The discussed paper states that the rigid column model is applied for a single air pocket and the nature of the used equations makes it difficult to be employed in case of several air pockets. The discussers do not agree with this assertion.In fact, other authors also use the rigid model approach. Liou and Hunt (1996) proposed a rigid column model of flow start-up in empty pipelines with undulating elevation profiles assuming a vertical interface between the air and water phases. They proposed a velocity-based criterion to justify the application of the rigid-column approach. Zhou et al. (2002) presented an experimental and numerical investigation on the description of the rapid filling of an empty horizontal pipe with limited ventilation. The numerical model was constructed using a lumped inertia approach and assumed a vertical interface separating the advancing waterfront and the air that initially filled the pipe.The discussers have developed a general model for the simultaneous analysis of entrapped air pockets within a pipeline with irregular profile (Fig. 1). Previous papers have paid attention to this problem from both theoretical (Fuertes et al. 1998;Izquierdo et al. 1999;Fuertes 2001) and experimental (Fuertes et al. 2000;Fuertes 2001) approaches. Moreover, and in order to identify the most significant parameters of the
Most numerical transient flow models that consider dynamic friction employ a finite differences approach or the method of characteristics. These models assume a single fluid (water only) with constant density and pressure wave velocity. But when transient flow modeling attempts to integrate the presence of air, which produces a variable density and pressure-wave velocity, the resolution scheme becomes increasingly complex. Techniques such as finite volumes are often used to improve the quality of results because of their conservative form. This paper focuses on a resolution technique for unsteady friction using the Godunov approach in a finite volume method employing single-equivalent twophase flow equations. The unsteady friction component is determined by taking into account local and convective instantaneous accelerations and the sign of both convective acceleration and velocity values. The approach is used to reproduce a set of transient flow experiments reported in the literature, and good agreement between simulated and experimental results is found.
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