Problem $2(30$ points$).$ A protein of molecular weight $300000$ is separated from the fermentation broth using an ultrafiltration membrane. The flow rate through a chamber $2cm$ in diameter and $50cm$ in length is $2\frac{L}{?}$ minutes. The flow is turbulent with a friction factor of $f=0\mathrm{.}0005.$ The inlet pressure is $2$atm. The concentration of protein in the solution and in the gel film are $30m\frac{g}{L}$ and $100\frac{g}{L}$ respectively.

a$)$ Determine the exit pressure

b$)$ Determine the transmembrane pressure drop

c$)$ If the mass transfer coefficient for the flux of protein is $5c\frac{m}{s},$ determine the flux of liquid through the membrane.

d$)$ If the resistance of the membrane is $0\mathrm{.}002$atm.$c{m}^2\frac{s}{c}{m}^3,$ determine the resistance of the gel layer.