# Difference between revisions of "Assignment 3 - 2013"

 Due date(s): 11 October 2013 (at class) (PDF) Assignment questions (PDF) Assignment solutions - thanks Dominik and Ahmed

<rst> <rst-options: 'toc' = False/> <rst-options: 'reset-figures' = True/> Assignment objectives

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To use ideas and formulas related to mechanical separation units.

.. |micron| replace:: :math:\mu \text{m}

#. Prove that for a spherical particle, :math:S = \displaystyle \frac{6}{d} = specific surface area of particle per volume of solid particle, with units of :math:\text{m}^{-1}.

#. Calculate this value for spherical particles of 50 |micron| and 100 |micron|.

#. What is the theoretical value(s) of voidage for spheres?

#. Calculate :math:\alpha, the specific cake resistance value in a filtration system for spherical particles of 50 |micron| and 100 |micron|, where the solids have a density of 2500 :math:\text{kg.m}^{-3}.

#. Under what assumptions do filtration data from lab equipment plot as a straight line for :math:V versus :math:\dfrac{t}{V} axes?

#. Look up the terms "precoat" and "filter aids" in the context of solid-liquid plate-and-frame or vacuum rotary-drum filtration. Explain in an unambiguous manner the purpose they serve.

Your sister company seems to have no problem at their site with particulate pollutant discharge. Your site however experiences continual problems, despite using a similar process.

You request their flowsheet and notice an arrangement of cyclones as shown below (your flowsheet does not have any cyclones). Explain what this sequence might do to help achieve pollutant reduction.

.. image:: ../figures/separations/cyclones/clarifying-sequence.png :align: center :scale: 90% :width: 750px

The following filtration data are collected from a laboratory unit, using the same filter medium for all experiments. The objective is to determine the constants :math:\alpha_0 and :math:f in the equation for specific cake resistance, :math:\alpha = \alpha_0 \left(- \Delta P \right)^f, where :math:\alpha and :math:\alpha_0 are in units of :math:\text{m.kg}^{-1}, and :math:- \Delta P is in Pascals.

Test 1 was run at 36 kPa, test 2 run at 128 kPa, and test 3 run at 370 kPa. All tests were run with a slurry concentration of 25 kg dry solids per cubic meter of filtrate, and the viscosity was around :math:9.2 \times 10^{-4} Pa.s on a filter of 0.08 :math:\text{m}^2.

.. list-table:: :widths: 15 10 10 10 :header-rows: 1

* - Filtrate volume [L] - Test 1, Time [s] - Test 2, Time [s] - Test 3, Time [s] * - 0.25 - 20 - 13 - 4 * - 0.5 - 39 - 29 - 9 * - 1.0 - 99 - 70 - 26 * - 1.5 - 175 - 123 - 53 * - 2.0 - 276 - 207 - 83 * - 2.5 - -- - 365 - 128 * - 3.0 - -- - 399 - 182

Show all calculations made, including your assumptions. Work in a systematic manner.

After reading this article on the course website <http://learnche.mcmaster.ca/media/mcmaster/Hanly-Petchonka--Equipment-selection-for-Solid-Gas-Separation.pdf>_, describe