This work addresses the dependence of water depth upstream a permeable barrier, , with discharge per unit channel width, , in sub-critical flow regime. The barrier, that extends over the entire width of the channel, is composed by smooth cylinders of small aspect ratio vertically mounted on the bottom in a staggered pattern and fully submerged in the flow. The height of the cylinders above the bottom was kept constant for all runs. Several configurations were considered by varying systematically the cylinders diameter, , the number of cylinders per unit area of the bed, or density, , and the length of the barrier in the stream direction, . A one-dimensional model was developed to predict the observed values of and to obtain a sound basis taking into account the incidence of , , and . This model is based on fluid mechanics equations applied on a finite control volume for the flow in the test section, and it was deduced under simplifying assumptions physically-based. Finally, and based on the experimental results and the model predictions, the mechanical energy losses of the flow are analyzed. The main role played by a dimensionless number , that takes into account the barrier's resistance to the flow, is highlighted.