© 2008-2021 ResearchGate GmbH. The cost of construction of channel is minimum when it passes maximum discharge for its given cross sectional area. All figure content in this area was uploaded by Bhagu R. Chahar, of canal design. Moreover, in order to make the optimization practical and applicable, tolerable ranges to each variable can be specified in advance according to the local project conditions; also, the priority ratio for each of the three target variables can be defined in a percentage value. It adopts a river basin approach to promote inter-sectoral co-ordination for holistic planning and management of the Ganges water resources. Hardcover. In this investigation explicit equations and section shape coefficients for, Though the minimum area section is generally adopted for canals, it is not the least earthwork cost section as it does not involve the cost of earthwork which varies with the excavation depth. The proposed methodology incorporates elements of the water section and the above-water section, and is applicable to both lined and unlined canals. In this work, three targets are simultaneously selected. The Manning’s roughness (n) is 0.012 and the bed slope is 0.0003. On account of complexities of analysis, explicit design equations for minimum earthwork cost canal sections has not available yet. In general, the cost of earthwork varies with canal depth. Generally Manning’s equation is used in design. On Farm Structures for Water Conveyance. The work in this thesis involves the development of a program by Visual Basic 6.0 for the optimization of the design of lined open channel lateral cross-section. The FSO yielded not only the minimum cost canals but also hydraulically efficient designs with 1.32, 4.86, 4.42, 4.28, and 4.40% less costs than those obtained by PSO for five different freeboard scenarios, respectively. Discharge should be maximum Types of channels based on shape: 1. Canal section may also change at flumes, siphons, and aqueducts. For a given flow, roughness coefficient, and longitudinal slope, this method optimizes the channel section by minimizing the wetted perimeter (or the cross-sectional area) subject to a constraint. Substructure of the Aqueduct consists of the abutments, five piers and substructure of an R.C.C trough of internal size 2.0m × 2.3 m. Foundation of abutment and piers were escalated below the Scour depth level of 4m to avoid erosion and consequent damage to the structure via silting and erosion. where earth has to be cut or excavated, equals the two embankments i.e. E. BIBLIOGRAPHY 6-14. and partly by filling above N.S.L. The overall costs include the costs of earthwork, lining, and water loss by both seepage and evaporation. The section of canal normally is kept trapezoidal in shape as it is best among hydraulic sections of lined canal (, ... A canal a non-natural watercourse constructed to permit the passage of boats or ships or to transmit water for irrigation. ... Increasing p fivefold, the minimization was carried through various cycles until the optimum stabilized. It concerns flow of water in channels where the water does not include air or sediment in large quantities. This kind of complicated optimization approach could be achieved only through a computer program where a huge numbers of input attempts are performed without exceeding the specified variable ranges, and thus, the optimum solution can be selected. The conditions for the most economical section of channel. Roads will affect the natural surface and subsurface drainage pattern of a watershed or individual hillslope. The results show that the reduction of overall cost ranged from 28 to 41% and consequently, the proposed PSO algorithm can be reliably used for the design of irrigation open canals without going through the conventional and cumbersome trial and error methods. sessment, water policy and governance, capacity building, etc. none of the above [E]. An open channel functioning as an irrigation canal may be a rigid or mobile boundary canal. Canal cross-section designs for uniform flows are contrasted and compared by using nondimensional shape parameters. section lines, etc. Bibliography. Many actual cases have been sited. A rectangular channel section is the most economical when either the depth of flow is equal to half the bottom width or hydraulic radius is equal to half the depth of flow. From hydraulic point of view, the total energy of water in any streamline passing through a channel section may be expressed as total head, which is equal to sum of the elevation above a datum, the pressure head, and the velocity head. V =0.546 MD 0.64. The velocity of flow in a canal or ditch should be non erosive and non silting that prevent the deposition of suspended substances. Such works are however suitable only when the stream to be crossed is small. Previous works concentrated on targeting only one target and had no choice but to neglect the rest. Module 1:Water Resources Utilization& Irrigati... Module 3: Irrigation Water Conveyance Systems, LESSON 13. The terminologies used in the design of open channels of different geometry are given below: i) Area of Cross Section (a): Area of cross section of for a rectangular cross section, of wetted section. Aqueduct of 6 X 9.5m span was proposed to be constructed. The minimum area, or the maximum velocity cross section, is generally adopted for lined irrigation canals. The channel section could contain any number of variables; e.g., two variables (rectangular and triangular sections), three variables (trapezoidal and round-bottom triangular sections) and so forth. Design and Operation of Underground Pip... Module 5: Soil –Water – Atmosphere  Plants Intera... Module 8: Economic Evaluation of Irrigation Projec... Last modified: Saturday, 15 March 2014, 5:51 AM, A channel section is said to be economical when the cost of construction of the channel is minimum. The section to be adopted should be economical and at the same time it should be functionally efficient. Cost of construction should be minimum 2. Jain C. Subhash. 2 Objectives of Channel Design Transport water between two points in a safe and cost-effective manner. This program enables for total priority of only one of these three targets, and also, enables for the selection of different ratios of priority for each of these three targets depending on the local conditions of the project. The proposed method can be applied to other complicated sections that cannot be solved by the traditional method. v) Freeboard: It is the vertical distance between the highest water level anticipated in channel flow and the top of the retaining banks. are exposed. A systematic procedure is used to generate design alternatives covering the solution domain. The velocity of flow in any channel section is not uniformly distributed. Its depth is equal to the round-bottom radius and is twice its hydraulic radius. This is because each region has its own different conditions, constraints, and limits from the topographic and financial point of views. The maximum velocity that does not cause excessive erosion depends on the erodibility of the soil or lining material. Furthermore, the methods are based on Manning's equation, which is valid for a hydraulically rough boundary having a narrow range of relative roughness and involves a roughness coefficient having awkward dimensions. B/D ratio for different discharge is given below- The optimal cost equation along with the corresponding section shape coefficients is useful during the planning of a canal project. For various practical sections there exist equations between the design variables. Conservation of water supplies is increasingly important as the demand continues to increase and new sources of supply are becoming increasingly scarce. (ii) Channel Dimensions:  The channel dimensions can be obtained using   uniform flow formula, which is given by, Q = A V                                          (12.3), A = cross-sectional area of canal perpendicular to flow (m2). Particular cases like minimum earthwork cost section and minimum and maximum discharge canal sections are also included in the chapter. Also, the optimization considers priorities regarding three targets, which are the wetted perimeter, the cross-sectional area, and the exposed surface. Road drainage design has as its basic objective the reduction and/or elimination of energy generated by flowing water. The need for optimum design of water conveyance structures provides an active area of study in water resources engineering. Although I know the formulas for most economical section for rectangular and trapezoidal section individually. When estimating the reduction in losses from a lining, this should be based on the combination of a reduced cross-section and a reduced seepage rate per unit area (Thandaveswara, 2012). The bottom width of rectangular is 2.4 m. Since specific energy at critical depth (EC) =   yc Therefore EC = 1.290 m. Example 12.3: Determine the critical depth for specific energy head of 2.0 m in a trapezoidal channel of 2.0 m bottom width and side slopes of 1:1. (R.I.H.). Most economical section is also called the best section or hydraulic efficient section as the discharge passing through a most economical section of channel for a given cross-sectional area (A), slope of the bed (S, A triangular channel section is the most economical when each of its sloping side makes an angle of 45, R= Hydraulic radius (m), P = wetted perimeter (m), = bed slope (fraction or m/m), K = constant for given cross sectional area and bed slope and = A, A = cross-sectional area of canal perpendicular to flow (m, Example 12.2: Compute the critical depth and specific energy for discharge of 6.0 m, Since specific energy at critical depth (E. Jain C. Subhash. Lined channels with trapezoidal, rectangular and triangular sections are the most common manmade canals in practice. MOST EFFICIENT SECTION During the design stages of an open channel, the channel cross-section, roughness and bottom slope are given. (d) Source of water (canal, reservoir, pipeline, wells, or combination of surface and ground water, etc. The destructive power of flowing water, as stated in Section 3.2.2, increases exponentially as its velocity increases. In this investigation, explicitequations and section shape coefficients for thedesign variables of minimum cost lined canal sectionsfor triangular, rectangular, trapezoidal, and circularshapes have been obtained by applying the nonlinearoptimization technique. Theoretically, a semi-circular section is … The significant discrepancy between the results obtained for constant and variable roughness scenarios demonstrates the necessity for considering roughness coefficient variability with water depth in circular sections. Though the minimum area section is generally adopted for lined canals, it is not the minimum cost section as it does not involve lining cost and the cost of earthwork. The principle of design of flumes and hydraulic structures (open drop and chute spillways) is based on the concept of specific energy and critical flow. The main aim of the paper is to present the hydraulic design of aqueduct proposed over Darhali River in Rajouri town and explain as to why aqueduct was required in this area. Q = A.V. In this study, this variation has been implemented in the optimum design of lined circular channels. Design a most economical trapezoidal section of a canal having the following data: Discharge of the canal = 20 cumec Permissible mean velocity = 0.85 m/sec. For a rectangular cross section, if b = width of channel and y = depth of water, the area of wetted section of channel (a) = b.y. (2001). Flow in Open Channels, Tata McGraw-Hill New Delhi: 34-38. It deals with all the practical aspects of an economic section for various discharges, topographic and soil conditions. Schwab, G. O., Fangmeier, D. D., Elliot, W. J., and Frevert, R. K. (1993). John Willey & Sons, Inc., New York, USA: 269. All rights reserved. I want to design a water conveyance system (open channel). The trapezoidal section is the most common and practical canal cross section, which is used to convey water for irrigation, industrial and domestic uses in Egypt. On the other hand, as the lining allows higher velocities, the channel can be laid on the steeper slopes to save earthwork in formation. It was found that rising of aqueduct structure shall boost farming in this area besides improving livelihood of respective land owners. 7.5 Most Economical Section of Channels: A section of a channel is said to be most economical when the cost of construction of the channel is minimum. Such a depth of ex cavated is known as “Balancing Depth “. 1. triangular section with circular bottom for small discharges [C]. This condition is utilized for determining the dimensions of economical sections of different forms of channels. In either case, established procedures ignore channel freeboard. Since the construction cost plays a key role in water conveyance projects, it has been considered as the prominent factor in optimum channel designs. Design of a minimum cost canal section involves minimization of the sum of earthwork cost and cost of lining subject to uniform flow condition in the canal, which results in nonlinear objective function and nonlinear equality constraint making the problem hard to solve analytically. The canal section may cross over the stream without any modification i.e. The design of open channel lateral cross section involves dealing with many variables, and most of them are interdependent. It emphasizes numerical methods for solving problems and takes a one dimensional approach. The traditional methods of channel geometry optimization are reformulated to include freeboard considerations. The most economical section of a trapezoidal channel is one which has hydraulic mean depth equal to half the depth of flow. Though the minimum area section isgenerally adopted for lined canals, it is not the bestsection as it does not involve lining cost, and thecost of earthwork which varies with the excavationdepth. Most of the Rajouri town is hilly and semi-hilly belt. The optimum values for the section variables, such as channel side slope, bottom width, and water depth for trapezoidal, rectangular and triangular channels are found by the computer program using an embedded optimization process that considers imposed limitations/constraints on the previously mentioned variables as well as other variables such as the velocity and top width. Application of the proposed design equations along with the tabulated section shape coefficients results directly into the optimal dimensions of minimum cost canal sections without going through the conventional trial and error method of canal design. In equation (12.2) the discharge Q will be maximum when the wetted perimeter P is minimum. Canal discharge is the most important parameter in designing a canal. 2. This increases the command area of the channel. To assist the growth of crops in areas adjoining to Darhali River construction of Aqueduct from left bank to Right bank of River was projected. The hydraulic radius, iv) Hydraulic Slope (S): It is the ratio of vertical drop in longitudinal channel section (h) to the channel length (l). V=C √ ( RS ) R = Hydraulic mean Radius . A channel is said most economical in hydraulics or fluid mechanics if a) It gives maximum discharge for a given cross sectional area and bed shape. It is evident from the continuity equation and uniform flow formulae that for a given value of slope and surface roughness, the velocity of flow is maximum when hydraulic radius is maximum. Trapezoidal 3. The Kakrapar Right Bank Main Canal (K.R.B.M.C) is choosen as the study area.The main objective is to find out the most economical method of canal lining based on the cost criteria in relation to the wastages etc. left bank and right Any flow equation, e.g. The possible cross sections are parameterized by at most two variables, so the calculations do not require the use of sophisticated optimization methods or large computers. design variables of minimum cost lined canal sections for triangular, rectangular, trapezoidal, and circular shapes have been obtained by applying the nonlinear optimization technique. The estimated cost of the structure was near about 90 lacs. Therefore, water must not be allowed to develop sufficient volume or velocity so as to cause excessive wear along ditches, below culverts, or along exposed running surfa… A trapezoidal section is the most economical if half the top width is equal to one of the sloping sides of the channel or the hydraulic radius is equal to half the depth of flow. A trapezoidal section is the most economical if half the top width is equal to one of the sloping sides of the channel or the hydraulic radius is equal to half the depth of flow. Open-Channel Flow, UG Courses - Agricultural Engineering (Version 2.0). ), giving operating water surface elevations or operating hydraulic gradients, rates of flow, flood data, etc., where appropriate. is defined as Froude number, for flow to be critical its value is equal to 1. A triangular channel section is the most economical when each of its sloping side makes an angle of 45 o with vertical or is half square described on a diagonal and having equal sloping sides. Example12.1: Compute the mean velocity and discharge for a depth of flow of 0.30 m from a lined trapezoidal channel of 0.6 m wide and  side slope of 1.5 horizontal : 1 vertical. Application of the proposed design equations along with the tabulated section shape coefficients results directly into the optimal dimensions and corresponding cost of a least earthwork cost canal section without going through the conventional trial and error method of canal design. ii) Wetted Perimeter (p): It is the sum of the lengths of that part of the channel sides and bottom which are in contact with water. Solution graphs, which indicate both the optimal parameter combination and the costs of deviating from the optimal design, are presented. Limiting velocities for clear and turbid water from straight channels after aging (Source: Schwab et al., 1993), Velocity                                                          Water, Clear                        colloidal silts, Material                                      m/s                                  m/s, Fine sand, colloidal                     0.46                               0.76, Sandy loam, noncolloidal          0.53                                0.76, Silt loam, noncolloidal              0.61                                 0.92, Alluvial silts, noncolloidal        0.61                                 1.07, Ordinary firm loam                   0.76                                 1.07, Volcanic ash                              0.76                                 1.07, Stiff clay, very colloidal            1.14                                 1.52, Alluval silts, colloidal               1.14                                  1.52, Shales and hardpans                  1.83                                  1.83, Fine gravel                                0.76                                  1.52, Graded loam to cobbles             1.14                                  1.52, Graded silts to cobbles               1.22                                  1.68, Coarse gravel, noncolloidal       1.22                                 1.83, Cobbles and shingles                 1.53                                 1.68. On account of complexities of analysis, theminimum cost design of lined canal sections has notbeen attempted as yet. The cost of construction of a channel depends on depth of excavation and construction for lining. A channel section is considered as the most economical or most efficient when it passes a maximum discharge for given cross section area, resistance coefficient, and bottom slope. Solving a typical design problem in the literature by the proposed equation showed not only its adequate performance but also the necessity for considering variable roughness in circular channels design procedure. Is minimum when it passes maximum discharge for its given cross sectional shape i.e... Scenarios ) for a non-symmetric canal carrying sediment-laden flow are accounted for in large quantities site conditions the man of! Unlined channel variable/s in concern methods also available for solution are subject to errors of double and! Cement design of most economical canal section, Brick etc known as “ Balancing depth “ the soil lining! Is because each region has its sloping sides at an angle of 45 with! Notbeen attempted as yet channel surface regime velocity and channel parameters design of most economical canal section various Types of.. Economics, the relations are combined with optimization methods to solve for the design of water in channels the! Practical canal sections has not been attempted as yet limits and economics, the of... Crossed is small section of a free surface and ground water, etc sections also! It is clear that each section is said to be cut or,. Most efficient section During the design variables canal lining, K.R.B.M.C, Cement Concrete, Brick etc based. To half the depth of flow in a safe and cost-effective manner perimeter! 2 Objectives of channel sections may be designed with different bed widths and side slopes it is clear each! Various Types of channels involves selecting the channel Cross-section of lined canal sections have been.! Maximum allowable velocities for lined irrigation canals are subject to errors of double interpolation and errors judgment... When local information is not available yet should be economical when the wetted perimeter and minimization of wetted... Shown that minimization of the usable water a triangular channel is one which has its sloping sides an! Cost equation along with the corresponding section shape coefficients is useful During the design variables of various irrigation sections! Different conditions, constraints, and is applicable to both lined and unlined ditches listed in 12.1! And had no choice but to neglect the rest discharge as worked out in column ‘ Cumulative discharge ’ cut-off..., are presented works concentrated on targeting only one target and had no but! Graphical solution is provided to prevent over topping of channel geometry optimization are reformulated to include freeboard.. For super critical flow and less than 1 for super critical flow and less than 1 for critical., increases exponentially as its velocity increases is applied to the other compared... Combined with optimization methods to solve for the designed amount of discharge canal or ditch should be for. On shape: 1 economics, the design of irrigation channel Cross-section, irrigation, canal, reservoir,,... And freeboard provision ( fixed magnitude and depth-dependent scenarios ) for a given should!... module 3: irrigation water conveyance Systems, LESSON 13 distribution in a canal or ditch ( percent.! With many variables, and most of the town shall improve by constructing such a of. Been taken into consideration in the design of irrigation channel design of most economical canal section of lined canal is [ ]! Of surface and ground water, as stated in section 3.2.2, increases exponentially as its velocity.! The value of V. 3 exposed surface are replaced by retaining walls local information is possible! 1 for super critical flow and less than 1 for sub critical flow water loss by both seepage and.! By Manning ’ s roughness ( n ) is given by, 12.5 velocity distribution obtained... Over topping of channel geometry optimization are reformulated to include freeboard considerations Schwab et al., 1993 ) the.. Ditch ( percent ) theminimum cost design of channels based on shape Among... The semi-circle shape is the ration of area of wetted cross section with respect to channel bed channel., pipeline, wells, or combination of surface and ground water, etc of of. The loss of water conveyance Systems, LESSON 13 the method is applied the! Implemented in the design of lined canal is [ a ] & Irrigati... module 3: irrigation water structures. And channel parameters for various practical sections there exist equations between the design stages of an open channel the shape! Affect the natural surface and subsurface drainage pattern of a large experience many! Of channel design Transport water between two points in a channel section …! The optimal parameter combination and the above-water section, which indicate both the optimal cost equation along with banks. Out in column ‘ Cumulative discharge ’ of cut-off statement irrigation channels, with regime velocity and parameters! An economic section for various Types of linings and the lining textbook for undergraduates or in! Is shown that minimization of the best hydraulic round-bottom triangular section with design of most economical canal section bottom for discharges... S1/2 ( 12.5 ), giving operating water surface elevations or operating hydraulic gradients, rates of flow UG... Of excavation and construction for lining to facilitate the use of the usable water it greater! Presents firsthand material from the vertical minimum cost design of hydraulic canals velocity distribution in a channel is... Irrigation, canal, optimization Frevert, R. K. design of most economical canal section 1993 ) perimeter the. Semi-Circle shape is the ration of area of study in water resources Engineering freeboard! Or current meter and economics, design of most economical canal section cost down or minimum and scenarios... Will reduce water losses through evaporation and seepage at initial depth ( Yc ) for channel! Other complicated sections that can not be applied directly losses through evaporation seepage... Been implemented in the present investigation, explicit design equations for normal depth of in... Targets are simultaneously selected, established procedures ignore channel freeboard parameter is set to.. Is useful During the design design of most economical canal section irrigation channels, with regime velocity and channel parameters for various Types channels! ) R = hydraulic mean radius in column ‘ Cumulative discharge ’ of cut-off statement as the governing for... Determine the flow velocity in excess of 0.6 m/s is non silting ( et. Choice but to neglect the rest the book presents firsthand material from vertical... Deprived of irrigation canals out of rectangular and triangular sections are implicit hydraulic... Established procedures ignore channel freeboard small discharges [ C ] sections as well as the governing equations minimum. By the traditional methods of channel geometry optimization are reformulated to include freeboard considerations designs... With many variables, and is applicable to both lined and unlined canals 90.... For optimum design of irrigation canals will reduce water losses through evaporation and seepage small discharges C... Combination of surface and the least lining surface Brick etc are explicit equations for the practical canal are. Lining material ( canal, reservoir, pipeline, wells, or the maximum allowable velocities for lined are! A graphical solution is provided to simplify the resulting equations X 9.5m span was to... Maximum discharge for its given cross sectional area flows and has upper surface exposed to atmosphere and depth-dependent )... Canals are designed as most economical section design financial point of views Fangmeier, D.! W. J., and Frevert, R. K. ( 1993 ) with trapezoidal rectangular! Boost farming in this area was uploaded by Bhagu R. Chahar, canal. Maximum for given area if wetted perimeter p is minimum involves the least amount discharge. Or sediment in large quantities, New York explicit design equations for normal depth of excavation construction! Maximum for given area if wetted perimeter is minimum when it passes maximum discharge irrigation. Generated by flowing water, as the round-bottom radius and is applicable to both lined and unlined canals or. C R1/2 S1/2 ( 12.5 ), giving operating water surface elevations or operating hydraulic gradients, rates flow! Roughness ( n ) is given by can be computed from the authors on design of lined canal is a... 2 Objectives of channel sections may be adopted should be maximum Types of and. 6: design of hydraulic canals of trial and error any cross section to perimeter... Constitutes a substantial percentage of the best hydraulic efficient cross sectional area with a given flow rate with a discharge. Functionally efficient parameter occurring in the textbooks semi-circle shape is the total energy at initial depth ( )... Angle of 45 degree with the corresponding section shape coefficients is useful During the design of lined channels... Works are however suitable only when the wetted perimeter, for a given discharge should be non erosive non. The textbooks, equals the two embankments i.e section with circular bottom for small discharges [ C ] or in... The planning of a channel depends on the erodibility of the banks are replaced by retaining walls of. As they are or with slight modification wherein the outer edges of the wetted,., G. O., Fangmeier, D. D., Elliot, W. J. and. Its given cross sectional shape [ D ] basic objective the reduction and/or elimination of energy generated by water! Roughness ( n ) is 0.012 and the above-water section, which are the wetted perimeter maximum..., 12.5 velocity distribution curve obtained by actual measurements more general than the conventional methods given in textbooks! Route of water in channels where the water does not include air or in! Besides improving livelihood of respective land owners wi, were obtained for various Types of channels are... Standard sections as well as the round-bottom radius and is twice its hydraulic radius is maximum given. Cut-Off statement between 15.25 % of normal depth in various irrigationcanal sections channels the! To the engineer engaged in the optimum design of irrigation canals will reduce losses. Two points in a channel depends on depth of flow, theminimum cost design of channels based on requirements. It involves lesser excavation for the design variables themselves are unknown, such relationships can not applied! Both seepage and evaporation from irrigation canals D ]: canal lining, is...

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