Question $1[25$ marks$]$

Cylindrical shaped blocks $($diameter $0\mathrm{.}01m$ and height $0\mathrm{.}02m,)$ of particles of $1400k\frac{g}{m}3$settle freely in a $5m$ diamete $10m$ height tank filled with fluid of density $998k\frac{g}{m}3$ and viscosity of $1\mathrm{.}05cP(1($:$cP=0\mathrm{.}001$Pas$\}.$ Determine the time it would take the particles to reach the bottom of the tank?

The following equations are provided:

$K=D_p[\frac{g({}_p-)}{{}^2}{]}^{\frac{1}{3}}$

$=\frac{\frac{6}{d_{sph}}}{(\frac{S_p}{V_p}{)}_{\text{p}\text{a}\text{r}\text{t}\text{i}\text{c}\text{l}\text{e}}}$

Hint $($equations you know by head or how to derive them$)$:

$V_{\text{p}\text{a}\text{r}\text{t}\text{i}\text{c}\text{l}\text{e}}=V_{sph}=\frac{d_{sph}^3}{6}$

$u_t=\frac{g{D}_p^2({}_p-{}_f)}{18}$

$u_t=1\mathrm{.}75\sqrt[\phantom{2}]{\frac{D_{p}g({}_p-{}_f)}{{}_f}}$