  We consider an isothermal gas flowing through a straight pipe and study the
effects of a two-way electronic valve on the flow. The valve is either open or
closed according to the pressure gradient and is assumed to act without any
time or reaction delay. We first give a notion of coupling solution for the
corresponding Riemann problem; then, we highlight and investigate several
important properties for the solver, such as coherence, consistence, continuity
on initial data and invariant domains. In particular, the notion of coherence
introduced here is new and related to commuting behaviors of valves. We provide
explicit conditions on the initial data in order that each of these properties
is satisfied. The modeling we propose can be easily extended to a very wide
class of valves.
