Explicit Solution for the Specific Flow Depths in Partially Filled Pipes

Abstract

This paper presents an explicit solution for the specific flow depths in partially filled pipes of circular cross-sectional area. Four depths encounter in most classical free-surface flow problems, namely the normal depth, the critical depth, the sequent depths from the specific momentum equation, and the alternate depths from the specific energy equation. This paper proposes new equations derived from dimensional analysis and gene expression programming to estimate directly those flow depths. The equations are examined over a wide range of flow and geometric conditions, providing satisfactory predictions when compared with the exact solution obtained from the governing hydraulic equations. Maximum error encountered in the critical and normal flow depths predictions is less than 1.25%, and maximum error encountered in the alternate and sequent flow depths predictions is less than 3.85%, which are acceptable in most hydraulic engineering practice. The equations are simple and would be useful in hydraulic engineering practice when quick and accurate estimates are needed of those depths, and can also be used to find the initial values for the flow depth in various theoretical and numerical schemes.