# Experimental Investigation in Drag Coefficient of Cubes
## 2 Experimental Facility and Procedure
\begin{table}
\begin{tabular}{c c} \hline
**Ref.** & **Prediction Model** \\ \hline [PERSON] et al. [11] & \(C_{D}=\frac{24}{Re}\frac{d_{A}}{d_{n}}\bigg{[}1+\frac{0.15}{\sqrt{c}}\left( \frac{d_{A}}{d_{n}}Re\right)^{0.687}\bigg{]}+\frac{0.42\left(\frac{d_{A}}{d_{ n}}\right)^{2}}{\sqrt{c}\bigg{[}1+4.25\times 10^{4}\left(\frac{d_{A}}{d_{ n}}Re\right)^{-1.16}\bigg{]}}\), \\  & where \(c=\pi d_{A}/P_{\text{p}}\). \\ \hline [PERSON] and [PERSON] [12] & \(C_{D}=\frac{24}{Re}\bigg{[}1+e^{2.3288-6.45816+2.4486\phi^{2}}Re^{0.0964+0.5565 \phi}\bigg{]}+\frac{4.905-13.8944+18.4222\phi^{2}-10.2599\phi^{2}Re}{Re\in c \in c\in 1.4861+2.2584\phi-20.732\phi^{2}+15.8585\phi^{2}}\), \\ \hline [PERSON] [13] & \(C_{D}=0.84\bigg{[}\frac{33.78}{(1+4.5\phi^{0.38})^{0.73}}Re^{0.65\phi}+\left( \frac{Re}{Re+700+1000\phi}\right)^{0.28}\frac{1}{\left(\phi^{4}+2\phi^{0.2} \right)^{0.175}}\bigg{]}\), \\  & where \(\beta=\frac{C}{\sqrt{AB}}\). \\ \cline{2-3}  & \(\frac{C_{D}}{K_{2}}=\frac{24}{ReK_{1}K_{2}}\bigg{[}1+0.1118(ReK_{1}K_{2})^{0.65 67}\bigg{]}+\frac{0.4305}{1+\frac{305}{ReK_{1}K_{2}}}\), \\ \hline [PERSON] [14] & \(\frac{\text{where }K_{1}=\left(\frac{1}{3}+\frac{2}{3}\phi^{-0.5}\right)^{-1}-2.25 \frac{d_{A}}{D}\) for isometric particles. \\ \cline{2-3}  & \(K_{1}=\left(\frac{1}{3}\frac{d_{A}}{d_{n}}+\frac{2}{3}\phi^{-0.5}\right)^{-1}-2.25\frac{d_{A}}{D}\) for non-isometric particles. \\ \cline{2-3}  & \(K_{2}=10^{1.8148(-\log\phi_{1})0.5743}\). \\ \hline [PERSON] [15] & \(C_{D}=\frac{30}{Re}+\frac{67.289}{\phi^{2}.000\phi}\). \\ \hline [PERSON] et al. [16] & \(C_{D}=\frac{15.21+\frac{1082}{Re}-\frac{0.144}{Re}}{Re}+\frac{13.41-\frac{10 64}{Re}-\frac{0.04}{Re}}{\sqrt{Re}}-8.82+\frac{5.70}{\phi}+\frac{0.23}{\phi^{2}}\). \\ \hline [PERSON] and [PERSON] [17] & \(C_{D}=\frac{8}{Re}\frac{1}{\sqrt{\phi_{II}}}+\frac{16}{Re}\frac{1}{\sqrt{\phi} }+\frac{3}{\sqrt{Re}}\frac{1}{\phi^{1/4}}+0.42\times 10^{0.4(-\log\phi)^{0.2}} \frac{1}{\phi_{\perp}}\). \\ \hline [PERSON] and [PERSON] [3] & \(\frac{C_{D}}{K_{2}}=\frac{24}{Re}\frac{K_{1}}{K_{2}}\bigg{(}1+0.125\Big{(}Re \frac{K_{2}}{K_{1}}\Big{)}^{2/3}\bigg{)}+\frac{0.46}{1+5330\left(Re\frac{K_{2} }{K_{1}}\right)}\), \\ \cline{2-3}  & where \(K_{1}\) and \(K_{2}\) is the same as the Ganser [14]. \\ \hline \end{tabular}
\end{table} 
Table 1: Widely used prediction model for drag coefficient of non-spherical partials. image, there is an uncertain value of 1 pixel point at this height, which is converted to an actual height of 0.2 mm. Therefore, the error in speed caused by the image resolution is (0.2 mm/50 mm) \(\times\) 100% = 0.4%. The test results will only be deemed valid if the velocity difference in particles between the first half and the second half of the capture area remains less than 5% and \(v_{p}\) is the average of the two values. A LED light was used as backlight to illuminate the test section. The LED light was installed with a white semitransparent glass diffuser to achieve a uniform white background. Particles were released beneath the free liquid surface without any air bubble to attach and were as close to the center of the tube as possible. A wire basket was placed near the bottom of the tube to retrieve the particles periodically. Since the temperature has a strong function of viscosity, four sets of twelve thermal resistances were arranged vertically on each side of the tank to monitor the temperature of the fluid during the experiment. Moreover, another moveable thermal resistance was used to record the room temperature and that of the center of the fluid. The temperature gradient over the tube will affect the results. To avoid errors arising due to this reason, a fan was blowing in the direction of the column to ensure the uniformity of the air temperature. Every run of the experiment was carried out within two hours to eliminate the effect of room temperature fluctuation. Water-glycerine mixtures of various concentrations were used as test liquids to cover a wide range of particle Reynolds numbers.