A gas absorption tower of diameter $2$ m contains ceramic Raschig

rings randomly packed to a height of $5$ m$.$ Air containing a small

proportion of sulphur dioxide passes upwards through the absorption

tower at a flow rate of $6$ m$3/$s$.$ The viscosity and density of the

gas may be taken as $1\mathrm{.}80$ x $10-5$ Pa$.$s and $1\mathrm{.}2$ kg$/$m$3$ respectively.

Details of the packing is given below:

Ceramic Raschig rings

Surface area per unit volume of packed bed is $190$ m$2/$m$3.$

Voidage of randomly packed bed $=0\mathrm{.}71$

$($a$)$ Calculate the diameter of a sphere with the same surface$-$volume

ratio as the Raschig rings.$($b$)$ Calculate the pressure drop across the packing in

the tower.$$