This paper presents a practical swarm navigation algorithm based on potential functions and properties of inviscid incompressible flows. Panel methods are used to solve the flow equations around complex shaped obstacles and to generate the flowlines, which provide collision-free paths to the goal position. Safe swarm navigation is achieved by following the generated streamlines. Potential functions are used to achieve and maintain group cohesion or a geometric formation during navigation. The algorithm is implemented and tested through numerical simulations, as well as experimental implementations on real robots in a laboratory environment in two settings, in which the flowlines are calculated either offline or in real time. The algorithm is easy to implement and can serve as an effective tool for cohesive navigation of robotic swarms.