Appropriate network design is very significant for Underwater Wireless Sensor Networks (UWSNs). Application-oriented UWSNs are planned to achieve certain objectives. Therefore, there is always a demand for efficient data routing schemes, which can fulfill certain requirements of application-oriented UWSNs. These networks can be of any shape, i.e., rectangular, cylindrical or square. In this paper, we propose chain-based routing schemes for application-oriented cylindrical networks and also formulate mathematical models to find a global optimum path for data transmission. In the first scheme, we devise four interconnected chains of sensor nodes to perform data communication. In the second scheme, we propose routing scheme in which two chains of sensor nodes are interconnected, whereas in third scheme single-chain based routing is done in cylindrical networks. After finding local optimum paths in separate chains, we find global optimum paths through their interconnection. Moreover, we develop a computational model for the analysis of end-to-end delay. We compare the performance of the above three proposed schemes with that of Power Efficient Gathering System in Sensor Information Systems (PEGASIS) and Congestion adjusted PEGASIS (C-PEGASIS). Simulation results show that our proposed 4-chain based scheme performs better than the other selected schemes in terms of network lifetime, end-to-end delay, path loss, transmission loss, and packet sending rate.