{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:58:15Z","timestamp":1750309095442,"version":"3.41.0"},"reference-count":13,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[1978,5,1]],"date-time":"1978-05-01T00:00:00Z","timestamp":262828800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[1978,5]]},"abstract":"<jats:p>This paper describes a computer program which evaluates, manipulates and identifies nondimensional numbers (pi terms, dimensionless numbers or factors) generated using the Buckingham Pi Theorem. Computations are performed using SYMBOLANG, an algebraic (symbol) manipulation package (solutions are kept in symbolic form). Manipulation occurs in two ways. First, many allowable combinations of pi terms (up to 720) are generated by changing the ordering of the dimensional equations which are solved. Second, a small group of operators (squaring, square-rooting, cube-rooting, reciprocating, and division of both the minimum and maximum exponent) are applied to each solution (these too are solutions and also kept in symbolic form). Numerical substitution into the symbolic forms produce scalars (evaluated solutions) for subsequent use (plotting, regression, factor analysis, etc.). Finally, every symbolic solution is compared with well-known nondminsional numbers (e.g., Reynold's, Weber's, etc.). If a match is not found, this information is displayed.<\/jats:p>","DOI":"10.1145\/1088261.1088266","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"21-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["The evaluation, manipulation and identification of nondimensional numbers"],"prefix":"10.1145","volume":"12","author":[{"given":"Morton A.","family":"Hirschberg","sequence":"first","affiliation":[{"name":"US Army Armament Research &amp; Development Command, MD"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[1978,5]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Sedov L. I. Similarity and Dimensional Methods in Mechanics. New York Academic Press 1959.  Sedov L. I. Similarity and Dimensional Methods in Mechanics. New York Academic Press 1959."},{"key":"e_1_2_1_2_1","unstructured":"Happ W. W. Private Communication January 1976.  Happ W. W. Private Communication January 1976."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1709041"},{"key":"e_1_2_1_4_1","unstructured":"Sloan A. D. and Happ W. W. \"Computer Program for Dimensional Analysis\" Electronics Research Center Cambridge MA NASA TN D-5165 April 1969.  Sloan A. D. and Happ W. W. \"Computer Program for Dimensional Analysis\" Electronics Research Center Cambridge MA NASA TN D-5165 April 1969."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0016-0032(71)90161-X"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(75)90035-3"},{"volume-title":"US Army Ballistic Research Laboratory Report No. 1824","year":"1975","author":"Hirschberg M. A.","key":"e_1_2_1_7_1"},{"key":"e_1_2_1_8_1","unstructured":"Land N. S. \"A Compilation of Nondimensional Numbers\" Washington DC US Government Printing Office NASA SP-274 1972.  Land N. S. \"A Compilation of Nondimensional Numbers\" Washington DC US Government Printing Office NASA SP-274 1972."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.4.345"},{"key":"e_1_2_1_10_1","unstructured":"Langhaar H. L. Dimensional Analysis and Theory of Models New York Wiley 1951.  Langhaar H. L. Dimensional Analysis and Theory of Models New York Wiley 1951."},{"key":"e_1_2_1_11_1","unstructured":"Housner C. W. and Hudson D. E. Applied Mechanics Dynamics. New York van Nostrand 1950.  Housner C. W. and Hudson D. E. Applied Mechanics Dynamics. New York van Nostrand 1950."},{"key":"e_1_2_1_12_1","unstructured":"Findler N. V. Pfaltz J. L and Bernstein H. J. Four High-Level Extensions of FORTRAN IV; SLIP AMPL-II TREETRAN SYMBOLANG. New York Spartan 305--387 1972.  Findler N. V. Pfaltz J. L and Bernstein H. J. Four High-Level Extensions of FORTRAN IV; SLIP AMPL-II TREETRAN SYMBOLANG. New York Spartan 305--387 1972."},{"key":"e_1_2_1_13_1","unstructured":"Hirschberg M. A. \"SYMBOLANG - A SLIP Extension for Algebraic Manipulation\" US Army Ballistic Research Laboratory Report No. 1749 November 1974.  Hirschberg M. A. \"SYMBOLANG - A SLIP Extension for Algebraic Manipulation\" US Army Ballistic Research Laboratory Report No. 1749 November 1974."}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1088261.1088266","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1088261.1088266","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T22:43:44Z","timestamp":1750286624000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1088261.1088266"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,5]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1978,5]]}},"alternative-id":["10.1145\/1088261.1088266"],"URL":"https:\/\/doi.org\/10.1145\/1088261.1088266","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1978,5]]},"assertion":[{"value":"1978-05-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}