QUESTION SET $1(5$ 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 $1\mathrm{.}3.$

$1.$ Pumping $(2$ points$)$

A centrifugal pump is used to transport the above suspension from tank A to tank B$.$

Both tanks are open to the atmosphere and have a liquid level difference of $5m.$ The suction pipe diameter is equal to the discharge pipe diameter $50mm.$ Total suction and discharge length is $20m.$ The friction coefficient is $0\mathrm{.}06$ and total local coefficient is $6.$ The pumping time to full fill tank B with a volume of $20m^3$ that is $1$ hour. Pump efficiency is $70\%.$

Calculate the required power of the pump in unit of hp$.$

$2.$ Agitation $(2$ points$)$

A paddle impeller with a diameter of $0\mathrm{.}5m$ is used to agitate the above suspension at

$200rpm.C$ and $m$ factors are $6\mathrm{.}8$ and $0\mathrm{.}2,$ respectively. Determine the required power of the agitator in unit of $hp.$

$3.$ Settling $(2$ points$)$

A gravity settling tank with a height of $5m$ is designed to settle the above suspension.

The velocity of the suspension flow into the tank is $0\mathrm{.}13\frac{m}{s}.$ Calculate the length of the

settling tank in unit of $m.$

$4.$ 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 $\frac{m^3}{h}.$

$5.$ 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 $\frac{m}{s}.$