  Many biological systems and artificial structures are ramified, and present a
high geometric complexity. In this work, we propose a space-averaged model of
branched systems for conservation laws. From a one-dimensional description of
the system, we show that the space-averaged problem is also one-dimensional,
represented by characteristic curves, defined as streamlines of the
space-averaged branch directions. The geometric complexity is then captured
firstly by the characteristic curves, and secondly by an additional forcing
term in the equations. This model is then applied to mass balance in a pipe
network and momentum balance in a tree under wind loading.
