Above all, this work deals with the contribution of analytical complex functions to the investigation of planar potential flows of incompressible fluids. Because the real fluid cannot flow with the velocity potential, one usually looks for another class of complex functions to study the plane flow of viscous fluid. This is how the areolar polynomials appear, which are separated from the general class of complex functions by means of the 'deviation level' of non-analytic functions defined by Bilimovitch [1] from analyticity. Using dynamic equations and the "deviation step" of the real fluid velocity field defined by Voronjec [2] has enabled us to find a new set of solutions of the Navier-Stokes equations.