# An Approach to Determine the Median Diameter of Droplets in a Water-Mist Spray
## 5 Results and Discussion  
In the first experiment, the flux density distribution of the spray was measured when the operating pressure, \(P_{1}\), was 34.5 bar. Then, the numerical simulation was conducted with the droplet sizes of 300, 350, 400 and 500 \(\upmu\)m, and the mass flux density distribution for each droplet size was calculated. The numerical results of the distribution of water spray were compared with that of the experimental data. When the numerical distribution data matched with the experimental data, the corresponding droplet size was taken to be the hypothetical median diameter of the droplets (\(dm_{1}\)) of the spray. A comparison of the numerical value with the experimental data is shown in Figure 5. The hypothetical median size of droplets of the spray in the first experiment was considered as 350 \(\upmu\)m at 34.5 bar.  
As mentioned in the methodology, a second experiment was carried out using a pressure, \(P_{2}\), of 75.8 bar, and the spray's corresponding flux density distribution data was measured. Afterwards, the expected \(dm_{2}\) of the spray was calculated for \(P_{2}\) by using Equation (2). The calculated median diameter of droplets for the spray in the second experiment was 275 \(\upmu\)m. Now, this droplet size and the corresponding pressure were used in the FDS software to generate the spray, and the flux density distribution of water spray was computed in the model. The numerical distribution data of flux density were compared with the experimental data. The results are presented in Figure 6. It was found that the numerical data closely matched the experimental measurement. As a result, it  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Orifice diameter & 1.524 & mm \\ Orientation (azimuthal angle) & 0 & degree \\ Flow pressure (\(P_{1}\)) & 34.5 & bar \\ Flow pressure (\(P_{2}\)) & 75.8 & bar \\ Spray height & 2.3 & m \\ Spray angle & 65 & degree \\ Spray pattern type & Solid cone & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: The input variables for the numerical model.  
Figure 4: Flow chart of the numerical analysis.  
appears that the hypothetical median diameter of droplets of 350 and 275 \(\upmu\)m are the actual median diameter of droplets in the experiments at pressures 34.5 and 75.8 bar, respectively.  
The standard uncertainty analysis of the experimental measurement is discussed here. A statistical analysis has been performed to calculate the uncertainty of measurements based on the least-squares method described in reference [26]. Measurements of the distribution of flux densities produced by the spray have an average experimental uncertainty of \(0.103\) L/m\({}^{2}\)/min, as also discussed in the previous article of these authors [3]. As a result, the levels of this uncertainty imply that the measured data from the experiments may vary by as much as the equivalent level of uncertainty.  
Therefore, the method presented in this paper can be useful to determine the median size of droplets of a water spray. The reasonable accuracy of this method is supported by [PERSON]'s [27] principle of consilience of inductions, which relies on the concordance of evidence from different sources. In this case, evidence converges from both the empirical relationship between the operating pressure and the median diameter of the droplets, and the distribution of simulated mass flux generated by the spray nozzle operating under the hypothesised conditions.