USE OF THE MANNING EQUATION TO ESTIMATE STREAM DISCHARGE THROUGH NATURAL SLOT CANYONS AND ARTIFICIAL SLOTS

Stream discharge through narrow, deep slot canyons can be a major source of groundwater recharge in the arid Southwest. However, these canyons are normally dry except during flash floods, making stream velocity nearly impossible to measure. Various state and federal agencies, including the Utah Department of Natural Resources (UDNR) use the empirical Manning Equation to predict the discharge through artificial slots created for diversion of rivers around coal mines. The advantage of the Manning Equation is that estimated discharge is based solely on the channel geometry, depth of the water, slope of the stream bed and an empirically-derived roughness coefficient, without the need to directly measure stream velocity on-site. However, it is not obvious that the Manning Equation could be applied to slot canyons or artificial slots as the data base used for development of the Manning Equation did not include either natural streams or artificial structures for which most of the friction occurs along the sides of the channel. The objective of this research is to develop an empirical formula for estimating the Manning roughness coefficient for flow through narrow, deep slots. The objective is being addressed by measuring stream discharge through natural slot canyons in southern Utah that are fed by perennial streams, springs or dam outlets. Based on measurements at ten sites along eight streams, the best estimate for the Manning roughness coefficient is n = 0.873n_J exp(5.108A/w²) where A is stream cross-sectional area, w is stream width, and n_J = 0.39S^0.38R^-0.16 is the roughness coefficient estimated by Jarrett (1984) for high-gradient streams, in which S is slope of the stream bed and R is hydraulic radius (ft). The new formula estimates stream discharge with a mean accuracy of 44%. On the other hand, Jarrett’s (1984) formula underestimates stream discharge by 1-2 orders of magnitude for aspect ratios A/w² in the range 0.6-0.7. The new formula will be refined by measurements on additional natural slot canyons in southern Utah and northern Arizona, on a laboratory hydraulics bench, and on artificial slot diversions created by UDNR for Lower Robinson Creek and Kanab Creek near Alton, Utah, and for Crandall Canyon Mine in Bear Canyon, Utah. It is hoped that the new formula will lead to a more realistic design for artificial slot diversions.