Page 38 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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parameters influence the value to be calculated. For example we know that the
partial heat transfer coefficient or is a function of the following parameters:

(99)

The dimensional analysis is a very powerful method not only to find the
form of the necessary equation, but also to give information about the limits of
its validity.
The basic theorem of the dimensional analysis is the n theorem of
Buckingham which states that the general dependence between » values at m
basic dimension units can be presented as a function of (M-»I) dimensionless
ratios of these values, and in case of similarity, of (n-m) criteria of similarity.
If for example a given phenomenon can be described as a function of
five values

f(a,fl,r,T,fi).

and if these values are expressed using e.g. 3 basic units, £-for size, T- for time,
and M- for mass, based on the n theorem the number N of the dimensionless
ratios is

N=m-n-=5-3=2.

I.e., the necessary equation can be presented in the form of a function of two
terms.

A simpler example of the application of dimensional analysis can be
given in case of 4 values with 3 basic units.

f(a,p,Y.t), (100)

or

a = f 1(j3,y,T), (101)