A membrane filtration system is designed for the winter demand. Can the system meet the summer demand with the same area of membrane? The winter and summer design conditions are:

a$.$ Maximum transmembrane pressure $($TMP$)=200$kPa

b$.$ Operating TMP $=75\%$ of maximum TMP

c$.R_m=3\mathrm{.}2{10}^{-12}{m}^{-1}$

d$.$ Winter temperature $=5C$

e$.$ Summer temperature $=20C$

a$.$ What is the operating flux in the winter, based on the membrane resistance and water temperature?

b$.$ What membrane area is required to meet the winter operating flux and winter demand?

c$.$ What is the operating flux in the summer, based on the membrane resistance and water temperature?

d$.$ Is the membrane area calculated in part $b$ sufficient to meet the summer conditions? If not, how would you change your design?