in most important works needs a model study). For excessive silt entry into the off take channel. Fig. 13.3.
Design Criteria 1. Waterway The effective waterway of head regulator should not be less than 60% of bed width of off taking channel and mean velocity should not exceed 2.5 m / sec. 2. Crest level Crest level of the distributary head regulator is generally kept 0.3 m to 0.6 m higher than crest level of cross regulator (C.R.). The crest level of C.R. is provided at bed level of parent canal. H e should be worked out from the formula Q C B e H e3/2
(4.1)
where C
Coefficient of discharge
B e
Effective length of crest B t 2 N K p K a H e
B t
Net length of the crest Number of piers
N K p
K a
Pier contraction coefficient Abutment contraction coefficient 2
(4.2)
Hydraulic Structures – Head and Cross Regulators
December 12, 2010
Table: Coefficients of contraction for piers and abutments.
Type of pier
Square nosed pier Round nosed pier Pointed nosed pier
K p
Type of abutment
0.02 0.01 0.01 K a
Square abutment Round abutment
0.2 0.1
Square nosed pier
Round nosed pier
3. Coefficient of discharge (C ) The coefficient of discharge C is 1.84 for crests of width less than or
equal to 23 H e . In case of submerged falls, C should be reduced
Pointed nose pier
depending on the drowning ratio, see Fig. 6.5. C 1.840
(H.R. crest)
C 1.705
(C.R. crest) . . . He
>2/3 He Broad Crested Weir 4. Shape of crest The u.s face of the crest should be given a slope of 1:1. The d.s. sloping glacis should not be steeper than 2:1.
5. Crest width should be kept equal to 23 H e . 6. Vertical cut-offs The cut-off should be provided at the end of u.s. and d.s. floors for safety against scour, undermining and exit gradient. Due to Lacey’s scour depth
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Hydraulic Structures – Head and Cross Regulators
December 12, 2010
Table 6.1 Minimum depth of u.s. and d.s. cut-offs
Min. depth of u.s. cut-off below bed level or G.L. whichever is lower ( m) 1.0 1.2 1.5 1.8
Canal capacity cumec
Up to 3 cumec 3.1 - 30 30.1 - 150 Above 150
Min. depth of d.s. cut-off below bed level or G.L. whichever is lower ( m) 1.0 1.2 1.5 1.8
7. Thickness of top coat
Table 6.2 Thickness of top coat.
Canal capacity ( cumec) Q 1.5
Thickness of top coat ( mm) 100
1.5 Q 30 30 Q 150 Q 150
150 200 300
8. Freeboard Table: Minimum Freeboard
Canal capacity ( cumec) Q 1.0
Freeboard ( m) 0.3
1 Q 10 10 Q 30 30 Q 150 Q 150
0.4 0.6 0.8 1.0
9. Protection works Downstream of floor, properly designed filter loaded by concrete blocks should be provided. The length of inverted filter is kept equal to 2 D ( D is the depth of d.s. cut-off below d.s. bed). Details of minimum thickness of the filter are given in Table 6.3. The width of gabs between the blocks shall not be more than 50 mm which should be packed with biggest size of pebbles available. Beyond the filter, an apron of 1.5 D length shall be provided. Similar protection is also provided in the u.s. in a length equal to D. the cubic content of material in
launching apron should be equal to 2.25 D m 3 m m length.
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Hydraulic Structures – Head and Cross Regulators
December 12, 2010
Design Example Design a cross regulator and a suitable head for a distributary which takes off at an angle of 60º from a canal which discharges 120 cumec. Discharge of distributary Bed width of distributary Water depth of distributary Full supply level of distributary Full supply level of parent channel (F.S.L.)
= 10 cumec = 10 m = 1.2 m = El. 310.2 m u.s. 311.00 m
Bed width of parent channel
Depth of water in parent channel
Safe exit gradient (G.E.)
d.s. u.s. d.s. u.s. d.s.
310.85 m 60 m 56 m 2m 2m
1 5
Solution A. Design of Cross Regulator 1. Fixation of crest level and waterway of cross regulator Crest level of C.R. F.S.L. of parent channel - water depth
311-2 309 m hd T.E.L.u.s. T.E.L.d.s.
311 310.85 0.15m H e F.S.L.u.s. crest level
=311 309 2 m Degree of submergence hd 0.15 0.075 H e 2 From Fig. 6.5 C s 0.56, where C 1.705 C C s 1.705 0.56 0.95 Q CB e H 3/2 3/2
120 0.95 B e 2
Be 44.66 m say 45 m
Assume 6 bays of 8 m each = 48 m 5
Hydraulic Structures – Head and Cross Regulators
December 12, 2010
B t B e 2(N K p K a )H e
45 2 5 0.01 0.2 2 46 m 48 m O.K. Provide 5 piers with rounded nose of width 1.6 m each. Total waterway 6 8 5 1.6 56 m O.K. 2. Level and length of downstream floor Q 120 cumec q
Q B e
120 48
2.5 m 3 / sec / m
H L T.E.L.u.s. T.E.L.d.s. F.S.L.u.s. F.S.L.d.s.
(v 2 2 g is negligible)
311 310.85 0.15m From Blench Curves, Fig. 3.5 Ef 2 1.435 m
d.s. floor level F.S.L.d.s. Ef 2
310.85 1.435m 309.415 m Actual cistern level 310.85 2 308.85 m lower than 309.415 m O.K. Cistern length Lc 5 D 2 D1 firm soil
6( D 2 D1 ) weak soil Ef 1 Ef 2 H L 1.435 0.15 1.585 m
From energy of flow curves (Fig. 2.7) Ef 1 1.575 m gives D1 0.534 m Ef 2 1.435 m gives
D 2 1.3 m
Lc 5 1.3 0.534 3.83 m
3. Vertical cutoffs Q 120cumec
Referring to table 6.1, the minimum depth of u.s. and d.s. cutoff = 1.5 m. u.s. cutoff is at El. 309 1.5 307.5 m 4. Total floor length and exit gradient H 1 G E d H F.S.L.u.s. G.L.d.s.
311 308.85 2.15m Trial and error d (m) 1.5 1.6
λ
α
L d (m)
5.20 4.57
9.15 8.08
14 12.93
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Hydraulic Structures – Head and Cross Regulators
1 5
2.15
1
1.6
December 12, 2010
, =4.57 1/2
2 2 1 1
1/2
2 2 457 1 1 Total floor length L d
8.08
8.081.6 12.93 m say 13m d.s. cutoff is at El. 308.85 1.6 307.25 m d.s. floor length d.s. glacis length with (2H:1V) slope u.s. floor length Total floor length
= 6.5 m = 2(309-308.85) = 0.3 m = 6.2 m = 13 m
5. Pressure calculation a. Upstream cutoff d 1.5 m ,b 13 m
1
d
1.5
0.115 b 13 D1 100 20 80% C 1 100 28 72%
Correction of C for floor thickness
t
D C d 0.6 80 72 3.2% 1.5
C corrected 72 3.2 75.2% of H b. Downstream cutoff d 1.6 m , b 13 m 1
d
1.6
b 13 E 31%
0.123
D 22%
Correction of E for floor thickness
0.6 1.6
E corrected 31 3.38 27.62% of H
7
31 22 3.38%
Hydraulic Structures – Head and Cross Regulators
December 12, 2010
6. Floor thickness a. d.s. floor 1. at 2 m from d.s. end
% pressure 27.62
75.2 27.62 12
1.5
33.6%of H Head H % pressure =2.15
33.6 100
0.722 m of water
Minimum concrete thickness t min
Head
c w
0.722 2.25 1
0.58 m
Provide 0.6 m thick concrete floor for 1.5 m. 2. at 4.5 m from d.s. end % pressure 27.62
75.2 27.62 12
4.0
43.48%of H Head H % pressure =2.15
t min
43.48
0.934 m of water 100 Head 0.934 0.75 m c w 2.25 1
Provide 0.8 m thick concrete floor for 2.5 m. 3. at 6.5 m from d.s. end 75.2 27.62 % pressure 27.62 6.0 12 54.41%of H t min
2.15 0.5141
0.9 m 2.25 1 Provide 1.0 m thick concrete floor for the rest of the glacis. 7. Upstream protection i. Block protection (inverted filter) Length of protection = depth of cutoff ( D) =1.5 m Provide 2 rows of 0.8 m 0.8 m 0.6 m C.C. blocks over 0.6 m thick inverted filter. ii. Launching apron 3 2 Volume per meter length 2.25 D m m m
If thickness is 1.0 m, then the required length Provide 3.5 m long launching apron. 8
2.25 D 1.0
2.25 1.5 1
3.37 m
Hydraulic Structures – Head and Cross Regulators
December 12, 2010
8. Downstream protection i. Block protection Length of protection 2 D 2 1.6 3.2 m
Provide 4 rows of 0.8 m 0.8 m 0.6 m blocks over 0.6 m inverted filter. ii. Launching apron
Volume per meter length 2.25 D m 3 m m 2 If thickness is 1.0 m, then Required length
2.25 D
2.25 1.6
3.6 m 1.0 1 Provide 4.0 m long launching apron. Provide 0.4 m thick and 1.2 deep toe wall between filter and launching apron. B. Design of distributary head regulator 1. Fixation of crest and waterway The crest level should be provided 0.5 m higher than upstream floor level. Crest level 309 0.5 309.5 m H e 311 309.5 1.5 m hd 311 310.2 0.8 m hd
H e C s C
0.8 1.5
0.533
0.98 (From Fig. 6.5)
C s 1.84 0.98 1.80
The effective width of waterway is found by Q C B e H e
1.5 1.5
10 1.8 B e 1.5 B e 3 m
Provide 60% of distributary width
60
10 6 m 100 Provide 2 bays of 3 m each separated by 1 m thick pier. Therefore, the overall waterway 2 3 1 7 m 2. Level and length of d.s. floor Q 10 cumec , waterway 6 m q
10 6
1.67 m sec
Head loss H L 311 310.2 0.8 m Using Blench curves (Fig. 3.5)
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Hydraulic Structures – Head and Cross Regulators
December 12, 2010
Ef 2 1.37 m
gives D 2 1.32 m
Ef 1 Ef 2 H L 1.37 m
gives D1 0.32 m
Cistern length Lc 5 D 2 D1
5 1.32 0.32 5.0 m Provide cistern length = 6 m Floor level required T.E.L.d.s. Ef 2
310.2 1.37 308.83m Provide d.s. floor level at El. 308.8 (Ground Level) 3. Vertical cutoffs a. u.s. cutoff Provide u.s. cutoff depth 1.5 m
The bottom of cutoff 309 1.5 307.5 m b. The minimum d.s. cutoff depth = 1.2 m 4. Total floor length and exit gradient Maximum static head F.S.L.u.s. F.L.d.s.
311 308.8 2.2 m Exit gradient G E
H
1
d 1/2
2 1 1 2
1 5
2.2
1
1.2
With trial and error d (m)
λ
α
L d (m)
1.2 1.4 1.6 1.7
8.50 6.26 4.75 4.24
15.99 11.47 8.50 7.42
19.00 16.05 13.62 12.60
Get L 13 m ,d 1.7 m
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Hydraulic Structures – Head and Cross Regulators
December 12, 2010
= 6.0 m
d.s. floor length (cistern length) d.s glacis length 2H:1V slope
2 309.5 308.8
= 1.4 m
Crest length
23 H e 23 1.5
= 1.0 m
u.s. glacis length 1H:1V slope
1 309.5 309.0
= 0.5 m
u.s. floor length
= 4.1 m
Total floor length
= 13 m
5. Pressure calculations a. Upstream cutoff d 1.5 m ,b 13 m
1
d
1.5
0.115 b 13 D1 100 20 80% C 1 100 28 72%
Assuming the u.s. floor thickness = 0.6 m Correction of C for floor thickness
0.6 1.5
80 72 3.2%
C corrected 72 3.2 75.2% of H b. Downstream cutoff d 1.7 m , b 13 m 1
d
1.7
b 13 E 32%
0.13
D 22%
Correction of E for floor thickness
0.6 1.7
32 22 3.5%
E corrected 32 3.5 28.5% of H 6. Floor thickness a. d.s. floor 1. at 2 m from d.s. end
% pressure 28.5
75.2 28.5
12 34.33%of H
1.5
Minimum concrete floor thickness t min
0.3433 2.2
2.25 1 Provide 0.6 m thick concrete floor for 1.5 m length. 11
0.6 m
Hydraulic Structures – Head and Cross Regulators
December 12, 2010
2. At 4 m from d.s. end Provide 0.8 m thick concrete floor for 2.5 m. 3. At the toe of glacis (beginning of the hydraulic jump) 5.5 %pressure 28.5 75.2 28.5 12 49.9%of H Unbalanced head 0.499 2.2 1.095 m Unbalanced head due to dynamic condition 50% D 2 D1 toe H L
1
1.32 0.32 2 0.898 m t min
49.9 100
0.8
1.095
0.88 m 2.25 1 Provide floor thickness 1.0 m. b. d.s Floor thickness Same as provided in u.s. floor for the cross regulator (minimum thickness of 0.6 m in the u.s. which should be thickened under the crest). 7. u.s Protection Same as provided in the u.s. of cross regulator. 8. d.s. protection i. Block protection (inverted filter) Length of filter 2 D 2 1.7 3.4 m Provide 6 rows of 0.6 m 0.6 m 0.4 m C.C. blocks over 0.4 m thick graded filter. ii.Launching apron
Volume per meter length 2.25 D 2.25 1.7 3.825 m 3 m Assume thickness of launching apron = 0.8 m, then 3.8 Required length 4.75 m 0.8 Provide 5.0 m long launching apron. Masonry toe wall 0.4 m thick and 1.2 deep shall be provided between filter and launching apron.
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Hydraulic Structures – Head and Cross Regulators
December 12, 2010
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Hydraulic Structures – Head and Cross Regulators
December 12, 2010
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