Page 39 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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when the described value is a.
According to the JT theorem the number of the dimensionless ratios is
N=3-2=L
If all values are expressed in one system of measurements, for example
the international system of units (SI), the dimensionless form of a can be
presented as

y
y .T') , (102)

where x, y and z are the powers at the respective values. Later it is shown how
to determine them.
Let the dimensions of the values in Eq. (102) be respectively:

a b c
[aJ = [L T M J (103)

e
d
f
= [L T M ] (104)
i
h
s
= [L T M J (105)
a r
[Tj = [L T"M j (106)

From Eqs. (101) to (106) it follows

g
h
f x
e
<i
i y
c
r
b
n
p
[IfT M ] = [L T M ] .[L T M ] .[L T M ]*, (107)
or
b
x+g +nz
FIfT M C J = jf y J iex+I 'y+P2 j>fi+ty+rz f 108)
Because the equation (105) is dimensionless, the following conditions
should be fulfilled:
a=dx+gy+nz (109)
b=ex+hy+pz (110)