The Saint-Venant equations of the continuity and momentum principles of one-dimensional, unsteady, open-channel flow are expressed in terms of the phase velocities of constant depth, velocity, and discharge, which results in unique relationships between these phase velocities and channel velocity. A case study shows that these unique relationships developed in this study can be used as an indicator of precision of numerical solutions of the Saint-Venant equations. Further physical interpretation of these relationships and utilization to the numerical analyses of the Saint-Venant equations are to be investigated.