Question $3$

A Nevtonian fiquid in uniform laminar film flov, on the internal surface of

Iong vertical tube is contacted vith a gas in upv vara counterflow:

$($i$)$ Shov$/$ that the velocity profile in the film can be described by:

$u_x=[\frac{p_{\text{s}\text{u}\text{r}f}}{L}-\frac{g}{}][\frac{y^2}{2}-y]+\frac{{}_{\text{s}\text{u}\text{r}\text{f}}}{}y$

Where $x$ is the direction of motion, $p_{\text{s}\text{u}\text{r}}$ is the pressure at the surface of

the liquid film, $L$ is the length of the film, ${}_{\text{s}\text{u}\text{r}\text{f}}$ the magnitude of the

interfacial shear stress at the film surface and $$ the film thickness.

A vertical gas$-$liquid contactor is to accommodate a fixed fiquid

feedrate of $10k\frac{g}{h}r.$ The liquid, which flow$/$s in a uniform thin film dov$/$n

the internal surface of a tube, $25mm$ in internal diameter is contacted

with a gas in upvard countercurrent flov$/$

$$ Calculate the expected film thickness in the absence of any

gas flow.

$($ii$)$ Show that reversed flow in the film just commences at a gas

mass flovitate of $0\mathrm{.}015k\frac{g}{s}$ approximately.

You may assume that a constant friction factor of $0\mathrm{.}006$ apples to the

gas$-$iquid interface.

DATA:

Liquic Properties:

Density $p_L$

$,930k\frac{g}{m^3}$

Viscosity $({}_L)$

$,0\mathrm{.}005N\frac{s}{m^2}$

Gas Properties:

Density $({}_g)$

$,1\mathrm{.}2k\frac{g}{m^3}$