The unique abilities of magnetic resonance imaging (MRI) to provide detailed images of blood flow in the body, and without resorting to the injection of contrast agents, has provided the stimulus for the keen interest in this subject. In this paper we discuss a technique aimed at providing quantitative information on the distribution of velocity of blood flow across the lumen of a vessel. The technique is designed to reduce the signal from stationary material allowing for a much more accurate determination of the signal from moving material. A particular feature is that the physical phenomenon sensitized is time-of-flight displacements or "fresh spin inflow," and the technique does not rely upon phase-sensitive modulations. Further this technique produces a steady-state spatial distribution of magnetization, and hence a signal, which reflects both the time at which material enters the selected slice and how long the material remains in the slice. In this way, a single image will provide the information necessary to extract information on the velocities of interest.