Closure to 'Influence of Entrapped Air Pockets on Hydraulic Transients in Water Pipelines' by Ling Zhou, Deyou Liu, Bryan Karney, and Qinfen Zhang

摘要

The writers would like to thank the discussers for their interest in the discussed paper. The discussion provides valuable suggestions and recommendations for further research on this topic. The aim of this closure is to clarify some comments raised in the discussion. In the discussed paper, the authors assume that the liquid inertia and energy loss of a tiny water column ΔLw_i, adjacent to the air-water interface can be ignored, and 0.5Δx ≤ ΔLw_i< 1.5Δx (Δx is the method of characteristics grid length). Namely, only the water column with a length ΔLw, neglects inertia, and all other water regions consider inertia. A very short Δx (Δx = 0.001-0.01 m) is used in the proposed model for numerical stability.