The nodes in a wireless sensor network are generally energy constrained. The lifetime of such a network is limited by the energy dissipated by individual nodes during signal processing and communication with other nodes. The issues of modeling a sensor network and assessment of its lifetime have received considerable attention in recent years. This paper provides an analytical framework for placing a number of nodes in a linear array such that each node dissipates the same energy per data gathering cycle. This approach ensures that all nodes run out of battery energy almost simultaneously. It is shown that the network lifetime almost doubles with the proposed scheme as compared to other reported schemes. However, in practice, the nodes are not expected to be placed as per this theoretical requirement. The issue of random placement of nodes has also been investigated to obtain the statistics of energy consumption of a node. The analytical results for random node placement are validated through simulation studies.