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3.1 Introduction

= 0.5

Figure: Rode in to the hole example
Lets take a trivial example of fitting a rode into a circular hole (see Figure [*]). To have solve this problem, it is required to know two parameters; one the diameter of the rode and second the diameter of the hole. Actually it is required to have the only one parameter, the ratio of the rode diameter to the hole diameter. The ratio is a dimensionless number and with this number one can say that for a ratio larger than one, the rode will not enter the hole; and ratio smaller than one rode is too small. Only when the ratio is equal to one the rode is said to be fitting. This allows one to draw the situation by using only one coordinate. Furthermore, if one wants to deal with tolerances, the dimensional analysis can easily be extended to say that when the ratio is equal from 0.99 to 1.0 the rode is fitting, and etc. When one will use the two diameters description he will need more than this simple sentence to describe it.

In preceding simplistic example the advantages are minimal. In many real problems, including the die casting process, this approach can remove clattered views and put the problem in a focus. It also helps to use information from different problems to a `similar'' situation. Throughout the book the reader will notice that the systems/equations are converted to a dimensionless form to augment the understanding.


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