Abstract: At present, no mature analytical framework exists for describing the jet behavior of flowing artesian wells, including well discharge and jet height. This study conducted systematic theoretical work. First, based on the principles of well flow, jet flow, and water flow continuity, a steady flow analytical model for jet of a flowing artesian well was established, and a closed form solution was derived and its practical implications were discussed. Second, to characterize jet vigor, the concept of jet potential for a flowing artesian well was proposed, including apparent jet potential and substantial jet potential. For the quantitative analysis of substantial jet potential, the expression of jet power was derived. Third, through systematic theoretical deduction, an in-depth analysis was conducted on the impact of three basic hydraulic factors (flowing hydraulic head, specific well discharge, and wellhead area) on the inflow potential of a flowing artesian well. Finally, the theoretical results are validated through application to real-world cases. The results indicate that jet is entirely determined by three fundamental hydraulic factors. The apparent jet potential provides an intuitive measure of jet vigor and serves as an external functional indicator of artesian well performance, while the substantial jet potential can more accurately reflect the vitality of the well from a mechanistic perspective. The three basic hydraulic factors are sufficient and necessary conditions for the jet. Among them, the flowing hydraulic head is the source of energy and water, whose impact on jet is positively correlated and unbounded. The specific well discharge reflects the runoff channel and has a positive correlation and bounded impact on the jet potential. The area of the wellhead represents the drainage capacity of a flowing artesian well, and is also the "main switch" and "regulator" for jet, whose impact on jet potential is "bidirectional"; theoretically, it exists a "maximum jet potential wellhead area". Both theoretical derivation and case application demonstrate that this study not only reveals the hydraulic essence of jet in theory but also provides important guidance for the design and operation of flowing artesian wells, as well as for the inversion of hydrogeological parameters using jet observations.