Convergent hydraulic structures are found in different open-channel flow configurations, particularly in the courier of the surface spillway and in some stilling basins. In some cases, the convergent transition is followed by a prismatic part with the same slope and steps with a different slope. The work that is presented here focuses on the physical modeling of this flow configuration type under steady flow conditions. It has been performed in a laboratory flume, located in the hydraulic laboratory of the National Polytechnic School of Algiers. As far as we are concerned, there has not been any systematic scientific research for the conception of this configuration type so far. In particular, the slope change effect between the convergent transition and the stepped spillway has not been explored yet. According to the slope change and the flowrate, we are interested in the transverse wave propagation that arises at the convergent downhill and the maximum height of the transverse wave, We have measured water heights and instantaneous velocities (transverse and longitudinal profiles) by varying the flowrate from 2 to 20 l/s, the main channel slope (convergent transition and prismatic part) from 0° to 24.4° and the stairs slope from 0° to 45°.