# Traceability of the Micro Scale Pipe Viscometer for Traceable Calibration of Dynamic Viscosity
## 3 Results and Discussion
### Single Measurement Point Analysis  
The linear fit with forced zero intercept over a range of pressure drops as a function of flow rate is one method used to obtain the quotient \(\Delta\)P/Q. The reason for forcing the intercept to zero is to compare the result from the linear fit over the measured flow rate range in the laminar regime to the results obtained using single measurement point analysis. This means that the quotient \(\Delta\)P/Q is calculated from a single measurement. The results of the single measurement point analysis of the measurement with the pipe viscometer including the soda glass microtube and the reference liquid \"2 BW\" are listed in Table 9. The single measurement point analysis results are very consistent with the result from the linear fit analysis. Although the result for the lowest pressure drop of 0.56 bar shows a larger deviation, it is still consistent within the measurement uncertainty with the result of the linear fit over the full range.  
Figure 7: Pressure drop as a function of flowrate flow through the glassmicro tube of reference liquid 2 AW (blue open circles), reference liquid 2 BW (violet solid squares) and reference liquid 5 AW (dark blue open squares) with the corresponding linear fit with forced zero intercept.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method/Pressure Drop (bar)** & **n @ 21.3 °C (mPa-s)** & **Deviation to Reference (\%)** \\ \hline Linear fit/full range & & \\ \(\Delta\)P = 0.56–6.70 & 2.201 \(\pm\) 0.020 & 0.42 \(\pm\) 0.90 \\ Single point/\(\Delta\)P = 6.70 & 2.203 \(\pm\) 0.020 & 0.54 \(\pm\) 0.90 \\ Single point/\(\Delta\)P = 6.15 & 2.200 \(\pm\) 0.020 & 0.39 \(\pm\) 0.90 \\ Single point/\(\Delta\)P = 5.58 & 2.199 \(\pm\) 0.020 & 0.33 \(\pm\) 0.90 \\ Single point/\(\Delta\)P = 5.02 & 2.200 \(\pm\) 0.020 & 0.41 \(\pm\) 0.90 \\ Single point/\(\Delta\)P = 4.46 & 2.202 \(\pm\) 0.020 & 0.47 \(\pm\) 0.90 \\ Single point/\(\Delta\)P = 3.91 & 2.202 \(\pm\) 0.020 & 0.48 \(\pm\) 0.90 \\ Single point/\(\Delta\)P = 3.35 & 2.193 \(\pm\) 0.020 & 0.08 \(\pm\) 0.90 \\ Single point/\(\Delta\)P = 2.78 & 2.195 \(\pm\) 0.020 & 0.16 \(\pm\) 0.90 \\ Single point/\(\Delta\)P = 1.67 & 2.197 \(\pm\) 0.020 & 0.27 \(\pm\) 0.90 \\ Single point/\(\Delta\)P = 1.11 & 2.195 \(\pm\) 0.020 & 0.19 \(\pm\) 0.90 \\ Single point/\(\Delta\)P = 0.56 & 2.219 \(\pm\) 0.020 & 1.27 \(\pm\) 0.90 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Dynamic viscosity \(\eta\) of the reference liquid “2 BW” determined using a pipe viscometer with the soda glass microtube.  
Note that the pressure measurement downstream of the microtube is performed with a pressure sensor of maximum 10 bar and measures pressures of the order of tens of mbar with an uncertainty of 10 mbar. This might be the reason for the larger deviation at the lowest pressure drop. One option for improvement is the use of a pressure sensor downstream of the microtube with a lower maximum pressure at an order of 0.5 bar. Additionally, measurements at zero flow leading to zero pressure drop for the verification of the indication of the pressure sensors can be performed to investigate if there are systematic deviations due to short time drift.