Question Q2. A filter with an area of 1 m² operates at a constant pressure drop of 100 kPa to filter a mineral slurry. A test gives the following results with an incompressible cake: Volume of filtrate collected (litre) 1 10 50 100 200 Time (min) 0.01 0.11 0.75 2 6 If you run the above filtration test at a constant pressure drop of 50 kPa, predict the experimental outcomes: a) What time is required to collect 0.1 m² of filtrate? b) What are the filtration rates (volume flow rate of filtrate) at the start and end of the filtration, respectively? Comment on the change in the filtration rate as a function of time and briefly explain why. c) Immediately following the completion of the filtration, the resulting cake is washed using water. Estimate the time required to wash the cake with 0.1 m at a constant pressure drop of 25 kPa.

Sol Foom fundemental Flitection Equetion\frac{d t}{d v}=k v+cAP K=\frac{\mu P Q}{\triangle P A^{2}} \quad C=\frac{\mu \cdot R_{m}}{A D P}At Conslent \Delta p.\begin{array}{l}d t=k v d v+c d v \\t=\frac{k v^{2}}{2}+c v \\\frac{t}{v}=\frac{k v}{2}+c\end{array}Plot b / w \quad \frac{t}{v} vs v gues slope =\frac{k}{2} \& intercept =Con plotting y=1.6711 x+0.166 \quad \therefore \quad R^{2}=01.\begin{aligned}\frac{K}{2} & =1.6711 \quad C=0.166 \\K & =3.3422 \\\frac{\mu \alpha P}{\Delta P A^{2}} & =3.3422 \\\frac{\mu \alpha P}{A^{2}} & =33.4022 \quad \frac{M R m}{A}=16.6 .\end{aligned}(1) for \Delta p= soup.\frac{\mu \alpha P}{\Delta P A^{2}}=6.6844 \quad \frac{\mu R_{m}}{A \Delta P}=0.332 : t=\frac{6.6844}{2} v^{2}+0.332 Vfor V=0.1 \mathrm{~m}^{3}\begin{array}{l}t=0.03342+0.0332 \\t=0.06662 \mathrm{sec}=3.99 \mathrm{~min}\end{array}(2) At stete of Filtectiv V=0\begin{array}{l}\frac{d t}{d v}=K=\begin{array}{c}6.6844+0.332=0.332 \\(0)\end{array} q_{0}=\frac{d v}{d t}=\frac{1}{0.332}=\frac{1}{3.012}\end{array}At end. V=0.1 \mathrm{~m}^{3}\begin{array}{l}\text { At end } \\\frac{d t}{d v}=(6.6844) \times(0.1) \neq 0.332=1 . \\\frac{d v}{d t}=1 \mathrm{~m}^{3} / \mathrm{s}\end{array}Cleoly Rate Decreoscs wilh time Beceuse Rifaction Cove shesisbne invere as pilterto Procecds.(3)\begin{array}{l}=2 \cdot 5 / \mathrm{m}^{3} \\\end{array}Time t=\frac{V}{q}=\frac{0.1}{\frac{1}{2}}=0.2 \mathrm{sec} using given data and variables we can find the requied parameters for any doubts write in comments ...