eople are able to reason about the physical dynamics of everyday objects. One proposal for the computations underlying this ability is that people are running an approximate mental simulation of their environment. However, such a simulation must be limited in its resources. We applied the notion of a resource-bound simulation to a fluid reasoning task, and show people’s changing behavior can be explained by an approximate simulation that hits a resource limit after some time elapses. In Experiments 1 and 2, people performed well on tasks that asked them to estimate the time-to-fill and water level of different containers, when filled over short periods of time (1-7 seconds). Experiment 3 shows systematic biases in visual volume estimation, which further strengthens the proposal that people are using a simulation to solve the first two experiments. Experiment 4 extends the reasoning time for the time-to-fill task, and shows the existence of a ‘switch point’, as expected from a resource-bound simulation model. The model also accounts for individual differences: People who perform worse on a digit-span task have an earlier switch point.