We introduce a new approach for snapshot imaging of time-resolved, non-stationary 3D fluid flows. Based on Particle Imaging Velocimetry (PIV), a well-established technique for fluid flow analysis, we propose a novel approach for spectral encoding of the third dimension. To do so, we illuminate the flow volume with a stack of monochromatic light planes at different wavelengths (rainbow) : we call this novel approach Rainbow-PIV. With a single camera, we can record the third dimension, this is a completely new approach compared to the state-of-the-art.