  The problem of identifying an obstruction into a fluid duct has several
applications, one of them, for example in medicine the presence of Stenosis in
coronary vessels is a life threatening disease. In this paper, we formulate a
continuous setting and study from a numerical perspective the inverse problem
of identifying an obstruction contained in a 2D duct where a Stokes flow hits
on the boundary (Dirichlet and Navier--slip boundary conditions), generating an
acoustic wave. To be precise, by using acoustic wave measurements at certain
points on the exterior of the duct, we can identify the location, extension and
height of the obstruction. Thus, our framework constitutes an external approach
to solving this obstacle-inverse problem. Synthetic examples are used to verify
the effectiveness of the proposed numerical formulation.
