Question marks$)$

a$.$ Starting with the Carmen$-$Kozeny equation:

$u_o=\frac{1}{A}\frac{dV}{dt}=\frac{1}{K^{\text{'}\text{'}}}\frac{e^3}{(1-e{)}^2}\frac{-P}{S^{2}l}$

Equation $3$

derive the basic filtration equation:

$\frac{dV}{dt}=\frac{A^2(-P)}{rv(V+\frac{LA}{v})}$

Equation $4$

Explain why the Carmen Kozeny equation is an appropriate starting point and what assumptions

are made by using it$.$ Define all the symbols used.

b$.$ You need to specify filtration equipment for the de$-$watering of a slurry. You have been requested

to do some test work in the laboratory to characterise its suspension and cake characteristics first.

The equipment that you have available runs as a dead$-$end filter $($i$.$e$.$ the cake builds up through

the process$)$ with a constant pressure applied across it$.$ The filtration area has a diameter of $0\mathrm{.}5m.$

You find it operates well when you apply a pressure difference of $65$kPa across it$.$

The solids density is $1400kg*m^{-3}$ and the density of the liquid phase suspending it is $1050kg*m^{-3}.$

The viscosity was measured as $4$mPa$*s*m^{-2}.$ The suspension has a solids concentration of $320g*I^{-1}.$

Your colleague, who has done similar tests previously, suggested that the voidage of the cake is

$0\mathrm{.}42$ and the resistance of the filter medium may equate to $1\mathrm{.}5mm$ of cake thickness.

Table $1$: You collect the following data:

i$.$ Determine the volume of cake formed per volume of filtrate, $v.$

ii$.$ Determine the specific resistance, $r.$

iii. How would you confirm that the voidage you are using is an appropriate value?

iv$.$ Do you have confidence in the L value given? Justify your answer.

v$.$ When designing your large scale filtration equipment, the cake depth used is an

important consideration. Discuss the impact of cake depth on the size and operating

variables.