A feed stream at $87\backslash$deg C with composition $18$ wt$\%$ methanol and $82$ wt$\%$ water is seperated by continous distilation. The feed is saturated liquid. It is desired to fit a production rate of $100000$ ton$/$year $98$wt$\%$ pure methanol. The bottom product should not contain more than $1$ wt$\%$ methanol. Estimate the column diameter $($for base$)$ by using the given information below:

Reflux ratio $=2$

$$ Plate spacing$=0\mathrm{.}6$ m

$$

$$

Down comer area $=10\%$ of the total

Percentage flooding $=80\%$

At the bottom of Column:

T$=98\mathrm{.}9\backslash$deg C; Vapour density $=0\mathrm{.}7$ kg$/$m$3$; Liquid density $=976$ kg$/$m$3$; Surface tension $=20$ mN$/$m$.$