Methods are needed to non-invasively measure in vivo very slow flows, which govern many important physiological processes like brain glymphatic flow. In this study, a new stimulated echo-based phase contrast MRI sequence, robust to phase errors induced by gradient hardware, is used to measure 3D flows as slow as 1 μm/s. The method was validated using a controlled pipe flow experiment. In the absence of induced flow, the method revealed unusual natural convection flows in a water filled tube placed in a wide-bore magnet. The method may be applied to measure important slow flows in vivo.