## 4 Analysis of Results
### Factors Affecting the Viscosity of the Sunflower Oil
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sphere**} & \multirow{2}{*}{
\begin{tabular}{c} **Iron** \\ **Fillings** \\ **(g/mL)** \\ \end{tabular} } & \multirow{2}{*}{**B (T)**} & \multicolumn{6}{c}{\(\Delta\)**t (s)**} & \multicolumn{6}{c}{\(\mathbf{T_{amb}}\) (\({}^{\circ}\)C)} & \multicolumn{6}{c}{**RH (\%)**} \\ \cline{3-14}  & & & & & & & & & & & & & & & & \\ \cline{2-14}  & & 0 & 0.54 & 0.47 & 0.50 & 0.02 & 17.32 & 0.12 & \(-\)0.251 & 0.910 & 24.2 & 0 & - & - \\ \cline{2-14}
2 & 1.28 & 0 & 0.51 & 0.46 & 0.49 & 0.02 & 14.97 & 0.09 & 0.186 & 0.606 & 24.5 & 0.03 & \(-\)0.559 & 0.093 \\ \cline{2-14}  & 1.28 & 0.015 & 0.54 & 0.48 & 0.51 & 0.02 & 14.98 & 0.18 & 0.181 & 0.454 & 24.3 & 0 & - & - \\ \hline \multirow{3}{*}{3} & 0 & 0 & 0.40 & 0.36 & 0.37 & 0.02 & 17.4 & 0 & - & - & 24.2 & 0 & - & - \\ \cline{2-14}  & 1.28 & 0 & 0.40 & 0.36 & 0.38 & 0.02 & 15.4 & 0.16 & \(-\)0.065 & 0.868 & 24.5 & 0.03 & \(-\)0.490 & 0.181 \\ \cline{2-14}  & 1.28 & 0.015 & 0.44 & 0.37 & 0.40 & 0.02 & 17.2 & 0.05 & \(-\)0.434 & 0.211 & 24.5 & 0.03 & \(-\)0.023 & 0.949 \\ \hline \multirow{3}{*}{4} & 1.28 & 0 & 5.80 & 5.41 & 5.59 & 0.16 & 11.63 & 0.05 & 0.308 & 0.386 & 25.0 & 0 & - & - \\ \cline{2-14}  & 1.28 & 0.015 & 6.02 & 5.41 & 5.62 & 0.16 & 12.3 & 0 & - & - & 24.9 & 0 & - & - \\ \cline{1-1} \cline{2-14}  & 1.28 & 0.030 & 6.06 & 5.37 & 5.61 & 0.21 & 13.2 & 0.10 & \(-\)0.067 & 0.853 & 24.8 & 0.05 & 0.139 & 0.701 \\ \cline{1-1} \cline{2-14}  & 2.56 & 0.030 & 5.90 & 5.04 & 5.46 & 0.3 & 13.8 & 0.05 & 0.492 & 0.149 & 24.7 & 0 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistics of the fall of Spheres 2, 3, and 4 through the tube with sunflower oil. concentration of iron filings, and the magnetic field intensity. The results of this analysis are presented in Table 5. Considering a 95% confidence level, the effects of the sphere and the concentration of iron filings were significant, while the magnetic field intensity was far from having a significant effect on the motion of the spheres. The tracked series of the fall of Spheres 2 and 3 were fitted under all hypotheses to Equation (10) using least squares. The adjustment of the curves with an active magnetic field was performed only on the tracked points in the area of the coils. From the adjustment, the viscosity, the correction factor \(\zeta\) and the terminal velocity \(v_{t}\) were deduced. The variability of the measurements can be obtained through the root mean square error (RMSE) of a fitted curve to the displacement vs. time plot. The overall RMSE in the fitted curves was 0.127 cm. Figure 10 shows one of the adjusted series of the fall of Sphere 3. The results are shown in Table 6.  
A \(t\)-test was performed to compare the variations in dynamic viscosity and the correction factor across trials for each sphere. In the absence of an active magnetic field, both the variations in dynamic viscosity and the correction factor across trials for each sphere were not significant at the 95% confidence level. This indicates that the addition of iron filings had no substantial effect on either parameter. The measured dynamic viscosity values align with those reported in the literature (Figure 7). However, the correction factors obtained in this study are notably higher than those inferred from Figure 2, suggesting that the effective viscosity may depend not only on the sphere-to-tube diameter ratio but also on their absolute diameters. Figure 10: Adjusted series of the fall of Sphere 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **F Statistic** & \(p\)**-Value** \\ \hline Intersection & 25,391.036 & \textless{}0.001 \\ Sphere & 9466.206 & \textless{}0.001 \\ Iron filings & 3.318 & 0.041 \\ Magnetic field & 0.261 & 0.771 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the multifactorial ANOVA test. A \(t\)-test was performed to compare the variations in the terminal velocity and the dynamic viscosity across trials for Sphere 4.