Air is flowing through a packed bed containing a mixture of particles in the following percentages, sizes and shape factors:

$20\%,15mm,$ shape factor $0\mathrm{.}86$

$35\%,18mm,$ shape factor $0\mathrm{.}57$

$15\%,25mm,$ shape factor $0\mathrm{.}76$

$30\%,10mm,$ shape factor $0\mathrm{.}92$

The particles have a constant density of $1350k\frac{g}{m^3}.$ The bulk density of the overall packed bed is $900k\frac{g}{m^3}.$ The bed has a diameter of $0\mathrm{.}6$ m and a height of $2\mathrm{.}5$ m $.$

a$.$ Calculate the mean hydraulic radius $(r_H)$ of the particle mixture for the air flow.

$(8$ marks$)$

b$.$ The air enters the bed at $25C$ and $202\mathrm{.}65$ kPa abs at the rate of $0\mathrm{.}4k\frac{g}{s}.$ The average molecular weight of air is $28\mathrm{.}97.$ Air viscosity at the flow conditions is $1\mathrm{.}845{10}^{-5}Pa.$s$.$ Calculate the pressure drop of the air in the packed bed. $($Hint: First, guess the outlet pressure, $P_2$ of the air flow. If your guess is far away from the resulted $P,$ repeat your calculations up to $2$ trials only.$)$

$(10$ marks$)$

c$.$ Now, the packed bed containing the mixture of these particles is fluidized using the airflow at $25C$ and $202\mathrm{.}65$ kPa abs$.$ The void fraction at the minimum fluidizing conditions is $0\mathrm{.}5.$ If the height of the fluidized bed is $3\mathrm{.}6$ m $,$ has the bed expanded? Explain your answer briefly.

$(3$ marks$)$

d$.$ Calculate the pressure drop at minimum fluidizing conditions. In your calculations, use the air density you obtained in question $($b$).$

$(3$ marks$)$

$1$

KKKR$2363$

e$.$ Calculate the minimum velocity for fluidization by first calculating the Reynolds number at minimum fluidization velocity using the simplified equation with:

${}_S{}_{mf}^3$~~$\frac{1}{14}$

$\frac{1-{}_{mf}}{{}_S^2}{}_{mf}^3$~~$11$