A tubular UF membrane with a diameter of $1\mathrm{.}9cm$ and a permeability of $245\frac{\text{I}}{m^2}h$ atm is used to concentrate the

cheese protein at $45C.$ The osmotic pressure $()$ can be estimated with the equation:

$(atm)=4,3*{10}^{-3}c-1,6*{10}^{-6}{c}^2+7,8*{10}^{-8}{c}^3$ donde $c(\frac{g}{l})$; Average protein diffusivity $=5*{10}^{-7}c\frac{m^2}{s}.$

Calculate

ii$)$ The effect of $p$ on the flow of a new membrane if the feed rate is $1\mathrm{.}4\frac{m}{s}$ and the protein concentration is $10,20$ or

$40\frac{g}{\text{I}}$

ii$)$ If the permeability of the membrane is reduced $4$ times due to fouling. What is the effect on the flow?

Data: maximum concentration $(395\frac{g}{\text{I}},$ rejection is $100\%,$ density and viscosity equal to water