Numerical simulations of solar surface convection have predicted the existence of supersonic horizontal flows in the photospheric granulation. Recently, the detection of such flows in data from the Hinode satellite was reported. We study supersonic granular flows in detail to understand their signatures in spectral lines and to test the observational detection method used to identify these flows in the Hinode observations. We perform time-dependent 3D radiative MHD numerical simulations and synthesize the Fe i 6302 Å spectral lines at the resolution of the Hinode data for different viewing angles covering the center-limb variation. There is very large variation in the detailed shape of the emergent line profiles depending on the viewing angle and the particular flow properties and orientation. At the full simulation resolution the supersonic flows can even produce distinct satellite lines. After smearing to the Hinode resolution sufficient signature of supersonic motion remains. Our analysis shows that the detection method used to analyze the Hinode data is indeed applicable. However, the detection is very sensitive to ad hoc parameter choices and can also misidentify supersonic flows.