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 .