Potential flow theory is an alternative theory to simulate burden flow in a blast furnace. But a contour line of the flow function defined to solve the old potential flow model isn’t a stream line. In this paper, the old potential flow model is first developed to a three-equation model which should include the equations of motion and continuity, and it is proved that the contour lines of the flow function defined to solve this three-equation model are stream lines. Second, an equation capable of calculating the distribution of diameter of burden particles in blast furnace is derived from an assumption that all burden particles on a stream line has the same diameter. Finally, the developed potential flow model and the derived equation are used to simulate a final reduction reactor producing hot metal containing Cr, together with other needed transportation equations. These works would play an important improving and exemplary role in the application of potential flow theory to simulate blast furnace process and other iron-making process.