Currently Underwater Acoustic Sensor Network (UASN) is playing a vital role in exploration and monitoring operations in underwater environments that are difficult to reach. Underwater communication mainly relies on acoustic waves, which limits the performance of UASN due to its limited bandwidth, large propagation delays, and high path loss. In this paper, we present a comprehensive mathematical model for underwater sensor network communication compared to available mathematical models in the literature. We also investigate the tradeoffs between energy consumptions, end-to-end delay, and number of hops of UASN. The model obtained in this paper is used to determine the number of hops in energy efficient UASNs for underwater time-critical missions.