Abstract
The Lacey, Chang, and Lacey-divergence formulas are chosen to represent different empirical, rational, and mixed approaches available for the design of alluvial canals. Lacey formulas are applicable for specific values of sediment concentration C and resistance of bank material to erosion τs, whereas Chang formulas are applicable for all C values but for a specific value of τs. Lacey-divergence formulas are of general application for all practical values of discharge Q , bed material size d50 and τs. In the downstream direction along a canal system, the three operative conditions are (1) interdependence between P , R , and S , as indicated by the Lacey-divergence equation; (2) constancy of sediment concentration; and (3) minimum consumption of stream power. These three conditions remain the same in all canal systems, and, hence, in the exponential formulas for width, depth, and slope in terms of discharge, the indices 0.5, 0.33, and −0.167 remain the same; however, the coefficients change depending on the sediment concentration and strength of bank material, which vary from one canal system to another.
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