## 3 Results and Discussions
### Effect of Velocity and Sand Loading
As the angle was less than 90\({}^{\circ}\), it is believed that the particle impact would form a crater, and subsequent impingement would enlarge the crater and also pile up the material around it, eventually removing it from the surface. Figure 6 shows the craters and larger holes as a sign of significant removal of materials due to the combined effect of corrosion and erosion. This is due to corrosion-enhanced erosion, resulting in the removal of flakes formed by multiple impacts of sand particles [48]. Figure 11: SEM of specimen after erosion–corrosion impingement test (**a**) at 10 m/s and 600 mg/L; and (**b**) at 20 m/s and 300 mg/L. Figure 12: Surface of the specimen 2 mm away from the center after pure erosion test at 20 m/s and 600 mg/L. Empirical Regression Model That Relates the \(Twl\) and \(E_{0}\) with the Velocity and Sand Loading  
A two-level factorial experimental method in the design of the experiments (DOE) was used to develop an empirical regression model that represents the \(TWL\) and \(E_{0}\) as a function of velocity and sand loading. Each variable was assigned two levels, low and high, also designated as \(-1\) and \(+1\), resulting in four different combinations. All the experiments were repeated three times for validity. Table 4 shows the four different combinations of velocity and sand loading used to conduct the experiments. Table 5 shows the values of velocity and sand loading at low and high levels used to develop a mathematical model. The model was developed using MINITAB in a form as shown in Equation (4). In Equation (4), \(Y\) is the response variable, \(B_{0}\), \(B_{1}\), \(B_{2}\), \(B_{12}\) are constant regression coefficients of the model, \(X_{1}\), \(X_{2}\) are independent variables and \(X_{12}\) is the interaction between \(X_{1}\) and \(X_{2}\), the product of \(X_{1}\) and \(X_{2}\). \[Y=B_{0}+B_{1}X_{1}+B_{2}X_{2}+B_{12}X_{12} \tag{4}\]  
\[TWL=-15.70+2.4700\ V+0.02500\ S+0.001856\ V\times S \tag{5}\]  
\[E_{o}=-17.40+1.5667\ V+0.03211\ S+0.000778\ V\times S \tag{6}\]  
Figure 13 shows the results of experiments conducted with the four different combinations. The results show that erosion is the dominant factor for all combinations except for the combination of low velocity and low sand loading, where the E-C interaction contributed more to the weight loss. Equations (5) and (6) are the developed models for \(TWL\) and \(E_{o}\), respectively. These equations were derived under laboratory conditions for a velocity of 10 m/s to 20 m/s, sand loading of 300 mg/L to 600 mg/L, a temperature of 29-33 \({}^{\circ}\)C, an impingement angle of 90\({}^{\circ}\) in a 4-h time period. The models given in Equations (5) and (6) where \(V\) is velocity and \(S\) is sand loading for both \(TWL\) and \(E_{o}\), show that the velocity has more influence on the weight loss than the sand loading, as the velocity \(V\) has a larger coefficient than the sand loading \(S\). However, both velocity and sand loading have a significant influence on \(TWL\) and \(E_{0}\). \begin{table}
\begin{tabular}{c c c} \hline
**Run** & **V** & **S** \\ \hline
1 & \(-1\) & \(-1\) \\
2 & \(-1\) & \(+1\) \\
3 & \(+1\) & \(-1\) \\
4 & \(+1\) & \(+1\) \\ \hline \end{tabular}
\end{table} 
Table 4: Runs for \(2^{2}\) experiment design. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Factors**} & \multicolumn{2}{c}{**Levels Used**} \\ \cline{2-3}  & **Low (\(-1\))** & **High (\(+1\))** \\ \hline Velocity (m/s) & 10 & 20 \\ Sand Loading (mg/L) & 300 & 600 \\ \hline \end{tabular}
\end{table} 
Table 5: Variables and experimental design levels for conducting experiments. \(TWL\) and \(E_{0}\) as a function of velocity and sand loading for specific conditions. Translating the results of this model for the prediction of material loss in field conditions requires additional work which includes using the types of steel used in the field. In addition, future work should include the effect of field operational temperature, velocity, and the impingement angle on the pure erosion and erosion-corrosion.