The following information applies to questions $21-28.$

Potable water is to be produced at a rate of $48,000\frac{m^3}{d}$ from the brackish groundwater containing $10,000m\frac{g}{L}$ of total dissolved solids $($TDS$).$ For calculation purposes, the TDS can be assumed to be NaCl $($molar mass $58\mathrm{.}4\frac{g}{m}ol).$ The selected membrane can achieve a salt rejection of $98\%,$ and the water recovery is to be $50\%.$ Pilot tests have shown that a permeate flux of $25\frac{L}{m^2}-h$ can be achieved at a transmembrane pressure $P$ of atm$).$

etermine the surface area $(m^2)$ of membrane needed to provide the required potable water flow.

Question $25$

$\frac{0}{5}$ pts

Determine the average differential osmotic pressure $(atm).$ Evaluate the osmotic pressure of the feed and of the retentate and take the average, then subtract the osmotic pressure of the permeate. Because of the wide range of solute concentrations, the variation of the van't Hoff factor i with concentration should be taken into account; estimated i values are $1\mathrm{.}7$ in the feed, $1\mathrm{.}6$ in the retentate, and $1\mathrm{.}9$ in the permeate.

Question $26$

$\frac{0}{5}$ pts

Determine the water flux coefficient $k_w(\frac{L}{a}tm-m^2-h)$ of the membrane.

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Question $27$

$\frac{0}{5}$ pts

Determine the solute flux $J_s(\frac{g}{m^2}-h).$