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>