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32
95
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The scale multipliers being constants are taken before the
differentiation operator as follows:
^ m ^ . (96)
a. X at
From Eqs, (95) and (96) it is obtained
a.
J
arC l=- -^ = L (97)
By replacing in the similarity indicator (C») the scale multipliers with
the respective ratios of physical values, we obtain:
f t
(98)
mw
where the index (1) is for the similar system.
The comparison between Eqs. (88) and (98) shows that the obtained
ratio is the Newton number,
1,3.2. Dimensional analysis
As already mentioned the similarity theory gives the possibility to
obtain equations for calculation of a given class of phenomena based on
differential equations. Unfortunately, in industrial practice there are many cases,
especially the more complicated, for which it is impossible or very difficult to
write these equations. The theory of dimensional analysis helps to solve the
problem in these cases. For this analysis it is necessary to know only what
