# Effects of Velocity Profiles on Measuring Accuracy of Transit-Time Ultrasonic Flowmeter
## 4 Results
### Uncertainty Analysis  
The flowrate obtained by the weighing method is regarded as the standard to evaluate the measurement results of the ultrasonic flowmeter. Therefore, the experiment uncertainty of weighting method is analyzed and results for laminar and turbulent flow are shown in Tables 4 and 5, respectively. Collected time is controlled by an electronic timer, the uncertainty of time is 10 ms. Collected mass is weighed by an electronic scale, the uncertainty of mass is 1 g. The standard relative uncertainty of time is from 0.017% to 0.200%; from 0.001% to 0.233% of mass. The combined uncertainty is from 0.019% to 0.233%. The expanded uncertainty has been reported at \(k=2\), which from 0.039% to 0.466%.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Collected Mass**} & \multicolumn{2}{c}{**Collected Time**} & \multicolumn{2}{c}{**Combined**} & \multicolumn{2}{c}{**Expanded**} \\ \cline{2-9}  & **Estimate (M)(kg)** & **Uncertainty (\(\mu_{\text{M}}\))(\%)** & **Estimate (\(\mu_{\text{M}}\))(\%)** & **Uncertainty (\(\mu_{\text{M}}\))(\%)** & **Uncertainty (U)(\%)** \\ \hline
1 & 0.43 & 0.233 & 60 & 0.017 & 0.233 & 0.466 \\
2 & 0.524 & 0.191 & 60 & 0.017 & 0.192 & 0.383 \\
3 & 0.721 & 0.139 & 60 & 0.017 & 0.140 & 0.279 \\
4 & 0.965 & 0.104 & 50 & 0.020 & 0.106 & 0.211 \\
5 & 1.073 & 0.093 & 50 & 0.020 & 0.095 & 0.191 \\
6 & 1.005 & 0.100 & 40 & 0.025 & 0.103 & 0.205 \\
7 & 1.019 & 0.098 & 40 & 0.025 & 0.101 & 0.203 \\
8 & 1.219 & 0.082 & 40 & 0.025 & 0.086 & 0.172 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Experiment uncertainty for laminar flow.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Ultraconic Flowmeter**} & \multicolumn{2}{c}{**Weighing Method**} & \multicolumn{2}{c}{**Flowrate**} \\ \cline{2-9}  & **\(\Delta T\times 10^{9}\)** & **Flowrate (\(\mu_{\text{M}}\))(\%)** & **Time** & **Mass** (kg)** & **Flowrate (\(\mu_{\text{M}}\))(\%)** & **Velocity (m/s)** & **Re** & **Ratio \(\beta\)** & \(k_{\text{r}}\) & \(\delta_{2}\) (\%) \\ \cline{2-9}  & **(s)** & **(m’/s)** & **(s)** & **(kg)** & **(m’/s)** & **(m/s)** & **Re** & **\(n\)** & **= Q\({}_{2}\):Q\({}_{1}\)** & & \\ \hline
15 & 629.177 & 16.131 & 5 & 76.218 & 15.244 & 7.525 & 382256 & 8.5 & 0.945 & 0.944 & 0.106 \\
16 & 662.113 & 16.976 & 5 & 80.136 & 16.027 & 7.912 & 401906 & 8.5 & 0.944 & 0.944 & 0.000 \\
17 & 694.919 & 17.817 & 5 & 84.163 & 16.833 & 8.309 & 422102 & 8.6 & 0.945 & 0.945 & 0.000 \\ \hline \hline \end{tabular}
\end{table}
Table 3: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Collected Mass**} & \multicolumn{2}{c}{**Collected Time**} & \multicolumn{2}{c}{**Combined**} & \multicolumn{2}{c}{**Expanded**} \\ \cline{2-9}  & **Estimate (M)(kg)** & **Uncertainty (\(\mu_{\text{M}}\))(\%)** & **Estimate (\(\mu_{\text{M}}\))(\%)** & **Uncertainty (\(\mu_{\text{M}}\))(\%)** & **Uncertainty (U)(\%)** \\ \hline  
\hline \hline \end{tabular}
\end{table}
Table 5: Experiment uncertainty for turbulent flow.