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At the end of a filtration cycle, a total volume of

`4.50m^(3)`

is collected in a total time of

`272.6s`

. The cake is to be washed through washing in the plate-and-frame press using a volume of wash water equal to

`10%`

of the filtrate volume. From the filtration data intercept

`B=16.50(s)/(m^(3))`

and

`K_(p)=38.82(s)/(m^(6))`

Calculate 6.1 The time of washing 6.2 The total filter cycle time if cleaning the filter takes 20 minutes. For the filter the filtration rate is

`((dV)/(dt))_(f)=(1)/(4)(1)/((K_(p))(V_(f))+B)`

(in a plate and frame press, the flow of wash water is one quarter of the filtration rate.) 6.3 Aqueous slurry of

`CaCO_(3)`

is to be filtered in a rotary drum filter with

`25%`

submergence of area is covered by slurry). The available pressure drop is

`75kPa`

and the cycle time is 6 minutes. The slurry contains

`240kg`

solids per cubic meters of slurry and density of solids is

`2850k(g)/(m^(3))`

. The filter cake contains

`45%`

moisture on wet basis and the specific cake resistance is

`1.23\times 10^(11)(m)/(k)g`

. Calculate the filter area required to fijter 40 litres/minute. The resistance of the filter medium maybe neglected. Take

`\mu _(slury )=0.001k(g)/(m),s`

The expression for the area in terms of filtrate flow rate

`(V_(f))/(\theta _(c))`

is given below

`A=((V_(f))/(\theta _(c)))*\sqrt(((s\rho \mu \alpha _(ave)\theta _(c))/(2Pk_(f)(1-ms))))`

Where

`\theta _(c)`

is the cycie time and

`k_(f)`

is the fractional submergence