COORDINATION OF EMPIRICAL AND RATIONAL ALLUVIAL CANAL FORMULAS

The Lacey, Chang, and Lacey-divergence formulas are chosen to represen t different empirical, rational, and mixed approaches available for th e design of alluvial canals. Lacey formulas are applicable for specifi c values of sediment concentration C and resistance of bank material t o erosion tau(s), whereas Chang formulas are applicable for all C valu es but for a specific value of tau(s). Lacey-divergence formulas are o f general application for all practical values of discharge Q, bed mat erial size d(50) and tau(s). In the downstream direction along a canal system, the three operative conditions are (1) interdependence betwee n P, R, and S, as indicated by the Lacey-divergence equation; (2) cons tancy of sediment concentration, and (3) minimum consumption of stream power. These three conditions remain the same in all canal systems, a nd, 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 concentrat ion and strength of bank material, which vary from one canal system to another.