## 4 Conclusions  
In the present study, experiments were performed to examine the characteristics of the two-phase frictional pressure drop of an R410A refrigerant flowing vertically upward and downward. The cross-sections of copper test tubes were 0.5, 0.7, 1.0, 1.5, and 2.0 mm circular tubes, and rectangular and triangular tubes with hydraulic diameters of 1.04 and 0.88 mm, respectively. The characteristics of measured pressure drops were clarified by different inner diameter tubes, cross-section shapes, and flow directions. Some of the major conclusions from this paper are summarized below:  
1. Although wide range data from low mass flux to high mass flux were obtained, most of data were located on the laminar liquid condition. Therefore, the viscous force and the surface tension have a significant influence on the area between the fluid and channel;
2. As in the case of the conventional large circular tube, the measured frictional pressure drop in small circular tubes increased with increasing quality in the wide range with a maximum at around 0.8; after that, it mildly decreased with increasing quality to a quality of around 1.0. Moreover, increasing mass flux increased the frictional pressure drop, and decreasing the inner diameter of tube increased the frictional pressure drop. In addition, for the low mass flux (50 kg\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\) and 100 kg\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\)), the frictional pressure drop decreased with increasing quality in the low quality region, its values not being affected by the different mass flux or inner diameter;
3. As in the case of the circular tube, the measured frictional pressure drop in both the small rectangular and triangular tubes increased with increasing mass flux and quality. In addition, for the low mass flux condition (50 kg\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\) and 100 kg\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\)), the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Tube**} & \multirow{2}{*}{**N**} & \multicolumn{6}{c}{**MD \%**} \\ \cline{3-8}  & & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** \\ \hline Cir\_D0.5 & 26 & 53.5 & 68.1 & 24.6 & **16.0** & 37.2 & 26.2 \\ Cir\_D0.7 & 36 & 28.3 & 50.6 & 29.5 & **18.9** & 37.4 & 25.2 \\ Cir\_D1.0 & 69 & 34.2 & 51.4 & 22.4 & **14.3** & 33.3 & 48.1 \\ Cir\_D1.5 & 41 & 36.1 & 60.5 & **18.0** & 22.1 & 35.8 & 36.0 \\ Cir\_D2.0 & 4 & 25.2 & 48.1 & **12.1** & 25.5 & 24.4 & 20.4 \\ All Cir. & 176 & 36.1 & 55.7 & 22.9 & **17.5** & 35.1 & 36.7 \\ Rec. & 58 & 65.9 & 79.8 & **16.9** & 24.5 & 49.6 & 119.4 \\ Tri & 63 & 63.8 & 65.2 & **17.2** & 20.5 & 47.3 & 74.6 \\ Total & 297 & 47.8 & 62.4 & 20.5 & **19.5** & 40.5 & 60.9 \\ \hline \hline \end{tabular}
**Bold number** shows the best results.  
\end{table} 
Table 3: Percentage mean deviation \(MD\) of each modified Chisholm parameter. (upward and downward flow). frictional pressure drop indicated higher values in the low-quality region, and that value of \(\Phi_{1}\)\({}^{2}\) was approximately 10; after that, it decreased with increasing quality. In this region, the value of frictional pressure drop was not affected by the different cross-section shape and mass flux;
4. The cross-section shape was slightly affected by the high mass flux. On the other hand, the pressure drop of the non-circular tubes became smaller at 100 and 200 kg\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\), especially in the downward flow. Hence, it was supposed that the effect of the cross-section shape became non-negligible;
5. In each tube, the frictional pressure drops of the downward flow were higher than those of the upward flow in which the pressure drop decreased with increasing quality in the low-quality region. Regarding the circular tube, there were no adequate differences in the frictional pressure drop due to the different flow directions, where the pressure drop increased with increasing quality at the mid-quality region.