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We propose a novel methodology to identity flows in the solar atmosphere and classify their velocities as either supersonic, subsonic, or sonic. The proposed methodology consists of three parts. First, an algorithm is applied to the Solar Dynamics Observatory (SDO) image data to locate and track flows, resulting in the trajectory of each flow over time. Thereafter, the differential emission measure inversion method is applied to six AIA channels along the trajectory of each flow in order to estimate its background temperature and sound speed. Finally, we classify each flow as supersonic, subsonic, or sonic by performing simultaneous hypothesis tests on whether the velocity bounds of the flow are larger, smaller, or equal to the background sound speed. The proposed methodology was applied to the SDO image data from the 171 {\AA} spectral line for the date 6 March 2012 from 12:22:00 to 12:35:00 and again for the date 9 March 2012 from 03:00:00 to 03:24:00. Eighteen plasma flows were detected, 11 of which were classified as supersonic, 3 as subsonic, and 3 as sonic at a $70\%$ level of significance. Out of all these cases, 2 flows cannot be strictly ascribed to one of the respective categories as they change from the subsonic state to supersonic and vice versa. We labelled them as a subclass of transonic flows. The proposed methodology provides an automatic and scalable solution to identify small-scale flows and to classify their velocities as either supersonic, subsonic, or sonic. We identified and classified small-scale flow patterns in flaring loops. The results show that the flows can be classified into four classes: sub-, super-, trans-sonic, and sonic. The detected flows from AIA images can be analyzed in combination with the other high-resolution observational data, such as Hi-C 2.1 data, and be used for the development of theories of the formation of flow patterns., Comment: 13 pages, 7 figures, Accepted for publication in A&A