Question $2$

$($Show every steps and assumpotions made with every calcualtions done for all questions. P$.$s from the front cover from the question paper$)$

a$)$ Butanol flows at $12\mathrm{.}9ml{s}^{-1}$ as a film down the inside a vertical tube of

diameter $26\mathrm{.}7mm$ and length $117cm,$ entering the tube at $325\mathrm{.}5K.$

Butanol has a molecular weight of $74$ and a liquid density of

$810kg{m}^{-3},$ and $0\mathrm{.}115ml$ of butanol evaporates per second into $1\mathrm{.}67g$

$s^{-1}$ of a countercurrent air flow, with a molecular weight of $29$ and a

density which may be assumed to be $1\mathrm{.}2kg{m}^{-3}.$ The butanol leaves

the tube at $320\mathrm{.}75K$ due to evaporative cooling and the air

temperature may be assumed the same as the butanol at the same

vertical position. The pressure in the tube is $1\mathrm{.}08$atm and is assumed

constant. The vapour diffusivity is $0\mathrm{.}09c{m}^2{s}^{-1}$ and the Schmidt number

is $1\mathrm{.}9.$ Because of the temperature difference, the vapour pressure of

butanol is $0\mathrm{.}05$atm at the inlet and $0\mathrm{.}0378$atm at the exit. The

universal gas constant is $8\mathrm{.}314Jmo{l}^{-1}{K}^{-1}.$

$($i$)$ Calculate the molar flux of butanol in the air leaving at the top

of the tube.

$($ii$)$ For the situation described above, calculate the Reynolds

number of the air$-$vapour flow, the mass transfer driving forces

at inlet and exit, the mass transfer coefficient $,k_c,$ and the

Sherwood number.

$($iii$)$ Recalling that:

for laminar flow $f=\frac{16}{R}e$

for transitional flow $f=\frac{0\mathrm{.}0791}{R}{e}^{0\mathrm{.}25}$

for turbulent flow $f=\frac{0\mathrm{.}046}{R}{e}^{0\mathrm{.}2}$;

calculate the friction factor for the flow in the tube and use the

mass transfer data above to assess whether the analogy

between mass and momentum transfer appears accurate.

Explain your reasoning.