In this paper, the analysis of fast laminar transients in pressurized pipes is developed using a computational fluid dynamics (CFD) model, combined with the Zielke model and laboratory data. The systematic verification of the performance of the CFD model executed in the first part of the paper allows defining the most efficient set of the discretization parameters capable of capturing the main features of the examined transient. In this framework, the crucial role of radial discretization is pointed out. In the second part of the paper, the refined and efficient CFD model is used to examine some aspects of interest for understanding the dynamics of transients. Specifically, the uniformity of the instantaneous pressure distributions along the pipe radius, which validates the results of the most popular quasi-two-dimensional (2D) models, has been revealed. Moreover, it has been shown that the strongest link between the wall shear stress and the axial component of the velocity occurs in the region close to the pipe wall as well as that the time-shift between the wall shear stress and the local instantaneous flow acceleration increases significantly as time elapses.