## 4 Discussion  
Verification of the obtained parameters was carried out by comparing the results of the numerical study with the results of the physical test. In this case, the k-\(\varepsilon\) turbulence model [21] was chosen. \begin{table}
\begin{tabular}{c c c c} \hline
**Surface Roughness, \(\upmu\)m** & \(\mathbf{c_{2}}\)**, m/s** & \(\mathbf{m_{a}}\)**, m/s** & \(\mathbf{A}\)**, N** \\ \hline
0 & 392 & 0.0378 & 16.0 \\
3.2 & 372 & 0.0374 & 14.0 \\ \hline \end{tabular}
\end{table} 
Table 7: The numerical simulation results for the nozzle UDC32-450 with a critical diameter of 6 mm with hydraulic smooth walls and a rough inner surface. Figure 8: The impact of air consumption on the output surface roughness (K—roughness coefficient): points—calculated values; lines—approximation lines. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**No.** & \(\mathbf{\Delta p}\)**, MPa** & \(\mathbf{m_{a}}\)**, m/s** & **No.** & \(\mathbf{\Delta p}\)**, MPa** & \(\mathbf{m_{a}}\)**, m/s** & **No.** & \(\mathbf{\Delta p}\)**, MPa** & \(\mathbf{m_{a}}\)**, m/s** \\ \hline
1 & 0.58–0.60 & 0.0096 & 9 & 0.42–0.44 & 0.0056 & 17 & 0.26–0.28 & 0.0034 \\
2 & 0.56–0.58 & 0.0096 & 10 & 0.40–0.42 & 0.0050 & 18 & 0.24–0.26 & 0.0032 \\
3 & 0.54–0.56 & 0.0078 & 11 & 0.38–0.40 & 0.0050 & 19 & 0.22–0.24 & 0.0029 \\
4 & 0.52–0.54 & 0.0078 & 12 & 0.36–0.38 & 0.0046 & 20 & 0.20–0.22 & 0.0028 \\
5 & 0.50–0.52 & 0.0078 & 13 & 0.34–0.36 & 0.0046 & 21 & 0.18–0.20 & 0.0025 \\
6 & 0.48–0.50 & 0.0068 & 14 & 0.32–0.34 & 0.0043 & 22 & 0.16–0.18 & 0.0022 \\
7 & 0.46–0.48 & 0.0068 & 15 & 0.30–0.32 & 0.0037 & 23 & 0.14–0.16 & 0.0023 \\
8 & 0.44–0.46 & 0.0063 & 16 & 0.28–0.30 & 0.0034 & 24 & 0.12–0.14 & 0.0019 \\ \hline \end{tabular}
\end{table} 
Table 8: The experimental results for the cylindrical nozzle with an inner diameter of 20 mm, length of 22 mm, and pressure ratio \(\beta\) = 0.51. Considerable differences were obtained between the values of the actual jet reaction force of the Venturi nozzle and the ideal jet reaction force. The discrepancy between the value of the jet reaction force \(A\) obtained experimentally and the value of the pre-calculated real jet reaction force and output velocity was about 4%. This confirmed the correctness of the calculation results. It can be seen from the tables that speed values of the air-abrasive mixtures differed by up to 10% in the nozzles made of ceramics and metal. This indicates velocity losses caused by the nozzle's inner surface roughness, as discussed in the works [22; 23; 24; 25]. The obtained results showed that the roughness of the nozzle wall impacts the value of the working medium velocity; namely, the ceramic nozzle velocity is 15% higher at the output cross-section if compared with the metal surface with higher roughness. The consumption coefficients stay almost the same, correlating with the papers [17; 18; 19]. It was found that the Venturi nozzle is more sensitive to surface roughness since the differences in the values of its output velocity in the ideal and actual processes make up to 4 times. The reduction of the cylindrical nozzle length from 22 mm to 11 mm reduced metal surface processing time by 1.5 times, which the reduction of the nozzle hydraulic resistance can explain. Even if an increase in the cylindrical nozzle diameter does not change the processing time, the air-abrasive mixture consumption rises up to 4 times, which correlated with the papers [20; 26]. Notably, since a pneumatic abrasive unit consumes a significant amount of compressed air and abrasive material, it is economically impractical to perform surface treatment of materials using worn nozzles or nozzles with an increased internal diameter. The reduction of the fractional structure of the abrasive material causes a decrease in the roughness of the processed surface. Thus, the following recommendations may be the following: for removal of the dirt coating, the abrasive fraction of 0.2\(-\)0.5 mm should be applied.