Question $3(20$ marks$)$

a$)$ Air $(29k\frac{g}{k}$mol $)$ at about $20C$ and $1$atm with a viscosity of $1\mathrm{.}81{10}^{-5}Pa.s,$ passes upward through a fixed bed of $0\mathrm{.}8m$ long and $0\mathrm{.}1m$ diameter with a porosity of $0\mathrm{.}4.$ The bed is packed with small cubes $($each side is $6mm).$ At a superficial volumetric flow rate of $0\mathrm{.}0118\frac{m^3}{s},$ find the pressure drop across the bed. Assume at these conditions air behaves ideally and is incompressible.

b$)$ Was it reasonable to assume an incompressible case? Give your reasons.

$[14$ marks$]$

c$)$ How many particles make up the bed?

$[2$ marks$]$

$[4$ marks$]$

You are given the following equations:

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

$=\frac{V_{\text{p}\text{o}\text{r}\text{e}\text{s}}}{V_{\text{b}\text{e}\text{d}}}$

$\frac{P}{L}=\frac{150u_o(1-{)}^2}{{}^2{d}_{sph}^2{}^3}+\frac{1\mathrm{.}75u_0^2(1-)}{d_{sph}{}^3}$