3. Design of Channels General Definition of some terms CHAPTER THREE

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1 CHAPTER THREE. Design f Channels.. General The success f the irrigatin system depends n the design f the netwrk f canals. The canals may be excavated thrugh the difference types f sils such as alluvial sil, nn-alluvial sil etc. the design cnsideratin naturally vary accrding t the type f sil. Again, the velcity f flw in the canal shuld be critical. That means, the velcity shuld be nn-silting and nn-scuring. If the velcity becmes less than the critical velcity, then silting will take place and the capacity f the canal will be reduced. If the velcity becmes mre than the critical velcity then the scuring will take place and the channel will be damaged. S, determinatin f critical velcity is very imprtant in canal design. Based n the water requirements f the crps n the area t be irrigated the entire system f main canal, secndary canal, tertiary canal and field distributaries shuld be designed prperly fr a certain realistic value f peak discharge that must pass thrugh them, s as t prvide sufficient irrigatin t the cmmands. Again, the design f unlined and lined canals invlves different practical and ecnmical cnsideratin... Definitin f sme terms. Alluvial sil: The sil which is frmed by cntinuus depsitin f silt is knwn as alluvial sil. The river carries heavy charge f silt in rainy seasn. When the river verflws its banks during the fld, the silt particles get depsited n the adjining areas. This depsitin f silt cntinues year after year. This type f sil is fund in deltaic regin f a river. This sil is permeable and sft and very fertile.. Nn-alluvial sil The sil which is frmed by the disintegratin f rck frmatin is knwn as nn-alluvial sil. It is fund in the muntains regins f a river. The sil is hard an impermeable in nature. This is nt fertile.. Silt factr (f) In designing f a canal in alluvial sil, the suspended silt and the depsited silt in the canal bed shuld be taken int cnsideratin with great imprtance. During the investigatin wrk in varius canals in alluvial sil, Lecey established the effect f silt n the determinatin f discharge and the canal sectin. S, he intrduced a factr which is knwn as silt factr. It depends n the main particle size f silt. It is dented by f. Determined by the expressin f =. 76 m f Where m f = mean particle size f silt in mm. 4. Cefficient f rugsity (N)

2 The rughness f the canal bed affects the velcity f flw. The rughness cefficient, being a parameter representing the integrated effect f the channel crss sectinal resistance, value f N depends n the type f bed materials f the canal. 5. Mean velcity elcity distributin in a canal sectin usually varies frm ne pint t anther, this is due t shear stress at the bttm and at the sides and due t the presence f the free surface. Field bservatin shws that average velcity fr pen channel flw t be the average velcity measured at 0. and 0.8 f y frm the free water surface. 0. y y av = 6. Critical velcity ( ) When the velcity f the flw is such that there is n silting r scuring actin in the canal bed, then that velcity is knwn as critical velcity. Generally the critical velcity depends n the nature f the sil frmatin in which the water flws. Table belw shws the critical velcity fr different sil frmatins: Nature f sil Critical velcity m/s Sandy sil 0. t 0.6 Black cttn sil 0.6 t 0.9 Firm clay and lm 0.9 t.5 Gravel. Hard rck Mre than.0 Cncrete 6.0 Steel lining Critical velcity ratin (CR) The rati f the mean velcity t the critical velcity is knwn as critical velcity rati. It is dented by m. CR = = m When m equals there is n silting r scuring, when m >, scuring will ccur and when m < silting will ccur. S, by finding the value f m, the cnditin f the canal can be predicted whether it will have silting r scuring. 8. Hydraulic radius (R) Is the rati f the crss-sectinal area t the wetted perimeter f the channel A R = P

3 9. Full supply level (FSL) The maximum discharge capacity f the canal fr which it is designed, is knwn as full supply level. 0. Ecnmical sectin In irrigatin canal water flws under the frce f gravity, t fld the cmmand area left and/r side f the canals the FSL f the canal is generally kept abve the natural surface level (NSL). Naturally t hld the water in the channel it is partly excavated belw the NSL and partly abve the NSL. T be ecnmical the depth f excavatin is arranged that the quantity f the earth excavated frm the canal sectin is just sufficient t cnstruct the banks. The depth f excavatin is called balancing depth. In additin t that the cnveyance f the channel will be efficient when the channel sectin have minimum perimeter fr a given area, slpe and rughness cefficient are fixed. Fig: Balancing depth Y is balancing depth D is full supply depth H is height f the tp f bank abve the bed f bank T is tp width f the bank B is bed width f the cannel m: is side slpe in cutting n: is side slpe in filling Fr ecnmical sectin Cutting = filling in banks y( B + my) = ( H y)( T + n( H y)) Generally side slpe in cutting is kept : and filling kept as.5:.

4 . Regime channel When the characteristics f the bed material f the channel are same as that f the transprted material and when the silt charge and silt grade are cnstant, then the channel is said t be in its regime and the channel is called regime channel. A channel in which neither silting nr scuring takes place is called regime channel r stable channel. This stable channel is said t be in state f regime if the flw is such that silting and scuring need n special attentin... Design f nn-alluvial channels The nn-alluvial sils are stable and nearly impervius. Fr the design f canal in this type f sil, the cefficient f rugsity plays an imprtant rle, but the ther factr like silt factr has n rle. Here, the velcity f the flw is cnsidered very clse t critical velcity. S, the mean velcity given by Chezy,s expressin r Manning s expressin is cnsidered fr the design f canal in this sil. After alng investigatin in varius canals, Chezy and Manning have established the fllwing expressins fr finding the mean velcity flw. Chezy frmula = C RS Where C is a cefficient which depend n the nature f the surface and the flw and knwn as chezy cefficient, S is bed slpe f the channel. C can be calculated frm the fllwing frmula:. Pavlvski frmula C = n x R In which x= R ( n 0.) n and n is Manning s cefficient. Ganguiller and Kutter frmula n S C = n + + S R. Bazin s frmula 4

5 C = In which M is a cefficient dependant n the surface rughness + M R Channel M fr unlined channel M =.0 t.75, fr lined channel M = 0.45 t 0.85 Manning s frmula = R S n Where n is rughness cefficient knwn as Manning s n [L -/ T]. This cefficient is essentially a functin Q A f the nature f the bundary surface. = Where Q is design discharge m /s A crss sectinal area f the channel m mean velcity f flw Design prcedures f nn-alluvial channels. Start with a design discharge and select the permissible velcity. Determine the area f the channel by Q=A frmula. Cmpute fr the hydraulics radius by using Chezy r Mannings equatin 4. Write the hydraulics radius in terms f B and Y and equate it with result f step three 5. Write the area in terms f B and Y and substitute B f step 4 in this equatin, then yu will have quadratic equatin t slve fr the value f Y..4. Design f alluvial channels If the prcedure adpted fr the design f channels n nn-alluvial sil is applied ver alluvial channels, then the silt lad carried by the irrigatin water is nt cnsidered. The principle f design f a channel n alluvial sil is ttally different frm that f channel n nn-alluvial sils. Channels n alluvial sil carry appreciable silt and sand lad. When the channel water has excess silt lad silting ccur in the channel. On the cntrary when the water is silt free it picks up the silt frm the channel bed and sides, it results in ersin f channel sectin. Manning s and Chezy s equatin d nt cnsider this aspect. When silting takes place the channel sectin is reduced and cnsequently capacity f the channel is reduced. When scuring ccurs firstly the water level is lwered with in turn reduces the cmmand. Secndly the scured material is depsited at sme ther place t disturb the equilibrium cnditin there. Taking the prblem f silt transprtatin in t accunt it was necessary t evlve sme basis fr the design f a stable sectin with critical velcity. There are tw imprtant and mst cmmnly used theries. They are Kennedy s silt thery and Lacey s thery. After lng research in different canals and different cnditins R.G Kennedy, Punjab and Gerald Lacey have established sme theries fr the design f canals which are knwn as Kennedy s thery and Lacey thery. Thse tw theries are based n the characteristics f sediment lad (i.e silt) in canal water. The behavir f the silt lad is explained by the thery which is knwn as silt thery.4.. Kennedy s regime thery Kennedy established a relatin between nn scuring, nn silting velcity, termed as critical velcity f flw and the stage f flw n the basis f experimental wrk cllected frm channels n the upper Bari-Dab canal system in Punjab (Pakistan). Fr any given channel having a particular sil cnditin, the critical velcity rati which is a functin f silt charge and grade and rugsity cefficient is uniquely fixed. Kennedy had suggested a general frm f equatin fr critical velcity =CD n. The value f m depends upn the silt charge and silt grade. The cefficient C and the pwer 5

6 index n are nt cnstant and change frm site t site. The mst prevalent values f C and n as wrked ut by Kennedy are and 0.64 respectively. Kennedy pltted varius graphs between and depth f flw and finally gave a frmula t calculate. the frmula is 0.64 = 0.546D Kennedy als recgnized that sediment size plays an imprtant rle in determining the relatinship between velcity and depth. Hence, he prpsed that fr the sediment sizes ther than the ne fund in the upper Bari Dab canal system the abve equatin shuld be mdified t: 0.64 = m D Where critical velcity / nnsilting velcity [m/s] and Y full supply depth [m] and C is a cnstant. It depends n character f silt. Carser the material greater the value f the cnstant and n is sme index. It als depends n the type f silt. Where m is incrprated t shw the rle f sediment size m = = CR, fr curse sand value f m may be taken as. t.. Whereas fr finer material it may be kept 0.8 and 0.9. in additin t estimate the actual velcity he prpsed the use f Chezy s equatin with Kutter s cefficient N equal t 0.05 fr Punjab canals. is the actual velcity by Chezy Table: Typical n values fr kenedy regime thert Type f silt lad in the canal water alue f n Fine silt 0.5 Sandy silt 0.64 Limitatins f Kennedy s thery. In the absence f B/Y rati the Kennedy s thery d nt prvide a direct answer t fix the channel dimensin but by trial and errr.. perfect definitin f silt grade and silt charge are nt given. cmplex phenmena f silt transprtatin is nt fully accunted and nly critical velcity rati cncept is cnsidered sufficiently 4. there is n prvisin t decide lngitudinal slpe under the scpe f the thery Design f irrigatin channel by Kennedy thery When an irrigatin channel is t be designed by Kennedy thery it is essential t knw FSD Q, cefficient f regsity N, CR m and lngitudinal slpe f the channel. Then using the fllwing three equatins the channel sectin can be designed: = m D. Q = A. = C RS The prcedure f designing may be utlined in the fllwing steps a. Assume reasnable trial full supply depth Y b. Using equatin () find ut the value f = m D c. With this value f, using equatin and design discharge find ut A = Q d. Assume side slpe and frm the knwledge f A and Y find ut the bed width B e. Calculate R hydraulic radius f. Using equatin find the value f the actual velcity

7 g. When the assumed value f Y is crrect, the value f in step f will be the same as calculated in step b, if nt assume anther suitable value f Y and repeat the prcedure till bth values f velcity are the same..4.. Lindley s regime thery Lindley (99) analyzed data frm stable channels f Punjab and give the fllwing similar equatins like Kennedy fr nn-silting and nn-scuring velcity taking Mannings n=0.05 and side slpe 0.5: = 0.57Y 0.5 = 0.7B Equating the abve tw will give as.6 B = 7.80Y The nly mdificatin by Lindley is that he expressed an equatin fr nly B/y rati. He als develped equatin f taking depth y and B as a functin..4.. Lacey regime thery Better and mdified methd was develped by Lacey. His regime thery pstulates that dimensin f bed width; depth and slpe f canal attain a state f equilibrium with time which is called regime state. Lacey defined a regime channel as a stable channel transprting a minimum bed lad cnsistent with fully active bed. Accrding t him, a channel will be in regime if it carries a cnstant discharge and it flws unifrmly in unlined incherent alluvium f same character. Lacey als differentiated regime between the initial and the final regime cnditins f channel. The initial regime cnditin is attained shrtly after it is put int peratin after cnstructin and the channel begins t adjust its bed slpe either by silting r scuring althugh bed width is nt altered. The cannel then appears t have attained stability, but it is nt actually the final state f stability and hence it still represents the initial regime cnditin. Eventually cntinuus actin f water vercmes the resistance the resistance f the banks and sets up a cnditin such that the channel adjusts its cmplete sectin, then final r true regime cnditin is attained. Accrding t Lacey, there is nly ne lngitudinal slpe at which the cahannel will carry a particular discharge with a particular silt grade. Natural silt transprting channels havea tendency t assume semi-elliptical sectin. The carser the silt, greater the waterway f such channel with narrwer depth. the finer the silt, greater is the depth with narrw waterway as shwn belw: 7

8 Fig: Channel sectin accrding t Lacey s thery Lacey s regime equatins Lacey cllected a large number f data f stable channels in Ind-Gangetic plains. Analizing the data he gave the fllwing equatin f regime channel relating regime velcity, silting factr f, hydraulic radius R, area A, sediment size in mm and bed slpe S. Lacey pltted a graph between regime mean velcity and hydraulic mean radius and give the relatinship: = KR Where K is cnstant Lacey recgnized the imprtance f silt grade in the prblem and intrduced a cncept f functin f knwn as silt factr. Abve equatin is mdified as: = K Rf After study and pltting f large data t justify his thery Lacey gave fur fundamental equatins fr design f irrigatin channels. Af = 0.69 = 4. = 0.8R Rf... 5 S f =.76 d...4 Equatin is called regime flw equatin, it may be seen that the equatin desn t cntain the rugsity cefficient. Frm the abve fundamental Lacey equatins the fllwing equatins have been derived:. Relatin between -Q-f Multiplying equatin by gives ( ) 6 = 0.48 Qf used t determine the critical velcity. relatin between -C-R-f 8

9 Using equatin = 0.8R = 60 R S = 60R S R = 5.5 RS 0.5 chezy' s cns tan t RS ( C) It is cmpared Chezy s equatin R C = R C = 4 K f using equatin taking = K fr = 0.69 = 0.406Rf R =.46 f Rf. Relatin between P and Q Using equatin 4 = 0.69 Rf = f 4 f = 0.667R = A 0.667R A 4. = 0.667R R Substitute equatin Af = 4. 5 A 4.Q = 0.667R.Q = P P = 4.85 Q 9

10 By using the relatin between (S-Q f) 5 f S = is develped 6 6Q Many mre refer Irrigatin and Hydraulic Structure bk by S.R SAHASRABUDHE page 6-66 Design f irrigatin channel by Lacey s regime thery Thus when Q, n r C and f are knwn design can be dne in the fllwing steps: a. Find ut using 0.48( Qf ) 6 = b. Calculate value f R using R =.46 f c. Calculate wetted perimeter P = Q d. Calculate the crss-sectinal area Q=A e. Assuming side slpe and calculate the full supply depth frm A, P and R f f. Calculate the lngitudinal slpe S = 6Q 5 6 0

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