Breathability in dense building arrays with packing densities similar to those of typical European cities is investigated using laboratory measurements and numerical simulations. We focus on arrays made up by regularly spaced square buildings forming a network of streets with right-angle intersections. It is shown that breathability can be evaluated using building ventilation concepts (mean flow rate and age of air) and from vertical mean and turbulent fluxes quantifiable through a bulk exchange velocity. Mean age of air reveals that varying wind angles result in different ventilation, which we explain through mean flow streamlines and exchange velocity. For low wind angles (wind direction almost parallel to the axes of half of the streets of the network), vertical transfer and mean transversal transfers are at minimum and removal of pollutants is associated with mean longitudinal fluxes. Larger wind angles result in better ventilation due to an increase of transversal fluxes and vertical exchange. The latter, for which a formulation is derived, shows a non-negligible contribution of the mean flow which increases with increasing wind angle. Ventilation conditions can be further altered by small differences in the array geometry. These observations are useful for the development of simple urban dispersion models.