Basics of Fluid Mechanics, 2014a

9.1. INTRODUCTORY REMARKS 275
the relationships between the physical quantities (see the question why the sky is blue
story).
Osborne Reynolds (1842–1912) was the first to derive and use dimensionless parameters
to analyze experimental data. Riabouchunsky 2 proposed of relating temperature
by molecules velocity and thus creating dimensionless group with the byproduct of
compact solution (solution presented in a compact and simple form).
Buckingham culminated the dimensional analysis and similitude and presented it in
a more systematic form. In the about the same time (1915, Wilhelm Nusselt (November
25, 1882 – September 1, 1957), a German engineer, developed the dimensional analysis
(proposed the principal parameters) of heat transfer without knowledge about previous
work of Buckingham.
9.1.2 Theory Behind Dimensional Analysis
In chemistry it was recognized that there are fundamental elements that all the material
is made from (the atoms). That is, all the molecules are made from a combination of
different atoms. Similarly to this concept, it was recognized that in many physical
systems there are basic fundamental units which can describe all the other dimensions
or units in the system. For example, isothermal single component systems (which does
not undergo phase change, temperature change and observed no magnetic or electrical
effect) can be described by just basic four physical units. The units or dimensions
are, time, length, mass, quantity of substance (mole). For example, the dimension or
the units of force can be constructed utilizing Newton’s second law i.e. mass times
acceleration −→ ma = M L/t 2 . Increase of degree of freedom, allowing this system
to be non–isothermal will increase only by one additional dimension of temperature,
θ. These five fundamental units are commonly the building blocks for most of the
discussion in fluid mechanics (see Table of basic units 9.1).
Table -9.1.
Basic Units of Two Common Systems
Standard System
Old System
Name Letter Units Name Letter Unis
Mass M [kg] Force F [N]
Length L [m] Length L [m]
Time t [sec] Time t [sec]
Temperature θ [ ◦ C] Temperature T [ ◦ C]
Additional Basic Units for Magnetohydrodynamics
Continued on next page
2 Riabouchunsky, Nature Vol 99 p. 591, 1915