  We study the drag on a centimetric sphere in a uniform flow in the presence
of a free surface as a function of submergence depth. Through direct force
measurements in a custom benchtop recirculating flume, we demonstrate that the
drag can significantly exceed the corresponding drag in a single-phase flow and
achieves a peak at submergence depths just prior to complete immersion. The
additional drag in the partially immersed state is rationalized by considering
hydrostatic effects associated with the asymmetric surface height profile
induced by the obstacle in the flow direction which persists for flow speeds
below the minimum capillary-gravity wave speed. At these scales, the sphere's
wettability plays a pronounced role in determining the maximum possible drag
and results in hysteretic behaviors near touchdown and complete immersion. The
influence of flow speed, sphere size, and surface tension on the drag
characteristics are additionally explored through a combination of experiments
and numerical simulations.
