A noninvasive quantification of the hydrodynamics in a stirred tank in space and time using flow-sensitive phase-contrast magnetic resonance imaging (PC-MRI) at 7 Tesla (7 T) is demonstrated. The PC-MRI technique is able to characterize the unsteady periodic 3D flow velocities with acceptable spatial and temporal resolution and does not imply that optically transparent fluids are employed. PC-MRI is already widely used for medical diagnostics in order to determine the blood flow velocities, e.g., for cardiovascular applications. However, its utilization for engineering problems is still new, including process engineering. Therefore, it is important to check the suitability of PC-MRI to applications of practical interest in this field and complement other flow measurement and simulation techniques.