Page 35 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

30

(90)

Taking into account Eqs. (81) to (82), it can be written:

fi - T i _ m i - w i -
a
a
— — flp -o T; - m"' ~ w
T m W
f 2 2 2 2
That is why equation (90) can be presented as a dependence of the
similarity constants

J L
- - (91)

The value Q is called indicator of similarity, Eq. (91) gives the
possibility to define the first law of the similarity theory also in the following
way: for similar phenomena the indicators of similarity are equal to unity.
The first law allows to transform the differential equations which
describe physical phenomena and to present them as functions of criteria,
passing over the analytical solution.
If the constants of similarity are obtained from the conditions of
uniqueness, the criteria obtained from these constants are called determining
criteria.
The second theorem of the similarity theory solves the problem how to
present the solution of the differential equations as functions of similarity
criteria. According to this theorem, any dependence between the variables
which characterize the phenomenon can be presented as a function of similarity
criteria K pK 3,K 3....,...K n, called generalized criterion (dimensionless)
equation

f(K,.K .K , KJ = 0. (92)
3
2
Instead of similarity "criterion" usually "number" is used.