Modern programmable graphics hardware offers sufficient computing power to suggest the implementation of traditional algorithms on the graphics processor. This paper describes a complete implementation of a standard technique to solve the incompressible Navier-Stokes fluid equations running entirely on the GPU: the SMAC (Simplified Marker And Cell) method. This method is widely used in engineering applications. The described implementation works with general rectangular domains, with or without obstacles, and with a variety of boundary conditions. Furthermore, we show that our implementation is about sixteen times faster than a reference CPU implementation running on similar cost hardware. Finally, we discuss simple extensions to the method to deal with more general situations, such as free boundary-value problems and three-dimensional domains.