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The distinction between U and E is significant in fluid dynamics.
Maybe I'm missing something, but AFAICT the «internal energy» is
not conserved. To see this, consider the contrast:
a) One parcel expands in such a way as to compress a neighboring
parcel. U is conserved in this situation. So far so good.
b) One parcel expands in such a way as to /lift/ a neighboring
parcel. It seems to me that U is not conserved.