An additive manufacturing system that retains a print head for printing a three-dimensional part in a layer-by-layer manner using an additive manufacturing technique, where the retained print head is configured to receive a consumable material, melt the consumable material, and extrude the molten material. The system also includes a velocimetry assembly configured to determine flow rates of the molten material, and a controller assembly configured to manage the extrusion of the molten material from the print head, and to receive signals from the velocimetry assembly relating to the determined flow rates.