Simulations of the gas flow in a variety of two-dimensional barred spiral galaxies have shown that vortices in the gas appear, when viewed from above, in the corotation frame of the bar. These low-density vortices generally appear at or near the L4 and L5 Lagrangian points. We show that these gas vortices in our models are the hydrodynamic analogs of closed, long-period orbits centered on L4 and L5. Secondary but high-density vortices can appear along the L1-L2 axis. The presence of the vortices at or near L4 and L5 leads to a possible practical application, namely, the determination of the corotation radius. Our models have shown that, when viewed in the rotating frame of the perturbation, vortices are present at or very close to corotation and with position angles approximately 90° with respect to the perturbation. As the viewing frame angular velocity is changed, both the radial positions and the position angles of the vortices change. If a gas-rich, barred spiral galaxy were observed in H I with sufficient resolution and signal-to-noise ratio, and if the gas velocities in that region are transformed so that they are "observed" in a rigidly rotating frame, having its origin at the galaxy's center, a pair of vortices should appear with position angles approximately 90° with respect to the bar when the angular velocity of the observing frame equals the pattern speed of the bar. Based upon these simulations, we estimate that the pattern speed and corotation radius can be deduced to within approximately 5%-25% of their true values depending upon the quality of the observations.