A model of the flow at the inlet of narrow passages, based on the theory of potential flows, is presented. No free surface is supposed to exist. A boundary layer is carried by a moving boundary; the impact of the fluid with the frontal surface of the other body, at rest, generates various flow patterns, as well as a pressure head at the entrance of the gap. A complete theory is presented, then a simplified model is shown, and flow mappings are obtained. The pressure head is calculated and shows an important dependence on the pressure gradient at the inlet of the passage.

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