CHANNEL DESIGN TO MINIMIZE LINING MATERIAL COSTS

ABSTRACT: A direct algebraic technique is developed to determine open chan-nel cross-sectional designs which minimize lining material costs when base and side wall unit costs are different. Solution graphs, which indicate both the optimal parameter combination and the costs of deviating from the optimal design, are presented. The graphs or analytical technique are also effective in designing any trapezoidal channels. Use of the technique shows that mod-erate deviations from optimal designs are not costly. inrrnoDuc-noN The material cost of channel linings depends upon the volume of lining ma-terial used. On a per unit length basis, the material costs are a function of the lining thickness and perimeter length, which, in turn, depends upon the channel cross-sectional shape. The capacity of a channel constructed on a given slope will also be a function of the cross-sectional shape. Using this interrelationship, cross sections that minimize lining material costs can be determined. If the channel is lined with one material of uniform thickness, the problem reduces to one of determining the best hydraulic section (1). However, if material or lining thickness is changed along the perimeter, the problem becomes much more complex. This paper will present a solution to the cost minimization prob-lem when the material cost per unit surface area of the base of trapezoidal (or rectangular) channels is different from the material cost of the sides. This analysis does not deal with placement or other construction costs. If they can be evaluated in terms of surface area, they can be combined with material costs. Otherwise, they must be considered separately. The technique will thus be most useful when long channel sections are to be constructed, allowing con-struction procedures to be oriented toward minimizing material costs or when labor costs are low relative to material costs, such as is the case in developing countries