  This paper is devoted to the extension to the full $3\times3$ Euler system of
the basic analytical properties of the equations governing a fluid flowing in a
duct with varying section. First, we consider the Cauchy problem for a pipeline
consisting of 2 ducts joined at a junction. Then, this result is extended to
more complex pipes. A key assumption in these theorems is the boundedness of
the total variation of the pipe's section. We provide explicit examples to show
that this bound is necessary.
