# Assignment 3 - 2013

 Due date(s): 11 October 2013 (at class) (PDF) Assignment questions

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Assignment objectives

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To use ideas and formulas related to mechanical separation units.

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

.. question:: :grading: 8

#. 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}.

.. question:: :grading: 4

.. From Seader, 3rd edition

#. 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.

.. question:: :grading: 5

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. Explain what this sequence might do to help you achieve pollutant reduction.

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

.. question:: :grading: 20

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.

.. 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.

.. question:: :grading: 12

The following is laboratory size distribution data for the feed, oversize and undersize of an industrial sieve stack are given.

.. image:: ../figures/separations/screens/particle-size-results.png :align: center :scale: 55x% :width: 750px

#. Calculate the overall efficiency. #. Calculate the cut size.

.. question:: :grading: 8

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

#. what a venturi scrubber does #. draw a sketch of how it looks #. give an advantage relative to another separation unit that achieves a similar purpose #. give a disadvantage relative to another separation unit that achieves a similar purpose.

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