## 3 Results and Discussion
### Discussion
However, in the previous work, the relationship between these two variables and the velocity reached by the water was not known: the novelty of the present research also lies in providing a relationship between the mass of explosive to be used and the diameter of the container to obtain a certain velocity, in the form of a regression equation valid for the range of study. It will be interesting to expand this range in future studies in order to determine in which proportions of \"Mass of Explosive\"-\"Diameter\" the effectiveness is lost, either because this ratio is very high or very low, thus providing an additional tool for the operator to calibrate the optimal device, based on the IED to be deactivated. Moreover, another topic of study would be the minimum velocity of the water front necessary to penetrate different materials. Figure 14: Contour plot of the effect of “Explosive Specific Mass” and “Diameter” factors over the response variable. Figure 13: Interaction plot of “Diameter” and “Inner Tube Resistance”. In Figure 12 (right), the interaction plot of \"Mass of Explosive\" and \"Density\" is depicted. A high level of \"Mass of Explosive\" improves the response with a low level of water density, finding the optimum combination at the cut-off point of the lines. If we take into account that a high density of water will make it more incompressible, this contrasts the results obtained with the numerical simulation method by [PERSON] [13], where it was concluded that \"calculations for an incompressible fluid yield higher values of pressure and velocity\". The results of DoE also contrast the recommendation given in [7], where it is mentioned that it is advisable to use water with additives that lower the freezing point. However, according to the experiments, we found that the latter is not recommended to obtain a higher water speed, as long as the additive increases the density. The interaction between the \"Diameter\" and \"Resistance of the Inner Tube\", plotted in Figure 13, indicates that a combination of a low level of one factor improves the response with a high level of the other. This can be related to the good operation of an explosive, maintaining the confinement of the gases [22], either by the presence of the water wall (related to the diameter) or by the resistance of the inner tube. However, excessive resistance due to the combined effect of a large diameter with high inner tube resistance can cause a loss of gases through the upper part of the device and, thus, a lower velocity of the projected water front. Finally, the analysis of the residuals allows us to demonstrate the goodness of the model, since the residuals follow a normal distribution (Figure 15, left). In addition, they present a constant variance with the variation of the response variable, without following a defined pattern and without outliers (Figure 15, right), where standardized residual errors are considered outliers with a value greater than 2 or less than \(-2\). The final purpose of this study is to obtain a mathematical model in the form of a regression equation, establishing a relationship between the predictors and the response, with values of the model terms comprised between the established levels. The regression equation obtained for the response variable (water projection velocity) as a function of the most significant factors and interactions is the following:  
\[v=294.5+84.36\cdot B+45.01\cdot A-17.50\ BC-15.06\cdot AD+4.72\cdot C+3.43 \cdot D \tag{5}\]  
where \(v\) is the speed in m\(\cdot\)s\({}^{-1}\); \(A\), \(B\), \(C\), and \(D\) are the values of the defined levels for \"Diameter\", \"Explosive Specific Mass\", \"Density\", and the \"Resistance of the Inner Tube\", respectively. Equation (5) can be simplified, due to the low significance of factors \(C\) and \(D\), giving the following equation:  
\[v=294.5+84.36\cdot B+45.01\cdot A-17.50\cdot BC-15.06\cdot AD \tag{6}\]  
Figure 15: (**Left**): Normal probability plot of standardized residuals. (**Right**): Plot of standardized residuals vs. fitted values.