  The observed velocities of the gas in barred galaxies are a combination of
the azimuthally-averaged circular velocity and non-circular motions, primarily
caused by gas streaming along the bar. These non-circular flows must be
accounted for before the observed velocities can be used in mass modeling. In
this work, we examine the performance of the tilted-ring method and the DiskFit
algorithm for transforming velocity maps of barred spiral galaxies into
rotation curves (RCs) using simulated data. We find that the tilted-ring
method, which does not account for streaming motions, under/over-estimates the
circular motions when the bar is parallel/perpendicular to the projected major
axis. DiskFit, which does include streaming motions, is limited to orientations
where the bar is not-aligned with either the major or minor axis of the image.
Therefore, we propose a method of correcting RCs based on numerical simulations
of galaxies. We correct the RC derived from the tilted-ring method based on a
numerical simulation of a galaxy with similar properties and projections as the
observed galaxy. Using observations of NGC 3319, which has a bar aligned with
the major axis, as a test case, we show that the inferred mass models from the
uncorrected and corrected RCs are significantly different. These results show
the importance of correcting for the non-circular motions and demonstrate that
new methods of accounting for these motions are necessary as current methods
fail for specific bar alignments.
