The main objective of conducting numerical simulations of flows in rivers with vegetation is to investigate the complex flow dynamics involved in non-equilibrium conditions. In such cases, it is inappropriate to apply the drag coefficient CD, which is typically derived based on uniform flows involving groups of infinitely long cylinders. This paper presents a method for evaluating the drag forces acting on emergent obstacles for non-uniform open-channel flows. This method is devised based on two sets of experiments: on flows with small-diameter cylinders, focusing on the water surface profiles through the group; and on flows with large-diameter cylinders, focusing on the local pressure distribution and local water surface profile around a target cylinder. In addition to the conventional drag force expression that includes CD, two new terms are proposed to account for the effects of water surface variation and pressure gradient in non-uniform open-channel flow on the drag. The first of these terms, which introduces the use of the Froude number to account for the effect of water surface variation, is derived theoretically and evaluated against past and present experimental results under uniform-flow conditions. On the other hand, the second of these terms, which includes the representative length of the separation zone to evaluate the effect of pressure gradient, is confirmed to be a necessity through numerical calculation of the longitudinal water surface profile in emergent cylinders. The incorporation of these two terms using a simple unified expression can help improve the accuracy of numerical simulations for practical problems of flows with emergent obstacles.

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