This paper presents a new technique for shape and topology optimization of fluid channels using generative design synthesis methods. The proposed method uses the generative abilities of graph grammars with simulation and analysis power of conventional computational fluid dynamics methods. The graph grammar interpreter GraphSynth is used to carry out graph transformations, which define different topologies for a given multiple-inlet multiple-outlet problem. After evaluating and optimizing the generated graphs, they are first transformed into meaningful three-dimensional shapes. These solutions are then analyzed by a computational fluid dynamics solver for final evaluation of the possible solutions. The effectiveness of the proposed method is checked by solving a variety of available test problems and comparing them with those found in the literature. Furthermore, by solving very complex large-scale problems, the robustness and effectiveness of the method is tested. To extend the work, future research directions are presented.