The following design parameters and data are provided:

$(\frac{x}{d_p}{)}_i=0\mathrm{.}000927$ micron

sphericity $=0\mathrm{.}60$

viscosity of air $=1\mathrm{.}78{10}^{-4}\frac{g}{cm-s}($air at $21C)$

viscosity of air $=4\mathrm{.}42{10}^{-4}\frac{g}{cm-s}($air at $816C)$

density of air $=0\mathrm{.}0012\frac{g}{c{m}^3}($air at $21C)$

density of air $=3\mathrm{.}25{10}^{-4}\frac{g}{c{m}^3}($air at $816C)$

density of solids $=2\mathrm{.}4\frac{g}{c{m}^3}$

voidage ${}_{mf}=0\mathrm{.}5$

bed height at minimum fluidization, $100cm$

reactor diameter $=0\mathrm{.}3048m$

Determine the following;

a$)$ Mean particle size of bed material, in $cm$

b$)$ Minimum fluidization velocity, $c\frac{m}{s}$

c$)$ Terminal velocity, $c\frac{m}{s}$

d$)$ Volumetric flow rate $(\frac{m^3}{hr})$ at operating temperature of $816C$

e$)$ Pressure drop through gasifier reactor in $cm$ of water