Question $4$

$[1)$ Demonstrate your understanding of discretisation as part of the

finite volume method. For your ansver briefly address the

folloving points:

a$.$ Why is discretisation carried out as part of finite volume analysis

b$.$ Hov is aiscretisation implemented?

c$.$ What are the potential negative effects of discretisation?

a$.$ Hov are discretised equations solved?

A chemical reaction is to be aerated at a rate of $1k\frac{g}{s}$ in a gas$-$liquid

contactor $[$oubble column$].$ It may be assumed that the average rate

of aeration from the gas to the liquid phase is proportional to the

interfacial surface area according to the folloving equation:

$q_{\text{c}\text{e}\text{r}\text{r}\text{a}\text{t}\text{i}\text{o}\text{n}}=0\mathrm{.}0072(a)$

Where $q_{\text{a}\text{e}\text{r}\text{a}\text{t}\text{i}\text{o}\text{n}\text{t}}$ is the aeration rate in the column $(k\frac{g}{s}),$ and $a$ is the

interfacial area betv$/$een the gos and liquid phases per unit mixture

volume $\frac{m^2}{m^3}.$

$[$i$)$ Determine the air flowmate required to the column to achieve the

required aeration rate of $1k\frac{g}{5}$

$($ii$)$ Evaluate the impact upon the aeration rate if the gas flovurate is

coubled

$[$iv$]$ Explain your physical interpretation of the result you obtained in

part $[$ili$]$

Data:

Column Details

Head pressure

Diometer

Fluid Height

Liouid Properties:

Density

Viscosity

Surface Tension

Air Properties:

Density $($at $p_{\text{a}\text{t}\text{m}})$

Viscosity

$101325($absolute$)$

$0\mathrm{.}8$

$-,1\mathrm{.}2$

$,1180k\frac{g}{m^3}$

$,1\mathrm{.}3{10}^{-3}N\frac{s}{m^2}$

$,0\mathrm{.}06\frac{N}{m}$

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

$,1\mathrm{.}9{10}^{-5}N\frac{5}{m^2}$