Discussion of "Explicit solutions of the Manning equation for partially filled circular pipes"

Abstract

The discusser has read with interest the work on sewer design based on the Manning equation. Two distinctly different conditions have to be considered, namely the “full-flowing” and the “partially filled” sewer flows. According to European standards, a sewer should be designed based on the Colebrook and White equation for the full-flowing condition. The Manning equation is currently in use, however, for predicting the flow characteristics in the partially filled sewer flow regime. Stable flow in partially filled sewers The discusser conducted a study on the historical development and currently accepted design guidelines of the partially filled sewer flow (Hager 1991a, 1991b). Curves for relative discharge in terms of sewer filling have been in use since the 1880s, before Robert Manning (1816–1897) presented his equation. A large number of experimental studies on the flow of water in partially filled pipes were conducted in the 20th century based on deviations between the measurements in existing sewers and the results furnished by the Manning equation. Notable works were presented by Ackers (1961a, 1961b) and Sauerbrey (1969). The following conclusions were drawn by Hager (1991a, 1991b):  The full-flowing condition in sewers is an important notion in sewer design, although it may not occur in nature.  The characteristics of full-flowing sewers should be computed with the Colebrook and White equation, thereby accounting for the effects of Reynolds number and relative roughness.  The Manning equation approximates the previous relation in the turbulent rough flow regime; it may be useful for designing partially filled sewers.  The air flow close to the sewer top has a small effect on the water flow in a sewer.  Filling diagrams are limited towards the sewer top; flow above the filling limit is hydraulically unstable.  The transition from free surface to pressurized sewer flow is abrupt; the stable upper limit corresponds to the maximum free surface discharge condition.  The findings of Sauerbrey (1969) appear to account in the best way for the effective flow characteristics in circular, partially filled sewers. The author did not account for observations made with sewers; instead, he accepted the relations furnished by the Manning equation without recourse to previous investigations. When plotting the relative discharge Q/Qv versus the relative filling y = h/D (where Q is the discharge, Qv is the discharge for the full-flowing condition, h is the uniform flow depth, and D is the sewer diameter), the condition Q/Qv is attained twice, namely for y = 1 as required from the scalings and for y ≅ 0.85; the latter condition was identified as the full-flowing condition in practice because it furnishes a discharge identical to that of the condition y = 1, in the stable flow pattern. A sewer flow is unstable in the upper filling region, typically for 0.85 ≤ y ≤ 1. Therefore, this region was excluded in sewer design. Circular profile computations