# Effects of Nozzle Exit Angle on the Pressure Characteristics of SRWJs Used for Deep-Hole Drilling
## 4 Experimental Results and Discussion
### Preliminary Non-Dimensional Analysis  
In order to provide further clarification on the pressure characteristics of SRWJs affected by the exit angle of the organ-pipe nozzle under different inlet pressures, a non-dimensional analysis of the \(P_{max}\) and \(P_{a}\) was performed. \(P_{max}\) and \(P_{a}\) were non-dimensionalized by \(P_{i}\); and the standoff distance was non-dimensionalized by \(D_{e}\), which has been defined as the characteristic parameter of the organ-pipe nozzle in the previous studies of SRWJs [10; 12; 20]. The dimensionless \(P_{max}\) and \(P_{a}\) against the dimensionless \(S\) under the two inlet pressures are plotted in Figures 7 and 8, respectively, and the correlation coefficients are also displayed. Moreover, for each exit angle, the differences in the dimensionless peaks and amplitudes under the two inlet pressures were calculated and plotted in Figures 9 and 10, respectively. Figure 7: The dimensionless \(P_{max}\) against dimensionless \(S\). As shown in Figure 7, it is clear that the inlet pressure can hardly affect the development trends of \(P_{max}\), as the curves of the same color have the same shapes. More specifically, for the exit angle \(\theta\), the inlet pressure can be increased by \(\sim 0.05\), which is consistent with the increase in the inlet pressure. Figure 8: The dimensionless pressure oscillation amplitude against dimensionless standoff distance. Figure 10: The differences in dimensionless amplitudes against dimensionless standoff distance. Figure 9: The differences in the dimensionless \(P_{max}\) against dimensionless \(S\). of \(\theta=0^{\circ}\), the development trends of \(P_{max}\) can be described by a quadratic convex function, which is \(y=-4\times 10^{-4}x^{2}+2.89\times 10^{-3}x+1.163\). For the other exit angles, the trends are fitted by quadratic concave functions. For example, when the exit angle was \(30^{\circ}\), the trend of the \(P_{max}\) fits the function of \(y=7\times 10^{-4}x^{2}-0.059x+1.3\). Furthermore, when combined with Figure 9, it was found that the dimensionless values of \(P_{max}\) at the two inlet pressures were very close when the exit angle was \(0^{\circ}\) or \(45^{\circ}\), because the differences were the closest to the red dashed line of 0. In addition, it is of interest to find that the dimensionless values of \(P_{max}\) at an inlet pressure of \(P_{i}=10\) MPa were always greater than those at an inlet pressure of \(P_{i}=20\) MPa under the exit angles of \(\theta=45^{\circ}\) and \(60^{\circ}\), and the greatest differences occurred when the exit angle was \(60^{\circ}\). However, at the exit angles of \(\theta=30^{\circ},75^{\circ}\), and \(90^{\circ}\), the dimensionless peaks at \(P_{i}=10\) MPa were smaller than those at \(P_{i}=20\) MPa, and the exit angle of \(\theta=75^{\circ}\) resulted in the greatest differences. With respect to the dimensionless \(P_{a}\) shown in Figure 8, the development trends were almost the same as those of the dimensionless \(P_{max}\) under the tested organ-pipe nozzles of different exit angles. That is to say, both \(P_{max}\) and \(P_{a}\) have a convex quadratic relationship with the standoff distance for the exit angle of \(\theta=0^{\circ}\) and have a concave quadratic relationship with the standoff distance for the exit angles of \(\theta=30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\), and \(90^{\circ}\). Moreover, the dimensionless values of \(P_{a}\) under the two inlet pressures were rather close at the testing standoff distances when the exit angle was \(30^{\circ}\) and \(75^{\circ}\), as shown in Figure 10. In addition, the dimensionless pressure oscillation amplitudes at an inlet pressure of \(P_{i}=10\) MPa were always greater than those at \(P_{i}=20\) MPa when the exit angle was \(45^{\circ}\) and \(60^{\circ}\), while at the other exit angles, the relative magnitudes of the amplitudes under the two inlet pressures fluctuated with the standoff distance.