  The net radial flow velocity of gas is an important parameter for
understanding galaxy evolution. It is difficult to measure in the presence of
the elliptical orbits of an oval distortion because the mathematical model
describing the observed velocity is degenerate in the unknown velocity
components. A method is developed in this paper that breaks the degeneracy
using additional information about the angular frequency of the oval
distortion. The method is applied to the neutral hydrogen in the oval
distortion of NGC 4736. The neutral hydrogen is flowing inward at a mean rate
of -6.1 $\pm$ 1.9 km s$^{-1}$. At this rate, it takes 400 Myr, or 1.7 rotations
of the oval distortion, for the neutral hydrogen to travel the 2.5 kpc from the
end to the beginning of the oval distortion. The mean mass flow rate of the
neutral hydrogen in this region is -0.25 $\pm$ 0.11 $M_\odot$ yr$^{-1}$, which
is similar to estimates for the star formation rate reported in the literature.
