Energy-constraint is a crucial problem in wireless sensor networks (WSNs). Many sensor node (SN) placement schemes and routing protocols are proposed to address this problem. In this paper, we first present how to place SNs by use of a minimal number to maximize the coverage area when the communication radius of the SN is not less than the sensing radius, which results in the application of regular topology to WSNs deployment. With nodes placed at an equal distance and equipped with an equal power supply, we discuss the energy imbalance problem and then give the mathematical formulation for maximizing network lifetime in grid-based WSNs. The formulation shows the problem of maximizing network lifetime is a non-linear programming problem and NP-hard even in the 1-D case. We discuss several heuristic solutions and show that the halving shift data collection scheme is the best solution among them. We also generalize the maximizing network lifetime problem to the randomly-deployed WSNs which shows the significance of our mathematical formulation for this crucial problem.