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Through detailed analysis of energy consumption of wireless sensor network with uniform node distribution, it is proved that the assumption of network where the density of sensor nodes in the same circular ring is uniform can cause inaccurate analysis of energy consumption. A more accurate theoretically analytical method for avoiding energy hole is proposed for wireless sensor networks with non-uniform node distribution. The main conclusions in this paper are presented below: We prove that unbalanced energy consumption among sensor nodes is unavoidable (namely the energy hole problem is unavoidable) in the circular wireless sensor networks with uniform distribution and constant data reporting. if the density of sensor nodes varies from one region to another, the network can achieve suboptimal energy efficiency. If the density of sensor nodes in inner circular ring is greater than that in outer circular ring. However, the density ratio of sensor nodes in inner circular ring to that in outer circular ring is not a geometric proportion, but related to the sensor node's distance from the base station and the radius of circular ring.