Deep learning models have demonstrated remarkable capabilities at producing fast predictions of complex flow fields. However, incorporating known physics is essential to ensure that physical solutions can generalize to flow regimes not used for training. In this work, a novel architecture that (by construction) enforces both flow incompressibility and no-penetration boundary conditions is introduced. The method is a hybrid approach, combining recent deep learning techniques with more classical computational fluid dynamics methodologies. Differently from the soft-constraints variants, a hard-constraints architecture can enforce physical conditions not only during training but at inference too. Furthermore, our model is more data efficient and allows for significantly smaller neural networks, being more suitable for real world problems where data and computational resources are often limited. The new ψ − flow model is compared with the well-known physics-informed neural net- work (PINN) model, and a baseline (no physics) NN model. Canonical test cases as well as a more challenging airfoil problem are considered. The robustness of the model is an important contribution to the state-of-the-art of scientific machine learning for flow predictions, which can target a wide range of applications, from super-resolution to topological optimization.