It has been proposed recently that the combined action of inertia and non-linear viscoelasticity may be the origin of very peculiar behaviors with dramatic changes of flow type. Two examples are the problem of delayed die swell and the orientation of elongated particles sedimenting in solutions of wormlike micelles. These solutions give rise to well defined viscoelastic properties which can be tuned precisely by changing the surfactant weight fraction. Our analysis does not rely on any constitutive equation and our results strongly support the interpretation that delayed die swell and sedimentation of long bodies in wormlike micellar solutions are ruled by a change of flow type from subcritical to supercritical.