Transmission range plays an important role in the deployment of a practical underwater acoustic sensor network (UWSN), where sensor nodes equipping with only basic functions are deployed at random locations with no particular geometrical arrangements. The selection of the transmission range directly influences the energy efficiency and the network connectivity of such a random network. In this paper, we seek analytical modeling to investigate the tradeoff between the energy efficiency and the network connectivity through the selection of the transmission range. Our formulation offers a design guideline for energy-efficient packet transmission operation given a certain network connectivity requirement.