Channel Design. Design of Channels

Transcription

1 Channel Design Hydrmechanics VVR090 Design f Channels lined channels minimizing lining material csts unlined channels maximum permissible velcity and threshld f mvement (stable hydraulic sectin) Cncrete-lined channel Unlined channel 1

2 Objectives f Channel Design Transprt water between tw pints in a safe and cst-effective manner. Includes ecnmical, safety, and esthetics aspects. Here, mainly hydraulic aspects are cnsidered. General bservatins: Cnveyance f a channel increases with the hydraulic radius (wetted perimeter deceases). Frm Manning s frmula. The best hydraulic sectin is a semicircle (fr a given area it has the minimum wetted perimeter). Fr a specific crss sectin, the prprtin that prduce the best hydraulic sectin (maximum flw) might be derived. The best hydraulic sectin might nt be the best frm an ecnmical pint f view. Best Hydraulic Crss Sectin I Maximize the flw fr a given crss-sectinal shape and area. Frm the Manning frmula: 1 Q = AR S n 2/3 1/2 Qn S = AR 2/3 Thus: Qn 2/3 max = AR shuld be fund fr a given S A 2

3 Best Hydraulic Crss Sectin II Optimum gemetries fr different crss sectins. Rectangular crss sectin: best hydraulic crss sectin when the water depth is half the channel width. Practical Cnsideratins fr Best Hydraulic Sectin The area needed t excavate the best hydraulic sectin might be larger than the area required t achieve the flw area It may nt be pssible t cnstruct a stable best hydraulic sectin in the natural material The cst f excavatin depends n ther things than the amunt f material remved (e.g., access t the site, cst f dispsing material) The slpe f the channel must als be cnsidered. 3

4 Channel Design General Aspects 1. The minimum permissible velcity is the lwest velcity that will prevent sedimentatin and vegetative grwth (crude estimates: m/s fr sedimentatin and 0.75 m/s fr vegetatin). 2. The side slpes depend primarily n the engineering prperties f the material thrugh which the channel is excavated. 3. The freebard refers t the vertical distance between either the tp f the channel r the tp f the channel lining and the water surface (design flw at nrmal depth). Side Slpes 4

5 Channel Freebard I Lined channel Channel Freebard II Preliminary estimate f freebard (unlined channel): F = Cy F: freebard (ft) y: design depth (ft) C: cefficient (=1.5 fr 20 ft 3 /s and 2.5 fr 3000 ft 3 /s) 5

6 Flw Arund a Channel Curve I Flw Arund a Channel Curve II Rise in water surface at the uter bank: 2 ub Δ h = gr b: channel width R: distance frm center f curve t centerline f channel Take int accunt velcity variatin: 2 u R Δ h = 2.3 lg g Ri R i : inner radius R : uter radius 6

7 Use f Lined Channels Lined channels may be used: t permit transmissin f water at high velcities thrugh areas f deep r difficult excavatin t permit transmissin f water at a reduced cnstructin cst t decrease channel seepage t reduce peratin and maintenance csts t ensure stability f the channel sectin Typical Lined Channel Crss Sectins 7

8 Design Prcedure fr Lined Channels Minimize the cst f the lining material. Identical t find best hydraulic sectin, if unifrm thickness f the lining material is emplyed. Design prcedure: 1. Estimate n 2. Cmpute the value f the sectin factr 3. Fr apprpriate expressin fr A and R, cmpute y N 4. Cmpute channel prperties 5. Check minimum permissible velcity and Frude number 6. Estimate height f lining abve surface and freebard 7. Summarize results with dimensined sketch Design fr Different Lining Thickness r Material The base f the channel and the sides f the channel might be lined with different material f same material with different thickness. Design prcedure invlves minimizing the ttal cst (C) f the lining material: ( C) = ( C + C ) min min b s C b : material cst fr channel base (per unit length) C s : material cst f sides (per unit length) 8

9 Design f Stable, Unlined, Earthen Channels Find a stable crss sectin => One where neither scur nr depsitin cnstitutes a prblem. Three types f unstable sectins: 1. Scuring ccur but n depsitin 2. Depsitin ccur but n scuring 3. Bth scur and depsitin ccur Maximum Permissible Velcities 9

10 Theretical Apprach t Stable Crss Sectin I Bed shear stress (balance between gravity and frce due t flw resistance): τ =ρgrs Fr a wide channel, τ =ρgyns R y N, giving: The shear stress is nt unifrmly distributed alng the perimeter. Cmplex prblem t determine crrect distributin, but fr trapezidal crss sectin the fllwing applies: τ =ρgy S maximum alng bttm τ = 0.76 ρ maximum alng side slpes max N max gyns Maximum Unit Tractive Frce Channel side Channel bttm (in terms f ρgy S ) N 10

11 Theretical Apprach t Stable Crss Sectin II Study a particle in equilibrium, just befre mbilizatin. Emply a balance between the shear frce mbilizing the sediment and the resisting frce depending n the material. Balance fr particles alng the bed: τ A = W tan α L e s W τ L = A s e tan α A e : effective area W s : submerged particle weight a: angle f frictin (= angle f repse) Angle f Respse The angle t the hrizntal at which grains start t rll n a flat bed f sediment that is gradually tilted frm the hrizntal. A representative value n the angle f repse is 32 deg. 11

12 Theretical Apprach t Stable Crss Sectin III Balance fr particles n the side slpes: ( ) ( ) 2 2 τ A + W sin Γ = W csγtan α S e s s Ws tan τ S = csγtan α 1 A tan e 2 2 Γ α Tractive frce rati: 2 2 S tan sin K = τ = csγ 1 Γ = 1 Γ 2 2 τl tan α sin α Angle f Repse tana 12

13 Maximum Unit Tractive Frce fr Different Materials nn-chesive chesive Typical Channel Crss Sectins 13

14 Design Prcedure fr Unlined Channels Find a stable crss sectin. Design prcedure: 1. Estimate n 2. Estimate angle f repse fr channel material Cnsult French fr the prcedure. Example : Water Surface Prfile Upstream an Obstructin Water flwing at the nrmal depth in a rectangular cncrete channel that is 12 m wide encunters an bstructin (see figure), causing the water level t rise abve the nrmal depth at the bstructin and fr sme distance upstream. The water discharge is 126 m 3 /s and the channel bttm slpe is The depth f water just upstream frm the bstructin is 4.55 m. Find the distance upstream t the pint where the surface is at the nrmal depth. 14

15 Nrmal water depth: 1 Q = AR S n 2/3 1/2 2/3 1 12y N 126 = 12yN yN 1/2 2/3 12y N = yN yn y N = 2.95 m (by trial and errr) Critical water depth: y cr 2 1/3 2 q /3 = = = 2.24 m g y N > y cr => subcritical flw at nrmal water depth Start at bstructin and calculate upstream thrugh the step methd. Δ x = i 2 2 ( y+ u /2 g) ( y+ u /2g) i+ 1 i 2 2 4/3 S ( n u / R ) i+ 1/2 15

16 Table fr Step Calculatin 16