Regular inspections are crucial to maintaining waste-water pipelines in good condition. The challenge is that inside a pipeline the space is narrow and may have a complex structure. The conventional methods that use pipe robots with heavy cables are expensive, time-consuming, and difficult to operate. In this work, we develop an amphibious system that combines a quad-copter with a surface vehicle, creating a hybrid unmanned aerial floating vehicle (HUAFV). Nonlinear dynamics of the HUAFV are modeled based on the dynamic models of both operating modes. The model is validated through experiments and simulations. A PI controller designed and tuned on the developed model is implemented onto a prototype platform. Our experiments demonstrate the effectiveness of the new HUAFV's modeling and design.