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Finding an optimal routing path in adverse underwater environment in an Underwater Sensor Network (UWSN) has always been a challenging task. Maintaining the network life for a longer duration by utilizing nodes' energy is also critical. By taking these issues into consideration we propose an Energy optimized Path Unaware Layered Routing Protocol (E-PULRP) for dense underwater 3D sensor networks. An up-link transmission is considered, where a set of underwater sensor nodes report events to the stationary sink node. E-PURLP consists of two phases. In the first phase (layering phase), a layering structure is presented which is a set of concentric spheres, around a sink node. The radii of the concentric spheres as well as the transmission energy of the nodes in each layer are chosen considering probability of successful packet transmissions and minimum overall energy expenditure. In the second phase (communication phase), we propose a method to choose intermediate relay nodes and on the fly routing algorithm for packet delivery from source node to sink node across the identified relay nodes. The energy analysis of the E-PULRP has been carried out and shown that it is energy efficient. The performance in terms of throughput and delay is also analyzed.