The pressure and flow rate of an argon line embedded within a stopper rod serve as useful industrial indicators and control factors for mitigating air aspiration into the Submerged Entry Nozzle (SEN) during the continuous casting of steel. This manuscript investigates several challenges associated with interpreting monitored argon line pressures and gas flow rates, including variations in gas pressure during delivery, actual volumes of gas entering the nozzle, argon leakage, and air aspiration. To address these issues, a new one-dimensional (1D) analytical model of compressible argon flow in the stopper rod was developed, incorporating gas dynamics and heat transfer. This concise 1D model was validated using data from a continuous casting simulator (CCS) employing a low-melting-point Bi-Sn alloy (melting point 137 °C). Pilot trials were conducted to replicate various industrial casting scenarios, generating datasets for model validation and demonstration of real-time operation. The 1D model predictions were compared with those from a CFD-based compressible flow model under CCS operating conditions. Following validation, parametric studies were conducted to explore realistic industrial scenarios (e.g., gas flow rate < 5 SLPM, nozzle diameter < 5 mm), including extreme conditions such as air aspiration and choking: a critical nozzle diameter (1.223 mm) corresponds to choked flow, limiting the maximum achievable gas flow rate to 5 SLPM. Additionally, the real-time prediction capabilities of the model were demonstrated using measured argon line pressures and flow rates from CCS trials. The proposed 1D model thus provides a practical tool for accurately interpreting SEN flow conditions from monitored argon pressures and effectively estimating argon bubble injection by clarifying actual gas pressures and flow rates at the stopper injection point.