In this study, we present speed and displacement measurements of micro-fluid in a hollow-core optical fiber, where an optical interference signal is created by two guided beams reflected at a fixed facet and a moving fluid end. By counting the number of intensity oscillations of the signal, the movement of the fluid end is successfully traced with high accuracy. Furthermore, we could detect the change in curvature diameters of the fluid end depending on the flow direction by monitoring the visibility of the interference signal.