  The steady-state solution of fluid flow in pipeline infrastructure networks
driven by junction/node potentials is a crucial ingredient in various
decision-support tools for system design and operation. While the nonlinear
system is known to have a unique solution (when one exists), the absence of a
definite result on the existence of solutions hobbles the development of
computational algorithms, for it is not possible to distinguish between
algorithm failure and non-existence of a solution. In this letter, we show that
for any fluid whose equation of state is a scaled monomial, a unique solution
exists for such nonlinear systems if the term solution is interpreted in terms
of potentials and flows rather than pressures and flows. However, for gases
following the CNGA equation of state, while the question of existence remains
open, we construct an alternative system that always has a unique solution and
show that the solution to this system is a good approximant of the true
solution. The existence result for flow of natural gas in networks also applies
to other fluid flow networks such as water distribution networks or networks
that transport carbon dioxide in carbon capture and sequestration. Most
importantly, our result enables correct diagnosis of algorithmic failure,
problem stiffness, and non-convergence in computational algorithms.
