USE OF THE MANNING EQUATION FOR ESTIMATING THE DISCHARGE OF HIGH-GRADIENT CANALS AND NATURAL STREAMS

The Manning Equation is an empirical equation for estimating stream discharge based upon the water slope (S), hydraulic radius (R), and a Manning roughness coefficient (n). Jarrett (1984) proposed that, for high-gradient (S > 0.002) streams, n could be estimated using the formula n = 0.34S^0.36R^-0.16 based upon 21 high-gradient stream sites in Colorado. The important question is why such a formula works at all, since it does not take into account sediment size or roughness. The answer is most likely that, for high-gradient streams, stream slope and hydraulic radius are predictors of sediment characteristics. However, that relationship should depend upon the rock type. In fact, separating the 21 sites into those incising clastic sedimentary rocks and those incising crystalline (igneous and metamorphic) rocks shows that the formula underestimates n for crystalline rocks, which is consistent with the larger sediment that should result from weathering of crystalline rocks, and that a more accurate formula for clastic sedimentary sites alone is n = 0.21S^0.26R^-0.25 (r² = 0.58). The objective of this study has been to develop a formula for estimating n at high-gradient stream sites that takes into account rock type. Stream discharge, water slope and hydraulic radius were measured at nine high-gradient stream sites in Haiti incising crystalline rocks, three sites in Haiti incising carbonate rocks, 16 sites in Utah incising carbonate rocks, and 16 sites in Utah on rock-lined or concrete canals, and were used to calculate the Manning roughness coefficient. The crystalline sites in Haiti were best fit with the formula n = 22.93S ^0.79R ^0.97 (r² = 0.46), while the carbonate sites in Haiti and Utah were best fit with the formula n = 3.82S ^0.78R ^0.82 (r² = 0.66). The major distinction among rock types is that n is a negative function of R for clastic sites and a positive function of R for crystalline or carbonate sites. The distinction probably results from the smoother sediment that occurs at crystalline or carbonate sites, so that turbulence is induced by increasing depth, as opposed to sediment roughness, which is suppressed by deeper water. For high-gradient canal sites, n is larger than would be predicted based upon the lining material, which is probably due to the roughening of the lining material that occurs at supercritical flows.