Cardiovascular disease represents a leading cause of death worldwide, drawing significant attention from various research fields. Mathematical models dedicated to patient-specific scenarios [1] and/or designed for standardized benchmarks [2] offer valuable tools to analyze blood flow in critical regions and in specific conditions. This presentation leverages the incompressible Navier-Stokes equations at full order level to analyze flow dynamics in both patient-specific vessels and in the Food and Drug Administration (FDA) nozzle benchmark. Full order solutions are obtained in both scenarios using the finite volume method. The employement of a Reduced Order Model (ROM) combined with the lifting function method [3] for the outflow pressure is the main novelty introduced for the study of blood flow in vessels. Neural networks are integrated into the ROM framework to enable the prediction of reduced order solutions for any outflow pressure value, enhancing its generalization capabilities. The flow analysis in the FDA benchmark is carried out using a stabilized ROM to accurately recover neglected data. The reduced model incorporates the effects of viscosity [4] only at reduced level, and a comparative evaluation is conducted between constant and linear kernel approaches from mid to high Reynolds numbers. In both cases, several analyses are performed varying various parameters and emphasizing strengths and limitations. Qualitative and quantitative comparisons are carried out for pressure and velocity by reaching good agreements between FOM and ROM solutions. REFERENCES [1] Siena, P., Girfoglio, M., Ballarin, F. and Rozza, G. Data-driven reduced order modelling for patient- specific hemodynamics of coronary artery bypass grafts with physical and geometrical parameters. Journal of Scientific Computing, 94(2):38, 2023. [2] Girfoglio, M., Quaini, A. and Rozza G. A POD-Galerkin reduced order model for a LES filtering approach. Journal of Computational Physics, 436:110260, 2021. [3] Star, K. S., Stabile, G., Belloni, F., Rozza, G. and Degroote J. A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems . Communications in Computational Physics, 30(1):34, 2021. [4] San, O. and Iliescu., T. A stabilized proper orthogonal decomposition reduced-order model for large scale quasigeostrophic ocean circulation. Advances in Computational Mathematics, 41:1289, 2015.