Memorandum from Raymond L. Murray to Dr. Clifford K. Beck

%MurNBsize060651; ]> Memorandum from Raymond L. Murray to Dr. Clifford K. Beck [a machine-readable transcription] Murray, Raymond L. Creation of machine-readable version: Russell S. Koonts Creation of digital images: Russell S. Koonts Conversion to TEI.2-conformant markup: NCSU Science and Technology Electronic Text Center. ca. 9 kilobytes NCSU Libraries. Raleigh, NC. Modern English, MurNBsize060651

Available from: NC State University Archives

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URL: http://www.lib.ncsu.edu/archives/etext/engineering/reactor/murray/

2000

Nuclear Reactor Digitization Project

Raymond L. Murray Reactor Project Notebook

Illustrations have been included from the print version. Scanned by Russell Koonts with Photoshop 5.0 software. Memorandum from Raymond L. Murray to Dr. Clifford K. Beck <author>Raymond L. Murray</author> <respStmt> <resp/> <name/> </respStmt> </titleStmt> <editionStmt> </editionStmt> <extent>2 pp.</extent> <publicationStmt> <publisher></publisher> <pubPlace></pubPlace> <date></date> <idno>Manuscript copy consulted: NCSU Libraries call number UA105.16</idno> </publicationStmt> <seriesStmt> </seriesStmt> <notesStmt> <note></note> </notesStmt> </biblFull> </sourceDesc> </fileDesc> <encodingDesc> <projectDesc> Prepared for the NCSU Libraries Science and Technology Electronic Text Project. </projectDesc> <editorialDecl> Spell-check and verification made against printed text using Notetab spell checker. The lineation of the manuscript has been maintained and all end-of-line hyphens have been preserved. The images exist as archived TIFF images, one or more JPEG versions for general use, and thumbnails. Keywords in the header are a local Electronic Text Center scheme to aid in establishing analytical groupings. </editorialDecl> <refsDecl> 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. </refsDecl> <classDecl> <taxonomy id="LCSH"> <bibl> <title>Library of Congress Subject Headings June 6, 1951 English non-fiction; prose LCSH 24-bit color; 400 dpi Memorandum from Raymond L. Murray to Dr. Clifford K. Beck Typescript 2 pp. June 6, 1951 MurNBsize060651

June 6, 1961 NCSC-20 TO: Clifford K. Beck FROM: Raymond L. Murray SUBJECT: Reactor Size and Mass

It has been suggested that changes in the volume of the reactor core from the original proposal be made to accomodate possible larger necessary masses. Consideration should be given to the following facts, however: 1. The critical mass is a rather insensitive function of the water content in the region around NH/NU= 400. An estimate of the variation from the minimum, Mo, from bare-reactor theory

is plotted in Figure 1. Taking the minimum critical mass to occur at NH/NU = 360, there is no more than a 10% increase in going as low as 250 or as high as 470. 2. The solution volume for a given mass of uranium varies inversely with the NH/NU ratio. Neglecting the presence of other elements and ignoring displacement, the relation is

The variation of volume is plotted on the same graph, using the relation

The conclusion is that if the critical mass of the N. C. State reactor is actually higher than the expected 915 grams, the excess material may still be easily accomodated by the container, providing a slightly lower NH/NU be used. On the other hand, if the mass turns out to be lower, the mixture can be diluted to fit the vessel.

Calculations leading to the formulas appear in the Appendix.

APPENDIX

Assumptions: 1. Bare spherical reactor of critical radius R, with pure U-235 in water. 2. Critical equation

---(1) where k is the infinite multiplication constant, ηf, where η = 2.1,

, m2 is the migration area ~ 34 cm2 for systems in the range of

3. Ratio of mass of U-235 to mass (and volume) of water

---(2) 4. Volume and mass of water

---(3)

Analysis: 1. Assume cross sections σU = 640 barns , σH = 0.31 barns. 2. Solve equations (1), (2) and (3) for MU, using the approximation that

, where the latter is 2065. The result is

---(4) 3. The minimum of this function occurs when the two terms in the denominator are equal, ie at NH/NU = 360 , which checks experiment fairly well. At that point MU = 3.2 kg = Mo which is a reasonable bare reactor mass. 4. The ratio of M in general to the minimum mass, as quoted in the body of this note, is computed to be

---(5) 5. The volume ratio is obtained from equations (2), (3), (5) as