Conjugate depths in partially filled sewers and pipes

Abstract

Partially filled pipes have many applications in hydraulic and environmental engineering; such as sewer and storm water collection pipes and circular culverts. Hydraulic jump can lead to scouring at hydraulic structures and thus excess energy should be dissipated to prevent scour and erosion. Calculation of conjugate depths in circular pipes and culverts is important in hydraulic engineering. The conjugate flow depths are commonly used to estimate the length of the hydraulic jump and the energy loss in the jump. Available relationships to estimate the conjugate depths in circular pipes are not accurate and wide application range. In comparison to easily available numerical solutions, a closed-form solution is a function of all input independent variables; and thus the dependence of the conjugate depth on each input independent variable can be easily interpreted. This study presents explicit solutions for the conjugate depths (pre- and post-jump depths) in partially filled pipes. The proposed solutions are examined over a wide range of the Froude number and geometric conditions, providing satisfactory estimations when compared with the exact solution obtained from the specific force relation. If the prejump flow depth of the hydraulic jump is known, the postjump flow depth can be determined using the proposed solution with a maximum relative error less than 1.4%. Inversely, if postjump flow depth is known, the prejump flow depth can be determined with a maximum relative error less than 2.3%. The proposed direct solutions are general, accurate, simple, and useful for studying the partially filled circular open channels.