The water electrolysis appears as a sustainable solution for hydrogen production. The proton exchange membrane electrolyzers (PEM-E) play an increasingly important role in the development of hydrogen technology. Fast analysis of PEM-E efficiency using a mathematical approach is an effective tool for the improvement of these devices. This work presents a closed-form solution of single cell PEM-E modelling. The approach considers charge and mass transport balances. The one-dimensional study focuses on the anodic and the cathodic catalyst layer and the membrane using only dimensionless parameters. The analytical model allows to describe the water management as a function of pressure gradient and current density using a dimensionless ratio of water transport process (ßm). This model is endorsed by experimental data. Dimensionless parameters like Thiele modulus (ßa,c) or Wagner number (Wa,C) are reached using numerical optimization methods. Changing values of dimensionless numbers, allow the observation of the impact of the two-phase flow regimes on the electrochemical performances.