Reynolds-Gauss theorem

If the Reynolds-Gauss theorem is applied to Eq. (2.12) and the integrals on the boundary of the control volume are written in terms of integrals over the control volume itself, it is straightforward to obtain... 

Using the Gauss divergence theorem, the Reynolds transport theorem (Eq. 2.27) can be rewritten as... 

See Arts (1962) for a rigorous derivation of the Reynolds-Gauss transport theorem. 

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