The dimensionless parameters generated by dimensional analysis
have an intereting significance: they may be interpreted as the ratio
of an external and an internal characteristic dimension of the
particular problem or phenomenon.
The outer characteristic dimension the usually the one a designer
designing a device based upon the phenomenon is free to choose. The inner
characteristic dimension is usually determined by the mechanism of the processes.
It is typical for processes in Nature that as a certain critical ratio of the two characteristic dimensions the
phenomenon in question changes its character. At a critical value of the Abbe number
(where
is the diameter of the aperture which limits the transverse dimension of a light beam,
is the wavelenght of the light) the laws of geometrical optics cease to be valid and
different laws of wave optics become relevant. Already mentioned
 | Fig.D-11 |
was a similar
meaning of the Knudsen number
, the critical value of which delimits the
region of validity for laws of superaerodynamics. Another
already mentioned nondimensional parameter is the Mach number
,
above a critical value of which the different
laws of supersonic aerodynamics. Event though in the present case of the
Reynolds number a meaning of the ratio of two characteristic dimensions is not so
immediately apparent, Figs D-10 and D-11
present a document that this number as a dimensionless parameter has actually quite similar meaning and
the importance of its critical value (Fig.12), delimiting validity of different laws of turbulent flow
is also very similar to what was mentioned in the case of Ab, Kn, and Ma.

Practical calculation procedure for
a frictional loss problem
1) Reynolds number is evaluated. This determines wheter laminar or tubulent laws apply.
2) Suitable formula is chosen in
Fig.D-12 and the coefficient of friction loss
is evaluated.
3) The Weisbach formula, Fig. D-4 is used to compute the loss (drag) coefficient
.
4) The amount of dissipated ("lost") energy is calculated according to Fig.D-2.
5) This result is inserted to the right-hand side of integrated Bernoullis' Theorem
equation.
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This is page Nr. D06 from textbook
Vaclav TESAR : "BASIC FLUID MECHANICS"
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