A side$-$stream membrane bioreactor process $($influent flow rate, $Q_f=0\mathrm{.}44\frac{m^3}{s})$ is operating to

remove organic and inorganic compounds from the feed stream at $90\%$ recovery.

Membrane system

$1\mathrm{.}1$ Calculate $Q_p(\frac{m^3}{s})$

Calculate membrane surface area $(m^2)$ to get the constant permeate flux of $50\mathrm{.}9\frac{L}{m^2}\frac{?}{h}.$

If this system uses spiral wound membrane elements with a packing density of $2,000\frac{m^2}{m^3}$

and each element is $10cm$ in diameter and $95cm$ long. How many membrane elements would be

required?

If rejection efficiency of organic compounds $(C_f=100m\frac{g}{l})$ by the plant is $80\%,$ then

calculate concentration of organic compounds in the retentate stream $(C_r)$ in $m\frac{g}{L}.$

After one$-$month operation, transmembrane pressure $($TMP$)$ increased to $20$kPa. Calculate

the total resistance of membrane $(m^{-1})$ at $20C.$ Viscosity of water is ${10}^{-3}Pa*s.$