Please answer part A$,$B and C exactly as asked.?????

Various industrial processes require that a flat sheet be coated with a uniform liquid film. Dip coating is a procedure in which an immersed substrate is withdrawn through a liquid$-$gas interface. In the process in Figure $1,$ in which a substrate is pulled upward at a constant velocity $V,$ the coating achieves a uniform thickness $H$ at a certain height above the liquid. It is desired to predict $H$ from $V$ and the liquid properties $,$ and $).$

Figure $1.$ One side of a solid sheet being withdrawn upward from a liquid

a$)$ Representative values are $H=0\mathrm{.}02$ to $0\mathrm{.}2cm,V=0\mathrm{.}4$ to $3c\frac{m}{s},=0\mathrm{.}3$ to $2Pa*s,=900k\frac{g}{m^3},$ and $=30m\frac{N}{m}.$ By examining the ranges of dimensionless groups, show that viscosity, gravity, and surface tension are all important, but inertia is not. $($Use dimensionless group listed on Table $1\mathrm{.}6($Deen$))$

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b$)$ A theoretical result that is applicable here is

$H(\frac{g}{}{)}^{\frac{1}{2}}=0\mathrm{.}944(\frac{V}{}{)}^{\frac{2}{3}}(1-\frac{H^{2}g}{V}{)}^{\frac{2}{3}}$

Show that this may be rewritten as a relationship between $Bo$ and $Ca.$

Here is the definition of $Bo$ and $Ca.$

$Bo=\frac{g{L}^2}{}-=\frac{\text{G}\text{r}\text{a}\text{v}\text{i}\text{t}\text{a}\text{i}\text{o}\text{n}\text{a}\text{l}}{\text{S}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e}\text{T}\text{e}\text{n}\text{s}\text{i}\text{o}\text{n}}$

$Ca=\frac{U}{}-=\frac{\text{V}\text{i}\text{s}\text{c}\text{o}\text{u}\text{s}}{\text{S}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e}\text{T}\text{e}\text{n}\text{s}\text{i}\text{o}\text{n}}$

c$)$ If one group is chosen now as $N=(B\frac{o}{C}a{)}^{\frac{1}{2}}=[H^2\frac{g}{vV}{]}^{\frac{1}{2}}$ and $Ca$ is the second group, show that

$\frac{N}{(1-N^2{)}^{\frac{2}{3}}}=0\mathrm{.}944C{a}^{\frac{1}{6}}$

Use this to derive explicit expressions for $N$ for $Ca0$ and $Ca.$ How does $H$ vary with $V$ in these limits$?$