2. Objective Functions

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.