We consider an incompressible Stokes fluid contained in a box $B$ that flows around an obstacle $K\subset B$ with a Navier boundary condition on $\partial K$. I will present existence and partial regularity results for the minimization of the drag of $K$ among all profiles with certain constraints on the measure and perimeter of $K$, based on techniques that were developed for Griffith's fracture model in brittle materials. This is a joint work with Dorin Bucur, Antonin Chambolle and Alessandro Giacomini.