<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<?xml-stylesheet type="text/xsl" href="../../../styles/reactor.xsl" ?>
<!DOCTYPE TEI.2 SYSTEM "../../../dtds/teixlite.dtd" [
<!ENTITY % MurNBalliners052151 SYSTEM "MurNBalliners052151.ent" >
%MurNBalliners052151;
]>
<TEI.2 id="MurNBalliners052151">
<teiHeader type="aacr2">
<fileDesc>
<titleStmt>
<title>Memorandum from A. C. Menius, Jr. to C. K.  Beck</title>
<title>[a machine-readable transcription]</title>
<author>Menius, A. C., Jr.</author>
<respStmt>
<resp>Creation of machine-readable version: </resp>
<name>Russell S. Koonts</name>
<resp>Creation of digital images: </resp>
<name>Russell S. Koonts</name>
<resp>Conversion to TEI.2-conformant markup: </resp>
<name>NCSU Science and Technology Electronic Text Center.</name>
</respStmt>
</titleStmt>
<extent>ca. 9 kilobytes </extent>
<publicationStmt>
<publisher>NCSU Libraries.</publisher>
<pubPlace>Raleigh, NC.</pubPlace>
<idno type="ETC"> Modern English, MurNBalliners052151</idno>
<availability>
<p>Available from: NC State University Archives</p>
<p>Publicly-accessible</p>
<p n="public">URL: http://www.lib.ncsu.edu/archives/etext/engineering/reactor/murray/</p>
</availability>
<date>2000</date>
</publicationStmt>
<seriesStmt>
<p>Nuclear Reactor Digitization Project</p>
<p>Raymond L. Murray Reactor Project Notebook</p>
</seriesStmt>
<notesStmt>
<note>Illustrations have been included from the print version.</note>
<note>Scanned by Russell Koonts with Photoshop 5.0 software.</note>
</notesStmt>
<sourceDesc>
<biblFull>
<titleStmt>
<title>Memorandum from A. C. Menius, Jr. to C. K.  Beck</title>
<title level="m"/>
<author>A. C. Menius, Jr.</author>
<respStmt> <resp/> <name/>
</respStmt>
</titleStmt>
<editionStmt>
<p></p>
</editionStmt> <extent>1 p.</extent>
<publicationStmt>
<publisher></publisher>
<pubPlace></pubPlace>
<date></date>
<idno>Manuscript copy consulted: NCSU Libraries call number UA105.16</idno>
</publicationStmt>
<seriesStmt> <p/>
</seriesStmt>
<notesStmt>
<note></note>
</notesStmt>
</biblFull>
</sourceDesc>
</fileDesc>
<encodingDesc>
<projectDesc>
<p>Prepared for the NCSU Libraries Science and Technology Electronic Text Project.</p>
</projectDesc>
<editorialDecl>
<p>Spell-check and verification made against printed text using Notetab spell checker.</p>
<p>The lineation of the manuscript has been maintained and all end-of-line hyphens have been preserved.</p> 
<p>The images exist as archived TIFF images, one or more JPEG versions for general use, and thumbnails.</p>
<p id="ETC">Keywords in the header are a local Electronic Text Center scheme to aid in establishing analytical groupings.</p>
</editorialDecl>
<refsDecl>
<p>ID elements are given for each page element and are composed of the text's unique cryptogram and the given page number, as in NEprop033050a for the title page of Clifford Beck's Proposal.</p>
</refsDecl>
<classDecl>
<taxonomy id="LCSH">
<bibl>
<title>Library of Congress Subject Headings</title> </bibl>
</taxonomy>
</classDecl>
</encodingDesc>
<profileDesc>
<creation>
<date>May 21, 1951</date>
</creation>
<langUsage>
<language id="en">English</language>
</langUsage>
<textClass>
<keywords>
<term>non-fiction; prose</term>
</keywords>
<keywords scheme="LCSH">
<term>LCSH</term>
</keywords>
</textClass>
<textClass>
<keywords>
<term type="artist"/>
<term type="visual work"/>
</keywords>
<keywords>
<term>24-bit color; 400 dpi</term>
</keywords>
</textClass>
</profileDesc>
<revisionDesc>
<change> <date/>
<respStmt> <resp/> <name/>
</respStmt> <item/>
</change>
</revisionDesc>
</teiHeader>

<text id="MurNBalliners052151T">

<front><div1 type="summary" n="1">
<head><hi rend="bold"><hi rend="center">Memorandum from A. C. Menius, Jr. to C. K.  Beck</hi><lb/>
<bibl><abbr>Typescript</abbr><lb/> <extent>1 p.</extent> <lb/><date value="1951-05-21">May 21, 1951</date><lb/> <idno rend="suppress">MurNBalliners052151</idno></bibl></hi></head>
<p>

</p>
</div1>
</front>

<body>
<pb n=""/>
<p><seg><xref id="reactorlg/MurNBalliners052151a.jpg" rend="new">
<figure entity="MurNBalliners052151a"></figure></xref></seg></p>
<div1 type="memorandum" n="1">
<head>
<hi rend="italics">NCSC-19 <name type="person">Murray</name><lb/>
<date value="1951-05-21">May 21, 1951</date></hi>
</head>

<opener>To: <name type="person"><abbr expan="Clifford">C.</abbr> K. Beck</name><lb/>
From: <name type="person">A. C. Menius, Jr.</name><lb/>
Subject: Effect of Proposed Al Liners in Vicinity of Reactor</opener>

<p>In the present design 4" <abbr expan="internal diameter">I.D.</abbr> Al liners 1/8" thick are to traverse the<lb/>
reflector and reach the reactor vessel. There will be in all ten of these.<lb/>
In the reflector near the surface of the reactor there will be considerable<lb/>
contamination of the graphite due to this Al which will result in an increase in<lb/>
the amount of U235 needed for criticality as well as a distention of the flux in<lb/>
that region.
</p>
<p>If we consider a six inch section around the reactor 6" high and assume<lb/>
a homogeneous mixture, the following data is obtained (See Calculations):<lb/>
<table>
<row>
<cell><seg><xref id="reactorlg/MurNBalliners052151aa.jpg" rend="new">
<figure entity="MurNBalliners052151aa"></figure></xref></seg></cell>
</row>
</table>
For graphite &#x03A3; = 0.00036<lb/>
For graphite and Al &#x03A3; = 0.00095</p>
<p>This means that the diffusion length L is<lb/>
<seg rend='left'><figure entity="MurNBalliners052151form1"></figure></seg>

<hi rend="suppress"><formula notation="mathml"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <msub>
        <mrow>
          <msup>
            <mrow>
              <mi>L</mi>
            </mrow>
            <mrow>
              <mn>2</mn>
            </mrow>
          </msup>
        </mrow>
        <mrow>
          <mi>A</mi>
          <mi>l</mi>
          <mo>+</mo>
          <mi>c</mi>
        </mrow>
      </msub>
      <mo>=</mo>
      <mfrac>
        <mrow>
          <msub>
            <mrow>
              <mi>&Sigma;</mi>
            </mrow>
            <mrow>
              <mi>c</mi>
            </mrow>
          </msub>
        </mrow>
        <mrow>
          <msub>
            <mrow>
              <mi>&Sigma;</mi>
            </mrow>
            <mrow>
              <mi>c</mi>
              <mo>+</mo>
              <mi>A</mi>
              <mi>l</mi>
            </mrow>
          </msub>
        </mrow>
      </mfrac>
      <mi>&thinsp;</mi>
      <mi>&thinsp;</mi>
      <msup>
        <mrow>
          <mi>L</mi>
        </mrow>
        <mrow>
          <mn>2</mn>
        </mrow>
      </msup>
      <mo>=</mo>
      <mfrac>
        <mrow>
          <mn>0</mn>
          <mn>.</mn>
          <mn>0</mn>
          <mn>0</mn>
          <mn>0</mn>
          <mn>3</mn>
          <mn>6</mn>
        </mrow>
        <mrow>
          <mn>0</mn>
          <mn>.</mn>
          <mn>0</mn>
          <mn>0</mn>
          <mn>0</mn>
          <mn>9</mn>
          <mn>5</mn>
        </mrow>
      </mfrac>
      <msup>
        <mrow>
          <mrow>
            <mo>(</mo>
            <mn>5</mn>
            <mn>0</mn>
            <mo>)</mo>
          </mrow>
        </mrow>
        <mrow>
          <mn>2</mn>
        </mrow>
      </msup>
      <mo>=</mo>
      <mn>0</mn>
      <mn>.</mn>
      <mn>3</mn>
      <mn>8</mn>
      <msup>
        <mrow>
          <mrow>
            <mo>(</mo>
            <mn>5</mn>
            <mn>0</mn>
            <mo>)</mo>
          </mrow>
        </mrow>
        <mrow>
          <mn>2</mn>
        </mrow>
      </msup>
    </mrow>
  </mrow>
</m:math>
-->
</formula></hi><lb/>
=950<lb/>
L &#x2243; 31 cm.
</p>
<p>Calculations:<lb/>
<list>
<item>Volume of Al = 10(&#x03C0;10.16)(.32)(15) = 1530cm<hi rend="sup">3</hi></item>
<item>Mass = 1530(2.4) = 3670 gms</item>
<item><table>
<row>
<cell>Volume of region</cell><cell>= &#x03C0;(r<hi rend="sub">1</hi><hi rend="sup">2</hi> - r<hi rend="sub">2</hi><hi rend="sup">2</hi>) 15 cm</cell><cell>=</cell>
</row>
<row>
<cell></cell><cell>= &#x03C0;(30<hi rend="sup">2</hi> - 15<hi rend="sup">2</hi>) 15</cell><cell>= &#x03C0;15(900-225)</cell>
</row>
<row>
<cell></cell><cell></cell><cell>= &#x03C0;15(675)</cell>
</row>
<row>
<cell></cell><cell></cell><cell>= 47.2(675) = 31800 cm<hi rend="sup">3</hi></cell>
</row>
</table></item>
<item><seg rend='left'><figure entity="MurNBalliners052151form2"></figure></seg>

<hi rend="suppress"><formula notation="mathml"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow>
      <msub>
        <mrow>
          <mi>&rho;</mi>
        </mrow>
        <mrow>
          <mrow>
            <mrow>
              <mi>A</mi>
              <mi>l</mi>
            </mrow>
          </mrow>
        </mrow>
      </msub>
      <mo>=</mo>
      <mfrac>
        <mrow>
          <mn>3</mn>
          <mn>6</mn>
          <mn>7</mn>
          <mn>0</mn>
        </mrow>
        <mrow>
          <mn>3</mn>
          <mn>1</mn>
          <mn>8</mn>
          <mn>0</mn>
          <mn>0</mn>
        </mrow>
      </mfrac>
      <mo>=</mo>
      <mn>0</mn>
      <mn>.</mn>
      <mn>1</mn>
      <mn>1</mn>
      <mn>5</mn>
      <mi>&thinsp;</mi>
      <mi>g</mi>
      <mi>m</mi>
      <mo>/</mo>
      <msup>
        <mrow>
          <mi>c</mi>
          <mi>m</mi>
        </mrow>
        <mrow>
          <mn>3</mn>
        </mrow>
      </msup>
    </mrow>
  </mrow>
</m:math>
-->
</formula></hi></item>
<item>
<table>
<row>
<cell><seg rend='left'><figure entity="MurNBalliners052151form3"></figure></seg>
<hi rend="suppress"><formula notation="mathml"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow>
      <msub>
        <mrow>
          <mi>N</mi>
        </mrow>
        <mrow>
          <mi>c</mi>
          <mi>c</mi>
        </mrow>
      </msub>
      <mo>=</mo>
      <mfrac>
        <mrow>
          <mn>6</mn>
          <mn>.</mn>
          <mn>0</mn>
          <mn>2</mn>
          <mo>&times;</mo>
          <msup>
            <mrow>
              <mn>1</mn>
              <mn>0</mn>
            </mrow>
            <mrow>
              <mn>2</mn>
              <mn>3</mn>
            </mrow>
          </msup>
        </mrow>
        <mrow>
          <mn>2</mn>
          <mn>7</mn>
        </mrow>
      </mfrac>
      <mi>&thinsp;</mi>
      <mi>&thinsp;</mi>
      <mi>&rho;</mi>
      <mo>=</mo>
      <mfrac>
        <mrow>
          <mn>6</mn>
          <mn>.</mn>
          <mn>0</mn>
          <mn>2</mn>
          <mo>&times;</mo>
          <msup>
            <mrow>
              <mn>1</mn>
              <mn>0</mn>
            </mrow>
            <mrow>
              <mn>2</mn>
              <mn>3</mn>
            </mrow>
          </msup>
        </mrow>
        <mrow>
          <mn>2</mn>
          <mn>7</mn>
        </mrow>
      </mfrac>
    </mrow>
  </mrow>
</m:math>
-->
</formula></hi></cell>
<cell>0.115</cell>
<cell>= (0.222) 0.115x10<hi rend="sup">23</hi></cell>
</row>
<row>
<cell></cell>
<cell></cell>
<cell>= 0.0258x10<hi rend="sup">23</hi></cell>
</row>
<row>
<cell></cell>
<cell>N<hi rend="sub">cc</hi></cell>
<cell>= 2.6x10<hi rend="sup">21</hi></cell>
</row>
</table>
</item>
<item>&#x03A3; = 2.6x10<hi rend="sup">21</hi> &#x2022; 0.23x10<hi rend="sup">-24</hi></item>
<item>&#x03A3;<hi rend="sub">al</hi> = 0.59x10<hi rend="sup">-3</hi> = 0.00059</item>
<item>For graphite, assume no change in density,</item>
<item><list><item>&#x03A3;<hi rend="sub">c</hi> = 0.00036</item></list></item>
</list></p>
</div1>
</body>
</text>
</TEI.2>