An axial flow of an immiscible liquid past a nearly cylindrical liquid bridge of similar density influences the stability of the bridge. Laminar flow along a cylindrical interface can generate a differential pressure gradient across the interface that is equivalent to a steady axial gravitational acceleration. Ideally, this flow can be used to cancel the pressure gradient due to the density imbalance, allowing a longer cylindrical interface than would be statistically possible. Experimental results that show this effect and that are in qualitative agreement with predictions are presented.