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Dimensional Analysis

Dimensional Analysis


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About the Book

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: CHAPTER III ON THE USE OF DIMENSIONAL FORMULAS IN CHANGING UNITS We saw in the last chapter how to obtain the dimensional formula of any quantity in terms of the quantities which we chose by definition to make fundamental. Our method of analysis showed also the connection between the numerical magnitude of the derived quantity and the fundamental quantities. Thus if length enters to the first power in the dimensional formula, we saw that the number measuring that quantity is doubled when the unit of length is halved, or the numerical measures are inversely as the size of the unit, raised to the power indicated in the dimensional formula. Let us consider a concrete example. What is a velocity of 88 feet per second when expressed in miles per hour ? The dimensional formula of a velocity is LT1. Now if our unit of length is made larger in the ratio of a mile to a foot, that is, in the ratio of 5280 to 1, the velocity will be multiplied by the factor 1/5280, because length enters in the dimensional formula to the first power. And similarly, if the unit of time is made larger in the ratio of the hour to the second, that is, in the ratio of 3600 to 1, the velocity will be multiplied by the factor 3600, because time enters the dimensional formula to the inverse first power. To change from feet per second to miles per hour we therefore multiply by 3600/5280, and in this particular case the result is 88 X 3600/5280, or 60 miles per hour. Now the result of these operations may be much contracted and simplified in appearance by a sort of shorthand. We write sec. 1 sec. 1ft. =88X5280 60 hour 3600,3600 mile '5280 hour A little reflection, considering the relation of the dimensional formula to the operations by which we obtain the measuring number of any physical ...


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Product Details
  • ISBN-13: 9781459064553
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 40
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1459064550
  • Publisher Date: 20 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 91 gr


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