Reynolds' Transport Theorem I — Lesson 2

The discussion of balance laws continues, with Reynold’s law. The theorem looks purely mathematical and may not find many obvious applications, but some important concepts are defined using it. This theorem helps to derive other balance laws, such as the mass balance law. The derivation of the theorem starts in this video.

The derivation of Reynold’s transport theorem (RTT) continues, and it is applied to show the balance of mass in a body moving in space that is deforming while the mass is conserved.

The use of Reynold’s transport theorem will be demonstrated for other quantities, as was done for mass in the previous video. The quantity that is used here for demonstration is energy per unit mass. A similar approach can be used for momentum.

In this video, Reynold’s theorem will be applied to a vector field. Coordinate notations are used to give further insight. The use of Gauss Divergence along with Reynold’s transport theorem reveals the physical significance of this theorem. An overview of what this theorem can do is provided.

Answers to Frequently Asked Questions

In this video we will answer the following question:

  • How does this last interpretation of the RTT and the Gauss divergence theorem apply to vector or tensor fields?