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The book presents firsthand material from the authors on design of hydraulic canals. The book discusses elements of design based on principles of hydraulic flow through canals. It covers optimization of design based on usage requirements and economic constraints. The book includes explicit design equations and design procedures along with design examples for varied cases. With its comprehensive coverage of the principles of hydraulic canal design, this book will prove useful to students, researchers and practicing engineers. End-of-chapter pedagogical elements make it ideal for use in graduate courses on hydraulic structures offered by most civil engineering departments across the world.

### Chapter 1. Introduction

Abstract
Irrigation has been practiced since the beginning of civilization. A canal is used to convey water from a source to a destination for irrigation, industrial, or domestic use. The canal must be capable of transporting water between the source and the destination in a reliable and cost-effective manner. A brief history of developments in canals is presented. An outline of all chapters and scope of the book are also reported in the chapter.
P. K. Swamee, B. R. Chahar

### Chapter 2. Objective Functions

Abstract
The optimal design of a canal consists of minimization of an objective function which is subjected to certain constraints. The known parameters are flow discharge, longitudinal bed slope of canal, and the canal surface roughness. There are various objective functions such as flow area, earthwork cost, lining cost, seepage loss, evaporation loss, and their combinations. This chapter describes geometric properties and seepage loss functions of commonly used channel sections as well as computation of lining cost, earthwork cost, cost of water lost as seepage and evaporation loss, and capitalized cost. A unification of all these costs results in cost function of rigid boundary canals. A natural channel is a stream in equilibrium, which is neither silting nor scouring over a period of time. Such a stable channel develops a cross-sectional area of flow through natural processes of deposition and scour. Using Lacey’s equations for stable channel geometry and using geometric programming, an objective function for stable alluvial channels can be synthesized. Thus, this chapter formulates objective functions for rigid boundary canals and mobile boundary (natural) canals.
P. K. Swamee, B. R. Chahar

### Chapter 3. Basic Canal Hydraulics

Abstract
Canals are designed for uniform flow considering economy and reliability. Uniform flow is described by a resistance equation. This chapter describes uniform flow equations for viscous flow, turbulent flow, and sediment-transporting channels. Open-channel sections are used for transferring viscous fluids in chemical plants. The Navier-Stokes equations are the governing equations for viscous flow. For steady viscous uniform flow, the Navier-Stokes equation is reduced to two-dimensional form of Poisson’s equation, and solution for a rectangular channel has been included in the chapter. For turbulent flow in channels, different uniform flow equations are described with pointing out that Manning’s equation is applicable only to the fully rough turbulent flow and in a limited bandwidth of relative roughness. For other flow conditions, a more general resistance equation based on the Colebrook equation is more appropriate. Direct analytic solution of the normal depth in natural/stable channel section is not possible, as the governing equation is implicit and it requires a tedious method of trial and error. Explicit expressions for normal depth associated with viscous flow in rectangular channel and turbulent flow in triangular, rectangular, trapezoidal, circular, and natural channel sections are presented in the chapter. Furthermore, Chap. 3 describes canal operations through normal sluice gate, side sluice gate, and side weir. Moreover, canal discharge measurements using sharp- and broad-crested weirs and linear weir are addressed in the chapter. Finally, the chapter includes explicit critical depth relations for power law and trapezoidal and circular canal sections.
P. K. Swamee, B. R. Chahar

### Chapter 4. General Principles of Canal Design

Abstract
In design of canals, various factors are considered, for example, the kind of material forming the channel surface which determines the roughness coefficient; the minimum permissible velocity to avoid deposition of silt or debris; the limiting velocity to avoid erosion of the channel surface; and the topography of the channel route which fixes the channel bed slope. This chapter describes general principles of canal design, which includes essential input parameters, and safety and system constraints. Canal discharge is the most important parameter in designing a canal. The chapter presents how to determine design discharge for irrigation canals and power canals. Also, the detailed information on canal lining and material selection, drainage and pressure relief arrangements, requirements on canal banks and freeboard, longitudinal bed slope, canal section shape selection, typical canal layout, and necessity of cross-drainage works is included in this chapter.
P. K. Swamee, B. R. Chahar

### Chapter 5. Design for Minimum Flow Area

Abstract
A canal based on minimization of flow area objective function for a specified discharge and canal bed slope implies maximum flow velocity or best hydraulic section. The best hydraulic section provides maximum carrying capacity for a fixed cross-sectional area or minimum cross-sectional area and perimeter to pass a given discharge. A particular set of geometric proportions yield a best hydraulic section for the specific shape of channel. As it is a minimum area and minimum perimeter section, it provides maximum hydraulic radius and requires least cost in excavation and lining. In this chapter, design of minimum flow area or maximum flow velocity sections for viscous and turbulent flows and sediment carrying canals are covered. Both the objective function and constraint for minimum flow area sections are nonlinear, so optimization problem is hard to solve analytically. The problem was converted in the unconstrained form through penalty function. A nondimensional parameter approach has been used to simplify the analysis. The dimensionless augmented function was minimized using a grid search algorithm. Using results of the optimization procedure and error minimization, close approximations in explicit form have been obtained for optimal channel dimensions. The optimization method has resulted in the optimal geometric properties for circular, trapezoidal, triangular, and rectangular sections. Presented equations result in section dimensions in single-step computations. A design example involving different cases has been presented to demonstrate the simplicity of the method.
P. K. Swamee, B. R. Chahar

### Chapter 6. Minimum Cost Canal Section

Abstract
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. In general, the cost of earthwork varies with canal depth. 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. This chapter discusses the nonlinear optimization method to obtain explicit design equations and section shape coefficients for the design variables for minimum cost canal section for triangular, rectangular, trapezoidal, and circular shapes. These optimal design equations and coefficients have been obtained by analyzing a very large number of optimal sections resulted from the application of optimization procedure in the wide application ranges of input variables. The analysis consists of conceiving an appropriate functional form and then minimizing errors between the optimal values and the computed values from the conceived function with coefficients. Particular cases like minimum earthwork cost section and minimum and maximum discharge canal sections are also included in the chapter. The optimal design equations show that on account of additional cost of excavation with canal depth, the optimal section is wider and shallower than the minimum area section. 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.
P. K. Swamee, B. R. Chahar

### Chapter 7. Minimum Water Loss Canal Section

Abstract
An irrigation canal may be an unlined canal or a lined canal. The loss of water due to seepage and evaporation from canals constitutes a substantial part of the available water. The seepage loss results not only in depleted freshwater resources but also causes water logging, salinization, groundwater contamination, and health hazards. To minimize seepage and to transport water efficiently, lined canals were envisaged. A perfect lining would prevent all the seepage loss, but canal lining deteriorates with time. The thickness of the lining material is small and cracks may develop anywhere on the perimeter. The seepage from a canal with cracked lining is likely to approach the quantity of seepage from an unlined canal. The quantity of seepage is affected by the presence of a drainage layer. This chapter deals with the design of canal sections considering seepage and evaporation water losses for triangular, rectangular, trapezoidal, parabolic, and power law canals. The chapter also includes special cases, for example, minimum seepage loss sections without drainage layer and minimum seepage loss sections with drainage layer at shallow depth. The resultant explicit equations for the design variables of minimum water loss sections have been obtained using nonlinear optimization technique. The proposed equations along with tabulated section shape parameters facilitate easy design of the minimum water loss section and computation of water loss from the section without going through the conventional and cumbersome trial and error method. Design examples have been included to demonstrate the simplicity of the method.
P. K. Swamee, B. R. Chahar

### Chapter 8. Overall Minimum Cost Canal Sections

Abstract
Design of a minimum cost canal section involves minimization of the sum of earthwork cost, cost of lining, and cost of water lost as seepage and evaporation subject to uniform flow condition in the canal. Essentially, it is a problem of minimization of a nonlinear objective function subject to a nonlinear equality constraint. This chapter highlights design equations for the least cost canal sections considering earthwork cost which may vary with depth of excavation, cost of lining, and cost of water lost as seepage and evaporation from irrigation canals of triangular, rectangular, and trapezoidal shapes passing through a stratum underlain by a drainage layer at shallow depth. Using nonlinear optimization technique on augmented function, generalized empirical equations and section shape coefficients have been obtained for the design of minimum overall cost canal sections of triangular, rectangular, and trapezoidal shapes. The optimal dimensions for any shape can be obtained from proposed equations along with tabulated section shape coefficients. The optimal design equations are in explicit form and result into optimal dimensions of a canal in single-step computations that avoid the trial and error method of canal design and overcome the complexity of the minimum cost design of canals by a constrained nonlinear optimization technique. The optimal design equations show that the optimal section becomes wider and shallower than the minimum area section due to additional cost of excavation with canal depth, while reverse is the case due to cost of water lost as evaporation. On the other hand, for increased lining cost and/or the excavation cost at ground level, the optimal canal section approaches to the minimum area section, while for increased cost of water lost as seepage, it approaches to the minimum seepage loss section. Design examples with sensitivity analysis demonstrate the simplicity of the proposed design equations.
P. K. Swamee, B. R. Chahar

### Chapter 9. Design of Canal Transitions

Abstract
A canal from source to destination may be of several hundred kilometers. The discharge in the canal varies along the length due to diversion and losses; therefore, a reduced canal section matching with the discharge is adopted. Canal section may also change at flumes, siphons, and aqueducts. A canal transition involving an expansion or contraction of the section is required whenever there is change in the canal section. A transition is a structure of short length; thus, the cost aspect of transitions is not considered in their design. This chapter gives design procedure for both contraction and expansion transitions.
P. K. Swamee, B. R. Chahar

### Chapter 10. Optimal Design of Transmission Canal

Abstract
A transmission canal conveys water from the source to a distribution canal. Many times, the area to be irrigated lies very far from the source, requiring long transmission canals. Though there is no withdrawal from a transmission canal, it loses water on account of seepage and evaporation. Hence, it is not economical to continue the same section throughout the length of a long transmission canal. Instead, a transmission canal should be divided into subsections or reaches, and the cross section for each of the subsections must be designed separately. This would result in reduced cross sections in the subsequent reaches. The reduced cross section not only results in cost saving for earthwork, lining, and water lost but also requires less cost in land acquisition, construction of bridges, and cross-drainage works. This chapter addresses the problem of design of transmission canal. Using the least-cost section equations presented in Chap. 8 and applying grid search method, equations for computation of the optimal subsection length and corresponding cost of a transmission canal have been obtained. The optimal subsection length of the transmission canal is independent of the length of the transmission canal. The optimal design equations along with the tabulated section shape coefficients provide a convenient method for the optimal design of a transmission canal. The present method can be extended in developing equations for the optimal design of a transmission canal having unequal cost of transitions and unequal length of subsections. The suggested equations are applicable for all the regular canal shapes. The section shape coefficients to be used in designing a transmission canal have been obtained for triangular, rectangular, and trapezoidal canals. The method can be extended to find the coefficients in the optimal design equations for other shapes such as the circular section, parabolic section, rounded corner trapezoidal section, etc., if the corresponding seepage functions are developed. Direct optimization procedures may be adopted for the optimal design of irrigation canal sections and for the transmission canal, but they are of limited use and require considerable amount of programming and computation. On the other hand, using the optimal design equations along with the tabulated section shape coefficients, the optimal design variables of a canal can be obtained in single-step computations.
P. K. Swamee, B. R. Chahar

### Chapter 11. Salient Features of Canal Route Alignment

Abstract
An alignment of a canal route mainly depends on the topography. The total cost of a canal project depends upon the alignment. A canal has to be aligned in such a way that it covers the entire area proposed to be irrigated with the shortest possible length, and at the same time, its cost including the cost of cross-drainage works is a minimum. Several alignments between the source and the destination may be possible. Out of many alignments, few may not be feasible to construct due to construction-related problems. Deep cutting or high embankments are generally avoided by suitable detouring after comparing the overall costs of the alternative alignments. Land cost varies with land use pattern, resettlement and rehabilitation cost, environmental cost, and alignment of the canal; cost of canal falls/drops/cross-drainage works varies with type and size of structure. The maximization of economy is achievable by minimization of the total cost of canal route alignment considering all possible cost factors. This type of canal alignment problem is addressed in this chapter. Formulation of cost function comprising earthworks is difficult due to undulating terrain. In this chapter, the topography of a given area is expressed as a double Fourier series for overcoming this problem. A cost function is formulated along a canal route incorporating the depth of cutting to be extracted from the equation of the terrain and bed level of the canal. To arrive at a minimum cost route of a canal, several alignments can be evaluated by subdividing each alignment into segments. The chapter includes canal alignment algorithm, which can be followed to arrive at optimal canal route alignment.
P. K. Swamee, B. R. Chahar