This study investigates the accuracy of deep learning models for the inference of Reynolds-averaged Navier–Stokes (RANS) solutions. This study focuses on a modernized U-net architecture and evaluates a large number of trained neural networks with respect to their accuracy for the calculation of pressure and velocity distributions. In particular, it is illustrated how training data size and the number of weights influence the accuracy of the solutions. With the best models, this study arrives at a mean relative pressure and velocity error of less than 3% across a range of previously unseen airfoil shapes. In addition all source code is publicly available in order to ensure reproducibility and to provide a starting point for researchers interested in deep learning methods for physics problems. Although this work focuses on RANS solutions, the neural network architecture and learning setup are very generic, and applicable to a wide range of partial differential equation boundary value problems on Cartesian grids.