Page 32 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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Geometrical similarity exists when the corresponding angles of two
similar objects are equal and the ratios between the values of each two similar
sizes are the same for all of them.
If the geometrical sizes of two objects are respectively:

L h L 2, L 3... L n ,and l h /* 4 /, , (80)

in case of geometrical similarity the following conditions are fulfilled:

(81)

where a, is a dimensionless parameter called similarity constant or scale
multiplier.
In case of geometrical similarity of movable systems, their similar
points move on similar trajectories.
In case of time similarity the similar points of the geometrically similar
systems, move on similar trajectories for time intervals the ratio between which
is constant for all points

T T T
- ^ = - ^ =....... = - ^ = a r = const., (82)

where T T and t are the time intervals of the two similar systems, and a T is the
respective similarity constant.
The physical similarity requires that in the similar points of similar
systems the ratios between the physical values are constant too,

^ = ^ = = ^L = a u= const, (83)
u, u 2 «„

where U and w are the physical values in the two similar system, and a u is a
similarity constant, e.g. constant of viscosity, density, and so on.
Consequently, in similar systems the respective fields of physical
properties are also similar.