Constant Pressure Drop Batch Plate and Frame Filtration

Problem $24\mathrm{.}2-1.$

a$)$

Constant$-$Pressure Filtration and Filtration Constants. Data for the filtration of

$CaC{O}_3$ slurry in water at $298\mathrm{.}2K(25C)$ are reported as follows $($R$1,$ R$2,$ M$1)$ at a

constant pressure $(-p)$ of $46\mathrm{.}2\frac{kN}{m^2}(6\mathrm{.}70a).$ The area of the plate$-$and$-$frame

press was $0\mathrm{.}0439m^2(0\mathrm{.}473f{t}^2)$ and the slurry concentration was $23\mathrm{.}47\frac{kg\text{s}\text{o}\text{l}\text{i}\text{d}}{m^3}$

filtrate. Calculate the constants $$ and $R_m.$ Data are given as $t=$ time in $s$ and

$V=$ volume of filtrate collected in $m^3.$

Ans. $,=1\mathrm{.}106{10}^{11}\frac{m}{k}g(1\mathrm{.}65{10}^{11}f\frac{t}{l}{b}_m)$

$,$

b$)$ For an increase in filter area to $10m^2$ and increase in constant pressure drop $(-p)$ to $200$

$\frac{kN}{m^2},$ determine the new values of $K_p$ and $B$ and then calculate the filtration time to collect $3m^3$

of filtrate?

c$)$ Determine the wash time using $10\%$ of the filtrate volume from part b$)?$