This research aims to demonstrate the existence of a velocity field (expressed in cylindrical coordinates) that can model the velocity profile at any position within a pipe, through which water circulates a laminar flow undergoes a process cooling after full hydrodynamic development. To determine that field, we have proceeded to particularize a field of initial velocity, based on boundary conditions of the flow inside a pipeline, in addition to this has been always the constant reference to the geometry of the different velocity profiles, especially in the hydrodynamic region after full development. Only for display purposes it has proceeded to draw the different velocity profiles using MATLAB. Finally observing the different velocity profiles obtained, it was found that the calculated velocity field expresses very well the behavior of the velocity profiles within the pipe, thereby valid...