Problem #$2$: Each pressure vessel $($containing $200m^2$ of membrane area$)$ in a proposed design for desalination of

seawater dissolved salt concentration$)$ is rated for $35\%$ recovery at flow rates between $850$ and $1,300$

$\frac{m^3}{d}.$ Design a multi$-$stage array system that will yield $2,000\frac{m^3}{d}$ of pure water for a town of $5,000$ people at a

total permeate recovery of $50\%.$ In your design it is suggested to operate with flows to each pressure vessel on the

conservative side of the flow range allowed to provide a design safety factor. The mass transfer coefficient for

water flux of $7{10}^{-4}\frac{m^3}{d}*m^2*kPa,$ and assume $100\%$ rejection of salts by the membranes.

$($a$)$ For each stage of the array system, determine the number of pressure vessels to operate in parallel and

the minimum required net transmembrane pressure $($in kPa $).$

$($b$)$ Estimate the dissolved salt concentration in the reject stream from the multi$-$stage array system.

$($c$)$ Sketch the system diagram.