Please answer all three questions if possible showing all work. Thank you! An engineer is designing a new nanofiltration membrane for water purification. If testing shows the

membrane has a porosity of $0\mathrm{.}52,$ thickness of $32m,$ and hydraulic permeability for water of $0\mathrm{.}1350$

$cmmmH{g}^{-1}h{r}^{-1},$ estimate the effective pore size of the membrane in microns, assuming the pores are

straight rectangular channels and water viscosity is $0\mathrm{.}0008Pa$ s$.$

A biotechnology company is developing a new membrane filtration system to purify proteins from

complex mixtures. If the transmembrane pressure across the membrane is $60mmHg$ and the pressure

on the permeate side is $20mmHg,$ with an osmotic pressure of retained proteins being $25\mathrm{.}6mmHg,$

estimate the filtration rate across a membrane with an area of $1\mathrm{.}25m^2$ and a hydraulic permeability of

$6\mathrm{.}96mLmi{n}^{-1}mmH{g}^{-1}{m}^{-2}.$

A hollow fiber dialysis system contains hollow fiber membranes with a total surface area of $1\mathrm{.}5m^2.$

During treatment of a patient, the blood pressure inside the fibers averaged $120mmHg$ and the

dialysate pressure surrounding the fibers averaged $-150mmHg.$ If the observed ultrafiltration rate was

$1000m\frac{L}{h}r$ and proteins were retained completely by the membrane, estimate the hydraulic

permeability of the hollow fiber membrane in $mLhr{m}^{-1}mmH{g}^{-1}.$