In wireless sensor networks an attack to the base station (sink) can render the whole network useless. Hence, concealing the physical location of the sink may be necessary in certain circumstances. Previous studies addressing this challenging problem assume a weak adversary model. The problem has not been studied in the presence of an eavesdropper who has global knowledge for the entire network. Here, a naive solution is to employ fake sinks so that nodes send their data not only to the real sink but also to other locations. An alternative solution with less overhead could be provided when all nodes including base station equalize the values of their total incoming and outgoing flows as well as their energy expenditure. This way, no information about the sink location is revealed even when all communication within the network is monitored. In this paper, through a Linear Programming (LP) framework we analyze and compare lifetime limits of wireless sensor networks preserving sink location privacy with the aforementioned two approaches.