Question $3($getting a close to an accurate answer is important, but partial

credit will be given for thoughtful working towards an answer$)$

You are in a zombie apocalypse and are the only engineer in your little band of survivors.

The available water supplies are polluted and you are very happy to find a reverse osmosis

system which can keep you supplied with water free from small molecule pollutants as well

as pathogens.

A$)$ What kind of precautions would you take or improvements you wish to make to ensure

$-$ Longevity of the individual membrane filters?

$-$ How can you improve on the notorious waste of water by RO filters?

$-$ What is a relationship that shows the permeate rate depends on the pressure drop

across a filter and the filter cross$-$sectional area? What other parameters does the

permeate rate depend on$?$ Write down the relationship.

$[9$ marks$]$

B$)$ The cross$-$section of the filters is $10$ cm$2,$ their length is $20$ cm$,$ and you find a note another

engineer has tested them and found they behave as homogeneous filter blocks of the same

shape with a membrane permeability of $6\mathrm{.}4\backslash$times $10-14$ m$2.$ You have a pump that can apply

$20$ bar input pressure to the filter casing. Consider an adult needs about $2$ L of water per

day and you can run the system for $20$ hrs$/$day and are purifying $30$ oC fresh water with

negligibly low salt content. Find out the permeate rate and therefore the number of people

your system can support.

$[10$ marks$]$

C$)$ After a month of relative peace, your fresh water source is destroyed in a zombie attack.

You are forced to move to a location near the ocean and need to use seawater as a source

for the RO drinking water system. You have enough RO filters to last a while, but you have

to redesign the RO system for the new environment. Calculate the new pump pressure

needed $($and potentially the number of systems you might need$)$ for water for the same

number of people.

Assume for simplicity that seawater only contains NaCl at a level of $35000$ ppm $($or $35$ g$/$L$)$

on a weight $/$volume basis and that the seawater is at a temperature of $10$ oC and viscosity

of $0\mathrm{.}0014$ Pa$$s$.$

Calculate first the type of pump pressure you would need in the ideal case when there are

no polarization effects.

Then, calculate the pump pressure and RO water production with polarization effects,

considering the polarization factor $\backslash$Gamma defined by the concentration at the membrane interface

CSi vs the bulk feed concentration CSf$,$ is

R$$

$($CSi$$CSf$)/$CSf

$=0\mathrm{.}2$