Peer-to-peer (P2P) systems are complex to analyze, due to their large number of users who connect intermittently, and to the frequency of requests for files or Web objects.In this paper we propose a mathematical model where request streams are represented as fluid flows and apply it to analyze Squirrel, a recent P2P cooperative Web cache. Our fluid model provides a low-complexity means to estimate the performance of Squirrel (hit probability, latency) and exhibits some key qualitative properties of this system. A comparison with discrete-event simulation validates the accuracy of our model.