In this paper we investigate the problem of uneven energy consumption in a large class of many-to-one sensor networks. In a many-to-one sensor network, all sensor nodes generate constant bit rate (CBR) data and send them to a single sink via multihop transmissions. This type of sensor network has many potential applications such as environmental monitoring and data gathering. Based on the observation that sensor nodes sitting around the sink need to relay more traffic compared to other nodes in outer sub-regions, our analysis verifies that nodes in inner rings suffer much faster energy consumption rates (ECR) and thus have much shorter expected lifetimes. We term this phenomenon of uneven energy consumption rates as the “energy hole” problem, which may result in severe consequences such as early dysfunction of the entire network. We proposed analytical modeling for this problem, which can help understand the relevance of different factors on energy consumption rates. Using this model, we study the effectiveness of several existing approaches towards mitigating the “energy hole” problem, including deployment assistance, traffic compression and aggregation. We have used simulation results to validate our analysis.