Modern research and engineering rely on numerical simulations to predict the behaviour of fluids and some derived physical quantities of interest. These predictions are often strewn with errors and uncertainties. In this talk we focus on controlling the deterministic (approximation) errors committed on a functional of interest. Thus, an a priori error estimator (EE) associated to a quantity of interest will be presented. This EE will be a basis for adaptive control of the flow via automatic mesh adaptivity. We present an algorithm for combining a fully anisotropic goal-oriented mesh adaptation with the transient fixed point method for unsteady problems. The minimization of the error on a functional provides both the density and the anisotropy (stretching) of the optimal mesh. This method is used for specifying the mesh for a time sub-interval from the state and the adjoint. The interaction of this method with UQ will be stressed. Applications to unsteady blast-wave Euler flows and Navier-Stokes flows are presented.