Hydraulic Structures –Hydraulic Design of Syphon February 1, 20111 Cross Drainage Works 1. Aqueducts: If the bed level of the channel is higher than H.F.L. of the drain, the structure is an aqueduct. Otherwise, the structure is either syphon or culvert. 2. Culvert If there is no restriction downstream, the structure will have two slopes S 1 and S 2 , then, the structure will be a culvert. 3. Syphon If there is any restriction downstream the structure will have three slopes, therefore the structure is a syphon. Hydraulic Design of Syphon Design a syphon with the following data a. Canal Discharge = 40 cumec Bed width = 18 m Full supply depth = 2.1 m Bed level = 250 m Side slope = 1½ H: 1 V b. Drain Flood discharge = 100 cumec Bed level = 251.8 m Depth = 1.45 m H.F.L. = 253.25 m 16 m 44.5 m 8 m Roadway Roadway Drain Hydraulic Structures –Hydraulic Design of Syphon February 1, 2011 2 Design 1. Drainage waterway Lacey’s Formula 4.83 , wetted perimeter 4.83 100 48.3 P Q P m = = = = Total length of barrels 8 44.5 16 68.5 70m = + + = = Provide bed width of the drain at crossing 44.5m = High flood level of the drain= 253.25 m 2. Canal waterway Velocity of approach ( ) 2 40 0.9 1.5 2.1 18 2.1 Q m s A = = = + × Maximum fluming is 40%, 0.4 18 7.2m × = Let the canal waterway be reduced from 18 m to 7.3 m such that two barrels each 3.5 m with 0.3 m thick wall. Let the height of the barrel = 2.5 m ( ) ( ) ( ) 40 2.29 2 ~ 3 3.5 2.5 2 2.29 0.46 1 1, 0.4 ~ 0.6 9.81 2.5 Q V m s V m s A V Fr Fr gD = = = = × × = = = < < × The flow is subcritical in the barrel. 3. Head loss and bed levels at different sections: Provide 2 in 1 splay in contraction, and 3 to 1 splay in expansion, and 3 in 1 splay in expansion: Length of contraction 18 7.3 2 10.7 2 m ÷ = × = Length of expansion 18 7.3 3 16.05 2 m ÷ = × = At section 4 2 2 0.9 Velocity head 0.041 2 2 9.81 a a V h m g = = = × R.L. of bed = 250 m 3.5 m 2.5 m 0.3 m Hydraulic Structures –Hydraulic Design of Syphon February 1, 2011 3 R.L. of water surface = 250+2.1=252.1 m R.L. of T.E.L. = 252.1+0.041 = 252.141 m At section 3 Provide water depth = 3 m Area of section 2 3 7.3 21.9m = × = ( ) 2 2 3 40 Velocity 1.83 21.9 1.83 Velocity head 0.17 2 2 9.81 Q m s A V m g = = = = = = × Loss of head in expansion from section 3 to section 4 2 2 2 2 3 4 2 1.83 0.9 0.3 0.039 2 2 9.81 V V K m g | | | | ÷ ÷ = = = | | × \ . \ . El. of T.E.L. at section 3 252.141 0.039 252.18m = + = R.L. of water surface 252.18 0.17 252.01m = ÷ = R.L. of bed 252.01 3 249.01m = ÷ = Head loss through barrels 2 1 2 1 2 L V f f R g | | = + + | \ . where, f 1 = constant for syphon mouth =0.08 for bell mouthed syphon 2 1 b f a R | | = + | \ . where a and b are constants depending on the material of the surface of barrels. For cement plaster, a = 0.00316 and b = 0.1. ( ) 2 3.5 2.5 3.5 2.5 2 2 A R P × × = = + × × 2 0.1 0.00316 1 0.036 0.729 f | | = + = | \ . Assume length of syphon barrels L= 70 m ( ) 2 2.29 70 1 0.08 0.0036 0.729 2 9.81 0.381 L h m | | = + + | × \ . = At section 2 Hydraulic Structures –Hydraulic Design of Syphon February 1, 2011 4 R.L. of T.E.L. R.L. of T.E.L. @ section 3 + head loss through barrels 252.18 0.381 252.561m = = + = R.L. of water surface 252.562 0.17 252.39m = ÷ = R.L. of bed 252.39 3 249.39 say 249.40 m m = ÷ = At section 1 2 2 2 1 1 2 2 in contraction transition 2 1.83 0.9 0.2 0.026 2 9.81 L V V h K g m | | ÷ = | \ . | | ÷ = = | × \ . R.L. of T.E.L. 252.561 0.026 252.587m = + = R.L. of water surface 252.587 0.041 252.546m = ÷ = R.L. of bed 252.546 2.1 250.446m = ÷ = Hydraulic Structures –Hydraulic Design of Syphon February 1, 2011 5 4. Transitions Because the depth is varying through the transition, Metra’s and Chutervedi’s formulae for transitions are not applicable, therefore Hinds’ method shall be used. The expansion transition is explained in more details, please refer to section 4.b. a. Contraction transition 2 1 1 w.s. @ sec.1 - w.s. @ sec. 2 2 252.546 252.4 0.073 2 length of transition 10.7 5.35 2 2 y C x y m x m = = ÷ = = = = = Substitute y 1 and x 1 in the equation to find C ( ) 2 2 0.073 5.35 0.0026 0.0026 C C y x = = = Contraction Transition [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] Dist. y El. of W.S. El. of T.E.L. Velocity head Velocity Side slope Area Bed level Depth Bed width (m) (m) (m) h v (m) V (m/s) s A (m 2 ) (m) D (m) B 0.0026x 2 Linear Interp. [4]-[3] (2g h v ) 1/2 Linear Interp. [3]-[9] A/D - s D 0.00 0.0000 252.400 252.500 0.017 1.83 0:1 21.86 249.40 3.0 7.30 2.50 7.53 5.35 9.06 8.00 14.56 10.70 0.0000 252.546 252.587 0.040 0.90 1.5:1 44.44 250.45 2.1 18.00 b. Expansion transition ( ) 1 1 1 2 2 2 252.1 252.01 0.045 2 16.05 8.025 2 0.045 8.025 0.0007 y m x m y C x y x ÷ = = = = = = = Hydraulic Structures –Hydraulic Design of Syphon February 1, 2011 6 Pucca Floor Expansion Transition [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] Dist. y El. of W.S. El. of T.E.L. Velocity head Velocity Side slope Area Bed level Depth Bed width (m) (m) (m) h v (m) V (m/s) s A (m 2 ) (m) D (m) B 0.0007x 2 Linear Interp. [4]-[3] (2g h v ) 1/2 Linear Interp. [3]-[9] A/D - s D 0.00 0.0000 252.010 252.180 0.170 1.826 0:1 21.86 249.01 3.00 7.30 3.00 0.0063 252.016 252.173 0.157 1.753 0.28:1 22.73 249.20 2.82 7.29 6.00 0.0252 252.035 252.165 0.130 1.596 0.56:1 25.48 249.38 2.66 8.09 8.02 0.0450 252.055 252.161 0.106 1.442 0.75:1 28.37 249.50 2.56 9.16 10.00 0.0252 252.075 252.156 0.081 1.262 0.93:1 31.75 249.63 2.44 10.71 13.00 0.0063 252.094 252.150 0.056 1.051 1.21:1 38.10 249.81 2.28 13.92 16.05 0.0000 252.100 252.140 0.040 0.886 1.5:1 44.44 250.00 2.10 18.00 5. Pucca floor Provide pucca floor in half the transition length in the upstream and 3/4 th the length of the expansion transition in the downstream. Length of pucca floor u.s. 10.7 5.35 say 6.0 2 m m = = 7 . 3 0 7 . 3 0 8 . 0 9 9 . 1 6 1 0 . 7 0 1 3 . 9 2 1 8 . 0 0 0 3 6 8.02 10 13 16.05 m x B e d w i d t h ( m ) 16.05 8.025 y 1 252.1 w.s. El. 252.01 PROFILE PLAN Bed level Hydraulic Structures –Hydraulic Design of Syphon February 1, 2011 7 6. Uplift pressure on the barrel floor and pucca floor a. Static uplift pressure i. At the bottom of barrel floor Level of bottom of barrel floor ( ) 251.8 0.6 0.3 2 2.5 248.1m = ÷ + × + = Static head 250 248.1 1.9 of water m = ÷ = ii. At the downstream end of barrel Floor level 249.01m = Assume floor thickness 249.01 1.5 247.51m = ÷ = Static head 250 247.51 2.49 of water m = ÷ = b. Seepage head on the barrel floor and the pucca floor Seepage head H.F.L. in the drain W.T. in the region (canal bed level) 253.25 250 3.25m = ÷ = ÷ = Total seepage path ( ) ( ) 1 3 0.6 2 0.3 2 2.5 1 8 13 11.3m = × + × + × + + × = i. At the bottom of barrel floor Seepage path to bottom of barrel floor 0.6 2 3.1 1 4.3m = × + × = 1 1 3.25 , 2.01 of water 11.3 4.3 11.3 H H m = = ÷ Total uplift in the barrel 1.9 2.01 3.91 of water m = + = ii. At d.s. end of barrel floor 4.3 6.97 Total seepage length = 11.3 m 3.25 H 1 H 2 Max. Seepage head Hydraulic Structures –Hydraulic Design of Syphon February 1, 2011 8 Seepage path 8 0.6 2 3.1 3 6.97m = × + ×+ = 2 2 3.25 , 1.25 of water 4.3 11.3 H H m = = Total uplift 2.49 1.25 3.74 of water m = + = Floor thickness 3.74 1.7 say 2.0 2.2 m m = = The remaining length of transition shall be provided with 0.8 0.8 0.6 m m m × × C.C. blocks over 0.6 m inverted filter. 4 rows of blocks resting on 1.2 m deep toe wall at ends. Hydraulic Structures –Hydraulic Design of Syphon February 1, 2011 9 and 3 to 1 splay in expansion.92 0. Drainage waterway Lacey’s Formula P 4. Let the height of the barrel = 2. 0.5 2 V 2.5m High flood level of the drain= 253.12 18 2.46 1 gD 9.1 Maximum fluming is 40%. Canal waterway Velocity of approach Q 40 0.83 Q 4.5 m V Q 40 2.5 m 0.29 Fr 0.05 m 2 R.6 The flow is subcritical in the barrel.81 18 7. 2011 Design 1.3 m .29 m s A 3. and 3 in 1 splay in expansion: Length of contraction Length of expansion At section 4 Velocity head ha Va2 0.5 m with 0.83 100 48. of bed = 250 m 2 .041 m 2 g 2 9.5 2.3 m thick wall.9 m s A 1.7 m 2 18 7.2m Let the canal waterway be reduced from 18 m to 7.5 16 68.5 V 2 ~ 3 m s Fr 1.5 m 3. Head loss and bed levels at different sections: Provide 2 in 1 splay in contraction.25 m 2.4 ~ 0.5 70 m Provide bed width of the drain at crossing 44. 0.3 3 16.3 m such that two barrels each 3.81 2.3 2 10. P wetted perimeter Total length of barrels 8 44.4 18 7.L.Hydraulic Structures –Hydraulic Design of Syphon February 1.5 2. 3.3 m 2. L.L.81 2g El.01m R.E.00316 and b = 0.729 Assume length of syphon barrels L= 70 m 70 2.08 for bell mouthed syphon b f 2 a 1 where a and b are constants depending on the R material of the surface of barrels.08 0.832 0.29 hL 1 0.L.729 2 9.039 m 2 9.18m R. of water surface 252. R A 2 3.3 21.00316 1 0.1+0. at section 3 252.036 0. of bed 252.1=252.81 Loss of head in expansion from section 3 to section 4 V 2 V42 1. of T.3 0.E. of T.9 2 V 2 1.L.L.01 3 249.0036 0.9m2 Velocity Q 40 1.18 0.041 = 252. 2011 R.L.17 252.5 2.83 m s A 21.141 m At section 3 Provide water depth = 3 m Area of section 3 7.81 0.1 f 2 0.039 252.Hydraulic Structures –Hydraulic Design of Syphon February 1.5 2 2 0.5 P 3.01m L V2 Head loss through barrels 1 f1 f 2 R 2g where.141 0. f1= constant for syphon mouth =0. of water surface = 250+2.83 Velocity head 3 0. = 252.92 K2 3 0.17 m 2 g 2 9.1 m R.1.5 2.381 m 2 At section 2 3 . For cement plaster. a = 0. of water surface 252.587 m R.026 252. of T.832 0.L.562 0.Hydraulic Structures –Hydraulic Design of Syphon February 1. 252.381 252.39 m At section 1 V 2 V12 hL in contraction transition K1 2 2g 1.40 m R. @ section 3 + head loss through barrels 252.446 m 4 . of T.561m R. 2011 R.L.39 3 249.L.1 250.587 0.026 m 2 9.546 m R.E.2 0.L.E.546 2.L.18 0. of bed 252.L.561 0.L.L. of bed 252.041 252.17 252.L.81 say 249. of T.92 0. of water surface 252.39 m R. R.L.E. [2] y (m) 0.1 .400 [3] El.587 0. 252.045 m 2 16.35 m 2 2 Substitute y1 and x1 in the equation to find C 0.546 252. a.073 m 2 length of transition 10.00 2 b. Metra’s and Chutervedi’s formulae for transitions are not applicable.Hydraulic Structures –Hydraulic Design of Syphon February 1.70 0.0 [11] Bed width B A/D . Contraction transition y C x2 w.s D 7.E.0026 x 2 Contraction Transition [1] Dist.44 250.53 9. @ sec.30 7.0026 y 0. 2011 4.1 0. therefore Hinds’ method shall be used.s.073 C 5. Transitions Because the depth is varying through the transition.017 [6] Velocity V (m/s) (2g hv)1/2 1.00 10.50 5. (m) Linear Interp.0000 252.0026x2 0.35 C 0.40 3. (m) [4] El.06 14.500 [5] Velocity head hv (m) [4]-[3] 0.56 18. The expansion transition is explained in more details.00 2. 0:1 [8] Area A (m2) [9] Bed level (m) [10] Depth D (m) [3]-[9] 21. of T.w.L.0000 252. of W.90 1.040 0. please refer to section 4.045 C 1 2 2 x 8. @ sec.01 0.86 249.025 m 2 y 0.05 x1 8.1 252.025 y1 y 0.5:1 44.35 8. 2 y1 2 252. Expansion transition 252.45 2.4 0.b.0007 x 2 5 .s.546 252.7 x1 5.S.83 [7] Side slope s Linear Interp. 30 9.66 2.016 252.75 38.44 2.262 1.040 [6] Velocity V (m/s) (2g hv)1/2 1. Length of pucca floor u.82 2.165 252.L.05 0.173 252.Hydraulic Structures –Hydraulic Design of Syphon 252. [2] y (m) 0.38 249.28:1 0.0063 0.1 y1 w.0000 252.157 0.0000 0. (m) [4] El.s D 7.05 Bed level PROFILE February 1.63 249.0007x2 0.30 8.0450 0.50 249.00 5.00 3.00 2.00 6. 252.01 249. of W.92 18.106 0.00 3.44 249.180 252.00 16. 10.93:1 1.056 0.02 10.70 13.00 13.37 31.56:1 0.21:1 1.753 1.09 7. of T.28 2.596 1.0063 0.s. 2011 Bed width (m) 10.s.0252 0.035 252.7 5.051 0. Pucca floor Provide pucca floor in half the transition length in the upstream and 3/4th the length of the expansion transition in the downstream.055 252. 0:1 0.S.16 PLAN x 0 3 6 8.86 22.0 m 2 Pucca Floor 6 .100 [3] El. (m) Linear Interp. 252.0252 0.10 44.150 252.75:1 0.156 252.130 0.20 249.010 252.71 13.29 8.48 28.170 0.01 8. El.10 [11] Bed width B A/D .73 25.09 9.025 16.886 [7] Side slope s Linear Interp.075 252.140 [5] Velocity head hv (m) [4]-[3] 0.05 m Expansion Transition [1] Dist.02 10 13 16.081 0.442 1.56 2.094 252.35 m say 6.16 10.161 252.92 18.826 1.E.30 7.00 7.81 250.00 8.5:1 [8] Area A (m2) [9] Bed level (m) [10] Depth D (m) [3]-[9] 21. s.01 3.5 247.01m Assume floor thickness 249. Uplift pressure on the barrel floor and pucca floor a.3 m ii.3 2 2.91 m of water Max.T.Hydraulic Structures –Hydraulic Design of Syphon February 1.25 250 3. H1 2.51m Static head 250 247.9 2.3 4.9 m of water ii.3m 3 i.6 0. At the downstream end of barrel Floor level 249.25 head H1 H2 4.11 4. At the bottom of barrel floor Seepage path to bottom of barrel floor 0.97 Total seepage length = 11.3 6.01 1.5 1 8 13 1 11.5 248.6 2 3. 2011 6. At d.51 2.3 11.1m Static head 250 248.3 Total uplift in the barrel 1. end of barrel floor 7 .49 m of water b. in the drain W.25 .L.8 0. At the bottom of barrel floor Level of bottom of barrel floor 251. in the region (canal bed level) 253.F.6 2 0.1 1. Static uplift pressure i.25m Total seepage path 0.01 m of water 11. Seepage head on the barrel floor and the pucca floor Seepage head H.3m H1 3. Seepage 3.3 2 2. 2 The remaining length of transition shall be provided with 0.25 .97 m 8 3 H 2 3.C.8 m 0.Hydraulic Structures –Hydraulic Design of Syphon February 1.0 m 2. H 2 1. 4 rows of blocks resting on 1. 2011 Seepage path 0.25 3.6 m inverted filter.7 m say 2.49 1.6 m C. 8 .74 m of water Floor thickness 3. blocks over 0.25 m of water 4.3 Total uplift 2.3 11.8 m 0.74 1.1 6.2 m deep toe wall at ends.6 2 3. 2011 9 .Hydraulic Structures –Hydraulic Design of Syphon February 1.