In the last decade, Underwater Wireless Sensor Networks (UWSNs) have been widely studied because of their peculiar aspects that distinguish them from common wireless terrestrial networks. In fact, most UWSNs use acoustic instead of radio-frequency based communications, and nodes are subject to high mobility caused by water currents. As a consequence, specialized routing algorithms have been developed to tackle this challenging scenario. Depth based Routing (DBR) is one of the first protocols that have been developed to this aim, and is still widely adopted in actual implementations of UWSNs. In this paper we propose a stochastic analysis that aims at evaluating the performance of UWSNs using DBR in terms of expected energy consumption and e...