# Effects of Nozzle Exit Angle on the Pressure Characteristics of SRWJs Used for Deep-Hole Drilling
## 3 Experimental Setup and Procedures
### Design of Organ-Pipe Nozzles  
To produce the tested organ-pipe nozzles, all the geometrical parameters shown in Figure 1 should first be acquired From Equation (4), it can be found that \(U_{j}\) should be obtained in order to get the value of \(L_{c}/D_{e}\), because the values of \(S_{d}\) and \(c\) are already known as 0.3 and 1450 m/s, respectively. The inlet, chamber, and exit diameters can be determined as 13 mm, 5 mm, and 2 mm, respectively, based on the previous results [13,14]. The process for getting the values of \(U_{j}\) corresponding to the two inlet pressures is shown below. Based on the Bernoulli equation, the relation between \(P_{i}\) and \(U_{j}\) can be obtained:  
\[\frac{P_{i}}{\rho g}=\frac{P_{o}}{\rho g}+\frac{U_{j}^{2}}{2g}+h_{f}+h_{j} \tag{7}\]  
where \(\rho\) is water density, \(g\) is the acceleration of gravity, \(P_{o}\) is the environment pressure (and here it can be neglected when compared with the inlet pressure), and \(h_{f}\) and \(h_{j}\) are the frictional and the local head losses, written as:  
\[h_{f}=\eta\frac{l}{d}\frac{u^{2}}{2g} \tag{8}\]  
\[h_{j}=k\frac{u^{2}}{2g} \tag{9}\]  
where \(\eta\) is the friction coefficient, \(l\) is the length of the flow channel (here it is the nozzle length), \(d\) is the channel diameter (here it is the nozzle diameter), \(u\) is the flow velocity, m/s, and \(k\) is the local resistance coefficient. For the case of a sudden area contraction, \(k\) is described as:  
\[k=\frac{1}{2}\Bigg{(}1-\bigg{(}\frac{A_{2}}{A_{1}}\bigg{)}^{2}\Bigg{)}^{2} \tag{10}\]  
where \(A_{1}\) and \(A_{2}\) are the cross-section areas at the area contraction. A preliminary calculation indicated that the frictional head loss was rather small and could be ignored. Therefore, the chamber lengths could finally be obtained by combining Equations (4), (6), (8), and (9), and were \(L_{c}\) = 21 mm and 15 mm, respectively, corresponding to inlet pressures of \(P_{i}\) = 10 MPa and 20 MPa. Six exit angles were employed in the experiment, which were \(0^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\), and \(90^{\circ}\), respectively. The geometrical parameters of the tested organ-pipe nozzles are shown in Table 3, and the typical profile and pictures of the testing organ-pipe nozzles are displayed in Figures 3 and 4, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & **Nominal Pressure (MPa)** & **Bust Pressure (MPa)** & **Accuracy** & **Influence Effects of Supply (10 V)** & **Influence Effects of Load (10 V)** & **Thermal Error (10 K)** \\ \hline BD Sensors & 45 & 100 & \(\pm\)0.5\% FS & 0.05\% FS & \(\pm\)0.2\% & \(\pm\)0.5\% FS \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters of the pressure transducer of DMK 331P. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & **Nominal Pressure (MPa)** & **Bust Pressure (MPa)** & **Frequency** & **Accuracy** & **Repeatability** & **Nonlinearity** \\  & **Pressure (MPa)** & **(MPa)** & **Response (KHz)** & **Accuracy** & **Repeatability** & **Nonlinearity** \\ \hline Measurement & & & & & & & \\ SPECIALITIESTM & 35 & 105 & 288 & \(\leq\)\(\pm\)0.25\% FS & \(\pm\)0.2\% & \(\pm\)0.25\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main parameters of the pressure transducer of XPM 10. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**\(P_{i}\) (MPa)**} & \multirow{2}{*}{\(L_{i}\) (mm)} & \multirow{2}{*}{\(L_{c}\) (mm)} & \multirow{2}{*}{\(L_{c}\) (mm)} & \multirow{2}{*}{\(L_{c}\) (mm)} & \multirow{2}{*}{\(L_{c2}\) (mm)} & \multirow{2}{*}{\(\Theta\)} & \multirow{2}{*}{\(D_{i}\) (mm)} & \multirow{2}{*}{\(D_{e}\) (mm)} & \multirow{2}{*}{\(D_{e}\) (mm)} \\  & & & & & & & & \\ \hline
10 & 10 & 21 & & 3 & \(0^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), & \(60^{\circ}\), \(75^{\circ}\), & \(90^{\circ}\) & 13 & 5 & 2 \\
20 & 10 & 15 & 2 & 3 & \(60^{\circ}\), \(75^{\circ}\), \(90^{\circ}\) & \(13\) & 5 & 2 \\ \hline \hline \end{tabular}
\end{table}