Your goal is to use the continous casting method to create a metal matrix composite. You have chosen

graphite as the reinforcement material and Al$-$alloy as your metal matrix. To the variations in densities

between the reinforcing material and matrix, a coating application needed on graphite's surface. The

densities of the materials follow:

Matrix:

${}_{Al}=2165k\frac{g}{m^3}$

Reinforcement:

${}_{\text{g}\text{r}\text{a}\text{p}\text{h}\text{i}\text{t}\text{e}}=2\mathrm{.}23\frac{g}{c}{m}^3$

Coating:

${}_{Ni}=8946k\frac{g}{m^3}$

Al$-$alloy contains $7\mathrm{.}55$ wt$.\%$ Si$,0\mathrm{.}16$ wt$.\%$ Mg$,1\mathrm{.}54$ wt$.\%$ Cu$,$ and rest Al$.$ The particles of graphite are

non$-$porous and spherical structures. The average particle size $($diameter$)$ of graphite is $85m$

In a crucible, the continous casting procedure will be carried out at $750C.$ You want to melt $13l{b}_{m}Al-$

alloy and add $1\mathrm{.}6$ wt$.\%$ reinforcement material.

During the coating process, a $1/3$ solid$-$to$-$liquid ratio $($i$.$e$.,1kg$ solid to $3L$ liquid$)$ with a solution of $0\mathrm{.}65pH$

will be used. The $Ni$ source of the coating process is $NiS{O}_4,$ and $13\%$ excess $Ni$ will be used. $H_{2}S{O}_4$

solution $(95\%\frac{w}{w}$ and $1\mathrm{.}83\frac{g}{c}{m}^3$ density$)$ will be added to adjust $pH,$ and the rest will be pure $H_{2}O$

$($density $1\mathrm{.}0\frac{g}{c}{m}^3).$

Calculate:

a$)$ amount of graphite $($g$)$ added to the solution,

b$)$ amount of $NiS{O}_4(g)$ added to the solution,

c$)$ amount of $H_{2}S{O}_4$ solution $(c{m}^3$ or $L)$ in the solution,

d$)$ amount of pure or $\{$:$L)$ in the solution,

e$)$ the average thickness of the $Ni$ coating $(m)$ coated on h$-BN,$

f$)$ the Ni content $($wt$.\%)$ after the slip casting process.