A space-averaged model of branched structures

•We present an original space-averaged model for conservation laws in branched systems.•The system is modeled by one-dimensional equations along characteristic curves related to the initial geometry.•A geometric forcing term accounts for branching and diameter variations in a continuous way.•This model accurately predicts mass balance in a pipe network and momentum balance in a tree under wind loading.•The derivation of this model is general and can be of use in a large variety of branched systems.