This paper presents a framework to segment planar or near-planar fluid flow and uses artificial neural networks to characterize fluid flow by determining the rate of flow and source of the fluid, which can be applied in various areas (e.g., characterizing fluid flow in surface irrigation from aerial pictures, in leakage detection, and in surgical robotics for characterizing blood flow over an operative site). For the latter, the outcome enables to assess bleeding severity and find the source of the bleeding. Based on its importance in assessing injuries and from a medical perspective in directing the course of surgery, fluid flow assessment is deemed to be a desirable addition to a surgical robot's capabilities. The results from tests on fluid flows generated from a test rig show that the proposed methods can contribute to an automated characterization of fluid flow, which in the presence of several fluid flow sources can be achieved by tracking the flows, determining the locations of the sources and their relative severities, with execution times suitable for real-time operation.