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How The Dimensional Analysis Work?

data:2017-05-18  Editor:佚名  Hits:

In dimensional analysis, the number of the effecting parameters is reduced to a minimum by replacing the dimensional parameters by dimensionless parameters. Some researchers point out that the chief advan-

tages of this analysis are “to obtain experimental results with a minimum amount of labor, results in a form having maximum utility. The dimensional analysis has several other advantages which include      

1) increase of understanding,

2) knowing what is important,

3) compacting the presentation. The advantage of compact of presentation allows one to “see’ the big picture with minimal efforts

 

Dimensionless parameters are parameters which represent a ratio which does not have a physical dimension. The experimental study assists to solve problems when the solution of the governing equation can not be obtained. To achieve this, experiments are designed to be “similar” to the situations which need to be solved or simulated. The base to this concept is mathematical. Two different sets of phenomena will produce similar result if the governing differential equations with boundaries conditions are similar. The actual experiments are difficult to carry out in many cases. Thus, design experiments with the same governing differential equations as the actual phenomenon is the solution. This similarity does not necessarily means that the experiments has be carried exactly as studied phenomena.It is enough that the main dimensionless parameters are similar, since the minor dimensional parameters, in many cases, are insignificant. An example to the last point, the Reynolds number is insignificant change in Reynolds number or large range on the friction factor.


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