Development of an Equation Independent of Manning's Coefficient n for Depth Prediction in Partially-Filled Circular Culverts

Abstract

In the design of culverts for fish passage, knowing the water depth is important as it relates to roughness. Engineers currently select roughness coefficients, such as Manning's n, from a table that has been calculated from full flow conditions for culvert design. It is known from previous investigations that Manning's n varies with depth. According to Lang et al. (2004), flows at half depth or lower are the typical flows that fish will encounter. If the designer is using constant Manning's roughness coefficients for full flow, a substantial error in calculating water depth could result (Lang et al. 2004). The objective of this research is to develop an equation to predict water depth inside of partially filled circular culverts independently from the Manning's equation. A new equation to predict depth (d) for a circular culvert, based on discharge (Q), slope (S), diameter (D), gravity (g), and absolute material roughness (Ks), has been developed. The new equation reduces the absolute mean error in calculating water depth by 37% compared to the previously published data. Data from five studies representing partially filled culvert conditions in concrete, clay, corrugated metal, PVC, and HDPE circular pipes with slopes and diameters ranging from 0.05 - 4% and 4 - 36 inches, respectively, were used in this study to establish the new equation. The new equation allows for the explicit solution of depth while the Manning's equation requires an implicit solution. The iterative solver used (Excel Goal-Seek) did not find a viable solution for predicted depth using the Manning's equation in 29% of the cases reported in the literature. The new equation predicts depth more frequently and with greater accuracy than the Manning's equation for the data analyzed; and is therefore, a more consistent method when used to design and assess culverts for fish passage.