# Traceability of the Micro Scale Pipe Viscometer for Traceable Calibration of Dynamic Viscosity
## 3 Results and Discussion
### Validation of the Pipe Viscometer with Reference Liquids  
The pipe viscometer was then validated by measuring the dynamic viscosity of reference liquids. These reference liquids have certificates for the density and dynamic viscosity as a function of temperature and are traceable to SI-units [22]. Three reference liquids with dynamic viscosities in the range from 1.5 mPa\(\cdot\)s to 4.0 mPa\(\cdot\)s were measured at the liquid temperature of 21.3 \({}^{\circ}\)C and their dynamic viscosities and densities are listed in Table 7. The certificates of the reference liquids contain the reference values at temperatures 20 \({}^{\circ}\)C, 23 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, 30 \({}^{\circ}\)C and 40 \({}^{\circ}\)C. A linear fit of the first order was applied to the data of the density and a linear fit of the second order was applied to the date of the dynamic viscosity to obtain the values at a measurement temperature of 21.3 \({}^{\circ}\)C, which corresponds to the liquid temperature in the tubing being measured using several temperature sensors. The three reference liquids \"2 AW\", \"2 BW\" and \"5 AW\" were calibrated using a pipe viscometer with the three microtubes in Table 4 and the results are listed in Table 8. The measurement data with the pipe viscometer including the soda glass microtube are shown in Figure 7, where the pressure drop is shown as a function of the flow rate. The data were fitted with a linear fit with forced zero intercept to obtain the slope \(\Delta\)P/Q. The dynamic viscosity was then calculated according to Equation (1) by taking into account the slope of the fit \(\Delta\)P/Q, the length and the inner diameter of the microtube. The calibration results are consistent with the reference values (Table 7) within the expanded uncertainty of this pipe viscometer, 0.90%. The calibration results of the three reference liquids lead to a deviation with respect to the reference values between +0.42% and +0.43%, which seems to be a systematic deviation, as the deviation is nearly the same for all three reference liquids. However, the deviations are smaller than the stated measurement uncertainty of 0.90%. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Reference Liquid Name** & **Dynamic Viscosity (mPa\(\cdot\)s)** & **Density (kg/m\({}^{3}\))** \\ \hline
2 AW & 1.5319 \(\pm\) 0.0031 & 751.2 \(\pm\) 0.1 \\
2 BW & 2.1913 \(\pm\) 0.0044 & 764.7 \(\pm\) 0.1 \\
5 AW & 4.0393 \(\pm\) 0.0081 & 785.3 \(\pm\) 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Reference liquids [22] with traceable density and dynamic viscosity at a temperature of 21.3 \({}^{\circ}\)C with the stated expanded (k = 2) uncertainty of 0.20% for the dynamic viscosity and 0.1 kg/m\({}^{3}\) for the density. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & & **2 AW** & **2 BW** & **5 AW** \\ \hline \multirow{4}{*}{Soda glass} & Dynamic viscosity & \multirow{2}{*}{1.5384} & \multirow{2}{*}{2.2005} & \multirow{2}{*}{4.0563} \\  & (mPa\(\cdot\)s) & & & \\  & Deviation incl. & & & \\  & uncertainty (\%) & & & \\ Stainless steel & Dynamic viscosity & \multirow{2}{*}{1.5090} & \multirow{2}{*}{2.1517} & \multirow{2}{*}{3.9797} \\  & (mPa\(\cdot\)s) & & & \\  & Deviation incl. & & & \\  & uncertainty (\%) & & & \\  & Dynamic viscosity & \multirow{2}{*}{1.5141} & \multirow{2}{*}{2.1671} & \multirow{2}{*}{3.9928} \\  & (mPa\(\cdot\)s) & & & \\  & Deviation incl. & & & \\  & uncertainty (\%) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The determination of the dynamic viscosities of reference liquids 2 AW, 2 BW, 5 AW [22] by means of a pipe viscometer in the laminar regime. The uncertainty (k = 2) of the pipe viscometer is 0.90%. The pipe viscometer with the stainless steel micro tube and the PEEK beige micro tube show larger deviations for all three reference liquids and are not consistent within the measurement uncertainties with the reference values.