Experimental study of the drag force applied by supercritical flows on emerging obstacles

Supercritical open channel flows are typically encountered in mountainous rivers, in tsunami break flood waves, or in steep flooded streets, where they can interact respectively with boulders, bridge piles, buildings, city blocks or urban furniture. Depending on the Froude number of the approaching flow and on the obstacle width compared to the water depth, the flow can either form a wall-jet like bow wave or a detached hydraulic jump, which are expected to modify the force applied on the obstacle. Thus, the present work aims to characterize the steady drag force applied on an emerging obstacle, and to provide a model of the corresponding drag coefficient. To that end, force measurements are performed on parallelepipedal obstacles within supercritical flows, for a wide range of Froude numbers and of obstacle width to water depth ratios. The drag coefficient increases with this ratio and decreases with the Froude number. A momentum-based hydraulic model explains these trends, basing on the specific force arriving on the obstacle. Once combined with the experimental asymptotic values for the very wide obstacles and large Froude numbers, the model results in a semi-empirical equation that provides accurate predictions of the drag coefficient. Strikingly, the same equation is efficient for the two kinds of flow, detached hydraulic jump and wall-jet like bow wave.