## 3 Results and Discussion
### Validation of MPY Data Through Electrochemical Techniques  
The reliability of the MPY data, which is critical for the accuracy of the regression model, was validated through multiple electrochemical techniques: Tafel extrapolation, VASP, and LPR tests. These methods provide complementary insights into corrosion behavior, ensuring the robustness of the data.  
The Tafel extrapolation method, a traditional technique, was used to estimate the corrosion current density (\(I_{corr}\)) and calculate the CR. Figure 5 presents the potentiodynamic curves plotted at flow velocities of 0.2 m/s, 0.8 m/s, and 1.6 m/s at 25 \({}^{\circ}\)C. As the flow velocity increased, the curves shifted the corrosion potential in the anodic direction, indicating enhanced oxygen diffusion to the metal surface and reduced concentration polarization [25; 26]. This behavior corresponds with the increased removal of iron oxide from the metal surface, leading to a higher CR. Specifically, at static conditions, the corrosion potential of carbon steel was \(-\)0.65 V, consistent with the potential of iron oxide formation on the surface [27]. As the flow velocity increased from 0.2 m/s to 1.6 m/s, the corrosion potential shifted from \(-\)0.54 V to \(-\)0.48 V, and \(I_{corr}\) also exhibited an upward trend, corresponding with the results from the LPR tests.  
Figure 4: Interaction effects of temperature, flow velocity, and pH on MPY.  
In addition to Tafel extrapolation, the VASP technique was employed to further validate the MPY data. Figure 6 compares the CR measured by LPR, Tafel extrapolation, and the VASP technique under nine different factor combinations, where only temperature and flow velocity were varied. These experiments were conducted using a neutral 3.5% NaCl solution, with the pH factor intentionally excluded to isolate the effects of temperature and flow velocity on CR.  
Figure 5: Potentiodynamic polarization curves at various flow velocities (static, 0.2 m/s, 0.8 m/s, and 1.6 m/s) measured at 25 \({}^{\circ}\)C.  
Figure 6: Comparison of CR measured by LPR, Tafel extrapolation, and VASP techniques under nine factor combinations, where only temperature and flow velocity varied.  
Both LPR and Tafel extrapolation techniques demonstrated that the CR increased with temperature and flow velocity, with both methods producing similar results. However, slight differences were observed due to the fundamental differences between the techniques. LPR measures corrosion current within a small polarization range, while Tafel extrapolation estimates corrosion current over a broader polarization range [28]. As a result, Tafel extrapolation often provides a more precise estimation of corrosion current, but it can introduce errors due to the experimenter's judgment during curve fitting and calculation.  
The VASP technique, however, yielded MPY values at least three times higher than the other electrochemical techniques. This disparity is attributed to the non-linear responses detected by VASP across a wider polarization range. While VASP is effective for evaluating corrosion resistance in coatings through electrochemical impedance spectroscopy (EIS), it is less suitable for bulk metal corrosion measurements [29; 30]. These results indicate that VASP may measure additional phenomena not directly related to the corrosion of carbon steel in this context, rendering it unsuitable for the present study.