Fractionating column design $(10$ points$)$

A continuous fractionating column is required to separate a mixture containing $0\mathrm{.}40$mol fraction

$n-$heptane $(MW=100)$ and $0\mathrm{.}60$mol fraction $n-$octane $(MW=114)$ into overhead products of $99$

mol$\%$ heptane and bottom products of $1$mol$\%$ heptane. The column is to operate at a pressure

$($at top$)$ of $101\mathrm{.}3k\frac{N}{m^2}$ with a pressure drop across the tower of $25$kPa. The feed is a saturated

mixture with $30\%$ vapor, and is supplied to the column at $0\mathrm{.}070$kmo$\frac{l}{s}.$ The reflux ratio $($L$/$D$)$ is

$2\mathrm{.}5$ and the fraction of the cross$-$sectional area available for vapor flow is $0\mathrm{.}88.$ If the vapor

velocity is $0\mathrm{.}8\frac{m}{s},$ determine the required diameter on stripping section based on the conditions

at the bottom of the tower, where you can use pure n$-$octane for the evaluation of vapor density.

Vapor pressure for n$-$octane

$ln{P}^{**}(kPa)=14\mathrm{.}2368-3304\mathrm{.}16/($T$($K$)-55\mathrm{.}2278)$

Gas constant $R=8314\frac{J}{k}$mol$K.$