Compute Critical and Normal Depths of Arch and Elliptical Pipes

Abstract

Arch and elliptical pipes are commonly used as roadway culverts. The pipe section is composed of three radii, which result in complex equations to compute cross-sectional geometry and hydraulic parameters, such as normal and critical depths. Basic sizing charts do not allow direct calculation of hydraulic properties of these pipe sections. Therefore, general formulas were developed to compute hydraulic properties for any given arch pipe cross section. An Excel workbook capable of calculating normal and critical depths for given flow rates was created using the developed formulas and the solver function. Worksheets to compute geometric properties and water surface profiles using the direct-step method were also developed. These user-friendly worksheets are useful for hydraulic design and analysis of arch and elliptical culverts. A case study was conducted on several standard pipe geometries to demonstrate the comparative results from the developed workbook and existing sizing charts.