This document studies the behavior of perfect fluids when passing around different surfaces that have been historically used for the design of wing profiles. In addition to that, some fluid potentials are represented over three-dimensional surfaces performed with pro-jections of the initial complex plane. Rather than taking a numerical approach, we follow here a completely analytical strategy, based on the theory of complex potentials and conformal transformations. In order to visualize the results we developed specific pieces of code based on the Wolfram Mathematica sotfware. The analysis thus obtained provides an analytical approach that can be an alternative to numerical simulation methods, or for some cases both strategies can also be complementary.