$30\mathrm{.}7.$ The following relation between $$ and $p$ for Superlight $CaC{O}_3$ has been de$-$

termined ${?}^{18}$ :

$=8\mathrm{.}8{10}^{10}[1+3\mathrm{.}36{10}^{-4}(p{)}^{0\mathrm{.}86}]$

where $p$ is in pounds force per square foot. This relation is followed over a pressure

range from $0$ to $1000I\frac{b_f}{i}n.{?}^2$ A slurry of this material giving $3\mathrm{.}0lb$ of cake solid per

cubic foot of filtrate is to be filtered at a constant pressure drop of $70l\frac{b_{}}{i}{n}^2$ and

a temperature of $70F.$ Experiments on this sludge and the filter cloth to be used

gave a value of $R_m=1\mathrm{.}2{10}^{10}f{t}^{-1}.$ A pressure filter of the tank type is to be used.

How many square feet of filter surface are needed to give $1400$ gal of filtrate in a

$1-$h filtration? The viscosity is that of water at $70F.$

$30\mathrm{.}8.$ The filter of Prob. $30\mathrm{.}7$ is washed at $70F$ and $70l\frac{b_f}{i}{n}^2$ with a volume of wash

water equal to one$-$third that of the filtrate. The washing rate is $85$ percent of the

theoretical value. How long should it take to wash the cake?