Abstract: Wireless sensor networks (WSNs) often consists of energy constrained sensor nodes and a data center, and data aggregation is often used to remove the redundant information from the data. However, no prior work studies the network lifetime under the aggregated data rate constraint. In this paper, a network flow model is proposed for data aggregated WSNs. By defining the loose factor for the aggregated data rate, the maximum network lifetime routing and the minimum aggregated data rate routing are combined. And a group of linear programming problems are designed to remove the loops in the routes. Extensive simulation results show the performances of the proposed routing algorithm. The relationships between the network lifetime and the aggregated data rate are also analyzed.