Direct determination of the width or the height for a box culvert applying dimensionless equations

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To determine dimensions of a rectangular culvert section, current design approaches need several trial calculations. It is a standard approach in the culvert section design to use nomographs provided by the Federal Highway Association. The height and the width of a box culvert are two basic unknowns. The approach proposed here assumes that the height or the width is known and the approach directly determines the other unknown variable without further trial calculations. The use of nomographs may be a major obstacle for computer modeling. It may also result in subjective errors when reading the graph. In order to find an explicit way of solving this problem, approximate relations of the hydraulic radius to shape factor was devised for a rectangular culvert. Then, the computational equations for the width or height of a box culvert were derived using dimensionless variables. Reasonable initial values were also proposed to solve the nonlinear computational equations. A verification test was performed by way of a worked example. Using the governing equations and the initial values, one can find a computer solution of box culvert dimensions.