What is a substantial derivative?

Also called material derivative, substantial derivative computes time’s rate of change of any quantity such as velocity or temperature for a portion of any material that moves with velocity. Flow patterns, which include velocity, temperature and pressure among others, are defined as a function of time and space.

What this means is that instead of tagging each particle in the flow, one simply needs to fix a volume in space to identify the properties of flow present in that particular space. This renders the particles that pass the volume irrelevant because that particle eventually resumes the flow property found in that space.