In this study, existing computational hydraulic engines are used to generate numerical solutions that are treated as 'noiseless' field data. Artificial neural networks (ANNs) are then used to transform this data into what are, in effect, numerical schemes, and these are used in their turn to generate the partial differential equations that govern the observed phenomena. Since it is thereby shown that the trained ANNs can reinstate the governing partial differential equations, it is argued that they contain the same knowledge, or have the same semantic content, as these equations. Besides raising confidence in the capabilities of ANNs in a future generation of sub-symbolic engines, this study opens up another way to mine data for knowledge discovery. Although introduced here only for a limited range of flow problems, the methods advanced here appear to be quite generally applicable.