Experiments at $25$C were performed to determine the permeabilities $($AW and AS$)$ of a cellulose

acetate membrane. The membrane area is Am $=4\mathrm{.}0\backslash$times $10-3$ m$2$

$,$ and its thickness is $0\mathrm{.}2\backslash$mu m$.$ The inlet

feed solution concentration of NaCl is CF $=10\mathrm{.}0$ kg NaCl$/$m$3$ solution and its density is $1004$ kg$/$m$3$

$.$

The water recovery is assumed to be low so the retentate concentration of salt CR is approximately

equal to CF$.$ The product solution contains $0\mathrm{.}50$ kg NaCl$/$m$3$ solution, and the density is

$997$ kg solution$/$m$3$

$.$ Permeate flow rate is $3\mathrm{.}80\backslash$times $10-8$ m$3$ solution$/$s$.$ The pressure differential of

$57$ atm is used. Calculate the following: $($mention appropriate SI units$)$

i$)$ Water flux $($Nw$,$ kg$.$m$-2$

$.$s$-1$

$)[4$ Marks$]$

ii$)$ Feed side osmotic pressure $[4$ Marks$]$

iii$)$ Water permeability of membrane $[4$ Marks$]$

iv$)$ Salt passage $[4$ Marks$]$

v$)$ Salt flux $($Ns$,$ kg$.$m$-2$

$.$s$-1$

$)[4$ Marks$]$

vi$)$ Permeate side osmotic pressure $[3$ Marks$]$

vii$)$ Salt permeability of membrane