Assignment 4 - 2012
| Due date(s): | 26 October |
| Link | [{{{questions_link}}} Assignment questions ] |
| Link | [{{{solutions_link}}} Assignment solutions] |
<rst> <rst-options: 'toc' = False/> <rst-options: 'reset-figures' = False/> Assignment objectives
=========
- Objectives**: Understanding membrane separation processes.
.. |micron| replace:: :math:`\mu \text{m}`
.. question:: :grading: 5; already answered as pop-quiz in class; do not re-submit a solution
A microfiltration membrane operating with pure feed of water produces a flux of 0.06 :math:`\text{kg}.\text{s}^{-1}\text{.m}^{-2}` when operated with a TMP of 30 kPa.
#. What is the resistance due to the membrane? Specify the units. #. If operated with a protein-water mixture at a 20 kPa pressure difference, a flux of :math:`216 \times 10^{-6}$ $\text{kg}.\text{s}^{-1}\text{.m}^{-2}` is measured at steady state. What is the resistance due to cake build-up? Specify the units.
.. question::
:grading: 10; already answered in midterm and in class; do not re-submit a solution
An asymmetric ultrafiltration membrane is used with the aim of separating dyes from a liquid stream and to achieve a more concentrated dye-water mixture. The feed waste stream arrives at a flow rate of 2.2\ :math:`\text{m}^{3}\text{.hour}^{-1}` with concentration of 1.2 :math:`\text{kg}\text{.m}^{-3}`. The membrane's operating characteristic was calculated from various experiments:
.. math::
J_v = 0.04 \ln \left(\frac{15}{C}\right)
where the bulk concentration :math:`C` has units of :math:`\text{kg}\text{.m}^{-3}` and flux is measured in :math:`\text{m}^{3}\text{.hour}^{-1}\text{.m}^{-2}`.
If two membrane modules, each of area 25 :math:`\text{m}^2`, are simply placed in series, give reasonable estimates of:
#. the dye concentration from the first membrane module? #. the permeate flow rate from the first membrane module? #. the dye concentration from the final membrane module? #. the permeate flow rate from the final membrane module? #. Then explain whether the above answers seem reasonable.
Please show all calculations, assumptions and relevant details.
.. raw:: latex
\vspace{0.3cm} \hrule \center{END} </rst>