Peer to peer file exchange systems such as BitTorrent are changing the way in which content is distributed in the Internet. Service capacity for a certain content adjusts dynamically as a function of peer population, thus achieving scalability. This dynamic behavior has been the subject of recent analytical studies. In this paper, we propose a partial differential equation model for BitTorrent-like systems, in which a fluid variable represents content and its distribution in the system is taken into account. This model allows for a variety of file sharing disciplines; we identify equilibrium properties that must hold regardless of this choice, and others that depend on a notion of efficiency. The equilibrium properties of many specific disciplines are described. Through a discretized ordinary differential equation model, we also present results on the stability of the equilibrium for a particular sharing policy that is suitable to model current BitTorrent systems.