Page 34 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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, dw
f = m—.
J
dT

The invariant of similarity which corresponds to this law is:

= idem. (87)
m.w

Such invariants of similarity expressing the ratio of heterogeneous
values are called criteria of similarity or numbers. Usually, they are called by
the names of eminent scientists. For example, the above written criterion is
called the Newton number.

ft
Jj— = Ne = idem. (88)
m.w

It is worth noting that all variants of similarity, simplexes, and criteria
are always dimensionless. The criteria of similarity express the very nature of
the physical phenomenon. To obtain them using the theory of similarity, it is
necessary to know the analytical description of the process.
The theory of similarity is based on three theorems. The first of them
determines the relation of the constants of similarity and gives the expressions
of the criteria of similarity. It states that the similar phenomena have equal
criteria of similarity.
Because the criteria of similarity in similar systems have equal values,
their ratios are always equal to 1. For example, for the Newton criterion

fi.h

1, (89)
ft* 2
m 2t 2

or