$8-4$ A new membrane plant is being designed. Pilot testing indicates that the membrane will be able to operate at a specific flux of $120\frac{L}{m^2}*h*$ bar at $20C.$ Water demand projections predict a summer peak$-$day demand of $90M\frac{L}{d}$ and a winter peak$-$day demand of $60M\frac{L}{d}.$ Historical records indicate that the source water has a minimum temperature of $3C$ in winter and $18C$ in summer.

a$.$ Which season will govern the size of the plant?

b$.$ What is the required membrane area, assuming the plant will operate at $0\mathrm{.}8$ bar, the online production factor is $95$ percent, and the recovery is $97$ percent?