The present work is realted to the mathematical modeling and computacional simulation of flow through hydrocyclons. The present model assumes the air core being a free surface of Young-Laplace type. As the characterisctic of the flow suggests, the model considers a turbuleny diffusion, this fact is essential to have a good agreement with experimental data. The velocity and pressure with the shape and localization of the interface are approzximated. For the above approximation a langrangian grid is used to characterize the free interface, and an eulerian grid for calculating the velocity and pressure fields thorough a finite-volume method. The approximation of the interface is achieved using an iterative procedure. An extensive comparison of model predictions against experimental data is presented together with some numerical results.