Velocimetry can be traced back to the days of Leonardo da Vinci, who would float grass seeds on a flow and sketch the resulting trajectories of the seeds that he observed (a Lagrangian measurement). Eventually da Vinci's flow visualizations were used in his cardio vascular studies, attempting to learn more about blood flow throughout the human body.
Methods similar to da Vinci's were carried out for close to four hundred years due to technological limitations. One other notable study comes from Felix Savart in 1833. Using a stroboscopic instrument, he sketched water jet impacts.
In the late 19th century a huge breakthrough was made in these technologies when it became possible to take photographs of flow patterns. One notable instance of this is Ludwig Mach using particles unresolvable by the naked eye to visualize streamlines. Another notable contribution occurred in the 20th century by Étienne-Jules Marey who used photographic techniques to introduce the concept of the smoke box. This model allowed both for the directions of the flow to be tracked but also the speed, as streamlines closer together indicated faster flow.
More recently, high speed cameras and digital technology has revolutionized the field. allowing for the possibility of many more techniques and rendering of flow fields in three dimensions.