## 5 Results and Discussion  
Tables 8 and 9 express the results of simulation 1, based on the manufacturing uncertainty, that maximize the actual volumetric flow rate and the standard volumetric flow rate, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference Flowrate (slpm)** & **Flowmeter Reading (slpm)** & **k** & **Uncertainty (\(\pm\)slpm)** \\ \hline
5.953 & 5.7 & 2.01 & 0.65 \\
50.05 & 49.6 & 2.01 & 0.59 \\
95.975 & 96.5 & 2.04 & 0.6 \\
137.85 & 138.4 & 2.18 & 0.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Automated flowmeter calibration sheet at sea level pressure. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Min** & **Max** & **Unit** \\ \hline \(p\) & 11,597 & 102,000 & Pa \\ \(T\) & 263.15 & 313.15 & \({}^{\circ}\)K \\ \(\Delta p\) & 0 & 10 & inH2O \\
**Errors (Manufacturers)** & **Min** & **Max** & **Unit** \\ \(u_{T}\) & \(-0.8\) & 0.8 & \({}^{\circ}\)K \\ \(u_{p}\) & \(-250\) & 250 & Pa \\ \(u_{\Delta p}\) (\(\Delta p<3.94\) inH2O) & \(-0.18\) & 0.18 & inH2O \\ \(u_{\Delta p}\) (\(\Delta p>3.94\) inH2O) & \(-0.3\) & 0.3 & inH2O \\
**Errors (Calibrations)** & **Min** & **Max** & **Unit** \\ \(u_{p}\) & \(-16\) & 16 & Pa \\ \(u_{\Delta p}\) & \(-0.04\) & 0.04 & inH2O \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Input variables and respective errors. Based on the calibrations uncertainty, Tables 10 and 11 express the results of simulation 2 that maximize the actual volumetric flow rate and the standard volumetric flow rate, respectively. The results of the MEMS calibration and the maximum errors that their manufactures claim to occur are presented in Table 12. Note that this MEMS do not have factory calibration, so it is natural that their manufacturers supply data with higher values of measurement errors in order to guarantee their clients medium/long time satisfaction. The maximum output errors were obtained in simulations that used ten million iterations. However, by analyzing the trend of the variables over each simulation, it was verified that the maximum output errors were obtained when the input values and respective errors take the limit values of their range. So, for this case, the iteration number (i) was negligible. In Table 13 there are presented the results obtained by the two simulations and by the calibration for the uncertainty of actual and standard volumetric flowrate. As has been said before, this flowmeter had a particular accuracy requirement established by the technical documentation delivered by the test bench manufacturer (\(\pm 1\%\) full scale). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(i\)} & \(\Delta p\) & \(u_{\Delta p}\) & \(T\) & \(u_{T}\) & \(p\) & \(Q_{a}\) & \(u_{Q_{a}}\) \\  & **(inHZO)** & **(inHZO)** & **(K)** & **(K)** & **(Ipm)** & **(Ipm)** & **(\% fs)** \\ \hline
10 M & 9.34 & 0.035 & 264.79 & \(-\)0.799 & 100,410 & 12.57 & 178.95 & 1.016 \\ - & 10.00 & 0.040 & 263.15 & \(-\)0.800 & 102,000 & 16.00 & 184.84 & 1.107 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Uncertainty of microelectromechanical systems (MEMSs). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(i\)} & \(\Delta p\) & \(u_{\Delta p}\) & \(T\) & \(u_{T}\) & \(Q_{a}\) & \(u_{Q_{a}}\) \\  & **(inHZO)** & **(inHZO)** & **(K)** & **(K)** & **(Ipm)** & **(\% fs)** \\ \hline
10 M & 3.96 & \(-\)0.299 & 265.45 & 0.791 & 72.633 & 3.559 \\ - & 3.94 & \(-\)0.300 & 263.15 & 0.800 & 72.782 & 3.598 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Simulation 1: actual volumetric flow rate. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(i\)} & \(\Delta p\) & \(u_{\Delta p}\) & \(T\) & \(u_{T}\) & \(Q_{a}\) & \(u_{Q_{a}}\) \\  & **(inHZO)** & **(inHZO)** & **(K)** & **(K)** & **(Ipm)** & **(\% fs)** \\ \hline
10 M & 9.94 & 0.039 & 263.15 & \(-\)0.778 & 166.89 & 0.636 \\ - & 10.00 & 0.040 & 263.15 & \(-\)0.800 & 167.67 & 0.644 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Simulation 2: actual volumetric flow rate.