A sieve$-$tray distillation column is to be designed to depropanise a multi$-$component hydrocarbon mixture. The following conditions at the column$-$bottom are used in the design:

Temperature: $125C$

Operating Pressure: $2000$ kPa absolute

Vapour: Mass flow rate $=16k\frac{g}{s},$ Average density $=58k\frac{g}{m^3}$

Liquid: Mass flow rate $=17\mathrm{.}5k\frac{g}{s},$ Average density $=435k\frac{g}{m^3},$ Surface tension $=2\mathrm{.}84{10}^{-3}\frac{N}{m},$

The column operates under counter$-$current mode. The column will have $21$ cross$-$flow plates at a spacing of $0\mathrm{.}6$ m $.$ The downcomer occupies $15\%$ of the column crosssectional area. The total hole area is $10\%$ of the plate active area. The hole diameter is $6$ mm and the plate thickness is $3\mathrm{.}4$ mm $.$ The height of the overflow weir on the plate is $51$ mm $.$

a$)$ Determine the required column diameter for operation at $80\%$ of flooding.

b$)$ Plate pressure drop for the given operating conditions in Pascals

Clearly state any assumptions made.