# Assignment 3 - 2013

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

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

Assignment objectives

###### =========

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. 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

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.

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.

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