QUESTION SET $1(2$questions$)$ please answer carefully all questions with detailed solution:

A suspension contains $30wt.\%$ of dispersed phase in water at $30C.$ The dispersed phase is particles with an average diameter of $300m$ and a specific gravity of $1\mathrm{.}3.$

$1.$ Filtration $(2$ points$)$

A plate and frame press filter is used to filter the above suspension at constant pressure. Filtration equation constants from the experiment which are $C=0\mathrm{.}14\frac{m^3}{m^2}$ and $K=0\mathrm{.}03\frac{m^2}{h}.$ The filter frame area is $0\mathrm{.}5m0\mathrm{.}5m.$ The number of frames or plates is $40.$Determine the product capacity of filtrate water in unit of $\frac{m^3}{h}.$

$2.$ Fluidization $(2$ points$)$

A fluidized bed equipment is used to dry the dispersed phase of the above suspension by a hot air stream at $100C$ and the atmospheric pressure. The initial porosity of the dispersed phase is $0\mathrm{.}4.$ Calculate the velocity of the hot air stream to bring the dispersed phase into the fluidized state in unit of $\frac{m}{s}.$