Please Solve this

An ultrafiltration module has a length of $0\mathrm{.}5$m$,$ diameter of $2$ cm$,$ flow of $2$ L$/$min with an

inlet pressure of $2$ bar. This crossflow membrane operates in the turbulent flow regime

$($Fanning$\text{'}$s friction factor $=0\mathrm{.}005)$ and the density of the fluid is $1020$ kg$/$m$3.$ The mass

transfer coefficient $($k$)$ is $5$ x $104$ m$/$s and the concentration of the protein in the gel laye

$($CG$)$ and bulk $($CB$)$ are $100$g$/$L and $30$ mg$/$L respectively. The filtrate side of the

membrane is open to atmosphere. Assuming the resistance of the membrane $($RM$)$ to be

$0\mathrm{.}002$ pa$.$s$/$m

a$.$ Exit pressure $(P_o)$ and the transmembrane pressure drop $(P_M)$

Calculate the liquid flux through the membrane $($J$)$

e$.$ Calculate the resistance of the gel layer $(R_G).$

d$.$ Determine the area of the membrane if a filtrate of $1000L$ must be filtered

from a batch of $3000L$ batch in one hour.

Use the following equations for calculations $($all parameters in SI units$)$:

$P=\frac{4fL{v}^2}{2D},P_M=p_i-\frac{1}{2}P$

$J=kln(\frac{C_G}{C_B})=\frac{P_M}{(R_G+R_M)}J.A=Q$