  With the advent of integrated sensor technology (smart flow meters and
pressure sensors), various new numerical algorithms for leak localization (a
core element of water distribution system operation) have been developed.
However, there is a lack of theory regarding the limitations of leak
localization. In this work, we contribute to the development of such a theory
by introducing an example water network structure with parallel pipes that is
tractable for analytical treatment. We define the leak localization problem for
this structure and show how many sensors and what conditions are needed for the
well-posedness of the problem. We present a formula for the leak position as a
function of measurements from these sensors. However, we also highlight the
risk of finding false but plausible leak positions in the multiple pipes. We
try to answer the questions of how and when the leaking pipe can be isolated.
In particular, we show that nonlinearities in the pipes' head loss functions
are essential for the well-posedness of the isolation problem. We propose
procedures to get around the pitfall of multiple plausible leak positions.
