In this paper, we propose a novel 3D Underwater Wireless Sensor Network Deployment scheme for solid detection in rivers. Our objective is to minimize the number of deployed underwater sensors within a target field installation while ensuring i) the required Quality of Monitoring (QoM) (i.e., differentiated probabilistic detection) and ii) wireless network connectivity. To generate the best topology, we propose a novel deployment heuristic, named 3D-UWSN-Deploy, based on a subcube tessellation of the monitored field installation and a mixed integer linear program optimization. To gauge the effectiveness of 3D-UWSN-Deploy, we compare it with the most prominent related strategies. Simulation results show that our proposal is scalable and obtains the best performance in terms of cost deployment, quality of monitoring and connectivity.