Question $2[25$ marks$]$

A fluidized $1\mathrm{.}5m3$ bed column containing $2\mathrm{.}3{10}^8$ spherical particles of $2mm$ diameter is operated. The solids density is $3100k\frac{g}{m^3}$ and the gas enters the bed at atmospheric pressure, its viscosity is $0\mathrm{.}001N\frac{s}{m^2},$ its average temperature $600K$ and its composition is given in Table $1$ below

Table $1$: Gas composition of inlet and outlet gas

$\backslash$table$[[$Component$,$mol$\%],[$Inlet$,$Outlet,MM$],[$A$,15,5,27],[$B$,50,60,42],[$C$,35,35,61]]$

At minimum fluidization velocity the height of the bed is measured and found to be $0\mathrm{.}5m.$ Calculate the minimum fluidization velocity; if at insipient fluidization the apparent weight and drag force resulting from the pressure drop are related by:

$P=g(1-)({}_p-)L$

You are also given the following equations:

$\frac{P}{L}=\frac{150u(1-{)}^2}{d_{\text{e}\text{f}\text{f}}^2{}^3}+\frac{1\mathrm{.}75u^2(1-)}{d_{\text{e}\text{f}\text{f}}{}^3}$