A case study:

Having missed your third year practical session, you decide to go see Alvira in the experiential lab to

see if you can be rescheduled for another day. As you wait for her, you find what looks like a

sedimentation tank containing a sediment of mixed powders, $x$ and $Y,$ in water. The powder has

sedimented, and as you take a closer look you observe that it is a mixture of $2$ metals. One brown$-$

orange metal mainly at the lower section of the tank, a greyish metal mostly seen towards the top of

the tank and what seems like a mixture of the two in between. You decide to put the concepts you

learned in block $1$ to the test, particularly the theory you learned for contacting of solid$-$fluid systems.

As luck would have it$,$ there is an empty packed bed tube, an elutriation tank and a stirred tank reactor.

As you inspect the sedimentation tank, you see a label on the side with the following information:

Spherical powder particles with.

$2\mathrm{.}1kg$ of powder $x$ with density $1538k\frac{g}{m^3}$

$3\mathrm{.}9kg$ of powder $Y$ with density $8960k\frac{g}{m^3}$

Powder $x$ and $Y$ particle size distributions are the same and as given in Table $1($ranging from

$10$ to $120m$ :

Table $1$:

Question $1(20$ marks$)$

Because you are a diligent chemical engineer in training, you remember that it is always easier to work

with single phase solids to simplify the tests you are about to carry out. So$,$ you decide to use the

elutriation tank to separate what you can of solid $x$ from solid $Y$ for different experiments. Assuming

free settling conditions, answer the following:

a$)$ What velocities would you apply in the elutriation tank to separate out the maximum amount

of purely powder $x$ from the mixture, and how much of this powder would you have collected

under these conditions.