Velocity and Depth of Flow Calculations in Partially Filled Pipes

Nomographs and tables are used to facilitate the application of Manning's equation for different flow conditions and pipe materials. Different computer programs are also used to avoid the laborious calculations required to find the optimum and economic design. There is no exact algebraic solution for the calculation of the depth of flow in a partially filled pipe when its diameter, slope, and flow rate are known. Therefore, iterative methods are applied to calculate the depth of flow. In this paper, a simple algebraic equation is proposed that will facilitate the calculation of the water surface angle and thus the depth of flow when the diameter, slope of the energy grade line, and the flow rate are known in partially filled pipes. The equation is valid for water surface angles less than or equal to 265°. The application of the proposed equation is illustrated by calculating the flow area, depth of flow, and velocity in a gravity-sewer example problem.